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Quantum-Well Structures for High-Speed Electronics
THIN FILMS, VOLUME 23
III-V Quantum-Well Structures for High-Speed Electronics E . R . B R O W N * AND K . A . M C I N T O S H
Lincoln Laboratory, Massachusetts Institute of Technology, 244 Wood St., Room E-124, Lexington, Massachusetts 02173- 9108
I. B a c k g r o u n d on Q u a n t u m - W e l l Infrared D e t e c t o r s . . . . . . . . . . . . . . . . . . . . . . . .
174
A. Direct D e t e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
174
B. H e t e r o d y n e Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
175
II. Q u a n t u m - W e l l D e t e c t o r Design and I n t e r s u b b a n d A b s o r p t i o n . . . . . . . . . . . . . . . . . A. Q u a n t u m - W e l l Energy Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
178 178
B. Epitaxial G r o w t h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
184
C. l n t e r s u b b a n d A b s o r p t i o n M e a s u r e m e n t T e c h n i q u e s . . . . . . . . . . . . . . . . . . . . .
i 85
D. l n t e r s u b b a n d A b s o r p t i o n Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
187
III. M Q W D e t e c t o r Fabrication and DC R e s p o n s e C h a r a c t e r i s t i c s
................
A. Fabrication and P a c k a g i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
188
B. Dark C u r r e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Spectral and Absolute Rcsponsivity D. P h o t o c o n d u c t i v e Gain
188 89
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190
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194
E. External Q u a n t u m Eflicicncy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
195
IV. Electrical B a n d w i d t h and O p t i c a I - H c t c r o d y n c E x p e r i m e n t s . . . . . . . . . . . . . . . . . .
196
A. P h o t o e l e c t r o n G e n e r a t i o n - R e c o m b i n a t i o n Noise T e c h n i q u c . . . . . . . . . . . . . . . .
196
B. D i o d e - L a s e r M i x i n g T e c h n i q u e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
198
C. M i c r o w a v e Rectification T e c h n i q u c
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D. D i s c u s s i o n of B a n d w i d t h and Lifetime
199
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200
E. H e t e r o d y n e Sensitivity M e a s u r e m e n t T e c h n i q u e . . . . . . . . . . . . . . . . . . . . . . .
201
F. H e t e r o d y n e Sensitivity Results
202
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V. A p p l i c a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
204
A. I n s t r u m e n t a l Resolution and Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . .
205
B. H i g h - R e s o l u t i o n M o l e c u l a r S p e c t r o s c o p y
207
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C. L o n g - R a n g e , H i g h - D a t a - R a t e C o m m u n i c a t i o n s
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210
VI. I m p r o v e m e n t s in M Q W H e t e r o d y n c Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . A. E n h a n c e m e n t of External Q u a n t u m Efficiency . . . . . . . . . . . . . . . . . . . . . . . . 1. 4 5 ~
211 211
Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
211
2. N o r m a l - I n c i d e n c e ( G r a t i n g - C o u p l e d ) Detector . . . . . . . . . . . . . . . . . . . . . . B. Design of Detectors Having L i f e t i m e - L i m i t e d Electrical B a n d w i d t h References
213 ..........
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214 216
*On leave of a b s e n c e to the D e f e n s e A d v a n c e d R e s e a r c h Projects Agency, 3701 N. Fairfax Dr., R o o m 850, A r l i n g t o n , Virginia 2 2 2 0 3 - 1 7 1 4 173 Copyright 0 1997 by MIT Lincoln Laboratory. All rights of reproduction in any form reserved. ISBN 0- i 2-533023-5, ISSN !079-4050/97 $25.00
E. R. BROWN AND K. A. MCINTOSH
174
I. Background on Quantum-Well Infrared Detectors A.
D I R E C T DETECTION
Since the initial observation of strong intersubband absorption in multiplequantum-well (MQW) structures (1), these structures have been used as the basis for several different types of midinfrared detectors, emitters, and modulators. One of the first successful detector designs used heavily doped n-type GaAs quantum wells and relatively thick AlxGa~_xAs barriers with the well thickness and barrier A1 fraction tuned so that only one bound state existed in each quantum well (2). The second state of each well lays at an energy level just above the band edge of the barriers, making it quasi-bound. The absorption mechanism in this detector was the bound-to-extended-state intersubband transition shown schematically in Fig. 1. The responsivity spectrum resulting from this transition was found to be Gaussian in form with a peak energy close to the bound-toextended-state separation and a spectral energy width roughly equal to one-third of the peak energy. The bound-to-extended detector has been found to behave like a classic photoconductor in the sense that the photocurrent I0 can be expressed as I~ =
r/~ hv
n=2
-- RoP,
( 1)
EXTENDED STATE - -
.
V
hv BOUNE STATE AIGaAs FIG. 1.
GaAs
AIGaAs
Bound-to-extended-state transition in a quantum well.
lll-V QUANTUM-WELL STRUCTURES F()R HIGH-SPEED ELECTR()NICS
175
where R 0 is the external responsivity. As in all photoconductors, the current noise is dominated by fluctuations in the generation and recombination rates (i.e., G-R noise) of electrons, leading to the power spectral density Sl =
4eg(I o + ID).
(2)
In these expressions, 7/o is the external quantum efficiency, e is the electron charge, P is the average optical power, h is Planck's constant, u is the optical frequency, It) is the dark current, and g is the photoconductive gain (which is usually much less than unity in MQW structures and is discussed more fully in Sec. III.E). The primary advantages of the GaAs MQW detector over the standard IR detectors made from HgCdTe are: (1) the peak wavelength Ap of the spectral response can be "engineered" through control of the quantum-well width and the barrier height, (2) GaAs substrates are relatively robust and are therefore more easily fabricated in arrays or other integrated circuits, and (3) GaAs and AIGaAs epitaxial layers are more robust because the constituent atoms diffuse much less with time or temperature than the volatile Hg component in HgCdTe alloys. One disadvantage of the MQW direct detector is that its dark-current density at 77 K is roughly three orders of magnitude higher than in good HgCdTe detectors. This higher density causes the specific detectivity D* of the MQW detectors to be roughly 100 times lower under low background radiation. To the best of the author's knowledge, the highest detectivity of an MQW detector reported to date at 77 K and 10-/.tm or longer wavelength is still D* = 2.6 • 10 ~ cm Hz~/-~W ~ (3). A second disadvantage is the polarization selection rule that results in a strong absorption of light only for the component of the incident IR electric field that is oriented perpendicular to the plane of the quantum wells. This disadvantage requires the fabrication of an angled facet in the substrate or two-dimensional gratings on the top surface of the wafer so that incident radiation can be efficiently absorbed within the MQW structure.
B.
HI';TER()I)YNF~ DF~TFA'TION
Neither of the previous disadvantages limits the performance of GaAs/AIGaAs MQW detectors in the optical-heterodyne, or coherent, mode. In this mode the output beam from a laser local oscillator (LO) is combined with radiation from another infrared source (signal) and both are coupled into the MQW structure, as depicted in Fig. 2. Because the detector response is inherently quadratic in the optical electrical field, the absorption of the combined beams results in the generation of photocurrent at the difference frequency (DF)
E. R. BROWN AND K. A. MCINTOSH
176
/
DETECTOR MESA
CO 2 L A S E R B E A M
(LOCAL OSCILLATOR)
QUANTUM/ WELLS .....
INPUT BEAM (SIGNAL) \
n+GaAs
SEMI-INSULATING s SUBSTRATE o
45 CLEAVED FACET BEAM COMBINER
FIG. 2. Schematic diagram of optical mixing process that occurs with angle-taceted MQW heterodyne detector.
between the LO and signal beams (4). The magnitude of the DF photocurrent (i~)v.) is proportional to the product of the time-averaged LO power (P~,~) and signal power (Ps) through the relation 9 llw
~
[2(r/oeg )2 Plx~Ps/(hv)2] I/2
(3)
where it has been assumed that vl.~ v s = v. Because P~,~ >> Ps, the magnitude of the DF photocurrent is much stronger than the signal photocurrent in the absence of an LO, which is why heterodyne is more sensitive than direct detection. Combining Eqs. (2) and (3), one can write the following relation for the DF signal-to-noise (S/N) power ratio" S N
")
9
2( r/0eg)-PsPi ()RA/ (h v)4eg(Ilx ~ + ID)RAAf + kTAAf --
2(r/~ . . . .. , 4eg(r/(legPlx~/(hv + II))RAAf + kTAAf
(4)
where R A is the amplifier input resistance and Af is the width of the DF passband. The last term in the denominator represents the amplifier noise power, with T A being the equivalent noise temperature. A more useful figure of merit for heterodyne performance is the noise equivalent power NEPH~.:T. This is defined as the value of Ps in Eq. (4) that yields a DF S/N ratio of unity, resulting in the expression NEP HEy
.
4eghv[r/~ .
.
.
.
+ IDhv]RAAf + kTAhuAf . . . 2(r/oeg)2pix)RA "
(5)
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
177
From Eqs. (4) and (5) it is clear why the disadvantages of MQW detectors in direct detection discussed in Sec. I.A do not necessarily limit the heterodyne performance. To overcome the dark-current disadvantage, one simply applies enough LO power that the photon-induced G-R noise dominates the darkcurrent and amplifier noise. In this case, PLO >> IDhv/rl0eg and PLO >> kTAhV / 4r/0(eg)2RA , so that the DF S/N ratio approaches the value rl0Ps/2hv and the NEPHET approaches 2hvAf/r/0. These values defined the photon-noise limit, which represents a maximum sensitivity that can be surpassed only by increasing r/0. To indicate how the magnitude of the NEPHET relates to this limit, a more convenient quantity is the effective-heterodyne quantum efficiency r/En, defined by ~EH ~ 2hvAf/NEPHET" This will be used henceforth to quantify the detector sensitivity. As an example, suppose one has a typical GaAs/A1GaAs MQW detector operating with 25% external quantum efficiency and a CO2-1aser LO at 10-/,m wavelength. In the photon-noise limit, we find NEPHET approaches 2hvAf/r/0 = 1.59 • 10 -19 W/Uz, and ~EH approaches 0.25. This NEP may strike some readers as a very small number, particularly when compared with the NEP values quoted for direct detection. Indeed, the same GaAs/A1GaAs MQW detector operating in direct detection would have a direct NEP of roughly 10- ~ W - Hz-~/2, with the noise being dominated by the darkcurrent fluctuations. The units are different because the heterodyne NEP is defined in the DF band before electrical rectification, and the direct NEP is defined after this rectification. Nevertheless, the much smaller heterodyne value represents a real improvement in sensitivity per Hz of electrical bandwidth. Physically, the low heterodyne NEP follows from the multiplication of the signal power by the LO power, as given by Eq. (4). This makes the heterodyne detector behave similarly to a linear amplifier, as first discussed in detail by Serber and Townes (5). It also allows one to relate the heterodyne and direct NEPs when their respective noise mechanisms are the same (i.e., when the LO power is low enough that the darkcurrent or amplifier noise dominates). The relationship is given by NEPHE T ~
NEPD'R p
9
(6)
I.()
By taking the typical NEPD!R of 1 0 *~ W / H z I/2 and the Pl.t) of 1 mW, this expression predicts NEPHET = 10 *'~W / Hz, in satisfactory agreement with the experimental results presented later in Sec. V. The polarization-rule disadvantage of MQW detectors does not limit the heterodyne performance because most laser LOs, particularly CO, lasers, emit in only one polarization. In this case, a high r/0 can be obtained simply by coupling the LO and signal through a 45 ~ facet lapped in the substrate, as shown in Fig. 2. This is the coupling technique proposed here. Because r/0 for a single polarization in MQW detectors can approach that of HgCdTe, the photon-noise limit of
E. R. BR()WN AND K. A. MCINT()SH
178
the two detector types should be comparable, provided that the HgCdTe is a photoconducive detector. If the HgCdTe is photovoltaic (e.g., a photodiode), then the photon-induced G-R noise term in Eqs. (4) and (5) is replaced by a full photon shot-noise term, 2eI~Af, and the photon-noise-limited NEPHET becomes huAf/r/0. This factor-of-two difference in sensitivity is a general result for all photovoltaic and photoconductive devices (4).
II. Quantum-Well Detector Design and Intersubband Absorption One of the key issues in using MQW structures for heterodyne detection is to design them so that the peak of the intersubband absorption lies within the laser LO band of interest, e.g., the CO~-laser band from 9 to 11 /.~m. For GaAs/ AIGaAs MQW structures, the key material design parameters are the quantumwell width and the barrier height (which is determined mostly by the A1 fraction). Along with the effective mass and the applied electric field, these parameters determine the energy of the two quantum states associated with the intersubband transition.
A.
QtJANTUM-WIilJ.
ENER(;Y
Ll:.Vlil.S
The energy levels are found by solving Schrodinger's equation. In a first pass, one usually applies the effective-mass approximation (EMA), whereby the full Bloch wave function in the quantum well or barriers is represented by the electronic envelope function q~, and the influence of the atomic core potentials is contained in the effective mass m*. The energy dependence of the effective mass associated with nonparabolicity in the band structure is ignored in solving for the envelope functions, but is accounted for in solving for the energy levels. A second assumption is that there is no internal electric field. With these three assumptions, the Schrodinger equation is -- h2 d2ff/
2m* 6x 2 = Ech,
(7)
and is subject to the conditions that ~ and (m*)-~ d~/dx be continuous at each point in the structure, particularly across the heterojunctions. The EMA has been found to be valid tbr electrons in most type-I heterostructures, such as GaAs/AIGaAs, in which the conduction band in the quantum-well material lies much closer to the conduction band of the barrier than to the valence band of the barrier. Exceptional cases, such as GaAs/AIAs (conduction band of GaAs ap-
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
179
proximately 1.0 and 2.0 eV from conduction and valence bands, respectively, of AlAs) can be handled by a generalization of the E M A known as the envelopefunction approximation, which is beyond the scope of this chapter. The lowest state of the well is strongly bound, so that the energy in any quantum well can be found to a satisfactory degree of accuracy by a straightforward solution to Eq. (7), assuming that no mixing occurs with the states in neighboring wells. The envelope function is given by cos(kwX) in the quantum well (x = 0 at the center of the well) and exp(--kBx) in the barriers, leading to the following implicit equation for the lowest energy: m*k B
tan(kwLw/2) = - - . m~kw
(8)
In this expression, m* is the effective mass in the well material, m~ is the effective
mass
k B - V'2m~(AE c -
in
the
E)/h. The
barrier
material,
kw = V'2m*E/h,
and
quantity AE c is the barrier height (i.e., the differ-
ence in conduction-band-edge energy between the well and barrier materials), and is given by AE c : E B - E w - a E V,
(9)
where E B and E~v are the band-gap energy of the barrier and well materials, respectively, and AE v is offset in the valence bands between these materials. At the typical detector temperature of 77 K, the band gap of AlyGal_yAS is approximately given by E G = 1.51 + 1.334y, valid in the range 0.0 < y < 0.45 where this band gap is known to be direct. The quantity AE v is usually determined by linear interpolation between the AE v values for AC and BC. Explicitly, if one denotes the quantum-well material as AxB ,_xC and the barrier material as AyB i_yC and assumes that y > x, then the valence-band offset between these two compounds is given by AEv{AxBI
xC/AyB,_yC} - ( y -
x)'AEv{BC/AC}.
(10)
The constituent binary compounds, GaAs and AlAs, are known to exhibit AE v ~ 0.50 eV (6,7,8), so that from Eqs. (9) and (10) one can write AE c = 0.834y. The interpolation procedure of Eq. (10) is known as Vegard's law (9). To proceed with the solution to Eq. (8), one must also account for band nonparabolicity and the composition dependence of the effective mass. The most important effect of the nonparabolicity is the energy dependence of the quantum-well effective mass. In the case of GaAs quantum wells, one can assume to a first approximation that m * = 0.067 9mo[1 + A(E/EG)].
(ll)
E. R. BROWN AND K. A. MCINTOSH
180
where m 0 is the free electron mass, E c is the gap energy, and A is a constant ( ~ 0.824). The compositional dependence of the effective mass in the barriers is given by m~ = (0.067 + 0.083y)m 0 where y is the A1 fraction. Nonparabolicity in the A1GaAs barriers is usually not addressed in MQW structures because of the relatively close proximity of the energy levels to the conduction band edge. In the first approximation, many body corrections from free carriers are generally ignored in the quantum well and barriers. The resulting values for the lowest energy level, E~, are plotted in Fig. 3 vs quantum-well width and parametrized by AI fraction in the barriers. The zero of energy is assumed to be the conduction band edge of the quantum-well material. The well width and AI fraction are varied over what is generally considered to be the practical range of these parameters. The plot shows two trends that are characteristic of quantum-size effects. First, the energy level decreases monotonically with increasing well width with a functional dependence that approaches an inverse quadratic as the well width increases. Second, for a given well width, the energy level increases monotonically with increasing AI fraction in the barriers. This can be understood in the classical limit as the increase in kinetic energy (the difference between the total energy and the conduction band edge) as-
110.00 100.00
f
.~26%
90.00 >
O
E >(9 n..
z
uJ
80.00 70.00 60.00 50.00 40.00 33.90
39.55
45.20
50.85 5( ;.50 WELL WIDTH (ANGSTROM)
62.15
67.80
FIG. 3. Theoretical curve of first-state energy (E~) in each quantum well of a G a A s / A l v G a ~ _ vAs M Q W structure plotted vs quantum-well width and parametrized by the A! fraction in the barriers. Each barrier is assumed to have a width of 40 nm.
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
181
sociated with an electron being reflected from more impenetrable walls. Note, however, that this increase is slower than the increase in AE c itself, so that the binding energy of the first level (i.e., the difference between AE c and E~) increases with increasing A1 fraction. A third and rather unusual effect shown in the plot is the inflection point in energy vs well width that occurs near L w = 3.5 nm. This is a ramification of band nonparabolicity in the quantum well, by which the energy increase is retarded with decreasing well width through the increase in the effective mass with energy. The solution for the second state in the quantum well is not as straightforward because it is usually either weakly bound or weakly extended, lying at an energy level just below or just above the barrier band edge, respectively. In either case, the envelope function can mix strongly with the functions in neighboring wells, causing the energy levels to be distributed over a miniband of significant range. In most cases, the miniband spans an energy range that is centered far below the second-state energy that would be found for an isolated quantum well having the same width and barrier height. The solution to Eq. (8) follows readily by assuming the MQW structure to be perfectly periodic and have infinite extent. One can then apply the well-known Kronig-Penny model of quantum mechanics. In this model, the lower edge of the miniband corresponds to an envelope function in the well of the form sin(kwX) and envelope functions in the barriers proportional to exp[kR(x - L w - Lr~)] + exp[-kBx] or exp[ik~(x - L w - L~)] + exp[-ik~x] for the bound and extended cases, respectively. In these expressions, L w and L b are the widths of the quantum well and barrier, respectively. They lead to the implicit eigenvalue equations tan(kwLw/2) =
m~kw coth(kBLs/2), m*k H
(12)
m~kw cot(ksLH/2) m~vkB
(13)
for the bound case, and tan(kwLw/2) =
for the extended case. The calculated energy value E 2, for the lower edge of the second-level miniband is plotted in Fig. 4 for the same ranges of well width and A1 fraction as in Fig. 3 and for L s = 40 nm. Also plotted is a curve for the upper edge of this miniband, as computed through the Kronig-Penny model. As expected intuitively, the solution for E 2 is monotonically increasing with decreasing well width. In addition, each A1 fraction has a transitional well width, above which the second level is bound and below which the second level is extended. In the bound range, E 2 decreases very rapidly with increasing well width; but near the transition, the rate of change of E 2 with well width decreases significantly and
E. R. BROWN AND K. A. MCINTOSH
182 250
L B -- 40 nm 230 _ . . _
~ 210 111 Z
uJ
AEc= 200.2 190 •Ec= 183.5 170
aEc= 16(~.9 150
33.90
39.55
45.20
50.85
56.50
WELL WIDTH (ANGSTROM)
62.15
67.80
FIG. 4. Theoretical curve for lower-edge energy (E~) of second-state miniband in each quantum well of a GaAs/AlvGa t vAs MQW structure plotted vs quantum-well width and paramctrizcd by the A! fraction in the barriers. Each barrier is assumed to have a width of 40 nm. The barrier height (measured in energy relative to the band cdgc of GaAs) for each A! fraction is shown as a horizontal dashed line.
approaches zero at the smallest widths. This "pinning" effect is caused primarily by the mixing action of the second-level envelope functions with the same functions in neighboring wells. To a much lesser extent, it is caused by the band nonparabolicity in the GaAs quantum wells. Another effect of the state mixing is the finite range of the miniband which, for each AI fraction, approaches 10 meV at the smallest well width of 33.9 ]k. The results of Figs. 3 and 4 can be combined to yield the intersubband energy, E 2 - E~, plotted in Fig. 5 in units of wavelength A -- hc/(E 2 - E~). This plot is useful because it serves as a design chart for bound-to-extended M Q W structures in the mid-IR spectral region. Similar plots have been published previously and used for the same purpose (10). For each AI fraction, the intersubband wavelength vs well width displays a minimum (i.e., the energy displays a maximum) very near the transition from a bound second level to an extended one. This is a result of two separate effects. Below the minimum, the decrease in A with increasing well width reflects the pinning action of the second level after it
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
183
is squeezed out of the well. The increase in A with well width above the minim u m reflects the fact that E 2 decreases faster with well width than E~ in this range. A simple explanation for this follows from the limit of a very deep quantum well, whereby E n = (nh)2/8m*L 2, with L w being the well width. In this case, the rate of decrease with increasing well width is four times greater for n = 2 than f o r n = 1. In addition, the transition from a bound to an extended second state, denoted by the dashed line in Fig. 5, moves toward smaller well thickness as the AI fraction increases. This is a simple consequence of the fact, stated earlier, that increasing A1 fraction increases the binding energy, so that a narrower quantum well is required to squeeze the second state out of the well. One effect that can be important in M Q W structures under operational conditions, but was ignored in the previous analysis, is the applied electric field. Under such a field, the potential energy term in Schrodinger's equation is no longer spatially constant, so that the envelope functions can not be sinusoids or simple exponentials, and the implicit eigenvalue equations given earlier are not correct. If the applied field is small, however, the change in the eigenvalues can be
FIG. 5. Theoretical inlersubband wavelength [;k = hc/(E 2 - El) ] for a G a A s / A l v G a I vAs M Q W structure plotted vs quantum-well width and parametrized by the AI fraction in the barriers. Each barrier is assumed to have a width of 40 nm. The squares represent data points for samples having a barrier width of 40 nm and an AI fraction of 22%.
E. R. BROWN AND K. A. MCINTOSH
184
neglected. A measure of the impact of the applied field is the potential energy drop induced by the field across the quantum well, AV = eFL w. As discussed in Sec. III, the bias field across MQW structures is generally kept rather low to keep the dark current at tolerable levels. In the present samples, the maximum internal electric field is estimated from the maximum bias voltage VmAx and the total length of the MQW s t r u c t u r e s LMQ w, through FMA x = VMAx/LMQW. This expression yields FMA x ~ 1.6 x 104V - cm-l for all three samples, so that the potential drop across the typical 4.5-nm-wide quantum well is AV ~ 7 meV. This is approximately 10% of the energy of the first energy level and less than 5% of the second level. These are small enough that the applied field is generally not addressed in the design of MQW structures but is treated as a second-order effect.
B.
EPITAXIAL GROWTH
Three MQW structures in this study were grown by molecular beam epitaxy (MBE) on semi-insulating GaAs substrates at a temperature of 600~ They differed in either the width L w or number N w of quantum wells, or in the width of the barriers. The essential properties are summarized in Table I. Sample 1 had 50 4.5-nm-wide wells separated by 20-nm-wide barriers; sample 2 had 50 5. l-rimwide GaAs quantum wells separated by 40-rim-wide barriers; and sample 3 had 100 4.5-nm-wide wells separated by 40-rim-wide barriers. In each sample, the center 2.5 nm of every well was doped n-type with Si to a density of approximately 2.5 X 10 TM cm-3, yielding a sheet density of 6 X 10 ~ cm 2. The contact layers below each MQW structure consisted of 750 nm of GaAs doped to 1.0 • 10 Is cm -3 followed by 250 nm of GaAs doped to 2.4 x 10 ~ cm --3. The
TABLE I MATF.R1AI. CHARACTH{ISTICS ~)t: THRF.F. GAAs/AI.GAAs MQW DvrE,:c'rr Quantity Nw L w (nm) Barrier aluminum fraction Barrier width (nm) LMQw (rim) Well sheet concentration
Sample 1
Sample 2
Sample 3
50
50
100
4.5
5.1
4.5
22%
22%
22%
20
40
40
1205
2295
4490
6 • 10 ~ cm 2
6 • 10 ~ cm 2
6 • 10 ~ cm 2
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
185
contact layer above the MQW structure consisted of 350 nm of GaAs doped to 2.5 X 1018 cm -3. The A1GaAs barriers in the MQW structure had a 22% A1 fraction and a thickness of 40 nm. The barrier thickness was chosen as a compromise between dark current and ease of fabrication. Experience has shown that the 40-nm barriers yield a significantly lower dark current than thinner barriers; however, the 40-nm barriers lead to an overall thickness in excess of 4 / x m (assuming N w = 100), which makes the fabrication somewhat difficult. The growth was carried out by MBE in a commercial machine (Intevac MOD GEN II) that had several features to facilitate the growth of MQW structures. First, it was designed for growth on 3-in. substrates that are mounted on solderless blocks during the growth process. Second, it has stable heating techniques for the substrate and the source (i.e., Ga, A1, As, and Si) effusion cells. Third, its sources, particularly the gallium, have very low defect density. These features provide excellent accuracy and uniformity of the temperature and source-flux across the substrate. Temperature and flux control play an important role in the given samples because of the relatively long growth times that were required. For example, at the average growth rate of 1 /zm/h, the 5.8-/xm-thick sample 3 required a growth time of 5.8 hours. Over such a duration, systematic temperature or flux drifts would have caused errors in the AI fraction or silicon doping, or introduced defects in the material. A third beneficial feature of the MBE machine is monitoring of the growth rate by in situ reflective high-energy electron diffraction oscillations. This monitoring is particularly important for obtaining the specified quantum-well width.
C. INTERSUBBAND ABSORPTION MEASUREMENT TECHNIQUES
The technique used to characterize the intersubband absorption was infrared transmission. Because intersubband transitions can be engineered to occur throughout the middle infrared, the transmission is usually measured with a broadband Fourier-transform spectrometer (FTS). The FTS used in the experiments at Lincoln Laboratory covers the spectral range 400 to 4800 c m ~ (2.1 to 25 /xm) and has two sample compartments and detectors. The primary sample compartment has fixed f/3.5 optics and a room-temperature pyroelectric detector, while the secondary compartment has adjustable f/1 optics and a liquid-nitrogencooled HgCdTe detector. Instrumental resolution is programmable over the range 2 to 32 cm-~. Polarization of the infrared beam is controlled by polarizers located in the sample compartments. To improve the S/N ratio in the data, multiple scans are coherently added. In addition, various smoothing, normalization, logarithmic-subtraction, and integration procedures are performed on the data to clarify the location and strength of
186
E. R. BROWN AND K. A. MCINT()SH
absorption features such as those due to intersubband transitions. Interfering features in the spectral region near the intersubband transition are removed to help interpret the transmission spectra. These features include absorption from free carriers in the substrate, higher-order phonons, surface oxide layers, contaminants on the samples, and Fabry-Perot interference fringes. Transmission measurements were made by normalizing the infrared signal measured with the MQW sample in the optical beam to that measured with a control sample. To accurately determine the center wavelength and width of the intersubband absorption feature, multiple-pass internal reflection (MIR) measurements were made. Small (3 • 10 mm) pieces were cleaved from each wafer and parallel 45 ~ facets were lapped and polished on two opposing ends, as shown in Fig. 6. The transmission spectra through these small 45 ~ parallelepipeds clearly show the intersubband absorption features because of the increased optical path length and the complete elimination of interference fringes. The polarization of the optical beam, which was incident along the normal to one of the end facets, could vary between parallel to the plane of the quantum well and at 45 ~ with respect to the well. Transmission data were obtained by dividing the optical power spectrum by a corresponding spectrum taken with a control sample, consisting of an identical MIR structure made from a bare SI-GaAs substrate. Multiple-pass measurements were limited to MQWs on semi-insulating substrates to avoid the possibility that strong free-carrier absorption in the substrate will dominate the intersubband absorption. Although MIR measurements increase the strength of the intersubband absorption and can help to identify weak absorption features, uncertainties in the number of passes and in the intensity distribution of the infrared beam at the quantum wells can lead to errors in measured absolute absorption strength.
FIG. 6. Cross-seclional view of GaAs parallelpiped used Io support multiple-pass internal rellection through a MQW epitaxial structure.
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
187
D. INTERSUBBAND ABSORPTION RESULTS The multiple-pass transmission spectra through the three samples were measured at room temperature and 77 K by F r l R transmission spectroscopy. Each spectra showed Gaussian-like absorption features, similar to those typically displayed by all GaAs/AIGaAs bound-to-extended MQW structures. The measured peak wavelength Ap and full width at half-maximum AA for the absorption profiles at 77 K were 9.70/.tm (127 meV) and 45 meV, respectively, for sample 2. The same quantities for samples 1 and 3 were Ap-- 10.53 /.tm (117 meV) and 10.19 /tim (121 meV), and AE = 43 and 42 meV, respectively. Each of these absorption profiles is largely contained within the CO 2 laser emission range of 9 to 11 ~ m (138 to 113 meV). They were also quite insensitive to temperature variations around 77 K. This insensitivity is consistent with the fact that the quantum wells in all of these samples were degenerately doped, making the sheet concentration in the first energy level practically insensitive to temperature variations around 77 K. The experimental values of peak wavelength for samples 2 and 3 are plotted in Fig. 5 in comparison with the theoretical curves for MQW structures having 40-nm-wide barriers. The experimental points lie at slightly lower wavelengths than the theoretical curve labeled 22%, the nominal Al fraction in these samples. This discrepancy is within the 1 to 2% experimental uncertainty in the Al fraction of these samples. The gratifying aspect of the comparison is that a line connecting the two data points has practically the same slope as the theoretical curves above and below it. This supports the argument given in Sec. II.A that the second-state miniband gets pinned just above the barrier conduction band edge, causing the difference in energy between this miniband and the ground (bound) level to increase (i.e., the wavelength to decrease) with increasing well width in the range below the bound-to-extended transition. For each sample, the transmittance at the center of the absorption feature was used to derive the fractional absorption per quantum well, sr, which is a useful figure of merit for the strength of intersubband transitions. The relation between transmission through the multiple-pass samples and fractional absorption is given by TVr
= T 2 (1 - ~') Nwp,
(14)
where T is the power transmission through the air-GaAs interface and P is the number of internal passes of the radiation through the MQW structure. For example, sample 2 had 50 quantum wells and, like the others, T = 0.7 (air-GaAs interface) and P = 4. Therefore, the measured peak absorbance of approximately 0.89 corresponds to TTOv = 0.13 and ~"= 0.007. This may seem small until one realizes that the absorption is taking place over a distance scale of LEvv = Lw/cOs 45 ~ which for this sample is 7.2 nm. Hence, the absorption coefficient is
188
E. R. BROWN AND K. A. MCINTOSH
approximately a - ~'/LEFF = 9.7 • 103 cm -1, which is comparable to the absorption coefficient at the band edge of some direct-gap semiconductors. It is interesting to compare the experimental values of peak fractional absorption to the theoretical value derived for a bound-to-bound intersubband transition in GaAs quantum wells (11), hOT
st(A~ = 27ri; s
[ 1024e2sin20] 2-7~~m*c j
(15)
In this formula, orT is the total sheet concentration in each well, 0 is the angle between the propagation vector and the perpendicular to the quantum wells, F s is the full width at half-maximum of the absorption profile (assumed to be induced by scattering), n is the optical refractive index, and m* is the effective mass of the quantum-well material. In applying Eq. (15) to the experimental results for sample 2, we have OrT=6X 1011cm-2, F s = 362 cm -~, sin20=0.5, m* = 0.067m, and n = 3.3, which yield ~"= 0.008, in good agreement with experiment. This agreement suggests that a single sum rule applies to both the bound-to-bound and bound-to-extended transitions. By this rule, the integrated absorption strength would be practically the same, but the peak absorption of the bound-to-extended transition would be weaker because of its greater broadening parameter. In practice, the bound-to-extended transition is roughly three to tour times broader than a bound-to-bound transition in a quantum well of comparable width, composition, and doping concentration.
III. MQW Detector Fabrication and DC Response Characteristics The fabrication and packaging of MQW detectors for heterodyne detection can have much greater consequences on the performance in heterodyne detection than in direct detection because of the effect of electrical bandwidth. Similarly, the effect of the responsivity is much more important in heterodyne detection than in direct detection because of its impact both through the LO and signal terms. Therefore, it is important to review the packaging and responsivity issues prior to discussion of the heterodyne or other high-frequency experiments.
A.
FABRICATION AND PACKAGING
After growth, detectors were fabricated by the following sequence of steps. First, 20-/zm-diam Ni/Ge/Au metal pads were patterned by optical lithography and metal liftoff techniques. This pad formed the ohmic-contact portion of the
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
189
top MQW-detector contact. Next, a 75-/~m-diam Ti/Au metal dot was defined concentric to the 20-/.~m dot. In the area outside of the smaller dot, the Ti/Au metallization formed the highly reflecting portion of the top contact. Then, 75/~m-diam detector mesas were defined by wet etching of the GaAs/AIGaAs layers using the Ti/Au as a self-aligned mask. Finally, an ohmic field metal was deposited on the exposed n + cladding layer below the MQW structure. After these steps, the wafers were cleaved into rectangular chips, and a 45 ~ facet was lapped into one edge of each chip to couple the infrared radiation to the M Q W structure. After fabrication, the chips were soldered onto copper mounting blocks and wire bonded or ribbon bonded to a microstrip transmission line. The separation between the mesa and the microstrip line was approximately 1 mm. Both types of bonds were attempted to maximize the high-frequency response of the detectors. Previous experience indicated that multiple wire bonds in parallel provided the highest bandwidth because this configuration yielded lower capacitance than a ribbon bond but less inductance than a single wire bond. Microwave power from the MQW device was transferred to a coaxial line using a stripline-to-coaxial adapter on the mounting block. For detector characterization experiments, the mounting block was fastened to the cold finger of a closed-cycle helium refrigerator, and the detector output was fed to outside electronics through a coaxial hermetic feedthrough connector. Note that the detectors fabricated from MQW samples 1, 2, and 3 will be called devices 1, 2, and 3, respectively, in the remainder of this chapter.
B. DARK CURRENT
Alter fabrication the dark current was measured for several 75-~m devices from each sample. Figure 7 shows the 77- and 4.2-K dark current vs voltage for devices 1, 2, and 3. A negative voltage was applied to the top contact because it produced lower dark current than an identical positive voltage, consistent with an expected small asymmetry in the doping profile in the samples. The dark current for device 1 changes by about one order of magnitude at most in cooling from 77 K to 4.2 K. In contrast, the dark current of device 2 decreases by over three orders of magnitude at low bias voltages, and the current of device 3 drops even more. The high 77-K current and weak temperature dependence of device 1 is consistent with strong defectrelated electron transport through the relatively thin barriers (20 nm) of this sample. The thicker barriers (40 nm) of devices 2 and 3 suppress this mechanism greatly, leading to much less 77-K dark current. The temperature sensitivity of the latter devices occurs because the predominant dark current mechanism in these devices becomes the thermionic emission of electrons out of the quantum wells, which has an Arrhenius dependence on temperature.
E. R. BROWN AND K. A. MCINTOSH
190
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Device 3 has practically identical dark current to device 2 at 77 K, except at the highest bias voltages. Upon cooling to 4.2 K, however, the dark current of device 3 drops by several orders of magnitude more than that of device 2. This is thought to occur because of the greater overall thickness of the MQW structure in device 3. Hence, at a given bias voltage the electric field across the MQW structure in device 2 is approximately twice that of device 3. This issue will be revisited in Sec. III.D. Much greater insight into the dark current through MQW structures and techniques for reducing its magnitude can be found in the recent review article by K. K. Choi and references therein (12).
C.
SPECTRAL AND ABSOLUTE RESPONSIVITY
Although there are many ways to measure the external responsivity R(), the technique shown schematically in Fig. 8 was applied at Lincoln Laboratory because of its accuracy and amenability to absolute calibration. The optical source
lll-V QUANTUM-WELL STRUCTURES F()R HIGH-SPEED ELECTRONICS
191
KBr-PRISM SPECTROMETER
MQW DETECTOR
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PINHOLE PYROELECTRIC DETECTOR
---, 9
! |
CHOPPER
ii
LOCK-IN AMPLIFIER
I
BLACKBODY SOURCE
AMPLIFIER FIG. 8. Block diagram of experimental setup used to measure the responsivity spectrum of MQW devices indirect detection.
for the measurements is a 1000~ blackbody filtered by a prism spectrometer. The blackbody provides much greater luminosity than a popular alternative, the incandescent globar, particularly at longer infrared wavelengths. The resolution of the prism spectrometer varies from approximately 16 cm t at 1000 cm ~ (10 /zm) to approximately 60 cm ~ at 2500 cm ~ (4 /xm). The detectors wcrc mounted on the cold finger of a closed-cycle helium refrigerator, and radiation emitted from the spectrometer was focused onto the detectors through the 45 ~ facet. For calibration purposes, a beamsplittcr located between the spectrometer exit slit and the input window on the refrigerator directs a portion of the infrared beam onto a pyroelectric detector. The pyroelectric detector has a specially treated surface of known area for constant and calibrated RI~ vs wavelength throughout the near and middle infrared regions. Hence, the true spectral variation of R 0 for the M Q W detector is obtained simply by normalization of the output of the M Q W detector to that of the pyroelectric detector at all wavelengths. Shown in Fig. 9 is the experimental result for device 2 at a bias voltage of 1 V. The spectral response curve was nearly Gaussian with a peak at 9 . 6 / x m and a full width at half-maximum of 45 meV. These are both close to the peak-absorption wavelength and width of the absorption results presented in Sec. II.D. Similar results were obtained for devices 1 and 3, suggesting that the response and absorption spectra in the present samples are practically identical.
192
E. R. BROWN AND K. A. MCINTOSH
A
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E x p e r i m e n t a l responsivity s p e c t r u m of device 2 al 77 K.
While the previous technique is useful for spectral response, the absolute response is better determined by illuminating the detector with a laser because of the much greater signal strength. At Lincoln Laboratory, R 0 was measured directly from the current-voltage (I-V) characteristics under laser illumination. Radiation from a waveguide CO~ laser was tuned to the wavelength nearest the peak of the spectral response curve. R 0 was then calculated as the difference in current at a constant voltage between the illuminated and dark I-V curves divided by the incident laser power. Plotted in Fig. I0 is the result for device 3. For each device, the responsivity at or near the peak wavelength displayed a well-defined maximum at a particular voltage, defined as V x. As listed in Table II, this maximum was 0.4, 0.28, and 0.25 mAJmW for devices 1, 2, and 3, respectively. The maximum bias voltages were 2.0, 4.0, and 7.5 V, respectively. As discussed in the following section, the maximum in the responsivity can be explained qualitatively through the bias dependence of the photoconductive gain. It should be mentioned that the decrease in responsivity at high bias voltages was initially thought to be associated with a current-dividing effect between the load resistance and the MQW differential resistance, which decreases rapidly at high
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
193
SAMPLE 3 T=77K
A
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0
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TABLE II St'ECTRAI. ANI) DC-RESP()NSE CHARACTERISTICS ()F THREE
MQW
SAMt'LES AND ASSC)CIATEI) DEVI('t:;S
Quantity
Sample 1
hp (~m)
10.53
AE (meV)
43
Sample 2 9.70 45
Sample 3 10.19 42
VMAx (V)
2.0
4.0
7.5
R 0 (mA/mW) @ VMAx
0.40
0.28
0.25
g
0.25
0.18
0.10
Xlo
19%
20%
34%
194
E. R. BROWN AND K. A. MCINT()SH
bias voltages from the increase in the dark current. This could lead to a reduction in the measured external responsivity if the load resistance were comparable to or greater than the differential resistance; however, the given values of responsivity were obtained from short-circuit load conditions, so that current dividing was not in effect.
D.
PHOTOCONDUCTIVE
GAIN
As in other photoconductive detectors, the gain in MQW structures can be defined by ~-/tx, where T is the photoconductive lifetime (i.e., capture time into a quantum well) and t f is the transit time of electrons across the MQW structure. Physically, the gain is the ratio of the electron transport rate through the detector load circuit to the incident photon flux over the detector area. It is generally less than unity in MQW structures because a photoelectron excited out of a quantum well usually relaxes into another quantum well long before arriving at the collecting contact; however, it can become greater than unity by reducing the number of wells far below the typical value of 50. An excellent discussion of the photoconductive gain under this and other interesting conditions can be found in a recent review article (13). With this cursory understanding, one can begin to explain the peaked behavior of responsivity vs bias voltage of Fig. 10 by a corresponding voltage dependence of the photoconductive gain. The rise in the gain at low bias voltages is expected from a decrease in the transit time t~. The transit time decreases because of increasing low-field drift velocity, given by t f = LM~W/ ~,~tt~LM~w/(/zF) ~ (LMt)W)2/(/zV), where F is the electric field across the MQW structure. Because of the increase in LM~w between samples 1 and 3, each corresponding device requires proportionately higher bias voltage to reach the maximum photoconductive gain. Note, however, that the electric field at the maximum bias voltage is practically the same in each sample, FMA x ~ 1.7 • 104V/cm. Within the same context, the decrease in gain at higher bias can be explained by the presence of a sharp maximum in the velocity-vs-field characteristic. In GaAs and AIGaAs (low AI fraction), the maximum velocity is about 2 • 10 7 cm/s at a bias field of roughly 1 • 104 V/cm (14). At fields just a factor of two above this peak, the velocity drops approximately two times and then saturates to approximately 6 • 10r cm/s. Such a maximum occurs in all III-V semiconductors and is caused by strong scattering between electrons and polar optical phonons. The absolute value of g was determined from the low-frequency photoinduced G-R noise power. According to theory, the power spectrum of G-R current noise is given by Eq. (2), so that a calibrated measurement of the noise power at low
lll-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
195
frequencies along with knowledge of the photocurrent I0 yields g. The low-frequency noise power was measured by a radiometric technique. The CO 2 laser was chopped while producing a known I0. The DF power of the MQW detector was measured using a chain of UHF low-noise amplifiers, a bandpass filter centered around 500 MHz, and a square-law detector. The rectified output of the square-law detector was synchronously detected with a lock-in amplifier at the laser-chop frequency. To calibrate the measurement, the M Q W detector was replaced with a calibrated noise diode and the square-law detector output remeasured. The resulting values of g are listed in Table II for each device biased at its respective Wmax. The maximum g of 0.25 occurs in device 1. The inferior g of 0.15 in device 2, and 0.11 in device 3 is consistent with the lower maximum responsivities in the same devices. This suggests that the degraded transport mechanisms discussed earlier become more effective as the total width of the MQW structure increases.
E. EXTERNAL QUANTUM EFFICIENCY
The primary means of determining the quantum efficiency in MQW detectors has been through the fundamental law of photoconductivity, Eq. (1), using the appropriate R 0, g, and h u values. The resulting values for the present three devices are listed in Table II. Devices 1 and 2 displayed comparable values of 77o (0.19 and 0.20, respectively), consistent with the fact that they had an equal number (50) of quantum wells and an equal electronic sheet concentration in each well. Device 3 had a much higher quantum efficiency of 0.34, consistent with its larger (100) number of wells. An alternative means of determining the quantum efficiency is through the optical absorption and transmission parameters according to the following expression applicable to MQW devices: 77o = T[ 1 - (1 - ~')NwP].
(16)
In this expression, T is the power transmission through the angled facet, P is the number of passes of radiation through the MQW structure, and ~"is the fractional absorption per quantum well, which depends on the wavelength and the angle of incidence of the radiation. For example, from Sec. II.D. we have sr ~ 0.007 for samples 2 and 3. Because of reflection from the GaAs-air interface at the 45 ~ facet, T ~ 0.7. In addition, because the top contact consisted of an alloyed ohmic metallization that is very absorptive at infrared wavelengths, P = 1. From these numbers, one finds r/0 ~ 0.35 for these samples. This is very close to the value derived earlier from the photoconductive gain and responsivity results.
196
E. R. BROWN AND K. A. MCINTOSH
IV. Electrical Bandwidth and OpticaI-Heterodyne Experiments A direct measurement of the bandwidth, BDF, of a MQW detector, or any photodetector for that matter, can be obtained by mixing two optical signals and offsetting their frequency in some fashion. In the infrared region where MQW detectors operate, a simple means of doing this is to use a CO 2 laser as one signal and a broadband thermal source, such as a blackbody, as the other signal. Provided that the electrical bandwidth of the MQW detector is just a small fraction of the optical frequency, the blackbody power spectrum will be practically flat and will provide a well-calibrated power density per spatial mode for mixing. The problem in applying it to MQW detectors is that at modest laser power levels their conversion efficiency is rather low (only about 10%). Hence, the low power per mode radiated by any practical blackbody is dominated by the noise of amplifiers that follow the MQW detector. This is particularly true at frequencies of 20 GHz or higher, where the wideband distributed amplifiers required for the MQW detector characterization typically have noise temperatures in excess of 1000 K. Because of this problem, we have investigated three other techniques to determine the electrical bandwidth. The first, conducted at Lincoln Laboratory, involves measurement of the laser-induced noise power spectrum to frequencies of 18 GHz (15). The second technique, conducted by H. C. Liu at the National Research Council (NRC) of Canada, involves the mixing of a CO~ laser with a tunable diode laser (TDL) up to offset frequencies of 26 GHz. The third technique, also conducted at NRC, entails a measurement of the de-rectified current in response to microwave power injected through the bias port as a function of frequency.
A. PHOTOELECTRON GENERATION-RECOMBINATION NOISE TECHNIQUE
When the RC time constant of the MQW detector is much less than the photoelectron lifetime, and the parasitic load reactance is negligible, the lifetime limits the electrical bandwidth. This allows one to determine the bandwidth unambiguously by direct measurement of the photo-induced generation-recombination (GR) noise spectrum. According to photoconductivity theory, the power spectrum is given by 4egI~ S I = 1 + oJZT2'
(17)
where T is simply related to the 3-dB-down bandwidth through the relation B T = (21rT) -l.
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
197
The G-R noise power spectrum was measured using the setup shown in Fig. 11. The CO 2 laser beam is chopped, while the power in the DF passband is measured using a spectrum analyzer with its video output fed to a dual-channel lock-in amplifier. To correct for the frequency-dependent gain of the amplifiers, white noise from a microwave noise diode is injected into the amplifier chain using a directional coupler. The noise diode is chopped at a frequency fd that is approximately 10 times higher than the mechanical chopper frequency f~. The spectrum analyzer is scanned in frequency between 0.5 and 20 GHz, and its video output is fed into the lock-in amplifier in which one channel is synchronously detected at frequency fd and the other channel at frequency f. Finally, the signal at f~ is divided by the signal at fo using the normalization option of the lock-in amplifier. Figure 12 shows the measured photocurrent noise spectrum for devices 1 to 3. For device 2, the measured power is relatively flat out to about 7 GHz, drops about 6 dB at 8 GHz, rises to a local peak at around 11 GHz, and then drops monotonically at higher frequencies. The power at 16 GHz is down 10 dB below
SQUARE-LAW
BANDPASS
ISOLATOR
BIAS VOLTAGE
CLOSED-CYCLE REFRIGERATOR
DIRECTIONAL COUPLER
SPECTRUM ANALYZER
NOISE DIODE
Go LENS
LOW-NOISE AMPLIFIER
SQUARE-WAVE GENERATOR
BLACKBODY
/
/
I
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LOCK-IN AMPLIFIER
FIG. 11.
Schematic diagram of setup used to measure high-frequency G-R noise and heterodyne sensitivity up to frequencies of 26 GHz (after Ref~ 15).
E. R. BROWN AND K. A. MCINTOSH
198
A
INTERPOLATION
1.0
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3
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20
FREQUENCY (GHz) FIG. 12. Photoinduced G-R noise spectrum fl~r devices 1, 2, and 3 biased 77 K (after R~f 15).
at VMA X
and operating at
the low-frequency power. These undulations are attributed to parasitic reactance and loss in the microwave circuit (wire bond, microstrip pad, and microstrip-tocoaxial adapter) between the MQW detector and the external electronics. Smoothing through the drop at 8 GHz and peak at 11 GHz, we estimate a 3-dB bandwidth of device 2 of 9 GHz. Device 3 displayed qualitatively similar characteristics with an estimated 3-dB bandwidth of 13 GHz. The greater bandwidth of device 3 is attributed to its lower capacitance.
B.
DIODE-LASER MIXING TECHNIQUE
In the optical mixing experiments, a CO 2 laser and a lead-salt TDL were used as the infrared sources in the arrangement described in Ref. (16). The CO 2 laser frequency (wavenumber) was fixed at 32.22 THz (1075 cm-~) by grating selection, while the TDL frequency was tuned by varying its operating temperature. Both infrared beams were polarized in the plane of incidence with respect to the quantum wells (p-polarized). The tuning rate for the TDL used in the temperature range of 30 to 32 K was about 15 GHz/K. As in previous experiments with
lli-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
199
TDLs, the output spectrum was not a single frequency but a superposition of longitudinal modes separated by about 90 GHz. To minimize spurious mixing, we selected and followed one relatively strong mode. This was done by first adjusting the TDL so that the frequency of the strong mode coincided with the CO 2 frequency (within 1 GHz), and then varying the TDL temperature to increase the difference frequency. In this scheme, other modes of the TDL do not give rise to observable signals in the measurement range of 1 to 26.5 GHz. The heterodyne signal vs. frequency was measured for device 2 at a few bias voltages and was corrected for the signal and connector and cable losses, but not for impedance mismatch (16). The signal was also normalized with respect to TDL power. With the highest bias voltage of 6 V, the measured signal power decreased by about 10 dB between low frequencies and 8 GHz, dropped to a local minimum about 25 dB down at 11 GHz, came back up to a local peak around 14 GHz, and then dropped to a deep minimum at around 18 GHz. Between 1 and 25 GHz, the measured power decreased by approximately 35 dB. The rolloff with frequency is much faster than in the photocurrent noise spectrum of Fig. 12. The heterodyne signal for device 3 also decreased much more slowly with frequency than that of device 2; however, the measured signal power still undulated, showing local minima around 4, 13, and 17 GHz. By 25 GHz, the heterodyne signal was down approximately 25 dB relative to low frequencies. In contrast to device 2, the roll-off in the heterodyne power spectrum of device 3 was quite similar quantitatively to the photocurrent noise spectrum.
C. MICROWAVE RI,;CTIFICATION TECHNIQUE
A third measure of the electrical bandwidth can be obtained by coupling a microwave signal directly to the device and observing the response. The basis tbr this technique is the nonlinearity present in the I-V curves of all MQW detectors associated with the transport of electrons in the absence of infrared radiation. Because of this nonlinearity, the microwave signal is rectified and the response is thc measured change of the bias current. A microwave source (Wiltron 68174A) fixed at a power of + 10 dBm was used for this experiment. The rectified current vs frequency was measured for device 2 at a few voltages. The rolloff behavior was similar qualitatively to that of the photocurrent noise in Fig. 12 and to the diode-laser mixing spectrum; however, the rate of rolloff of the microwave rectification spectrum is much slower than that of the laser mixing, and more nearly equal to the rolloff of the photocurrent noise. The difference in the rolloff behaviors may be significant and is discussed in the next section. Unlike device 2, the microwave rectification spectrum of device 3 was very similar in rolloff characteristics to the photoelectron-noise and heterodyne-signal
200
E. R. BROWN AND K. A. MCINTOSH
spectra. For example, the dip at 17 GHz is observed in all three spectra. This also demonstrates the need to fabricate M Q W detectors in monolithic integrated circuits for operation much beyond 10 GHz. Note that the microwave rectification technique represents a new and potentially very useful means of measuring the electrical bandwidth of M Q W detectors. In general, microwave rectification probes electrons involved in the dark current. Thus, if the dark electrons and the photoelectrons follow the same transport path, then the microwave-rectification bandwidth and the heterodyne bandwidth should be the same, as in device 3. Because of the rather large microwave amplitude that can be imposed on the M Q W detector, the sensitivity can be about as high as for the optical heterodyne technique, but the simplicity will be comparable to the photoelectron-noise technique.
D.
DISCUSSION
OF B A N D W I D T H
AND LIFETIME
In general, the electrical bandwidth of photoconductors is governed by two independent time constants" (1) the RC time associated with the capacitance of the M Q W structure and the differential resistance of the load circuit, and (2) the photoelectron lifetime. Individually, each of these causes the magnitude of the photocurrent to decay at a rate of approximately 3 dB/octave past a corner frequency, which is (2-n'RC) ~-- BRf for the RC time constant and (2rrr) -~ ---- B for the photoelectron lifetime. Given the parameters listed in Table I, one can estimate these time constants and frequencies as follows. Knowing g, one can estimate -r using g - "r/tT and the approximation t T ~ LMQw/Vd, where v o is the drift velocity ( ~ 1 • 10 7 cm]s) in the AIGaAs barriers. This leads to -r = 3.1, 3.4, and 4.9 ps, and B = 51, 47, and 33 GHz, for devices 1, 2, and 3, respectively. These values are listed in Table III. In contrast, separate derivations of the lifetime in similar MQW structures have usually resulted in somewhat longer electron lifetimes (17). For example, using the careful measurements of the saturated meanfree path of electrons in GaAs/AIGaAs of about 0.8/xm (13) and assuming the same drift velocity as stated earlier, one obtains an electron lifetime of 8 ps. One can estimate the RC time constant of the present devices using the fact that under bias the M Q W detectors are similar electrostatically to parallel-plate capacitors, so that C ~ eA/LMQw, where A is the detector lateral area. Thus, with e = 12 and A = 4.4 • 10 -5 cm 2, one finds C ~ 0.38, 0.20, and 0.10 pF for devices 1, 2, and 3, respectively. This leads to R C - 1 9 , 10, and 5 ps, and BRC = 8.4, 16, and 31 GHz, for devices 1, 2, and 3, respectively. Because the estimated knee frequencies are substantially higher than the corresponding BD~., one must conclude that parasitic circuit reactance is limiting the electrical band-
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
201
width of the devices. It is thought that the ribbon (or wire) bond to the detector is the source of this reactance. A surprising result of this study is the discrepancy between the photoelectronnoise and heterodyne-signal spectra for device 2. The discrepancy may indicate that the photoelectron noise is not purely G-R noise. Thermal (i.e., JohnsonNyquist) noise also occurs in photoconductors and becomes more important relative to G-R noise when the dark current is high or, equivalently, the differential resistance is low, as in most MQW detectors at 77 K or higher temperatures. In principle, the power spectrum of thermal noise is flat out to a frequency of approximately (2"tr'rp) - l , w h e r e ~'p is the momentum relaxation time. Because % is probably less than "r in MQW detectors by roughly one order of magnitude, we expect that the bandwidth of the thermal noise will be much greater than the G-R noise bandwidth. Therefore, a roughly equal combination of thermal and G-R noise would have a significantly larger bandwidth than G-R noise alone.
E. HETERODYNE SENSITIVITY MEASUREMENT TECHNIQUE The heterodyne sensitivity at microwave DF frequencies was measured by mixing the CO 2 laser with a calibrated blackbody (18). Such mixing generates power over a very broad DF band, because the blackbody is essentially a thermal noise source. The portion of the infrared power that appears in the DF band is approximately u _+ Af, where the plus and minus signs denote the upper and lower sidebands, respectively. These sidebands are shown schematically in Fig. 13. For a blackbody of absolute temperature TBB and emissivity e, the infrared spectral density in the single polarization and spatial mode of the laser is given by hvE
Sp = eh~/kT....--1"
(18)
The power generated in the DF band is given by Eq. (18) times the optical transmittance between the blackbody and the MQW detector. Equation (18) provides a means of calibrating the heterodyne sensitivity as quantified by NEPH~.:T. The relationship between NEPHET and the experimental parameters is given by {
huET
NEPHE T = 2Af (eh, ,/kT,,,, _
hveT }N l) - (e h"/k~., -- l) S'
(19)
where TRT is the ambient temperature. As derived in Sec. I.B, this is related to the effective heterodyne quantum efficiency through the relation, "r/EH -----2hu Af/NEPHEv.
E. R. BROWN AND K. A. MCINT()SH
202
D nc I-O 111 13. O9 or" UJ
0 II.
MICROWAVE REGION-
- ~
~
. . . .
INFRARED REGION
"~
CO2-LASER LOCAL OSCILLATOR
DIFFERENCE-FREQUENCY BAND
LOWER SIDEBAND
UPPER SIDEBAND
3x1013 FREQUENCY
(Hz)
FIG. 13. Infrared and microwave power spectra associated with the L(), the signal and the differonce-frequency band of the optical hctcrodync process.
F. HETEROI)YNI:. SI'~NSITIVITY RI'~SUI.TS One of the important parameters in operating an MQW detector in heterodyne mode is the bias voltage. Figure 10 shows a comparison of the integrated blackbody-heterodyne response (measured over a 100-MHz bandwidth, centered at a low difference frequency) to the direct-detection response of device 3. Like the direct-detection curve, the heterodyne response displays a maximum just above 7 V. The other devices displayed a similar maximum in the heterodyne response with respect to bias voltage. In each device, the maximizing voltage was the same for both modes of detection. The other important factor in heterodyne detection is the LO power. To determine this, the heterodyne signal was measured at a low difference frequency and compared directly to the photocurrent, dark-current, and amplifier noise powers at the same frequency. This resulted in an experimental S/N ratio, which was converted to an NEP using Eq. 19 and to an effective heterodyne quantum efficiency using the relation r/EH = 2hu AffNEPH~:T. Figure 14 shows the results obtained for device 1 with LO powers of 1, 2, 5, and 10 mW (17). Clearly, there is
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
203
100
A
"rio
>. O 10 z u,I ,..,. (J IL IL U,I I--" Z
PLO = 10 m W
o f
.......... 9
'TIE H r "
0,
9 =2mW 1
\o
= 1 mW
L O C A L O S C I L L A T O R W A V E L E N G T H - 10.2 p m D E T E C T O R O P E R A T I N G T E M P . = 77 K
0.0
I
1
0.5
1.0
I
1.5 BIAS
I
I
I
I
2.0
2.5
3.0
3.5
VOLTAGE
4.0
(V)
FIG. 14. Heterodyne sensitivity (quantified by 'rlEH) for device 1 plotted vs bias voltage and paramctrizcd by CO,-lascr LO power (after Re./'. 17).
a rapid increase in "qH~between 1 and 5 mW. Between 5 and 10 mW, ~EH begins to saturate as it approaches B0" At this point the photocurrent noise induced by the LO power begins to dominate the other noise mechanisms, as expected from the discussion of Sec. I.B. Table III summarizes the heterodyne sensitivity results for all three devices. The bias voltage is the value for peak responsivity and P~.~ is 2 and 10 mW. The amplifier noise is set equal to 100 K, consistent with the noise figure of the UHF preamplifier (1.2 dB) used in these experiments. The results for detectors 1 and 2 are identical at P~.~ = 8 mW but differ at the lower power. The superiority of detector 2 at P~(~ = 2 mW reflects its lower dark current. Hence, less LO power is required to make the photocurrent noise dominate. Detector 3 displays the best performance at all values of LO power and the highest values of BEH"At PL~ = 8 mW, the ~EH of this detector is 0.18, which represents the most sensitive heterodyne detection achieved with an MQW detector.
E. R. BROWN AND K. A. MCINTOSH
204
TABLE III HIGH-SPEED AND HETERODYNE CHARACTERISTICS OF THREE MQW SAMPLES Sample 1
Quantity a- (ps)
Sample 2
3.1
B (GHz)
BDF (GHz) hLO
4.9
51
47
33
7
9
13
10.24
hVLo
3.4
Sample 3
121
9.50 131
9.56 130
"qEH(PLo = 2 mW)
6%
8%
9%
qqEH(PLo = 8 mW)
11%
1 1%
18%
Note that the sensitivity of all three devices approaches roughly 55% of the photocurrent-noise limit with 8 mW of LO power. This power corresponds to approximately 80 mW of CO2-1aser power incident on the diplexer in Fig. 2. This is a substantially larger LO power than required by HgCdTe heterodyne detectors because of the lower responsivity of the MQW device; however, it poses no practical problem because CO~ lasers generally provide a great excess of power, and because the MQW detector has a high dynamic range. The dynamic range stems in part from the small r, which inhibits current saturation and spacecharge effects in the active region of the device. It also stems from the thermal conductivity of GaAs, which is substantially higher than that of HgCdTe (but less than that of Si). Up to 100 mW of LO power has been applied on MQW devices, with no degradation in the detector characteristics.
V. Applications The MQW detector will enable applications that were previously impossible with HgCdTe detectors, whose maximum electrical bandwidth was (and remains) approximately 3 GHz. For example, when using a CO2-1aser LO with a HgCdTe detector for atomic or molecular spectroscopy, the atomic or molecular line of interest must fall within roughly 3 GHz of a CO 2 emission line. Because these emission lines are typically separated by at least 30 GHz, the vast majority of frequency space between 9 and 11 t*m is undetectable. Similarly, when using a HgCdTe detector as a front-end mixer in a coherent laser communications re-
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
205
ceiver, the maximum digital transmission rate is approximately 1 GBit/s. With the MQW detector, these drawbacks are greatly alleviated because of its roughly 10-times-greater electrical bandwidth. Alternative means of alleviating these shortcomings, such as the use of a frequency-tunable diode laser as an LO in molecular spectroscopy, or the use of very high-speed (often room-temperature) photoconductive detectors, have been largely unsuccessful because of the deleterious excess noise of these devices.
A.
INSTRUMENTAL RESOLUTION AND SENSITIVITY
Before embarking on the system implementations that the MQW detector enables, it is important to compare heterodyne and direct detection in terms of instrumental spectral resolution and instrumental sensitivity. Because of the coherent nature of the optical mixing process, the lower limit on the resolution of a heterodyne instrument is the intrinsic width of the LO emission line, and the upper limit is just BoF. The actual value is usually determined to be somewhere between these limits by electrical filtering in the DF band. In contrast, the resolution of a direct-detection instrument is either the intrinsic spectral bandwidth of the direct detector or the resolution of the optical-filtering instrument in front of it, whichever is finer. Provided that the LO emission is unimodal (e.g., from a CO~ laser), the heterodyne instrument will typically have a higher resolution by several orders of magnitude. Resolution is important not only from the standpoint of positively identifying the spectral feature of interest, but also because of its relationship to instrumental sensitivity. This relationship can be cast in general terms, quite independent of the type of detection, but is strongly dependent on the spectral linewidth of the signal being measured. Under many conditions, the output signal of a spectroscopic instrument can be written as the convolution ~c t"
S(f) - /I0(v)e-"ZR(v - f) dv d
(20)
0
where I0(v) is the source spectrum, a is the frequency-dependent absorption or emission coefficient associated with the spectral feature, R is the instrumental responsivity, and z is the physical length of the absorbing medium. For simplicity, but without loss of generality, we assume that I0(u) is spectrally flat over the ranges of variation of oLand R, and that R can be represented by the box function R(v) = R ~
(f - A f / 2 ) ] . 0 [ ( f / 2 ) - v], Af
(21)
E. R. BROWN AND K. A. MCI NT O SH
206
where 0 is the Heaviside step function and Af is the instrumental resolution. The /.
expression (21) is normalized, / R(u) d r = 1, so that the instrumental response J
0
to the flat background is simply S0(f) = R0I 0. For analytical purposes only, we assume that the spectral feature is optically thin, or e -"z ~ 1 - oe z, and a can be represented by the Lorentzian function (applicable to homogeneously broadened features, e.g., pressure broadened), so that cff 1,') =
a~ (v -- v0 )2 + F 2/4'
(22)
where F is the broadening parameter. Upon substituting (21) and (22) into (20), we find
{z%F[2(f+Afl2-vo)
S(f) = R o I o 1 -
Af
a tan
A
-
a tan
2(f-
Af/2F
v~
(23)
....I , J
The instrumental sensitivity can be defined as the maximum difference, AS, between the signal response without absorption S 0 and the signal with absorption. Clearly, the maximum offset of S(f) from S o occurs at f - v 0, so that AS -- S 0 - S(u0) = R 0 1 0 [ - - ~ - a tan
-- R0101%z[3],
(24)
where 13 is a correction factor that depends on the ratio of the instrumental resolution to the spectral linewidth. From this expression, it is clear why heterodyne instruments have a substantial advantage over direct-detection instruments when the spectral signal linewidth is relatively narrow. For example, if the linewidth is such that F/Af -- 0.1 for the direct instrument and F/Af = 10 for the heterodyne, then we find [3 = 0.147 for the direct instrument and 0.997 for the heterodyne. In other words, the sensitivity of the heterodyne instrument is effectively 0.997/0.147 or 6.8 times greater than that of the direct instrument. Note that this sensitivity advantage goes beyond the S/N benefit of heterodyne detection discussed in Sec. I.B. The latter benefit was a consequence of the amplifying effect of the LO power on the signal power. The former effect results from spectral bandwidth matching in the presence of noise. Put more intuitively, the heterodyne instrument can usually be operated so that its resolution bandwidth is less than or equal to the signal bandwidth. In this case, the instrument
|II-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
207
will not measure any more noise (either internal or external) than contained within the signal bandwidth, and the S/N ratio will be optimal. On the other hand, direct-detection instruments are usually operated with instrumental resolution substantially greater than narrow signal spectra. Hence, they measure much more noise than contained in the signal bandwidth, and the S/N is degraded.
B. HIGH-RESOLUTION MOLECULAR SPECTROSCOPY
To demonstrate the advantages of the MQW detector in the heterodyne mode, it has been configured in the tabletop spectrometer setup shown in Fig. 15. The setup consists of a 1000~ blackbody as a broadband source illuminating a 10cm-long gas cell. A beamsplitter is used to combine the input blackbody and laser LO beams and direct them to the MQW detector. A chopper modulated the blackbody beam and, hence, the difference-frequency power spectrum, which was amplified and measured with the combination of a scanning microwave
FIG. 15. Tabletop setup of high-resolution spectrometer used to measure gas absorption lines that occur in the C O : l a s e r band (approximately 9 to 1 I ~m).
E. R. BROWN AND K. A. MCINTOSH
208
spectrum analyzer (0.1 to 18 GHz) and lock-in amplifier. The spectrum analyzer had a maximum sampling bandwidth of 2 MHz. Background scans measured without gas in the cell were used to normalize scans with gas. The first molecular absorption line examined was one of NH 3 located approximately 8.5 GHz from the 9P38 CO2-1aser line. The NH 3 was at a partial pressure of 2 torr in a gas cell that was backfilled with 1 atm of N 2. Figure 16 shows the measured infrared transmission through the cell from a conventional FTIR instrument having 2-cm -~ resolution. The inset of Fig. 16 shows the transmission spectrum through the same cell measured with the M Q W heterodyne detector. The sloped lines between the inset and the main figure show the portion of the FTIR spectrum covered by the MQW spectrometer when using the 9P38 laser line. Because of its superior frequency resolution, the M Q W spectrometer detects a strong absorption feature having a minimum transmission of 25% at 927.32 cm -~. At this same wave number in the FI'IR scan, there is a nearly imperceptible dip in the transmission of roughly 1%. The broader feature in the F r l R spectrum centered at around 931 cm -~ is a series of NH 3 absorption lines that is merged into one continuous band by the FTIR instrument.
i
1.00
Z 0.95 O === ~0 g3
o0 Z 0.90 r
/"
B
--
1 0.8
0.6
F--
0.4
0.2 ~-
0.85 "
0" 927.20
927.30
HETERODYNE
927.40
927.50
SPECTRUM
,,lll,,l,,,I,,,I,,,l,,,l,,,I,,,l,,,l,,,l,,,I,,,I,,,I, 920
930
FREQUENCY
940
(cm "1)
FIG. 16. High-resolution transmission spectrum (inset) through NH~ at a partial pressure of 2 torr and broadened to atmospheric pressure by nitrogen. The main plot shows the transmission spectrum through the same NH.~ gas sample but measured by a Fourier-transform spectrometer having relatively low spectral resolution.
III-V QUANTUM-WELLSTRUCTURES FOR HIGH-SPEED ELECTRONICS
209
Of course, because the resolution of the MQW-detector-based instrument can, in principle, be made as narrow as the CO2-1aser emission line, such an instrument could also be very useful in detection of low-pressure molecular lines of interest in fundamental chemistry and in the astrophysics of the interstellar and extraterrestrial medium. Here, the molecular or atomic absorption features are usually Doppler broadened and, hence, relatively narrow. To demonstrate the capability of the GaAs/A1GaAs M Q W detector in this application, we have used the same setup as in Fig. 15 but eliminated the background nitrogen to yield 2 torr of NH 3 alone. The NH 3 absorption feature in the resulting transmission spectrum is plotted in Fig. 17a. Without the 1 atm of broadening gas, the full width at half-maximum shrinks to approximately 0.2 GHz. Even at this narrow width, the M Q W heterodyne spectrometer is resolving the line with much greater resolution than required. To demonstrate this point, the pressure of the NH 3 was reduced further to a level of 0.1 torr, as plotted in Fig. 17b. Although the maximum absorption of the sample starts to drop rapidly as the pressure is lowered, it is clear that the absorption feature is fully resolved in each case.
1.2 2 TORR NH 3 .,
.::/'' -
LU
O Z
,,r II-.
0.8
-
0.6
-
0.4
-
0.2
-
.,..,,
i
orj Z
BROADENED
SELFBROADENED ~'~
0 7.5
8.5 DIFFERENCE
WITH
Na
. 9i "[
i
I
9.5
10.5
11.5
FREQUENCY
12.5
(GHz)
(a) High-resolution transmission spectra measured by MQW-heterodyne spectrometer through NH3 under two different gas conditions: (1) 2 torr of NH3 broadened to atmosphere by N~, and (2) 2 torr of NH~ without further pressure broadening.
FIG. 17.
E. R. BROWN AND K. A. MCINT()SH
210
1.2 1 0.8 r
0.6 0.4
,"-"
0.2
9
9.2
DIFFERENCE
9.4
, 9.6
FREQUENCY
9.8
10
(GHz)
(b) High-resolution transmission spectra through NH~ under low-pressure, I)opplcr-broadcncd conditions.
FIG. 17. Cmuintwd
Besides ammonia, there are many other molecules of scientific interest that occur at frequencies far away from the nearest CO~-laser line. These include a class of lightweight, atmospheric molecules involved in ozone depletion, global warming, and toxic waste. Among these are O~ (ozone), CCIeF: (Freon), AsH~ (arsine), PH~ (phosphine), CH~Br (methyl bromide), CH~CI (methyl chloride), CH~CN (acetonitrile), OCS (carbonyl sulfide), and C:HsCI (ethyl chloride). All of the absorption lines from these molecules are pressure broadened under atmospheric conditions, leading to signal linewidths of 1 GHz or more. With a HgCdTe detector, this would be a great deterrence, because the limited BDI: would prevent the absolute resolution of the line and, hence, the positive identification of the molecule. With the MQW detector, the large B~. is, again, beneficial, allowing one to fully resolve the molecular line while maintaining nearly photon-noise-limited sensitivity.
C. LONG-RANGE, HIGH-DATA-RATE COMMUNICATIONS
In pioneering work conducted by Hughes Aircraft Co. and NASA in the 1970s
(19), it was recognized that the high spectral and spatial purity of the CO~ laser made it well suited to long-range, point-to-point communication links between
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
211
orbiting satellites or between a satellite and ground stations (in the absence of cloud or fog cover). When such systems were developed experimentally, the data rate was limited to approximately 1 GBit/s by the 2-GHz bandwidth of HgCdTe photodiodes. Present-day HgCdTe detectors would not improve this performance substantially; however, the MQW detectors combined with modem GaAs-based transistors and microelectronics could extend this data rate at least up to the limit of CO2-1aser modulator technology, which is approximately 10 GHz. The advantages of a CO2-1aser communications system over near-infrared or visible laser systems are in S/N ratio per unit watt of transmitter power. These advantages are expressed through the fact that the quantum-limited sensitivity of any system using a conventional laser LO (i.e., a laser operating in a coherent state, not a squeezed state) is given by an NEP of huAf, where Af is the measurement bandwidth. Thus, the minimum NEP is roughly ten times lower for the CO2-1aser system because of its substantially longer wavelength.
VI. Improvements in MQW Heterodyne Detectors The experimental results presented in Secs. III and IV suggest that the performance of MQW heterodyne detectors could be substantially improved by straightforward changes in the material design or packaging techniques. This section investigates changes aimed at improving the external quantum efficiency (dc and heterodyne) and the electrical bandwidth. The investigation is not intended to be complete and, therefore, good approaches for improving other MQW detector characteristics, such as the dark current (12), are not considered. A good overview of these approaches has been given in the review article by Levine (18).
A. ENHANCEMENT OF EXTERNAL QUANTUM EFFICIENCY
1. 45~
Detector
From the discussion of Sec. III.E and Eq. (16), it is clear that the detector structures having a 45 ~ facet and top ohmic contact could be improved substantially through the addition of an antireflection (AR) coating on the facet and by making the ohmic contact highly reflecting in the A = 10/.Lm region. These embellishments are shown in cross section in Fig. 18. The antireflection coating raises the transmission through the facet from 0.7 to approximately 1.0. The reflecting ohmic contact raises the number of passes [i.e., P in Eq. (16)] from 1 to 2. The effect of these changes on the external quantum efficiency is listed in Table IV, using device 3 as a baseline. Both changes would increase ~0 from
E. R. BROWN AND K. A. MCINTOSH
212
Ti/Au REFLECTING METALLIZATION
MULTIPLE QUANTUM-WELL STRUCTURE
ANTIREFLECTION COATING
INCIDENT
Ni/Ge/Au OHMIC
METALLIZATION
F L
.
.
.
.
.
.
.
.
_
_
45 ~ CLEAVED FACET
/
SEMI-INSULATING GaAs SUBSTRATE
RADIATION FIG. 18.
_nLGa_As_
Cross-sectionalview of MQW detector designed for high vl0.
0.34 tO 0.74, which is comparable to the quantum efficiency of the best detectors operating in the 10-~m region. Another straightforward means of improving r/0 is to increase the number of quantum wells N w. Table IV lists the effect of increasing N w from 100 to 400, again using device 3 as a baseline. For example, 200 quantum wells would increase 7/o from 0.34 to 0.52; but, there is little gained with more wells as 7/o saturates to the facet transmission of 0.7. With the AR coating added, r/()thus increases much more rapidly with N w, surpassing 90% at 400 wells. The combination of AR coating and reflecting ohmic yields a very fast increase of 7/o with well number, 93% being reached with just 200 wells. Of these two techniques, the AR coating and reflecting ohmic are preferred because they improve the performance with no deleterious effect on other as-
TABLE IV EXTERNAl. QUANTUM EFFICIENCY FOR PROP()SEI) IMPROVEMENTS IN THE
MQW
DEVlCE
Nw
l"lo(t=0"7, P= 1)
11o(t= 1.0, P= 1)
"q0(t= 1.0, P-~2)
100
0.34
0.49
0.74
200 300 400
0.52 0.61 0.65
0.74 0.87 0.93
0.93 0.98 0.99
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
213
pects of the detector performance. Increasing N w has the drawback of reducing the photoconductive gain because of its inverse dependence on LMQw. Hence, more LO power is required to make the detector sensitivity approach the photonnoise limit, because the photon-noise term in the denominator of Eq. (4) is scaled down relative to the amplifier thermal-noise term. This drawback is not as severe for the dark-current noise because it, too, scales down with the reduction in g. While a significant increase in LO power would likely be a problem for a high-speed HgCdTe detector, it should not hinder the operation of the MQW detector because of its relative robustness with respect to strong photocarrier and thermal generation. 2. Normal-Incidence (Grating-Coupled) Detector
To reduce the power requirements and still maintain high %, GaAs/A1GaAs MQW detectors can be designed and fabricated with a topside grating coupler instead of the 45~ coupling shown in Fig. 18. The grating coupling is configured in the manner shown in Fig. 19. It consists of a two-dimensional array of squares etched into the top surface of the MQW structure and covered with reflecting metal, as first demonstrated by Andersson et al. (20,21). Radiation is incident on the MQW structure from the bottom side of the wafer, passes through the quantum wells without absorption, and is reflected off the top grating at large angles from the normal. This leads to a strong absorption of the reflected radiation consistent with the intersubband polarization selection rules. At the bottom of the MQW structure, a thick AlAs layer provides total internal reflection of
(a}
MESA
TOP OHMIC C O N T A C T
GRATIN
t
............................'~' ~ A N T I R E F L E C T I O N COATING
FIG. 19. (a) Cross-sectional view of MQW detector. (b) Top view of grating-coupled detector mesa.
214
E. R. BROWN AND K. A. MCINTOSH
radiation after its first pass. The radiation then propagates through the MQW structure, again at large angles from the normal; however, on encountering the grating once again, some fraction of the radiation is diffracted back near the normal and propagates through the MQW structure without further absorption. One thus expects that this structure will support at least two passes of the radiation through the MQW structure. Experimental investigation of the two-dimensional grating structure has shown that it is capable of providing a peak internal quantum efficiency in excess of 90% for only 50 quantum wells in the structure (21). This represents an improvement of approximately three times over a single-pass 45~ detector having the same number of quantum wells. The physical reason for this improvement is that the grating can diffract much of the incident radiation into larger angles away from the perpendicular than 45 ~. Because the absorption strength in the quantum wells varies as sin20, the improvement in absorption strength per pass can increase twofold between 45 ~ and 90 ~ propagation angle. The penalty for the increased quantum efficiency is a narrowing of the spectral response compared to the 45~ detector. This has been a problem for these structures in direct detection (e.g., staring arrays), because in this application the relevant performance criterion is the quantum efficiency integrated over a substantial spectral range, typically 8 to 12/xm. In heterodyne detection, however, the peak quantum efficiency is more important, because the operational spectral range is just the CO~-laser frequency plus and minus the electrical bandwidth of the detector. Aside from the issue of spectral narrowing, other deleterious effects can lead to degradation in the internal quantum efficiency. Two such effects are lateral spread in the periodicity of the grating and nonideal reflection from the metal above it (20). To counteract these effects and ultimately obtain internal quantum efficiencies approaching 100%, we propose to increase the number of quantum wells in the grating-coupled detector to as many as 200. This has the additional benefit of reducing the specific capacitance of the detectors, allowing the RC time constant to be very small in detectors of acceptable size (i.e., diameters greater than or equal to about 50/xm).
B. DESIGN OF DETECTORS HAVING LIFETIME-LIMITED ELECTRICAL BANDWIDTH One benefit of the high-quantum-efficiency detectors proposed in Sec. VI.A is that they will naturally yield a very low RC time constant. From the parallelplate approximation, the capacitance of any of the 300-well GaAs/A1GaAs sam-
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
215
pies listed in Table IV is estimated to be 35 fF, leading to RC = 1.7 ps and BRC = 92 GHz. The photoelectron lifetime should be comparable to the values deduced for the samples in Table III, yielding B ~ 35 GHz; however, when connected to the load circuit through a bond wire, the real electrical bandwidth of the proposed detectors is likely to be much less than these values because of the parasitic reactance. To reduce the reactance and increase the bandwidth, a monolithic M Q W detector circuit could be produced, such as that shown in Fig. 20. In this circuit, the detector and output transmission line are fabricated on the same substrate, so that the two can be brought into very close proximity. The interconnection between the two can then be made by a metallic air bridge whose total length is 100 ~ m or less. This short length makes the magnitude of the parasitic reactance roughly one order of magnitude less than in the best possible ribbon or wire bond. The output transmission line is a coplanar waveguide (CPW), which on a semi-insulating GaAs substrate is useful well into the millimeter-wave band. The CPW is transformed to coaxial line by a 50-GHz stripline-to-coax adapter. The bias tee and low-noise preamplifier required for all applications can then be coaxial components and would likely be mounted on the same cold finger as the MQW detector.
FIG. 20. Perspective view of monolithic MQW detector designed for lifetime-limited electrical bandwidth.
216
E. R. BROWN AND K. A. MCINTOSH
References 1. L. C. West and S. J. Eglash, Appl. Phys. Lett. 46, 1156 (1985). 2. B. F. Levine, C. G. Bethea, G. Hasnain, V. O. Shen, E. Pelve, R. R. Abbott, and S. J. Hsieh, Appl. Phys. Lett. 56, 851 (1990). 3. B. E Levine, A. Zussman, S. D. Gunapala, M. T. Asom, J. M. Kuo, and W. S. Hobson, J. Appl. Phys. 72, 4429 (1992). 4. R. H. Kingston, Detection of Optical and Infrared Radiation, Sec. 6.1, Springer, New York, 1978. This reference, like most others on the subject, refers to the difference frequency as the intermediate frequency, mostly for historic reasons. 5. Serber and Townes. 6. J. Tersoff, Phys. Rev. B. 30, 4874 (1984). 7. E L. Schuermeyer, P. Cook, E. Martinez, and J. Tantillo, Appl. Phys. Lett. 55, 1877 (1989). 8. Y. Tsou, A. Ichii, and E. M. Garmire, IEEE J. Quantum Electron, 5, 1261 (1992). 9. L. Vegard, Z. Krist67, 239 (1928). 10. K. K. Choi, J. Appl. Phys. 73,5230(1993). 11. E. R. Brown and S. J. Eglash, Phys. Rev. B. 41, 7559 (1990). 12. K. K. Choi, "Multiquantum-Well Structures for Hot-Electron Phototransistors" in Thin Films: Homojunction and Quantum-Well hlfrared Detectors (M. H. Francombe and J. L. Vossen, eds.) Academic, San Diego, p. 239, 1995. 13. S. D. Gunapala and K. M. S. Bandara, "Recent Developments in Quantum-Well Infrared Photodetectors," in Thin Fihns: Hontojutwtion and Quantum-Well h(h'ared Detectors, (M. H. Francombe and J. L. Vosscn, Acadcmic, San Dicgo, p. 114, 1995. 14. S. M. Szc, Physics of Semiconductor Devices, Wiley, New York, p. 46, 198 !. 15. E. R. Brown, K. A. Mclntosh, K. B. Nichols, E W. Smith, and M. J. Manfra, "CO,-laser hcterodyne dctection with GaAs/AIGaAs MQW structurcs," in Quantum Well lntersuhbaml l)evices, (H. C. Liu, B. F. Lcvine, and J. Y. Andcrsson, eds.) NATO ARW Series, Kluwcr, Dordrccht, pp. 207- 220, 1994. 16. H.C. Liu, J. Li, E. R. Brown, K. A. Mclntosh, K. B. Nichols,and M. J. Manfra, Appl. Phys. Lett. 67, 1594 (1995). / 7. B. F. Levine, J. Appl. Phys. 74, R 1 (1993). 18. E. R. Brown, K. A. Mclntosh, F. W. Smith, and M. J. Manfra, Appl. Phys. Lett. 62, 1513 (1993). /9. J. H. McElroy, N. McAvoy, E. H. Johnson, J. J. Degnan, F. E. Goodwin, D. M. Hcndcrson, T. A. Nussmeier, L. S. Stoker, B. J. Peyton, and T. Flattau, Proc. IEEE 65, 22 I. 20. J.Y. Andersson, L. Lundqvist, and Z. F. Paska, Appi. Phys. Lett. 58, 2264 ( 1991 ). 21. J.Y. Andcrsson and L. Lundqvist, Appl. Phys. Lett. 59, 857 (1991).
III-V Quantum-Well Structures for High-Speed Electronics E . R . B R O W N * AND K . A . M C I N T O S H
Lincoln Laboratory, Massachusetts Institute of Technology, 244 Wood St., Room E-124, Lexington, Massachusetts 02173- 9108
I. B a c k g r o u n d on Q u a n t u m - W e l l Infrared D e t e c t o r s . . . . . . . . . . . . . . . . . . . . . . . .
174
A. Direct D e t e c t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
174
B. H e t e r o d y n e Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
175
II. Q u a n t u m - W e l l D e t e c t o r Design and I n t e r s u b b a n d A b s o r p t i o n . . . . . . . . . . . . . . . . . A. Q u a n t u m - W e l l Energy Levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
178 178
B. Epitaxial G r o w t h . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
184
C. l n t e r s u b b a n d A b s o r p t i o n M e a s u r e m e n t T e c h n i q u e s . . . . . . . . . . . . . . . . . . . . .
i 85
D. l n t e r s u b b a n d A b s o r p t i o n Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
187
III. M Q W D e t e c t o r Fabrication and DC R e s p o n s e C h a r a c t e r i s t i c s
................
A. Fabrication and P a c k a g i n g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
188
B. Dark C u r r e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Spectral and Absolute Rcsponsivity D. P h o t o c o n d u c t i v e Gain
188 89
..............................
190
......................................
194
E. External Q u a n t u m Eflicicncy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
195
IV. Electrical B a n d w i d t h and O p t i c a I - H c t c r o d y n c E x p e r i m e n t s . . . . . . . . . . . . . . . . . .
196
A. P h o t o e l e c t r o n G e n e r a t i o n - R e c o m b i n a t i o n Noise T e c h n i q u c . . . . . . . . . . . . . . . .
196
B. D i o d e - L a s e r M i x i n g T e c h n i q u e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
198
C. M i c r o w a v e Rectification T e c h n i q u c
..............................
D. D i s c u s s i o n of B a n d w i d t h and Lifetime
199
............................
200
E. H e t e r o d y n e Sensitivity M e a s u r e m e n t T e c h n i q u e . . . . . . . . . . . . . . . . . . . . . . .
201
F. H e t e r o d y n e Sensitivity Results
202
.................................
V. A p p l i c a t i o n s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
204
A. I n s t r u m e n t a l Resolution and Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . .
205
B. H i g h - R e s o l u t i o n M o l e c u l a r S p e c t r o s c o p y
207
..........................
C. L o n g - R a n g e , H i g h - D a t a - R a t e C o m m u n i c a t i o n s
.......................
210
VI. I m p r o v e m e n t s in M Q W H e t e r o d y n c Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . A. E n h a n c e m e n t of External Q u a n t u m Efficiency . . . . . . . . . . . . . . . . . . . . . . . . 1. 4 5 ~
211 211
Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
211
2. N o r m a l - I n c i d e n c e ( G r a t i n g - C o u p l e d ) Detector . . . . . . . . . . . . . . . . . . . . . . B. Design of Detectors Having L i f e t i m e - L i m i t e d Electrical B a n d w i d t h References
213 ..........
...............................................
214 216
*On leave of a b s e n c e to the D e f e n s e A d v a n c e d R e s e a r c h Projects Agency, 3701 N. Fairfax Dr., R o o m 850, A r l i n g t o n , Virginia 2 2 2 0 3 - 1 7 1 4 173 Copyright 0 1997 by MIT Lincoln Laboratory. All rights of reproduction in any form reserved. ISBN 0- i 2-533023-5, ISSN !079-4050/97 $25.00
E. R. BROWN AND K. A. MCINTOSH
174
I. Background on Quantum-Well Infrared Detectors A.
D I R E C T DETECTION
Since the initial observation of strong intersubband absorption in multiplequantum-well (MQW) structures (1), these structures have been used as the basis for several different types of midinfrared detectors, emitters, and modulators. One of the first successful detector designs used heavily doped n-type GaAs quantum wells and relatively thick AlxGa~_xAs barriers with the well thickness and barrier A1 fraction tuned so that only one bound state existed in each quantum well (2). The second state of each well lays at an energy level just above the band edge of the barriers, making it quasi-bound. The absorption mechanism in this detector was the bound-to-extended-state intersubband transition shown schematically in Fig. 1. The responsivity spectrum resulting from this transition was found to be Gaussian in form with a peak energy close to the bound-toextended-state separation and a spectral energy width roughly equal to one-third of the peak energy. The bound-to-extended detector has been found to behave like a classic photoconductor in the sense that the photocurrent I0 can be expressed as I~ =
r/~ hv
n=2
-- RoP,
( 1)
EXTENDED STATE - -
.
V
hv BOUNE STATE AIGaAs FIG. 1.
GaAs
AIGaAs
Bound-to-extended-state transition in a quantum well.
lll-V QUANTUM-WELL STRUCTURES F()R HIGH-SPEED ELECTR()NICS
175
where R 0 is the external responsivity. As in all photoconductors, the current noise is dominated by fluctuations in the generation and recombination rates (i.e., G-R noise) of electrons, leading to the power spectral density Sl =
4eg(I o + ID).
(2)
In these expressions, 7/o is the external quantum efficiency, e is the electron charge, P is the average optical power, h is Planck's constant, u is the optical frequency, It) is the dark current, and g is the photoconductive gain (which is usually much less than unity in MQW structures and is discussed more fully in Sec. III.E). The primary advantages of the GaAs MQW detector over the standard IR detectors made from HgCdTe are: (1) the peak wavelength Ap of the spectral response can be "engineered" through control of the quantum-well width and the barrier height, (2) GaAs substrates are relatively robust and are therefore more easily fabricated in arrays or other integrated circuits, and (3) GaAs and AIGaAs epitaxial layers are more robust because the constituent atoms diffuse much less with time or temperature than the volatile Hg component in HgCdTe alloys. One disadvantage of the MQW direct detector is that its dark-current density at 77 K is roughly three orders of magnitude higher than in good HgCdTe detectors. This higher density causes the specific detectivity D* of the MQW detectors to be roughly 100 times lower under low background radiation. To the best of the author's knowledge, the highest detectivity of an MQW detector reported to date at 77 K and 10-/.tm or longer wavelength is still D* = 2.6 • 10 ~ cm Hz~/-~W ~ (3). A second disadvantage is the polarization selection rule that results in a strong absorption of light only for the component of the incident IR electric field that is oriented perpendicular to the plane of the quantum wells. This disadvantage requires the fabrication of an angled facet in the substrate or two-dimensional gratings on the top surface of the wafer so that incident radiation can be efficiently absorbed within the MQW structure.
B.
HI';TER()I)YNF~ DF~TFA'TION
Neither of the previous disadvantages limits the performance of GaAs/AIGaAs MQW detectors in the optical-heterodyne, or coherent, mode. In this mode the output beam from a laser local oscillator (LO) is combined with radiation from another infrared source (signal) and both are coupled into the MQW structure, as depicted in Fig. 2. Because the detector response is inherently quadratic in the optical electrical field, the absorption of the combined beams results in the generation of photocurrent at the difference frequency (DF)
E. R. BROWN AND K. A. MCINTOSH
176
/
DETECTOR MESA
CO 2 L A S E R B E A M
(LOCAL OSCILLATOR)
QUANTUM/ WELLS .....
INPUT BEAM (SIGNAL) \
n+GaAs
SEMI-INSULATING s SUBSTRATE o
45 CLEAVED FACET BEAM COMBINER
FIG. 2. Schematic diagram of optical mixing process that occurs with angle-taceted MQW heterodyne detector.
between the LO and signal beams (4). The magnitude of the DF photocurrent (i~)v.) is proportional to the product of the time-averaged LO power (P~,~) and signal power (Ps) through the relation 9 llw
~
[2(r/oeg )2 Plx~Ps/(hv)2] I/2
(3)
where it has been assumed that vl.~ v s = v. Because P~,~ >> Ps, the magnitude of the DF photocurrent is much stronger than the signal photocurrent in the absence of an LO, which is why heterodyne is more sensitive than direct detection. Combining Eqs. (2) and (3), one can write the following relation for the DF signal-to-noise (S/N) power ratio" S N
")
9
2( r/0eg)-PsPi ()RA/ (h v)4eg(Ilx ~ + ID)RAAf + kTAAf --
2(r/~ . . . .. , 4eg(r/(legPlx~/(hv + II))RAAf + kTAAf
(4)
where R A is the amplifier input resistance and Af is the width of the DF passband. The last term in the denominator represents the amplifier noise power, with T A being the equivalent noise temperature. A more useful figure of merit for heterodyne performance is the noise equivalent power NEPH~.:T. This is defined as the value of Ps in Eq. (4) that yields a DF S/N ratio of unity, resulting in the expression NEP HEy
.
4eghv[r/~ .
.
.
.
+ IDhv]RAAf + kTAhuAf . . . 2(r/oeg)2pix)RA "
(5)
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
177
From Eqs. (4) and (5) it is clear why the disadvantages of MQW detectors in direct detection discussed in Sec. I.A do not necessarily limit the heterodyne performance. To overcome the dark-current disadvantage, one simply applies enough LO power that the photon-induced G-R noise dominates the darkcurrent and amplifier noise. In this case, PLO >> IDhv/rl0eg and PLO >> kTAhV / 4r/0(eg)2RA , so that the DF S/N ratio approaches the value rl0Ps/2hv and the NEPHET approaches 2hvAf/r/0. These values defined the photon-noise limit, which represents a maximum sensitivity that can be surpassed only by increasing r/0. To indicate how the magnitude of the NEPHET relates to this limit, a more convenient quantity is the effective-heterodyne quantum efficiency r/En, defined by ~EH ~ 2hvAf/NEPHET" This will be used henceforth to quantify the detector sensitivity. As an example, suppose one has a typical GaAs/A1GaAs MQW detector operating with 25% external quantum efficiency and a CO2-1aser LO at 10-/,m wavelength. In the photon-noise limit, we find NEPHET approaches 2hvAf/r/0 = 1.59 • 10 -19 W/Uz, and ~EH approaches 0.25. This NEP may strike some readers as a very small number, particularly when compared with the NEP values quoted for direct detection. Indeed, the same GaAs/A1GaAs MQW detector operating in direct detection would have a direct NEP of roughly 10- ~ W - Hz-~/2, with the noise being dominated by the darkcurrent fluctuations. The units are different because the heterodyne NEP is defined in the DF band before electrical rectification, and the direct NEP is defined after this rectification. Nevertheless, the much smaller heterodyne value represents a real improvement in sensitivity per Hz of electrical bandwidth. Physically, the low heterodyne NEP follows from the multiplication of the signal power by the LO power, as given by Eq. (4). This makes the heterodyne detector behave similarly to a linear amplifier, as first discussed in detail by Serber and Townes (5). It also allows one to relate the heterodyne and direct NEPs when their respective noise mechanisms are the same (i.e., when the LO power is low enough that the darkcurrent or amplifier noise dominates). The relationship is given by NEPHE T ~
NEPD'R p
9
(6)
I.()
By taking the typical NEPD!R of 1 0 *~ W / H z I/2 and the Pl.t) of 1 mW, this expression predicts NEPHET = 10 *'~W / Hz, in satisfactory agreement with the experimental results presented later in Sec. V. The polarization-rule disadvantage of MQW detectors does not limit the heterodyne performance because most laser LOs, particularly CO, lasers, emit in only one polarization. In this case, a high r/0 can be obtained simply by coupling the LO and signal through a 45 ~ facet lapped in the substrate, as shown in Fig. 2. This is the coupling technique proposed here. Because r/0 for a single polarization in MQW detectors can approach that of HgCdTe, the photon-noise limit of
E. R. BR()WN AND K. A. MCINT()SH
178
the two detector types should be comparable, provided that the HgCdTe is a photoconducive detector. If the HgCdTe is photovoltaic (e.g., a photodiode), then the photon-induced G-R noise term in Eqs. (4) and (5) is replaced by a full photon shot-noise term, 2eI~Af, and the photon-noise-limited NEPHET becomes huAf/r/0. This factor-of-two difference in sensitivity is a general result for all photovoltaic and photoconductive devices (4).
II. Quantum-Well Detector Design and Intersubband Absorption One of the key issues in using MQW structures for heterodyne detection is to design them so that the peak of the intersubband absorption lies within the laser LO band of interest, e.g., the CO~-laser band from 9 to 11 /.~m. For GaAs/ AIGaAs MQW structures, the key material design parameters are the quantumwell width and the barrier height (which is determined mostly by the A1 fraction). Along with the effective mass and the applied electric field, these parameters determine the energy of the two quantum states associated with the intersubband transition.
A.
QtJANTUM-WIilJ.
ENER(;Y
Ll:.Vlil.S
The energy levels are found by solving Schrodinger's equation. In a first pass, one usually applies the effective-mass approximation (EMA), whereby the full Bloch wave function in the quantum well or barriers is represented by the electronic envelope function q~, and the influence of the atomic core potentials is contained in the effective mass m*. The energy dependence of the effective mass associated with nonparabolicity in the band structure is ignored in solving for the envelope functions, but is accounted for in solving for the energy levels. A second assumption is that there is no internal electric field. With these three assumptions, the Schrodinger equation is -- h2 d2ff/
2m* 6x 2 = Ech,
(7)
and is subject to the conditions that ~ and (m*)-~ d~/dx be continuous at each point in the structure, particularly across the heterojunctions. The EMA has been found to be valid tbr electrons in most type-I heterostructures, such as GaAs/AIGaAs, in which the conduction band in the quantum-well material lies much closer to the conduction band of the barrier than to the valence band of the barrier. Exceptional cases, such as GaAs/AIAs (conduction band of GaAs ap-
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
179
proximately 1.0 and 2.0 eV from conduction and valence bands, respectively, of AlAs) can be handled by a generalization of the E M A known as the envelopefunction approximation, which is beyond the scope of this chapter. The lowest state of the well is strongly bound, so that the energy in any quantum well can be found to a satisfactory degree of accuracy by a straightforward solution to Eq. (7), assuming that no mixing occurs with the states in neighboring wells. The envelope function is given by cos(kwX) in the quantum well (x = 0 at the center of the well) and exp(--kBx) in the barriers, leading to the following implicit equation for the lowest energy: m*k B
tan(kwLw/2) = - - . m~kw
(8)
In this expression, m* is the effective mass in the well material, m~ is the effective
mass
k B - V'2m~(AE c -
in
the
E)/h. The
barrier
material,
kw = V'2m*E/h,
and
quantity AE c is the barrier height (i.e., the differ-
ence in conduction-band-edge energy between the well and barrier materials), and is given by AE c : E B - E w - a E V,
(9)
where E B and E~v are the band-gap energy of the barrier and well materials, respectively, and AE v is offset in the valence bands between these materials. At the typical detector temperature of 77 K, the band gap of AlyGal_yAS is approximately given by E G = 1.51 + 1.334y, valid in the range 0.0 < y < 0.45 where this band gap is known to be direct. The quantity AE v is usually determined by linear interpolation between the AE v values for AC and BC. Explicitly, if one denotes the quantum-well material as AxB ,_xC and the barrier material as AyB i_yC and assumes that y > x, then the valence-band offset between these two compounds is given by AEv{AxBI
xC/AyB,_yC} - ( y -
x)'AEv{BC/AC}.
(10)
The constituent binary compounds, GaAs and AlAs, are known to exhibit AE v ~ 0.50 eV (6,7,8), so that from Eqs. (9) and (10) one can write AE c = 0.834y. The interpolation procedure of Eq. (10) is known as Vegard's law (9). To proceed with the solution to Eq. (8), one must also account for band nonparabolicity and the composition dependence of the effective mass. The most important effect of the nonparabolicity is the energy dependence of the quantum-well effective mass. In the case of GaAs quantum wells, one can assume to a first approximation that m * = 0.067 9mo[1 + A(E/EG)].
(ll)
E. R. BROWN AND K. A. MCINTOSH
180
where m 0 is the free electron mass, E c is the gap energy, and A is a constant ( ~ 0.824). The compositional dependence of the effective mass in the barriers is given by m~ = (0.067 + 0.083y)m 0 where y is the A1 fraction. Nonparabolicity in the A1GaAs barriers is usually not addressed in MQW structures because of the relatively close proximity of the energy levels to the conduction band edge. In the first approximation, many body corrections from free carriers are generally ignored in the quantum well and barriers. The resulting values for the lowest energy level, E~, are plotted in Fig. 3 vs quantum-well width and parametrized by AI fraction in the barriers. The zero of energy is assumed to be the conduction band edge of the quantum-well material. The well width and AI fraction are varied over what is generally considered to be the practical range of these parameters. The plot shows two trends that are characteristic of quantum-size effects. First, the energy level decreases monotonically with increasing well width with a functional dependence that approaches an inverse quadratic as the well width increases. Second, for a given well width, the energy level increases monotonically with increasing AI fraction in the barriers. This can be understood in the classical limit as the increase in kinetic energy (the difference between the total energy and the conduction band edge) as-
110.00 100.00
f
.~26%
90.00 >
O
E >(9 n..
z
uJ
80.00 70.00 60.00 50.00 40.00 33.90
39.55
45.20
50.85 5( ;.50 WELL WIDTH (ANGSTROM)
62.15
67.80
FIG. 3. Theoretical curve of first-state energy (E~) in each quantum well of a G a A s / A l v G a ~ _ vAs M Q W structure plotted vs quantum-well width and parametrized by the A! fraction in the barriers. Each barrier is assumed to have a width of 40 nm.
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
181
sociated with an electron being reflected from more impenetrable walls. Note, however, that this increase is slower than the increase in AE c itself, so that the binding energy of the first level (i.e., the difference between AE c and E~) increases with increasing A1 fraction. A third and rather unusual effect shown in the plot is the inflection point in energy vs well width that occurs near L w = 3.5 nm. This is a ramification of band nonparabolicity in the quantum well, by which the energy increase is retarded with decreasing well width through the increase in the effective mass with energy. The solution for the second state in the quantum well is not as straightforward because it is usually either weakly bound or weakly extended, lying at an energy level just below or just above the barrier band edge, respectively. In either case, the envelope function can mix strongly with the functions in neighboring wells, causing the energy levels to be distributed over a miniband of significant range. In most cases, the miniband spans an energy range that is centered far below the second-state energy that would be found for an isolated quantum well having the same width and barrier height. The solution to Eq. (8) follows readily by assuming the MQW structure to be perfectly periodic and have infinite extent. One can then apply the well-known Kronig-Penny model of quantum mechanics. In this model, the lower edge of the miniband corresponds to an envelope function in the well of the form sin(kwX) and envelope functions in the barriers proportional to exp[kR(x - L w - Lr~)] + exp[-kBx] or exp[ik~(x - L w - L~)] + exp[-ik~x] for the bound and extended cases, respectively. In these expressions, L w and L b are the widths of the quantum well and barrier, respectively. They lead to the implicit eigenvalue equations tan(kwLw/2) =
m~kw coth(kBLs/2), m*k H
(12)
m~kw cot(ksLH/2) m~vkB
(13)
for the bound case, and tan(kwLw/2) =
for the extended case. The calculated energy value E 2, for the lower edge of the second-level miniband is plotted in Fig. 4 for the same ranges of well width and A1 fraction as in Fig. 3 and for L s = 40 nm. Also plotted is a curve for the upper edge of this miniband, as computed through the Kronig-Penny model. As expected intuitively, the solution for E 2 is monotonically increasing with decreasing well width. In addition, each A1 fraction has a transitional well width, above which the second level is bound and below which the second level is extended. In the bound range, E 2 decreases very rapidly with increasing well width; but near the transition, the rate of change of E 2 with well width decreases significantly and
E. R. BROWN AND K. A. MCINTOSH
182 250
L B -- 40 nm 230 _ . . _
~ 210 111 Z
uJ
AEc= 200.2 190 •Ec= 183.5 170
aEc= 16(~.9 150
33.90
39.55
45.20
50.85
56.50
WELL WIDTH (ANGSTROM)
62.15
67.80
FIG. 4. Theoretical curve for lower-edge energy (E~) of second-state miniband in each quantum well of a GaAs/AlvGa t vAs MQW structure plotted vs quantum-well width and paramctrizcd by the A! fraction in the barriers. Each barrier is assumed to have a width of 40 nm. The barrier height (measured in energy relative to the band cdgc of GaAs) for each A! fraction is shown as a horizontal dashed line.
approaches zero at the smallest widths. This "pinning" effect is caused primarily by the mixing action of the second-level envelope functions with the same functions in neighboring wells. To a much lesser extent, it is caused by the band nonparabolicity in the GaAs quantum wells. Another effect of the state mixing is the finite range of the miniband which, for each AI fraction, approaches 10 meV at the smallest well width of 33.9 ]k. The results of Figs. 3 and 4 can be combined to yield the intersubband energy, E 2 - E~, plotted in Fig. 5 in units of wavelength A -- hc/(E 2 - E~). This plot is useful because it serves as a design chart for bound-to-extended M Q W structures in the mid-IR spectral region. Similar plots have been published previously and used for the same purpose (10). For each AI fraction, the intersubband wavelength vs well width displays a minimum (i.e., the energy displays a maximum) very near the transition from a bound second level to an extended one. This is a result of two separate effects. Below the minimum, the decrease in A with increasing well width reflects the pinning action of the second level after it
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
183
is squeezed out of the well. The increase in A with well width above the minim u m reflects the fact that E 2 decreases faster with well width than E~ in this range. A simple explanation for this follows from the limit of a very deep quantum well, whereby E n = (nh)2/8m*L 2, with L w being the well width. In this case, the rate of decrease with increasing well width is four times greater for n = 2 than f o r n = 1. In addition, the transition from a bound to an extended second state, denoted by the dashed line in Fig. 5, moves toward smaller well thickness as the AI fraction increases. This is a simple consequence of the fact, stated earlier, that increasing A1 fraction increases the binding energy, so that a narrower quantum well is required to squeeze the second state out of the well. One effect that can be important in M Q W structures under operational conditions, but was ignored in the previous analysis, is the applied electric field. Under such a field, the potential energy term in Schrodinger's equation is no longer spatially constant, so that the envelope functions can not be sinusoids or simple exponentials, and the implicit eigenvalue equations given earlier are not correct. If the applied field is small, however, the change in the eigenvalues can be
FIG. 5. Theoretical inlersubband wavelength [;k = hc/(E 2 - El) ] for a G a A s / A l v G a I vAs M Q W structure plotted vs quantum-well width and parametrized by the AI fraction in the barriers. Each barrier is assumed to have a width of 40 nm. The squares represent data points for samples having a barrier width of 40 nm and an AI fraction of 22%.
E. R. BROWN AND K. A. MCINTOSH
184
neglected. A measure of the impact of the applied field is the potential energy drop induced by the field across the quantum well, AV = eFL w. As discussed in Sec. III, the bias field across MQW structures is generally kept rather low to keep the dark current at tolerable levels. In the present samples, the maximum internal electric field is estimated from the maximum bias voltage VmAx and the total length of the MQW s t r u c t u r e s LMQ w, through FMA x = VMAx/LMQW. This expression yields FMA x ~ 1.6 x 104V - cm-l for all three samples, so that the potential drop across the typical 4.5-nm-wide quantum well is AV ~ 7 meV. This is approximately 10% of the energy of the first energy level and less than 5% of the second level. These are small enough that the applied field is generally not addressed in the design of MQW structures but is treated as a second-order effect.
B.
EPITAXIAL GROWTH
Three MQW structures in this study were grown by molecular beam epitaxy (MBE) on semi-insulating GaAs substrates at a temperature of 600~ They differed in either the width L w or number N w of quantum wells, or in the width of the barriers. The essential properties are summarized in Table I. Sample 1 had 50 4.5-nm-wide wells separated by 20-nm-wide barriers; sample 2 had 50 5. l-rimwide GaAs quantum wells separated by 40-rim-wide barriers; and sample 3 had 100 4.5-nm-wide wells separated by 40-rim-wide barriers. In each sample, the center 2.5 nm of every well was doped n-type with Si to a density of approximately 2.5 X 10 TM cm-3, yielding a sheet density of 6 X 10 ~ cm 2. The contact layers below each MQW structure consisted of 750 nm of GaAs doped to 1.0 • 10 Is cm -3 followed by 250 nm of GaAs doped to 2.4 x 10 ~ cm --3. The
TABLE I MATF.R1AI. CHARACTH{ISTICS ~)t: THRF.F. GAAs/AI.GAAs MQW DvrE,:c'rr Quantity Nw L w (nm) Barrier aluminum fraction Barrier width (nm) LMQw (rim) Well sheet concentration
Sample 1
Sample 2
Sample 3
50
50
100
4.5
5.1
4.5
22%
22%
22%
20
40
40
1205
2295
4490
6 • 10 ~ cm 2
6 • 10 ~ cm 2
6 • 10 ~ cm 2
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
185
contact layer above the MQW structure consisted of 350 nm of GaAs doped to 2.5 X 1018 cm -3. The A1GaAs barriers in the MQW structure had a 22% A1 fraction and a thickness of 40 nm. The barrier thickness was chosen as a compromise between dark current and ease of fabrication. Experience has shown that the 40-nm barriers yield a significantly lower dark current than thinner barriers; however, the 40-nm barriers lead to an overall thickness in excess of 4 / x m (assuming N w = 100), which makes the fabrication somewhat difficult. The growth was carried out by MBE in a commercial machine (Intevac MOD GEN II) that had several features to facilitate the growth of MQW structures. First, it was designed for growth on 3-in. substrates that are mounted on solderless blocks during the growth process. Second, it has stable heating techniques for the substrate and the source (i.e., Ga, A1, As, and Si) effusion cells. Third, its sources, particularly the gallium, have very low defect density. These features provide excellent accuracy and uniformity of the temperature and source-flux across the substrate. Temperature and flux control play an important role in the given samples because of the relatively long growth times that were required. For example, at the average growth rate of 1 /zm/h, the 5.8-/xm-thick sample 3 required a growth time of 5.8 hours. Over such a duration, systematic temperature or flux drifts would have caused errors in the AI fraction or silicon doping, or introduced defects in the material. A third beneficial feature of the MBE machine is monitoring of the growth rate by in situ reflective high-energy electron diffraction oscillations. This monitoring is particularly important for obtaining the specified quantum-well width.
C. INTERSUBBAND ABSORPTION MEASUREMENT TECHNIQUES
The technique used to characterize the intersubband absorption was infrared transmission. Because intersubband transitions can be engineered to occur throughout the middle infrared, the transmission is usually measured with a broadband Fourier-transform spectrometer (FTS). The FTS used in the experiments at Lincoln Laboratory covers the spectral range 400 to 4800 c m ~ (2.1 to 25 /xm) and has two sample compartments and detectors. The primary sample compartment has fixed f/3.5 optics and a room-temperature pyroelectric detector, while the secondary compartment has adjustable f/1 optics and a liquid-nitrogencooled HgCdTe detector. Instrumental resolution is programmable over the range 2 to 32 cm-~. Polarization of the infrared beam is controlled by polarizers located in the sample compartments. To improve the S/N ratio in the data, multiple scans are coherently added. In addition, various smoothing, normalization, logarithmic-subtraction, and integration procedures are performed on the data to clarify the location and strength of
186
E. R. BROWN AND K. A. MCINT()SH
absorption features such as those due to intersubband transitions. Interfering features in the spectral region near the intersubband transition are removed to help interpret the transmission spectra. These features include absorption from free carriers in the substrate, higher-order phonons, surface oxide layers, contaminants on the samples, and Fabry-Perot interference fringes. Transmission measurements were made by normalizing the infrared signal measured with the MQW sample in the optical beam to that measured with a control sample. To accurately determine the center wavelength and width of the intersubband absorption feature, multiple-pass internal reflection (MIR) measurements were made. Small (3 • 10 mm) pieces were cleaved from each wafer and parallel 45 ~ facets were lapped and polished on two opposing ends, as shown in Fig. 6. The transmission spectra through these small 45 ~ parallelepipeds clearly show the intersubband absorption features because of the increased optical path length and the complete elimination of interference fringes. The polarization of the optical beam, which was incident along the normal to one of the end facets, could vary between parallel to the plane of the quantum well and at 45 ~ with respect to the well. Transmission data were obtained by dividing the optical power spectrum by a corresponding spectrum taken with a control sample, consisting of an identical MIR structure made from a bare SI-GaAs substrate. Multiple-pass measurements were limited to MQWs on semi-insulating substrates to avoid the possibility that strong free-carrier absorption in the substrate will dominate the intersubband absorption. Although MIR measurements increase the strength of the intersubband absorption and can help to identify weak absorption features, uncertainties in the number of passes and in the intensity distribution of the infrared beam at the quantum wells can lead to errors in measured absolute absorption strength.
FIG. 6. Cross-seclional view of GaAs parallelpiped used Io support multiple-pass internal rellection through a MQW epitaxial structure.
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
187
D. INTERSUBBAND ABSORPTION RESULTS The multiple-pass transmission spectra through the three samples were measured at room temperature and 77 K by F r l R transmission spectroscopy. Each spectra showed Gaussian-like absorption features, similar to those typically displayed by all GaAs/AIGaAs bound-to-extended MQW structures. The measured peak wavelength Ap and full width at half-maximum AA for the absorption profiles at 77 K were 9.70/.tm (127 meV) and 45 meV, respectively, for sample 2. The same quantities for samples 1 and 3 were Ap-- 10.53 /.tm (117 meV) and 10.19 /tim (121 meV), and AE = 43 and 42 meV, respectively. Each of these absorption profiles is largely contained within the CO 2 laser emission range of 9 to 11 ~ m (138 to 113 meV). They were also quite insensitive to temperature variations around 77 K. This insensitivity is consistent with the fact that the quantum wells in all of these samples were degenerately doped, making the sheet concentration in the first energy level practically insensitive to temperature variations around 77 K. The experimental values of peak wavelength for samples 2 and 3 are plotted in Fig. 5 in comparison with the theoretical curves for MQW structures having 40-nm-wide barriers. The experimental points lie at slightly lower wavelengths than the theoretical curve labeled 22%, the nominal Al fraction in these samples. This discrepancy is within the 1 to 2% experimental uncertainty in the Al fraction of these samples. The gratifying aspect of the comparison is that a line connecting the two data points has practically the same slope as the theoretical curves above and below it. This supports the argument given in Sec. II.A that the second-state miniband gets pinned just above the barrier conduction band edge, causing the difference in energy between this miniband and the ground (bound) level to increase (i.e., the wavelength to decrease) with increasing well width in the range below the bound-to-extended transition. For each sample, the transmittance at the center of the absorption feature was used to derive the fractional absorption per quantum well, sr, which is a useful figure of merit for the strength of intersubband transitions. The relation between transmission through the multiple-pass samples and fractional absorption is given by TVr
= T 2 (1 - ~') Nwp,
(14)
where T is the power transmission through the air-GaAs interface and P is the number of internal passes of the radiation through the MQW structure. For example, sample 2 had 50 quantum wells and, like the others, T = 0.7 (air-GaAs interface) and P = 4. Therefore, the measured peak absorbance of approximately 0.89 corresponds to TTOv = 0.13 and ~"= 0.007. This may seem small until one realizes that the absorption is taking place over a distance scale of LEvv = Lw/cOs 45 ~ which for this sample is 7.2 nm. Hence, the absorption coefficient is
188
E. R. BROWN AND K. A. MCINTOSH
approximately a - ~'/LEFF = 9.7 • 103 cm -1, which is comparable to the absorption coefficient at the band edge of some direct-gap semiconductors. It is interesting to compare the experimental values of peak fractional absorption to the theoretical value derived for a bound-to-bound intersubband transition in GaAs quantum wells (11), hOT
st(A~ = 27ri; s
[ 1024e2sin20] 2-7~~m*c j
(15)
In this formula, orT is the total sheet concentration in each well, 0 is the angle between the propagation vector and the perpendicular to the quantum wells, F s is the full width at half-maximum of the absorption profile (assumed to be induced by scattering), n is the optical refractive index, and m* is the effective mass of the quantum-well material. In applying Eq. (15) to the experimental results for sample 2, we have OrT=6X 1011cm-2, F s = 362 cm -~, sin20=0.5, m* = 0.067m, and n = 3.3, which yield ~"= 0.008, in good agreement with experiment. This agreement suggests that a single sum rule applies to both the bound-to-bound and bound-to-extended transitions. By this rule, the integrated absorption strength would be practically the same, but the peak absorption of the bound-to-extended transition would be weaker because of its greater broadening parameter. In practice, the bound-to-extended transition is roughly three to tour times broader than a bound-to-bound transition in a quantum well of comparable width, composition, and doping concentration.
III. MQW Detector Fabrication and DC Response Characteristics The fabrication and packaging of MQW detectors for heterodyne detection can have much greater consequences on the performance in heterodyne detection than in direct detection because of the effect of electrical bandwidth. Similarly, the effect of the responsivity is much more important in heterodyne detection than in direct detection because of its impact both through the LO and signal terms. Therefore, it is important to review the packaging and responsivity issues prior to discussion of the heterodyne or other high-frequency experiments.
A.
FABRICATION AND PACKAGING
After growth, detectors were fabricated by the following sequence of steps. First, 20-/zm-diam Ni/Ge/Au metal pads were patterned by optical lithography and metal liftoff techniques. This pad formed the ohmic-contact portion of the
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
189
top MQW-detector contact. Next, a 75-/~m-diam Ti/Au metal dot was defined concentric to the 20-/.~m dot. In the area outside of the smaller dot, the Ti/Au metallization formed the highly reflecting portion of the top contact. Then, 75/~m-diam detector mesas were defined by wet etching of the GaAs/AIGaAs layers using the Ti/Au as a self-aligned mask. Finally, an ohmic field metal was deposited on the exposed n + cladding layer below the MQW structure. After these steps, the wafers were cleaved into rectangular chips, and a 45 ~ facet was lapped into one edge of each chip to couple the infrared radiation to the M Q W structure. After fabrication, the chips were soldered onto copper mounting blocks and wire bonded or ribbon bonded to a microstrip transmission line. The separation between the mesa and the microstrip line was approximately 1 mm. Both types of bonds were attempted to maximize the high-frequency response of the detectors. Previous experience indicated that multiple wire bonds in parallel provided the highest bandwidth because this configuration yielded lower capacitance than a ribbon bond but less inductance than a single wire bond. Microwave power from the MQW device was transferred to a coaxial line using a stripline-to-coaxial adapter on the mounting block. For detector characterization experiments, the mounting block was fastened to the cold finger of a closed-cycle helium refrigerator, and the detector output was fed to outside electronics through a coaxial hermetic feedthrough connector. Note that the detectors fabricated from MQW samples 1, 2, and 3 will be called devices 1, 2, and 3, respectively, in the remainder of this chapter.
B. DARK CURRENT
Alter fabrication the dark current was measured for several 75-~m devices from each sample. Figure 7 shows the 77- and 4.2-K dark current vs voltage for devices 1, 2, and 3. A negative voltage was applied to the top contact because it produced lower dark current than an identical positive voltage, consistent with an expected small asymmetry in the doping profile in the samples. The dark current for device 1 changes by about one order of magnitude at most in cooling from 77 K to 4.2 K. In contrast, the dark current of device 2 decreases by over three orders of magnitude at low bias voltages, and the current of device 3 drops even more. The high 77-K current and weak temperature dependence of device 1 is consistent with strong defectrelated electron transport through the relatively thin barriers (20 nm) of this sample. The thicker barriers (40 nm) of devices 2 and 3 suppress this mechanism greatly, leading to much less 77-K dark current. The temperature sensitivity of the latter devices occurs because the predominant dark current mechanism in these devices becomes the thermionic emission of electrons out of the quantum wells, which has an Arrhenius dependence on temperature.
E. R. BROWN AND K. A. MCINTOSH
190
10-1
--
s,:.
<
A v
I..Z LU nIZ: :3
S
ss s S s s s s I 77 K s I s s I s 1 s s 4.2K f s s
ss
SS SS
. . . . .
SAMPLE
..........
SAMPLE 2
1
SAMPLE 3
000000
~ S
If
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ee o
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e I'
,"
77K
eaeeeeeee~176
INSTRUMENTAL NOISE FLOOR 10. 9
! 0
I
l'~
.."
I
9 /
9 !
VOLTAGE
4.2 K
I (V)
l
I
-10
FIG. 7. Dark current vs bias w)ltage for mesa devices made fi'om three different MQW samples. The nmasurement temperatures are 77 and 4.2 K (after R
Device 3 has practically identical dark current to device 2 at 77 K, except at the highest bias voltages. Upon cooling to 4.2 K, however, the dark current of device 3 drops by several orders of magnitude more than that of device 2. This is thought to occur because of the greater overall thickness of the MQW structure in device 3. Hence, at a given bias voltage the electric field across the MQW structure in device 2 is approximately twice that of device 3. This issue will be revisited in Sec. III.D. Much greater insight into the dark current through MQW structures and techniques for reducing its magnitude can be found in the recent review article by K. K. Choi and references therein (12).
C.
SPECTRAL AND ABSOLUTE RESPONSIVITY
Although there are many ways to measure the external responsivity R(), the technique shown schematically in Fig. 8 was applied at Lincoln Laboratory because of its accuracy and amenability to absolute calibration. The optical source
lll-V QUANTUM-WELL STRUCTURES F()R HIGH-SPEED ELECTRONICS
191
KBr-PRISM SPECTROMETER
MQW DETECTOR
! !
PINHOLE PYROELECTRIC DETECTOR
---, 9
! |
CHOPPER
ii
LOCK-IN AMPLIFIER
I
BLACKBODY SOURCE
AMPLIFIER FIG. 8. Block diagram of experimental setup used to measure the responsivity spectrum of MQW devices indirect detection.
for the measurements is a 1000~ blackbody filtered by a prism spectrometer. The blackbody provides much greater luminosity than a popular alternative, the incandescent globar, particularly at longer infrared wavelengths. The resolution of the prism spectrometer varies from approximately 16 cm t at 1000 cm ~ (10 /zm) to approximately 60 cm ~ at 2500 cm ~ (4 /xm). The detectors wcrc mounted on the cold finger of a closed-cycle helium refrigerator, and radiation emitted from the spectrometer was focused onto the detectors through the 45 ~ facet. For calibration purposes, a beamsplittcr located between the spectrometer exit slit and the input window on the refrigerator directs a portion of the infrared beam onto a pyroelectric detector. The pyroelectric detector has a specially treated surface of known area for constant and calibrated RI~ vs wavelength throughout the near and middle infrared regions. Hence, the true spectral variation of R 0 for the M Q W detector is obtained simply by normalization of the output of the M Q W detector to that of the pyroelectric detector at all wavelengths. Shown in Fig. 9 is the experimental result for device 2 at a bias voltage of 1 V. The spectral response curve was nearly Gaussian with a peak at 9 . 6 / x m and a full width at half-maximum of 45 meV. These are both close to the peak-absorption wavelength and width of the absorption results presented in Sec. II.D. Similar results were obtained for devices 1 and 3, suggesting that the response and absorption spectra in the present samples are practically identical.
192
E. R. BROWN AND K. A. MCINTOSH
A
//i l-
.fi i__
w (/) z
O a. 0'J Lu
I:1:: n.-
o
I(.) uJ I.ILl
C~
I
12
I
10
I
8
I
6
WAVELENGTH (pm) FIG. 9.
E x p e r i m e n t a l responsivity s p e c t r u m of device 2 al 77 K.
While the previous technique is useful for spectral response, the absolute response is better determined by illuminating the detector with a laser because of the much greater signal strength. At Lincoln Laboratory, R 0 was measured directly from the current-voltage (I-V) characteristics under laser illumination. Radiation from a waveguide CO~ laser was tuned to the wavelength nearest the peak of the spectral response curve. R 0 was then calculated as the difference in current at a constant voltage between the illuminated and dark I-V curves divided by the incident laser power. Plotted in Fig. I0 is the result for device 3. For each device, the responsivity at or near the peak wavelength displayed a well-defined maximum at a particular voltage, defined as V x. As listed in Table II, this maximum was 0.4, 0.28, and 0.25 mAJmW for devices 1, 2, and 3, respectively. The maximum bias voltages were 2.0, 4.0, and 7.5 V, respectively. As discussed in the following section, the maximum in the responsivity can be explained qualitatively through the bias dependence of the photoconductive gain. It should be mentioned that the decrease in responsivity at high bias voltages was initially thought to be associated with a current-dividing effect between the load resistance and the MQW differential resistance, which decreases rapidly at high
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
193
SAMPLE 3 T=77K
A
, u
c DIRECT RESPONSE . . _ . ~ / (CO2-Laser Chop) / ,
/,
u
> r,/)
/
A
%
%,~
m
z
%
ii I
O
IX. U.I n-
HETERODYNE RESPONSE (Blackbody Chop)
0
I 4
2
I 6
I 8
BIAS (V)
I 10
I 12
FIG. 10. Responsivity vs bias w)ltage of device 3 to a CO, laser in direct detection. Also shown is integrated hetcrodync output of same device in response to a 1000"C blackbody mixing with a CO 2 laser.
TABLE II St'ECTRAI. ANI) DC-RESP()NSE CHARACTERISTICS ()F THREE
MQW
SAMt'LES AND ASSC)CIATEI) DEVI('t:;S
Quantity
Sample 1
hp (~m)
10.53
AE (meV)
43
Sample 2 9.70 45
Sample 3 10.19 42
VMAx (V)
2.0
4.0
7.5
R 0 (mA/mW) @ VMAx
0.40
0.28
0.25
g
0.25
0.18
0.10
Xlo
19%
20%
34%
194
E. R. BROWN AND K. A. MCINT()SH
bias voltages from the increase in the dark current. This could lead to a reduction in the measured external responsivity if the load resistance were comparable to or greater than the differential resistance; however, the given values of responsivity were obtained from short-circuit load conditions, so that current dividing was not in effect.
D.
PHOTOCONDUCTIVE
GAIN
As in other photoconductive detectors, the gain in MQW structures can be defined by ~-/tx, where T is the photoconductive lifetime (i.e., capture time into a quantum well) and t f is the transit time of electrons across the MQW structure. Physically, the gain is the ratio of the electron transport rate through the detector load circuit to the incident photon flux over the detector area. It is generally less than unity in MQW structures because a photoelectron excited out of a quantum well usually relaxes into another quantum well long before arriving at the collecting contact; however, it can become greater than unity by reducing the number of wells far below the typical value of 50. An excellent discussion of the photoconductive gain under this and other interesting conditions can be found in a recent review article (13). With this cursory understanding, one can begin to explain the peaked behavior of responsivity vs bias voltage of Fig. 10 by a corresponding voltage dependence of the photoconductive gain. The rise in the gain at low bias voltages is expected from a decrease in the transit time t~. The transit time decreases because of increasing low-field drift velocity, given by t f = LM~W/ ~,~tt~LM~w/(/zF) ~ (LMt)W)2/(/zV), where F is the electric field across the MQW structure. Because of the increase in LM~w between samples 1 and 3, each corresponding device requires proportionately higher bias voltage to reach the maximum photoconductive gain. Note, however, that the electric field at the maximum bias voltage is practically the same in each sample, FMA x ~ 1.7 • 104V/cm. Within the same context, the decrease in gain at higher bias can be explained by the presence of a sharp maximum in the velocity-vs-field characteristic. In GaAs and AIGaAs (low AI fraction), the maximum velocity is about 2 • 10 7 cm/s at a bias field of roughly 1 • 104 V/cm (14). At fields just a factor of two above this peak, the velocity drops approximately two times and then saturates to approximately 6 • 10r cm/s. Such a maximum occurs in all III-V semiconductors and is caused by strong scattering between electrons and polar optical phonons. The absolute value of g was determined from the low-frequency photoinduced G-R noise power. According to theory, the power spectrum of G-R current noise is given by Eq. (2), so that a calibrated measurement of the noise power at low
lll-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
195
frequencies along with knowledge of the photocurrent I0 yields g. The low-frequency noise power was measured by a radiometric technique. The CO 2 laser was chopped while producing a known I0. The DF power of the MQW detector was measured using a chain of UHF low-noise amplifiers, a bandpass filter centered around 500 MHz, and a square-law detector. The rectified output of the square-law detector was synchronously detected with a lock-in amplifier at the laser-chop frequency. To calibrate the measurement, the M Q W detector was replaced with a calibrated noise diode and the square-law detector output remeasured. The resulting values of g are listed in Table II for each device biased at its respective Wmax. The maximum g of 0.25 occurs in device 1. The inferior g of 0.15 in device 2, and 0.11 in device 3 is consistent with the lower maximum responsivities in the same devices. This suggests that the degraded transport mechanisms discussed earlier become more effective as the total width of the MQW structure increases.
E. EXTERNAL QUANTUM EFFICIENCY
The primary means of determining the quantum efficiency in MQW detectors has been through the fundamental law of photoconductivity, Eq. (1), using the appropriate R 0, g, and h u values. The resulting values for the present three devices are listed in Table II. Devices 1 and 2 displayed comparable values of 77o (0.19 and 0.20, respectively), consistent with the fact that they had an equal number (50) of quantum wells and an equal electronic sheet concentration in each well. Device 3 had a much higher quantum efficiency of 0.34, consistent with its larger (100) number of wells. An alternative means of determining the quantum efficiency is through the optical absorption and transmission parameters according to the following expression applicable to MQW devices: 77o = T[ 1 - (1 - ~')NwP].
(16)
In this expression, T is the power transmission through the angled facet, P is the number of passes of radiation through the MQW structure, and ~"is the fractional absorption per quantum well, which depends on the wavelength and the angle of incidence of the radiation. For example, from Sec. II.D. we have sr ~ 0.007 for samples 2 and 3. Because of reflection from the GaAs-air interface at the 45 ~ facet, T ~ 0.7. In addition, because the top contact consisted of an alloyed ohmic metallization that is very absorptive at infrared wavelengths, P = 1. From these numbers, one finds r/0 ~ 0.35 for these samples. This is very close to the value derived earlier from the photoconductive gain and responsivity results.
196
E. R. BROWN AND K. A. MCINTOSH
IV. Electrical Bandwidth and OpticaI-Heterodyne Experiments A direct measurement of the bandwidth, BDF, of a MQW detector, or any photodetector for that matter, can be obtained by mixing two optical signals and offsetting their frequency in some fashion. In the infrared region where MQW detectors operate, a simple means of doing this is to use a CO 2 laser as one signal and a broadband thermal source, such as a blackbody, as the other signal. Provided that the electrical bandwidth of the MQW detector is just a small fraction of the optical frequency, the blackbody power spectrum will be practically flat and will provide a well-calibrated power density per spatial mode for mixing. The problem in applying it to MQW detectors is that at modest laser power levels their conversion efficiency is rather low (only about 10%). Hence, the low power per mode radiated by any practical blackbody is dominated by the noise of amplifiers that follow the MQW detector. This is particularly true at frequencies of 20 GHz or higher, where the wideband distributed amplifiers required for the MQW detector characterization typically have noise temperatures in excess of 1000 K. Because of this problem, we have investigated three other techniques to determine the electrical bandwidth. The first, conducted at Lincoln Laboratory, involves measurement of the laser-induced noise power spectrum to frequencies of 18 GHz (15). The second technique, conducted by H. C. Liu at the National Research Council (NRC) of Canada, involves the mixing of a CO~ laser with a tunable diode laser (TDL) up to offset frequencies of 26 GHz. The third technique, also conducted at NRC, entails a measurement of the de-rectified current in response to microwave power injected through the bias port as a function of frequency.
A. PHOTOELECTRON GENERATION-RECOMBINATION NOISE TECHNIQUE
When the RC time constant of the MQW detector is much less than the photoelectron lifetime, and the parasitic load reactance is negligible, the lifetime limits the electrical bandwidth. This allows one to determine the bandwidth unambiguously by direct measurement of the photo-induced generation-recombination (GR) noise spectrum. According to photoconductivity theory, the power spectrum is given by 4egI~ S I = 1 + oJZT2'
(17)
where T is simply related to the 3-dB-down bandwidth through the relation B T = (21rT) -l.
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
197
The G-R noise power spectrum was measured using the setup shown in Fig. 11. The CO 2 laser beam is chopped, while the power in the DF passband is measured using a spectrum analyzer with its video output fed to a dual-channel lock-in amplifier. To correct for the frequency-dependent gain of the amplifiers, white noise from a microwave noise diode is injected into the amplifier chain using a directional coupler. The noise diode is chopped at a frequency fd that is approximately 10 times higher than the mechanical chopper frequency f~. The spectrum analyzer is scanned in frequency between 0.5 and 20 GHz, and its video output is fed into the lock-in amplifier in which one channel is synchronously detected at frequency fd and the other channel at frequency f. Finally, the signal at f~ is divided by the signal at fo using the normalization option of the lock-in amplifier. Figure 12 shows the measured photocurrent noise spectrum for devices 1 to 3. For device 2, the measured power is relatively flat out to about 7 GHz, drops about 6 dB at 8 GHz, rises to a local peak at around 11 GHz, and then drops monotonically at higher frequencies. The power at 16 GHz is down 10 dB below
SQUARE-LAW
BANDPASS
ISOLATOR
BIAS VOLTAGE
CLOSED-CYCLE REFRIGERATOR
DIRECTIONAL COUPLER
SPECTRUM ANALYZER
NOISE DIODE
Go LENS
LOW-NOISE AMPLIFIER
SQUARE-WAVE GENERATOR
BLACKBODY
/
/
I
I
LOCK-IN AMPLIFIER
FIG. 11.
Schematic diagram of setup used to measure high-frequency G-R noise and heterodyne sensitivity up to frequencies of 26 GHz (after Ref~ 15).
E. R. BROWN AND K. A. MCINTOSH
198
A
INTERPOLATION
1.0
B % ~
w e~
3 dB DOWN LEVEL
m L
S~LP
J
~~ 9
l e o o~,~ Ie
,m
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v
nu,i 0 el u.I r
0
0.1
SAMPLE
1
------
SAMPLE
2
....
SAMPLE
3
Z
20
FREQUENCY (GHz) FIG. 12. Photoinduced G-R noise spectrum fl~r devices 1, 2, and 3 biased 77 K (after R~f 15).
at VMA X
and operating at
the low-frequency power. These undulations are attributed to parasitic reactance and loss in the microwave circuit (wire bond, microstrip pad, and microstrip-tocoaxial adapter) between the MQW detector and the external electronics. Smoothing through the drop at 8 GHz and peak at 11 GHz, we estimate a 3-dB bandwidth of device 2 of 9 GHz. Device 3 displayed qualitatively similar characteristics with an estimated 3-dB bandwidth of 13 GHz. The greater bandwidth of device 3 is attributed to its lower capacitance.
B.
DIODE-LASER MIXING TECHNIQUE
In the optical mixing experiments, a CO 2 laser and a lead-salt TDL were used as the infrared sources in the arrangement described in Ref. (16). The CO 2 laser frequency (wavenumber) was fixed at 32.22 THz (1075 cm-~) by grating selection, while the TDL frequency was tuned by varying its operating temperature. Both infrared beams were polarized in the plane of incidence with respect to the quantum wells (p-polarized). The tuning rate for the TDL used in the temperature range of 30 to 32 K was about 15 GHz/K. As in previous experiments with
lli-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
199
TDLs, the output spectrum was not a single frequency but a superposition of longitudinal modes separated by about 90 GHz. To minimize spurious mixing, we selected and followed one relatively strong mode. This was done by first adjusting the TDL so that the frequency of the strong mode coincided with the CO 2 frequency (within 1 GHz), and then varying the TDL temperature to increase the difference frequency. In this scheme, other modes of the TDL do not give rise to observable signals in the measurement range of 1 to 26.5 GHz. The heterodyne signal vs. frequency was measured for device 2 at a few bias voltages and was corrected for the signal and connector and cable losses, but not for impedance mismatch (16). The signal was also normalized with respect to TDL power. With the highest bias voltage of 6 V, the measured signal power decreased by about 10 dB between low frequencies and 8 GHz, dropped to a local minimum about 25 dB down at 11 GHz, came back up to a local peak around 14 GHz, and then dropped to a deep minimum at around 18 GHz. Between 1 and 25 GHz, the measured power decreased by approximately 35 dB. The rolloff with frequency is much faster than in the photocurrent noise spectrum of Fig. 12. The heterodyne signal for device 3 also decreased much more slowly with frequency than that of device 2; however, the measured signal power still undulated, showing local minima around 4, 13, and 17 GHz. By 25 GHz, the heterodyne signal was down approximately 25 dB relative to low frequencies. In contrast to device 2, the roll-off in the heterodyne power spectrum of device 3 was quite similar quantitatively to the photocurrent noise spectrum.
C. MICROWAVE RI,;CTIFICATION TECHNIQUE
A third measure of the electrical bandwidth can be obtained by coupling a microwave signal directly to the device and observing the response. The basis tbr this technique is the nonlinearity present in the I-V curves of all MQW detectors associated with the transport of electrons in the absence of infrared radiation. Because of this nonlinearity, the microwave signal is rectified and the response is thc measured change of the bias current. A microwave source (Wiltron 68174A) fixed at a power of + 10 dBm was used for this experiment. The rectified current vs frequency was measured for device 2 at a few voltages. The rolloff behavior was similar qualitatively to that of the photocurrent noise in Fig. 12 and to the diode-laser mixing spectrum; however, the rate of rolloff of the microwave rectification spectrum is much slower than that of the laser mixing, and more nearly equal to the rolloff of the photocurrent noise. The difference in the rolloff behaviors may be significant and is discussed in the next section. Unlike device 2, the microwave rectification spectrum of device 3 was very similar in rolloff characteristics to the photoelectron-noise and heterodyne-signal
200
E. R. BROWN AND K. A. MCINTOSH
spectra. For example, the dip at 17 GHz is observed in all three spectra. This also demonstrates the need to fabricate M Q W detectors in monolithic integrated circuits for operation much beyond 10 GHz. Note that the microwave rectification technique represents a new and potentially very useful means of measuring the electrical bandwidth of M Q W detectors. In general, microwave rectification probes electrons involved in the dark current. Thus, if the dark electrons and the photoelectrons follow the same transport path, then the microwave-rectification bandwidth and the heterodyne bandwidth should be the same, as in device 3. Because of the rather large microwave amplitude that can be imposed on the M Q W detector, the sensitivity can be about as high as for the optical heterodyne technique, but the simplicity will be comparable to the photoelectron-noise technique.
D.
DISCUSSION
OF B A N D W I D T H
AND LIFETIME
In general, the electrical bandwidth of photoconductors is governed by two independent time constants" (1) the RC time associated with the capacitance of the M Q W structure and the differential resistance of the load circuit, and (2) the photoelectron lifetime. Individually, each of these causes the magnitude of the photocurrent to decay at a rate of approximately 3 dB/octave past a corner frequency, which is (2-n'RC) ~-- BRf for the RC time constant and (2rrr) -~ ---- B for the photoelectron lifetime. Given the parameters listed in Table I, one can estimate these time constants and frequencies as follows. Knowing g, one can estimate -r using g - "r/tT and the approximation t T ~ LMQw/Vd, where v o is the drift velocity ( ~ 1 • 10 7 cm]s) in the AIGaAs barriers. This leads to -r = 3.1, 3.4, and 4.9 ps, and B = 51, 47, and 33 GHz, for devices 1, 2, and 3, respectively. These values are listed in Table III. In contrast, separate derivations of the lifetime in similar MQW structures have usually resulted in somewhat longer electron lifetimes (17). For example, using the careful measurements of the saturated meanfree path of electrons in GaAs/AIGaAs of about 0.8/xm (13) and assuming the same drift velocity as stated earlier, one obtains an electron lifetime of 8 ps. One can estimate the RC time constant of the present devices using the fact that under bias the M Q W detectors are similar electrostatically to parallel-plate capacitors, so that C ~ eA/LMQw, where A is the detector lateral area. Thus, with e = 12 and A = 4.4 • 10 -5 cm 2, one finds C ~ 0.38, 0.20, and 0.10 pF for devices 1, 2, and 3, respectively. This leads to R C - 1 9 , 10, and 5 ps, and BRC = 8.4, 16, and 31 GHz, for devices 1, 2, and 3, respectively. Because the estimated knee frequencies are substantially higher than the corresponding BD~., one must conclude that parasitic circuit reactance is limiting the electrical band-
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
201
width of the devices. It is thought that the ribbon (or wire) bond to the detector is the source of this reactance. A surprising result of this study is the discrepancy between the photoelectronnoise and heterodyne-signal spectra for device 2. The discrepancy may indicate that the photoelectron noise is not purely G-R noise. Thermal (i.e., JohnsonNyquist) noise also occurs in photoconductors and becomes more important relative to G-R noise when the dark current is high or, equivalently, the differential resistance is low, as in most MQW detectors at 77 K or higher temperatures. In principle, the power spectrum of thermal noise is flat out to a frequency of approximately (2"tr'rp) - l , w h e r e ~'p is the momentum relaxation time. Because % is probably less than "r in MQW detectors by roughly one order of magnitude, we expect that the bandwidth of the thermal noise will be much greater than the G-R noise bandwidth. Therefore, a roughly equal combination of thermal and G-R noise would have a significantly larger bandwidth than G-R noise alone.
E. HETERODYNE SENSITIVITY MEASUREMENT TECHNIQUE The heterodyne sensitivity at microwave DF frequencies was measured by mixing the CO 2 laser with a calibrated blackbody (18). Such mixing generates power over a very broad DF band, because the blackbody is essentially a thermal noise source. The portion of the infrared power that appears in the DF band is approximately u _+ Af, where the plus and minus signs denote the upper and lower sidebands, respectively. These sidebands are shown schematically in Fig. 13. For a blackbody of absolute temperature TBB and emissivity e, the infrared spectral density in the single polarization and spatial mode of the laser is given by hvE
Sp = eh~/kT....--1"
(18)
The power generated in the DF band is given by Eq. (18) times the optical transmittance between the blackbody and the MQW detector. Equation (18) provides a means of calibrating the heterodyne sensitivity as quantified by NEPH~.:T. The relationship between NEPHET and the experimental parameters is given by {
huET
NEPHE T = 2Af (eh, ,/kT,,,, _
hveT }N l) - (e h"/k~., -- l) S'
(19)
where TRT is the ambient temperature. As derived in Sec. I.B, this is related to the effective heterodyne quantum efficiency through the relation, "r/EH -----2hu Af/NEPHEv.
E. R. BROWN AND K. A. MCINT()SH
202
D nc I-O 111 13. O9 or" UJ
0 II.
MICROWAVE REGION-
- ~
~
. . . .
INFRARED REGION
"~
CO2-LASER LOCAL OSCILLATOR
DIFFERENCE-FREQUENCY BAND
LOWER SIDEBAND
UPPER SIDEBAND
3x1013 FREQUENCY
(Hz)
FIG. 13. Infrared and microwave power spectra associated with the L(), the signal and the differonce-frequency band of the optical hctcrodync process.
F. HETEROI)YNI:. SI'~NSITIVITY RI'~SUI.TS One of the important parameters in operating an MQW detector in heterodyne mode is the bias voltage. Figure 10 shows a comparison of the integrated blackbody-heterodyne response (measured over a 100-MHz bandwidth, centered at a low difference frequency) to the direct-detection response of device 3. Like the direct-detection curve, the heterodyne response displays a maximum just above 7 V. The other devices displayed a similar maximum in the heterodyne response with respect to bias voltage. In each device, the maximizing voltage was the same for both modes of detection. The other important factor in heterodyne detection is the LO power. To determine this, the heterodyne signal was measured at a low difference frequency and compared directly to the photocurrent, dark-current, and amplifier noise powers at the same frequency. This resulted in an experimental S/N ratio, which was converted to an NEP using Eq. 19 and to an effective heterodyne quantum efficiency using the relation r/EH = 2hu AffNEPH~:T. Figure 14 shows the results obtained for device 1 with LO powers of 1, 2, 5, and 10 mW (17). Clearly, there is
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
203
100
A
"rio
>. O 10 z u,I ,..,. (J IL IL U,I I--" Z
PLO = 10 m W
o f
.......... 9
'TIE H r "
0,
9 =2mW 1
\o
= 1 mW
L O C A L O S C I L L A T O R W A V E L E N G T H - 10.2 p m D E T E C T O R O P E R A T I N G T E M P . = 77 K
0.0
I
1
0.5
1.0
I
1.5 BIAS
I
I
I
I
2.0
2.5
3.0
3.5
VOLTAGE
4.0
(V)
FIG. 14. Heterodyne sensitivity (quantified by 'rlEH) for device 1 plotted vs bias voltage and paramctrizcd by CO,-lascr LO power (after Re./'. 17).
a rapid increase in "qH~between 1 and 5 mW. Between 5 and 10 mW, ~EH begins to saturate as it approaches B0" At this point the photocurrent noise induced by the LO power begins to dominate the other noise mechanisms, as expected from the discussion of Sec. I.B. Table III summarizes the heterodyne sensitivity results for all three devices. The bias voltage is the value for peak responsivity and P~.~ is 2 and 10 mW. The amplifier noise is set equal to 100 K, consistent with the noise figure of the UHF preamplifier (1.2 dB) used in these experiments. The results for detectors 1 and 2 are identical at P~.~ = 8 mW but differ at the lower power. The superiority of detector 2 at P~(~ = 2 mW reflects its lower dark current. Hence, less LO power is required to make the photocurrent noise dominate. Detector 3 displays the best performance at all values of LO power and the highest values of BEH"At PL~ = 8 mW, the ~EH of this detector is 0.18, which represents the most sensitive heterodyne detection achieved with an MQW detector.
E. R. BROWN AND K. A. MCINTOSH
204
TABLE III HIGH-SPEED AND HETERODYNE CHARACTERISTICS OF THREE MQW SAMPLES Sample 1
Quantity a- (ps)
Sample 2
3.1
B (GHz)
BDF (GHz) hLO
4.9
51
47
33
7
9
13
10.24
hVLo
3.4
Sample 3
121
9.50 131
9.56 130
"qEH(PLo = 2 mW)
6%
8%
9%
qqEH(PLo = 8 mW)
11%
1 1%
18%
Note that the sensitivity of all three devices approaches roughly 55% of the photocurrent-noise limit with 8 mW of LO power. This power corresponds to approximately 80 mW of CO2-1aser power incident on the diplexer in Fig. 2. This is a substantially larger LO power than required by HgCdTe heterodyne detectors because of the lower responsivity of the MQW device; however, it poses no practical problem because CO~ lasers generally provide a great excess of power, and because the MQW detector has a high dynamic range. The dynamic range stems in part from the small r, which inhibits current saturation and spacecharge effects in the active region of the device. It also stems from the thermal conductivity of GaAs, which is substantially higher than that of HgCdTe (but less than that of Si). Up to 100 mW of LO power has been applied on MQW devices, with no degradation in the detector characteristics.
V. Applications The MQW detector will enable applications that were previously impossible with HgCdTe detectors, whose maximum electrical bandwidth was (and remains) approximately 3 GHz. For example, when using a CO2-1aser LO with a HgCdTe detector for atomic or molecular spectroscopy, the atomic or molecular line of interest must fall within roughly 3 GHz of a CO 2 emission line. Because these emission lines are typically separated by at least 30 GHz, the vast majority of frequency space between 9 and 11 t*m is undetectable. Similarly, when using a HgCdTe detector as a front-end mixer in a coherent laser communications re-
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
205
ceiver, the maximum digital transmission rate is approximately 1 GBit/s. With the MQW detector, these drawbacks are greatly alleviated because of its roughly 10-times-greater electrical bandwidth. Alternative means of alleviating these shortcomings, such as the use of a frequency-tunable diode laser as an LO in molecular spectroscopy, or the use of very high-speed (often room-temperature) photoconductive detectors, have been largely unsuccessful because of the deleterious excess noise of these devices.
A.
INSTRUMENTAL RESOLUTION AND SENSITIVITY
Before embarking on the system implementations that the MQW detector enables, it is important to compare heterodyne and direct detection in terms of instrumental spectral resolution and instrumental sensitivity. Because of the coherent nature of the optical mixing process, the lower limit on the resolution of a heterodyne instrument is the intrinsic width of the LO emission line, and the upper limit is just BoF. The actual value is usually determined to be somewhere between these limits by electrical filtering in the DF band. In contrast, the resolution of a direct-detection instrument is either the intrinsic spectral bandwidth of the direct detector or the resolution of the optical-filtering instrument in front of it, whichever is finer. Provided that the LO emission is unimodal (e.g., from a CO~ laser), the heterodyne instrument will typically have a higher resolution by several orders of magnitude. Resolution is important not only from the standpoint of positively identifying the spectral feature of interest, but also because of its relationship to instrumental sensitivity. This relationship can be cast in general terms, quite independent of the type of detection, but is strongly dependent on the spectral linewidth of the signal being measured. Under many conditions, the output signal of a spectroscopic instrument can be written as the convolution ~c t"
S(f) - /I0(v)e-"ZR(v - f) dv d
(20)
0
where I0(v) is the source spectrum, a is the frequency-dependent absorption or emission coefficient associated with the spectral feature, R is the instrumental responsivity, and z is the physical length of the absorbing medium. For simplicity, but without loss of generality, we assume that I0(u) is spectrally flat over the ranges of variation of oLand R, and that R can be represented by the box function R(v) = R ~
(f - A f / 2 ) ] . 0 [ ( f / 2 ) - v], Af
(21)
E. R. BROWN AND K. A. MCI NT O SH
206
where 0 is the Heaviside step function and Af is the instrumental resolution. The /.
expression (21) is normalized, / R(u) d r = 1, so that the instrumental response J
0
to the flat background is simply S0(f) = R0I 0. For analytical purposes only, we assume that the spectral feature is optically thin, or e -"z ~ 1 - oe z, and a can be represented by the Lorentzian function (applicable to homogeneously broadened features, e.g., pressure broadened), so that cff 1,') =
a~ (v -- v0 )2 + F 2/4'
(22)
where F is the broadening parameter. Upon substituting (21) and (22) into (20), we find
{z%F[2(f+Afl2-vo)
S(f) = R o I o 1 -
Af
a tan
A
-
a tan
2(f-
Af/2F
v~
(23)
....I , J
The instrumental sensitivity can be defined as the maximum difference, AS, between the signal response without absorption S 0 and the signal with absorption. Clearly, the maximum offset of S(f) from S o occurs at f - v 0, so that AS -- S 0 - S(u0) = R 0 1 0 [ - - ~ - a tan
-- R0101%z[3],
(24)
where 13 is a correction factor that depends on the ratio of the instrumental resolution to the spectral linewidth. From this expression, it is clear why heterodyne instruments have a substantial advantage over direct-detection instruments when the spectral signal linewidth is relatively narrow. For example, if the linewidth is such that F/Af -- 0.1 for the direct instrument and F/Af = 10 for the heterodyne, then we find [3 = 0.147 for the direct instrument and 0.997 for the heterodyne. In other words, the sensitivity of the heterodyne instrument is effectively 0.997/0.147 or 6.8 times greater than that of the direct instrument. Note that this sensitivity advantage goes beyond the S/N benefit of heterodyne detection discussed in Sec. I.B. The latter benefit was a consequence of the amplifying effect of the LO power on the signal power. The former effect results from spectral bandwidth matching in the presence of noise. Put more intuitively, the heterodyne instrument can usually be operated so that its resolution bandwidth is less than or equal to the signal bandwidth. In this case, the instrument
|II-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
207
will not measure any more noise (either internal or external) than contained within the signal bandwidth, and the S/N ratio will be optimal. On the other hand, direct-detection instruments are usually operated with instrumental resolution substantially greater than narrow signal spectra. Hence, they measure much more noise than contained in the signal bandwidth, and the S/N is degraded.
B. HIGH-RESOLUTION MOLECULAR SPECTROSCOPY
To demonstrate the advantages of the MQW detector in the heterodyne mode, it has been configured in the tabletop spectrometer setup shown in Fig. 15. The setup consists of a 1000~ blackbody as a broadband source illuminating a 10cm-long gas cell. A beamsplitter is used to combine the input blackbody and laser LO beams and direct them to the MQW detector. A chopper modulated the blackbody beam and, hence, the difference-frequency power spectrum, which was amplified and measured with the combination of a scanning microwave
FIG. 15. Tabletop setup of high-resolution spectrometer used to measure gas absorption lines that occur in the C O : l a s e r band (approximately 9 to 1 I ~m).
E. R. BROWN AND K. A. MCINTOSH
208
spectrum analyzer (0.1 to 18 GHz) and lock-in amplifier. The spectrum analyzer had a maximum sampling bandwidth of 2 MHz. Background scans measured without gas in the cell were used to normalize scans with gas. The first molecular absorption line examined was one of NH 3 located approximately 8.5 GHz from the 9P38 CO2-1aser line. The NH 3 was at a partial pressure of 2 torr in a gas cell that was backfilled with 1 atm of N 2. Figure 16 shows the measured infrared transmission through the cell from a conventional FTIR instrument having 2-cm -~ resolution. The inset of Fig. 16 shows the transmission spectrum through the same cell measured with the M Q W heterodyne detector. The sloped lines between the inset and the main figure show the portion of the FTIR spectrum covered by the MQW spectrometer when using the 9P38 laser line. Because of its superior frequency resolution, the M Q W spectrometer detects a strong absorption feature having a minimum transmission of 25% at 927.32 cm -~. At this same wave number in the FI'IR scan, there is a nearly imperceptible dip in the transmission of roughly 1%. The broader feature in the F r l R spectrum centered at around 931 cm -~ is a series of NH 3 absorption lines that is merged into one continuous band by the FTIR instrument.
i
1.00
Z 0.95 O === ~0 g3
o0 Z 0.90 r
/"
B
--
1 0.8
0.6
F--
0.4
0.2 ~-
0.85 "
0" 927.20
927.30
HETERODYNE
927.40
927.50
SPECTRUM
,,lll,,l,,,I,,,I,,,l,,,l,,,I,,,l,,,l,,,l,,,I,,,I,,,I, 920
930
FREQUENCY
940
(cm "1)
FIG. 16. High-resolution transmission spectrum (inset) through NH~ at a partial pressure of 2 torr and broadened to atmospheric pressure by nitrogen. The main plot shows the transmission spectrum through the same NH.~ gas sample but measured by a Fourier-transform spectrometer having relatively low spectral resolution.
III-V QUANTUM-WELLSTRUCTURES FOR HIGH-SPEED ELECTRONICS
209
Of course, because the resolution of the MQW-detector-based instrument can, in principle, be made as narrow as the CO2-1aser emission line, such an instrument could also be very useful in detection of low-pressure molecular lines of interest in fundamental chemistry and in the astrophysics of the interstellar and extraterrestrial medium. Here, the molecular or atomic absorption features are usually Doppler broadened and, hence, relatively narrow. To demonstrate the capability of the GaAs/A1GaAs M Q W detector in this application, we have used the same setup as in Fig. 15 but eliminated the background nitrogen to yield 2 torr of NH 3 alone. The NH 3 absorption feature in the resulting transmission spectrum is plotted in Fig. 17a. Without the 1 atm of broadening gas, the full width at half-maximum shrinks to approximately 0.2 GHz. Even at this narrow width, the M Q W heterodyne spectrometer is resolving the line with much greater resolution than required. To demonstrate this point, the pressure of the NH 3 was reduced further to a level of 0.1 torr, as plotted in Fig. 17b. Although the maximum absorption of the sample starts to drop rapidly as the pressure is lowered, it is clear that the absorption feature is fully resolved in each case.
1.2 2 TORR NH 3 .,
.::/'' -
LU
O Z
,,r II-.
0.8
-
0.6
-
0.4
-
0.2
-
.,..,,
i
orj Z
BROADENED
SELFBROADENED ~'~
0 7.5
8.5 DIFFERENCE
WITH
Na
. 9i "[
i
I
9.5
10.5
11.5
FREQUENCY
12.5
(GHz)
(a) High-resolution transmission spectra measured by MQW-heterodyne spectrometer through NH3 under two different gas conditions: (1) 2 torr of NH3 broadened to atmosphere by N~, and (2) 2 torr of NH~ without further pressure broadening.
FIG. 17.
E. R. BROWN AND K. A. MCINT()SH
210
1.2 1 0.8 r
0.6 0.4
,"-"
0.2
9
9.2
DIFFERENCE
9.4
, 9.6
FREQUENCY
9.8
10
(GHz)
(b) High-resolution transmission spectra through NH~ under low-pressure, I)opplcr-broadcncd conditions.
FIG. 17. Cmuintwd
Besides ammonia, there are many other molecules of scientific interest that occur at frequencies far away from the nearest CO~-laser line. These include a class of lightweight, atmospheric molecules involved in ozone depletion, global warming, and toxic waste. Among these are O~ (ozone), CCIeF: (Freon), AsH~ (arsine), PH~ (phosphine), CH~Br (methyl bromide), CH~CI (methyl chloride), CH~CN (acetonitrile), OCS (carbonyl sulfide), and C:HsCI (ethyl chloride). All of the absorption lines from these molecules are pressure broadened under atmospheric conditions, leading to signal linewidths of 1 GHz or more. With a HgCdTe detector, this would be a great deterrence, because the limited BDI: would prevent the absolute resolution of the line and, hence, the positive identification of the molecule. With the MQW detector, the large B~. is, again, beneficial, allowing one to fully resolve the molecular line while maintaining nearly photon-noise-limited sensitivity.
C. LONG-RANGE, HIGH-DATA-RATE COMMUNICATIONS
In pioneering work conducted by Hughes Aircraft Co. and NASA in the 1970s
(19), it was recognized that the high spectral and spatial purity of the CO~ laser made it well suited to long-range, point-to-point communication links between
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
211
orbiting satellites or between a satellite and ground stations (in the absence of cloud or fog cover). When such systems were developed experimentally, the data rate was limited to approximately 1 GBit/s by the 2-GHz bandwidth of HgCdTe photodiodes. Present-day HgCdTe detectors would not improve this performance substantially; however, the MQW detectors combined with modem GaAs-based transistors and microelectronics could extend this data rate at least up to the limit of CO2-1aser modulator technology, which is approximately 10 GHz. The advantages of a CO2-1aser communications system over near-infrared or visible laser systems are in S/N ratio per unit watt of transmitter power. These advantages are expressed through the fact that the quantum-limited sensitivity of any system using a conventional laser LO (i.e., a laser operating in a coherent state, not a squeezed state) is given by an NEP of huAf, where Af is the measurement bandwidth. Thus, the minimum NEP is roughly ten times lower for the CO2-1aser system because of its substantially longer wavelength.
VI. Improvements in MQW Heterodyne Detectors The experimental results presented in Secs. III and IV suggest that the performance of MQW heterodyne detectors could be substantially improved by straightforward changes in the material design or packaging techniques. This section investigates changes aimed at improving the external quantum efficiency (dc and heterodyne) and the electrical bandwidth. The investigation is not intended to be complete and, therefore, good approaches for improving other MQW detector characteristics, such as the dark current (12), are not considered. A good overview of these approaches has been given in the review article by Levine (18).
A. ENHANCEMENT OF EXTERNAL QUANTUM EFFICIENCY
1. 45~
Detector
From the discussion of Sec. III.E and Eq. (16), it is clear that the detector structures having a 45 ~ facet and top ohmic contact could be improved substantially through the addition of an antireflection (AR) coating on the facet and by making the ohmic contact highly reflecting in the A = 10/.Lm region. These embellishments are shown in cross section in Fig. 18. The antireflection coating raises the transmission through the facet from 0.7 to approximately 1.0. The reflecting ohmic contact raises the number of passes [i.e., P in Eq. (16)] from 1 to 2. The effect of these changes on the external quantum efficiency is listed in Table IV, using device 3 as a baseline. Both changes would increase ~0 from
E. R. BROWN AND K. A. MCINTOSH
212
Ti/Au REFLECTING METALLIZATION
MULTIPLE QUANTUM-WELL STRUCTURE
ANTIREFLECTION COATING
INCIDENT
Ni/Ge/Au OHMIC
METALLIZATION
F L
.
.
.
.
.
.
.
.
_
_
45 ~ CLEAVED FACET
/
SEMI-INSULATING GaAs SUBSTRATE
RADIATION FIG. 18.
_nLGa_As_
Cross-sectionalview of MQW detector designed for high vl0.
0.34 tO 0.74, which is comparable to the quantum efficiency of the best detectors operating in the 10-~m region. Another straightforward means of improving r/0 is to increase the number of quantum wells N w. Table IV lists the effect of increasing N w from 100 to 400, again using device 3 as a baseline. For example, 200 quantum wells would increase 7/o from 0.34 to 0.52; but, there is little gained with more wells as 7/o saturates to the facet transmission of 0.7. With the AR coating added, r/()thus increases much more rapidly with N w, surpassing 90% at 400 wells. The combination of AR coating and reflecting ohmic yields a very fast increase of 7/o with well number, 93% being reached with just 200 wells. Of these two techniques, the AR coating and reflecting ohmic are preferred because they improve the performance with no deleterious effect on other as-
TABLE IV EXTERNAl. QUANTUM EFFICIENCY FOR PROP()SEI) IMPROVEMENTS IN THE
MQW
DEVlCE
Nw
l"lo(t=0"7, P= 1)
11o(t= 1.0, P= 1)
"q0(t= 1.0, P-~2)
100
0.34
0.49
0.74
200 300 400
0.52 0.61 0.65
0.74 0.87 0.93
0.93 0.98 0.99
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
213
pects of the detector performance. Increasing N w has the drawback of reducing the photoconductive gain because of its inverse dependence on LMQw. Hence, more LO power is required to make the detector sensitivity approach the photonnoise limit, because the photon-noise term in the denominator of Eq. (4) is scaled down relative to the amplifier thermal-noise term. This drawback is not as severe for the dark-current noise because it, too, scales down with the reduction in g. While a significant increase in LO power would likely be a problem for a high-speed HgCdTe detector, it should not hinder the operation of the MQW detector because of its relative robustness with respect to strong photocarrier and thermal generation. 2. Normal-Incidence (Grating-Coupled) Detector
To reduce the power requirements and still maintain high %, GaAs/A1GaAs MQW detectors can be designed and fabricated with a topside grating coupler instead of the 45~ coupling shown in Fig. 18. The grating coupling is configured in the manner shown in Fig. 19. It consists of a two-dimensional array of squares etched into the top surface of the MQW structure and covered with reflecting metal, as first demonstrated by Andersson et al. (20,21). Radiation is incident on the MQW structure from the bottom side of the wafer, passes through the quantum wells without absorption, and is reflected off the top grating at large angles from the normal. This leads to a strong absorption of the reflected radiation consistent with the intersubband polarization selection rules. At the bottom of the MQW structure, a thick AlAs layer provides total internal reflection of
(a}
MESA
TOP OHMIC C O N T A C T
GRATIN
t
............................'~' ~ A N T I R E F L E C T I O N COATING
FIG. 19. (a) Cross-sectional view of MQW detector. (b) Top view of grating-coupled detector mesa.
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radiation after its first pass. The radiation then propagates through the MQW structure, again at large angles from the normal; however, on encountering the grating once again, some fraction of the radiation is diffracted back near the normal and propagates through the MQW structure without further absorption. One thus expects that this structure will support at least two passes of the radiation through the MQW structure. Experimental investigation of the two-dimensional grating structure has shown that it is capable of providing a peak internal quantum efficiency in excess of 90% for only 50 quantum wells in the structure (21). This represents an improvement of approximately three times over a single-pass 45~ detector having the same number of quantum wells. The physical reason for this improvement is that the grating can diffract much of the incident radiation into larger angles away from the perpendicular than 45 ~. Because the absorption strength in the quantum wells varies as sin20, the improvement in absorption strength per pass can increase twofold between 45 ~ and 90 ~ propagation angle. The penalty for the increased quantum efficiency is a narrowing of the spectral response compared to the 45~ detector. This has been a problem for these structures in direct detection (e.g., staring arrays), because in this application the relevant performance criterion is the quantum efficiency integrated over a substantial spectral range, typically 8 to 12/xm. In heterodyne detection, however, the peak quantum efficiency is more important, because the operational spectral range is just the CO~-laser frequency plus and minus the electrical bandwidth of the detector. Aside from the issue of spectral narrowing, other deleterious effects can lead to degradation in the internal quantum efficiency. Two such effects are lateral spread in the periodicity of the grating and nonideal reflection from the metal above it (20). To counteract these effects and ultimately obtain internal quantum efficiencies approaching 100%, we propose to increase the number of quantum wells in the grating-coupled detector to as many as 200. This has the additional benefit of reducing the specific capacitance of the detectors, allowing the RC time constant to be very small in detectors of acceptable size (i.e., diameters greater than or equal to about 50/xm).
B. DESIGN OF DETECTORS HAVING LIFETIME-LIMITED ELECTRICAL BANDWIDTH One benefit of the high-quantum-efficiency detectors proposed in Sec. VI.A is that they will naturally yield a very low RC time constant. From the parallelplate approximation, the capacitance of any of the 300-well GaAs/A1GaAs sam-
III-V QUANTUM-WELL STRUCTURES FOR HIGH-SPEED ELECTRONICS
215
pies listed in Table IV is estimated to be 35 fF, leading to RC = 1.7 ps and BRC = 92 GHz. The photoelectron lifetime should be comparable to the values deduced for the samples in Table III, yielding B ~ 35 GHz; however, when connected to the load circuit through a bond wire, the real electrical bandwidth of the proposed detectors is likely to be much less than these values because of the parasitic reactance. To reduce the reactance and increase the bandwidth, a monolithic M Q W detector circuit could be produced, such as that shown in Fig. 20. In this circuit, the detector and output transmission line are fabricated on the same substrate, so that the two can be brought into very close proximity. The interconnection between the two can then be made by a metallic air bridge whose total length is 100 ~ m or less. This short length makes the magnitude of the parasitic reactance roughly one order of magnitude less than in the best possible ribbon or wire bond. The output transmission line is a coplanar waveguide (CPW), which on a semi-insulating GaAs substrate is useful well into the millimeter-wave band. The CPW is transformed to coaxial line by a 50-GHz stripline-to-coax adapter. The bias tee and low-noise preamplifier required for all applications can then be coaxial components and would likely be mounted on the same cold finger as the MQW detector.
FIG. 20. Perspective view of monolithic MQW detector designed for lifetime-limited electrical bandwidth.
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References 1. L. C. West and S. J. Eglash, Appl. Phys. Lett. 46, 1156 (1985). 2. B. F. Levine, C. G. Bethea, G. Hasnain, V. O. Shen, E. Pelve, R. R. Abbott, and S. J. Hsieh, Appl. Phys. Lett. 56, 851 (1990). 3. B. E Levine, A. Zussman, S. D. Gunapala, M. T. Asom, J. M. Kuo, and W. S. Hobson, J. Appl. Phys. 72, 4429 (1992). 4. R. H. Kingston, Detection of Optical and Infrared Radiation, Sec. 6.1, Springer, New York, 1978. This reference, like most others on the subject, refers to the difference frequency as the intermediate frequency, mostly for historic reasons. 5. Serber and Townes. 6. J. Tersoff, Phys. Rev. B. 30, 4874 (1984). 7. E L. Schuermeyer, P. Cook, E. Martinez, and J. Tantillo, Appl. Phys. Lett. 55, 1877 (1989). 8. Y. Tsou, A. Ichii, and E. M. Garmire, IEEE J. Quantum Electron, 5, 1261 (1992). 9. L. Vegard, Z. Krist67, 239 (1928). 10. K. K. Choi, J. Appl. Phys. 73,5230(1993). 11. E. R. Brown and S. J. Eglash, Phys. Rev. B. 41, 7559 (1990). 12. K. K. Choi, "Multiquantum-Well Structures for Hot-Electron Phototransistors" in Thin Films: Homojunction and Quantum-Well hlfrared Detectors (M. H. Francombe and J. L. Vossen, eds.) Academic, San Diego, p. 239, 1995. 13. S. D. Gunapala and K. M. S. Bandara, "Recent Developments in Quantum-Well Infrared Photodetectors," in Thin Fihns: Hontojutwtion and Quantum-Well h(h'ared Detectors, (M. H. Francombe and J. L. Vosscn, Acadcmic, San Dicgo, p. 114, 1995. 14. S. M. Szc, Physics of Semiconductor Devices, Wiley, New York, p. 46, 198 !. 15. E. R. Brown, K. A. Mclntosh, K. B. Nichols, E W. Smith, and M. J. Manfra, "CO,-laser hcterodyne dctection with GaAs/AIGaAs MQW structurcs," in Quantum Well lntersuhbaml l)evices, (H. C. Liu, B. F. Lcvine, and J. Y. Andcrsson, eds.) NATO ARW Series, Kluwcr, Dordrccht, pp. 207- 220, 1994. 16. H.C. Liu, J. Li, E. R. Brown, K. A. Mclntosh, K. B. Nichols,and M. J. Manfra, Appl. Phys. Lett. 67, 1594 (1995). / 7. B. F. Levine, J. Appl. Phys. 74, R 1 (1993). 18. E. R. Brown, K. A. Mclntosh, F. W. Smith, and M. J. Manfra, Appl. Phys. Lett. 62, 1513 (1993). /9. J. H. McElroy, N. McAvoy, E. H. Johnson, J. J. Degnan, F. E. Goodwin, D. M. Hcndcrson, T. A. Nussmeier, L. S. Stoker, B. J. Peyton, and T. Flattau, Proc. IEEE 65, 22 I. 20. J.Y. Andersson, L. Lundqvist, and Z. F. Paska, Appi. Phys. Lett. 58, 2264 ( 1991 ). 21. J.Y. Andcrsson and L. Lundqvist, Appl. Phys. Lett. 59, 857 (1991).