AlSb quantum wells

~

Pergamon

Solid-State Electronics Vol. 37, Nos 4-6, pp. 1293-1295, 1994 Copyright ~ 1994 Elsevier Science Ltd 0038-1101(93)E0067-B Printed in Great Britain. All rights reserved 0038-1101/94 $6.00+0.00

INFRARED SPECTROSCOPY OF LATERAL-DENSITY-MODULATED 2DES IN InAs/A1Sb QUANTUM WELLS M. SUNDARAM1, S. J. ALLENJR l, C. NGUYEN2, B. BRAR2, V. JAYARAMAN2 and H. KROEMER2 )Quantum Institute, University of California, Santa Barbara, CA 93106 and 2Department of Electrical and Computer Engineering, University of California, Santa Barbara, CA 93106, U.S.A. Abstract--In infrared transmission experiments through a two-dimensional electron system with substantial lateral density modulation in an InAs quantum well, we directly observe plasmon absorption without the mediating help of a surface metallic grating. The plasmon frequency is determined by the average density, and its strength by the amplitude of the density modulation. It disperses in a magnetic field in predicted fashion.

We have observed plasmon absorption in lateral-density-modulated two-dimensional electron systems (2DES) in InAs quantum wells in far infrared spectroscopy. Its location and strength agree well with the dynamic conductivity a (q,co) that we explicitly derive for such a system. The dispersion of the plasmon frequency cop in a magnetic field agrees well with existing theory. Far infrared plasmon experiments on 2DES have traditionally relied on the fabrication of a surface metallic grating (of period a) to couple to plasmons with fixed wave vectors q = nn/a (n = 1,2. . . . )[1] in 2DES residing as inversion layers in Si MOSFETs or as accumulation layers in GaAs/AIGaAs heterojunctions and quantum wells[l,2]. Such measurements have shown the position, width, and strength of the plasmon resonance, and also its dispersion in a magnetic field B to agree with theory in detail. Non-local effects have manifested themselves in the plasmon B field dispersion via a coupling between the magnetoplasmon and the second harmonic of the cyclotron frequency 2coc[3]. Most of these experiments have been on 2DES with lateral uniformity. Measurements on 2DES with electron density laterally modulated with submicron spatial periodicity in both the Si MOSFET[4] and the GaAs/AIGaAs[3] systems reveal the resultant creation of minigaps in the plasmon dispersion, manifested as a splitting of the plasmon peak. Increase of the periodicity to micron levels appears to shift the plasmon to higher frequencies and cause the splitting to vanish[5]. Density modulation was achieved with modulated oxide thickness in the former material system[4]; it was a side-effect of a surface metallic grating[3] enhanced by illumination[5] in the latter system. The InAs/AISb system offers certain unique advantages in the study of laterally modulated 2DES. The electron density n S in an InAs quantum well sandwiched between AISb barriers is extremely sensitive to

both the composition of the cap layer and its separation from it[6]. Firstly, its 1.35 ev depth allows deep donors in the barriers and surface to drain electrons into it resulting in typical n~ values of 10~2cm -2. Secondly, the absence of a surface depletion layer allows the quantum well to be located closer to the surface than in the GaAs/A1GaAs system, resulting in substantially more sensitivity to it. Thirdly, the selection of a cap layer, either InAs or GaSb, can result in a difference of ns in excess of 100% by virtue of the difference in the surface Fermi level pinning in each cap[6]. Growing and laterally patterning a bilayer InAs/GaSb cap[7] and thereby modulating the surface Fermi level suggests itself as a logical means of impressing large lateral modulation on the 2DES residing in the quantum well a short distance below (Fig. 1). The sample for this experiment had the following epilayer sequence: on a semi-insulating (100) GaAs substrate were grown a GaAs buffer, AlAs and AISb nucleation layers, a 1/~m AISb buffer, a 10 x (2.5 nm GaSb + 2.5 nm A1Sb) short-period smoothing superlattice, a 20 nm AISb bottom barrier, followed by the 15 nm InAs quantum well, a 15 nm AISb top barrier, a 5 nm GaSb cap, a 10 nm AISb cap separator, and a 3 nm InAs cap (sufficiently thin that it contains no electrons, due to the large quantization of the ground state). The sample was not intentionally doped. More details on the growth procedure for this material system can be found elsewhere[8]. The periodic patterns of alternating InAs and GaSb cap layers were fabricated by conventional photolithography and selective etching. For the two samples investigated here, the period a is 4 g m , and the duty cycle t/a (t = opening in InAs cap) 0.5 and 0.75 (Fig. I). The samples were characterized by low-temperature (4.2 K) magnetotransport on conventional Hall bars both before and after the lateral patterning. The as-grown sample with the InAs cap had a

1293

M. SUNDARAMet al.

1294 a = 4p.m

0.20 t

~

A

I

I

I

lnAs S

I

I

I

I

I

(a)

b

I

I

t/a = 0.5

0.15

0.10 0.05

tA' u

t

Fig. 1. Lateral composition modulation of the cap layer can result in substantial lateral density modulation in an InAs quantum well. t/a is the duty cycle. Figure not to scale. 2DES with density n, = 5.2 x i0 II c m - : and mobility /1 = 170,000 cm2/Vs. Stripping this cap and exposing the GaSb cap caused these values to rise to 9.2 x 10 H cm : and 250,000 cm2/Vs, respectively. For the sample with t/a = 0.5, the low-field Hall resistance both along and across the lateral superlattice (LSL) gave an electron density ns = 7.2 x 10 ~ c m - : , exactly the average of the two unpatterned values. The mobilities dropped to 80,000 cm2/Vs across the LSL and 160,000cm-'/Vs along it. The high-field magnetotransport differed drastically in the two directions. F r o m these measurements the amplitude of the lateral potential modulation is calculated to be 30 meV[7]. Transmission measurements were performed with a conventional rapid-scan Fourier transform spectrometer with the radiation light-piped through the sample immersed in a cryostat at 4.2 K. The transmission T ( B ) was measured with a resolution of 1 c m - ~ at various magnetic fields B up to 8 T in steps of 0.2 T. Several absorption features are observed in a T(B)/T(O) trace. The 2D plasmon (B = 0 ) is observed only when the radiation is polarized perpendicular to the LSL (Fig. 2). Cyclotron resonances with identical lineshapes are observed in both polarizations; so also are the magnetoplasmons (since the B field mixes polarizations). The fractional change in transmission - A T ~ T = 1 - T(O)/T(B) for both samples show the high-frequency Drude tails with

l.l

I

I

I

0.00 0.20

B=5.6Tesla

' I

I

I

I

l

I

~ 0.050"100"15", , ~ ' <1,

0.00

I

10

I

20

I

I

I

t/a = 0.75

",~_ I

I

30

~

'/~ 1

40

50

I 1 ~ ~

60

k (cm-1) Fig. 3. Relative transmission for the sample with t/a = 0.5 (a) and for the sample with t/a = 0.75 (b). Dashed curves are obtained from eqn (2). The reference spectrum is T(B = 8.4 T).

plasmon absorptions at top = 49 and 52.5 cm-~ for the samples with t/a = 0.5 and 0.75, respectively (Fig. 3). The peak absorption is ~ 10% for the former sample, ~ 4 % for the latter. The polarization-dependence and the fit to theory (developed below) leave no doubt about the identification of these peaks as 2D plasmon resonances. - A T / T directly measures the real part of the dynamic conductivity of a 2DES[9]:

-AT/T=2Rea(to)/(Yo+

Y~)

(I)

where 110 and Ys are the wave admittances of free space and the host semiconductor, respectively. For a 2DES with lateral density modulation ns = n~o+ An~ocos(qy), where q = 2n/a, on the surface of a semiconductor with dielectric constant E~, we derive a (to) explicitly as:

I

2DP A perpendicular

' ,

o"0

~r (to) = - -

1 +itot AaoAto

2I(to ~ -- 2to 2) "+""to z ( 1 q- r 2(to ~ -- °9 2))]'

0.9 p lel

CR

where

0.8 top=

0'730

60

90

120

(2)

150

180

k (era-~) Fig. 2. Relative transmission spectra at B = 5.6 T for the lateral superlattice with t/a = 0.75 for both polarizations. The lower trace has been vertically offset for clarity.

/ n~oe2q / Ansoe2q " *-77-.-7- ; Atop= x/m (Eo+ ~) X/m*(Eo + ~J'

(3)

where top is the plasmon frequency, m* the electron effective mass, t the relaxation time, a 0 = en,o#o is the d.c. (to = 0) conductivity, Aa0 = cans0#0, and/% is the d.c. electron mobility. The first part on the right hand side of (2) is the Drude part and is determined solely

1295

Lateral-density-modulated 2DES by the average electron conductivity; the second part is the plasmon part: its pole determines the plasmon frequency to be COpgiven by the classic expression (3) for a 2DES with uniform density n~0[10] and its strength and shape are determined by An~0 and z respectively. F r o m (1) and (2) for COpz>> I, the peak absorption at COpsimplifies to:

250

---

I

I

I

I

I

I

200

I

°°4

¢.d

A T (CO = COp)~ eAn~o#o An~o T Yo+Y~ n~o

(4)

'~

and is seen to be directly fixed by the size of the density modulation. As expected, it also vanishes as the density modulation is tuned to zero. For a rectangular density modulation of period a and duty cycle t/a, with low and high (in the region t ) density values of ns~ and ns2, the average density n s 0 = n s l ( 1 - t / a ) + n s 2 ( t / a ), and the amplitude of the first Fourier component A n ~ o = ( 2 / n ) ( n a nsl)sin(nt/a). Using the values of n~l, ha, and measured above, an effective mass m * = 0.037 m0 (from the cyclotron resonance), and E~= 10.5 e0 for the thick AISb cladding layer, we calculate COpto be 49 and 52.2cm -~ for t/a values of 0.5 and 0.75, in exact agreement with measurement. Furthermore, the peak absorption strengths from (4) are respectively 10 and 5% for the two cases, again in close agreement with experiment. The detailed absorptions from (1) and (2) are plotted along with the measured spectra in Fig. 3. There are no adjustable parameters in the calculated trace in Fig. 3(a). For Fig. 3(b), the calculated trace assumes the d.c. mobility along the LSL to be 100,000 cm2/Vs to get a better fit to the Drude tail. The positions of all resonances for the sample with t/a = 0.5 are plotted as a function of magnetic field up to 8 T in Fig. 4. F r o m the cyclotron resonance frequencies we calculate an electron mass m * = O . O 3 7 m o. The magnetoplasmon resonances obey the relation[I 1]:

2-

~+CO~

COmp - - COc

I00

6~f

o,e..,.

I

0

I 0

I 2

I

I 4

I

I 6

8

B (Tesla) Fig. 4. Absorption frequencies at different magnetic fields, for the sample with t/a = 0.5. Closed circles denote cyclotron resonance, open ones the 2D plasmon resonance. The dashed line fit for the CR line assumes m* = 0.037 m0. Dashed curve for the plasmon dispersion is calculated from eqn (5). portional to a ' q , where a* is the Bohr radius. The higher Bohr radius for a 2DES in InAs together with a higher q should make this interaction appear in far infrared transmission measurements on such samples. These investigations will be reported elsewhere.

Acknowledgements--It is a pleasure to thank P. Pinsukanjana, A. Lorke and A. Wixforth for many illuminating discussions. This work was supported in part by the Office of Naval Research (ONR grant #N000 15-92-J-1452) through the Quantum Institute, and by the National Science Foundation (NSF grant #DMR-91-10430) through QUEST, a National Science and Technology Center, at the University of California, Santa Barbara.

(5)

very well, as indicated (Fig. 4). N o evidence is seen in these samples for the coupling of the magnetoplasmon resonance with harmonics of the cyclotron resonance. Measurements on LSLs with 2D modulation yielded results identical to the I D LSLs. In summary, we observe the absorption of 2D plasmons in I D and 2D lateral-density-modulated 2DES in an InAs q u a n t u m well sandwiched between AISb barriers. The density modulation is achieved by lateral modulation of the surface Fermi level with a periodic alternation of the composition of the cap layer between InAs and GaSb. In a LSL with 4/am period we observe up to 10% peak absorption at 49 c m - i . Both the location and strength of the plasm o n absorption, as well as the dependence of these quantities on the duty cycle, agree well with theory. Sub-micron periodicities achieved with holographic lithography should lift the plasmon absorption to higher frequencies, and make possible the observation of non-local effects, which, in first order, are pro-

REFERENCES

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