Infrared optical characterization of GaAsAlxGa1−xAs submicron heterostructures

0038-1098/81/390307-04502.00/0

Solid State Communications, Vol. 40, pp. 307-310. Pergamon Press Ltd. 1981. Printed in Great Britain.

INFRARED OPTICAL CHARACTERIZATION OF GaAs-AlxGaI_xAs SUBMICRON HETEROSTRUCTURES* M.S. Durschlag1" and T.A. DeTemple Electrical Engineering Research Laboratory, Department of Electrical Engineering, 1406 West Green Street, University of Illinois, Urbana, IL 61801, U.S.A.

(Received 27 April 1981 by A.A. Maradudin) Infrared optical characterization of submicron, multiple layers of AlxGaI_xAs-GaAs on a GaAs substrate is reported, demonstrating that layer resolved phonon frequencies, electron concentrations and mobilities can be obtained. RECENT REFINEMENTS and innovations in crystal growth technology have led to the development of a new class of semiconductor devices utilizing ultra-thin (quantum size) heterostructures [ 1--4]. Unfortunately, the dimensions and geometry of these structures place severe demands upon traditional analytical techniques for the determination of material parameters. Most notably, free carrier concentration and mobility determinations within the various regions are difficult to perform and interpret under the best of conditions. In situations such as these, a contactless optical characterization offers a potential alternative to the standard methodology. In particular carrier concentration, mobility, and polar phonon frequencies can be extracted from an analysis of the middle and far infrared reflectivities (20 < ~ < 100#m) [5, 6]. Results of optical determinations, in good agreement with more conventional measurements, have been reported in bulk and epitaxial samples of GaAs [7-9], AIxGal-xAs [ 10-12], multilayer [ 13 ], and even quaternary materials [14]. In this current work, it will be demonstrated that this approach is applicable even to multilayer GaAs-Alx Gal_x As heterostructures of much smaller dimensions than have been reported previously, yielding layer resolved phonon frequencies, electron concentrations and mobilities. Conceptually the procedure is quite straightforward. A simple Drude model [11, 14] is used to describe the dielectric function of each layer which is then used to determine the reflectivity of the structure in a manner similar to that used for multilayer dielectric mirrors. A general dielectric function of the form

* This research was supported by the National Science Foundation and by the University of Illinois Industrial At'tiliates ~ogram. 1" Present address: Raytheon Company, 28 Seyon Street, Waltham, MA 02154, U.S.A.

=

6.

+

2

~j60~oj

eeet.o2

j=l ~ o j -- 602 + iFjw

co(60-- iT)

(1)

is used for each layer where / = 1 refers to GaAs and / = 2 refers to AlAs. The ternary, AlxGal_xAs, requires the summation since it exhibits mixed mode behaviour. In equation (1), 60toj is the transverse optic phonon frequency, Fj the lattice damping constant, and Si is t h e / t h oscillator strength. For the electronic contribution, 60p is the plasma frequency and 3' the electron damping constant. The high frequency dielectric constant is 6.. which is assumed to vary linearly with alloy composition. From the lattice contribution, the longitudinal optic phonon frequency, COto,can be extracted with the aid of the Lyddane-Sachs-Teller relation [ 12]. Free carrier concentration is obtained from the plasma frequency, and mobility is related to the electron damping constant by

N e (cm -3) = 1.11

x

1013 m___~n6**602,

me /ae(cm2V-lsec-1) = 9.33 x 103me/(3"m*),

(2)

with all frequencies and rates expressed in wavenumbers (cm-1). Once the dielectric function is in hand for each layer including the substrate, it is a simple matter to generate the reflectivity as a function of frequency [ 15]. By adjusting the various layer parameters to obtain a "best fit" to the experimental reflectivity data, each layer in the assembly can, in principle, be characterized. Reflectivity data were obtained on a Beckman 720-M Fourier transform spectrophotometer used at near normal incidence. In practice, the substrate side was analyzed first. Because of its large thickness, the substrate was assumed to be semi-infinite in length so that it could be easily characterized and thus some variables could be eliminated when fitting the front surface data. As an initial demonstration of the effectiveness of the procedure, an epilayer of AlxGal_xAs (x = 0.35)

307

308

INFRARED OPTICAL CHARACTERIZATION OF GaAs-Al~Gal_xAs

Vol. 40, No. 3

Table 1. Sample parameters Layer No.

Parameter

1

AlxGal_xAs (cm -3) /ae (cm 2V-1 sec -1) e** t (#m) N e

~Otol 6O2ol ~to2 Wlo2 2

GaAs* r (h)

Are (cm -a) /ae (cm2V-lsec-l) AlxGal-xAs t

1WA

1WB

(x = 0.5)

(Jc = 0.6) 1.8 X 1017 (2 X 1017) 520 [9.46]

< 1016 (4 X 1017) 200 [9.7]

2WA (x = 0.45)

< 1016 (~ 1016) 200 [9.93]

[0.3]

[0.31

[0.31

267 290 336 377

262 277 354 374

269 285 347 382

[2001 1.5 x 1018 (5 x 1018) 5200

[1001 1.3 x 1018 (< 1016) 4500

[801 < 1016 (< 1016) ~ 4230

(x = 0.45)

(x = 0.6) [1.0/am]

(x = 0.35)

Same as 1

It]

[0.9/aml

[80AI

( 1016 Are (cm -a) Other parameters

(1.5 x 101') Same as 1

4

Same as Layer No. 2

5

Same as Layer No. 1

Buffer plus substrate

GaAs* substrate Are (cm -a) /ae (cm 2V-1 sec-l) t (mils)

[9 x 1017] [2400] [15]

[9 x 1017] [2400] [15]

[9 x 1017] [2400] [15]

* Lattice parameters for GaAs are fixed as shown in Fig. 2. t

Barrier parameters were fixed to those obtained for the AlxGal_xAs epitaxial layer previously analyzed.

( ) Nominal values estimated from growth conditions. [ ] Fixed values. on a GaAs substrate will be examined first. The reflectivity data for this sample are shown in Fig. 1. The procedure described above was used to calculate a least squares fit to these data and the result, after a convolution with the instrument lineshape function [ 16] to account for finite resolution, is shown as the solid line. Clearly evident in this figure is that at least two oscillators are required to characterize this alloy. The peak at 360cm -1 is the AlAs-like LO resonance and the strong structure at 270 cm -1 is associated with GaAs. The splitting of this lower frequency peak is due to the shift in the LO phonon frequency of the epilayer from that of the substrate and is repeated in Fig. 2. The experimental thickness obtained as a result of the optical measurement, 5.6/am, agrees very well with the 5.4/am

value determined by standard methods. The main results of this test are, however, the phonon frequencies. These are illustrated in Fig. 2 as open circles and it is apparent that even for layers much thinner than those reported in the literature (100-200/am) [10, 12] the optical characterization is still accurate. This technique, then, can provide a corroborative approach for determining epilayer alloy composition in structures of this type. Next, three metalorganic chemical vapor deposition (MO-CVD) grown samples containing quantum-size heterostructures [see Fig. 3(a)] and that were separately operated as CW 300 K lasers [3] were analyzed in the same manner [17, 18]. Since the resulting reflectivity spectra were similar in most respects, only one set of

INFRARED OPTICAL CHARACTERIZATION OF GaAs-AlxGal_xAs

Vol. 40, No. 3 u

1.0

i

309

i

AIxGal_xAS ( x = O . 3 5 )

?

Z

_o p0 LtJ nl It. nl

0.5

re

!

0"0150

, Ga, 0 AIxGal

1.0

.

AIxGal.xAS . . . .

"~" ~ • ~

~

350

t

o . -~lAI

X

rr

UJ 3 4 0 (n

A

Z UJ

~

2911 280

270

26¢

250 . . 0.O

.

.

.

•

e

.

. . 0.5

u

.

P-

~UJ 0 . 5 .d ii nan n"

I

I

"~ v/

i

200

\

3~o

40O

(cm I )

Fig. 3. (a) Schematic of a single well sample. (b) Experimental data and theoretical fit (sohd line) to the sample in lWA. The dashed line is the calculated curve obtained by using bulk material phonon frequencies.

D 'E

i

WAVENUMBER

3,0

•

u

_o

0"0100

,

3'0/'.° 8 u:

u

Z

390

360

I

450

Fig. 1. Experimental data and theoretical fit of the reflection spectra of a Al~Gat_xAs epilayer on GaAs. For these data, a 12 cm -f resolution was used. For the fits the following were found: 1-'~= 3.2 cm -1, 1"2 = 7.7 cm -t, epilayer thickness of 5.6/.tm and the phonon frequencies are shown in Fig. 2.

.

iiiiiiiiii!iiii....... ~ttratili /iiii i ........................... ......

"

WAVENUMBER (cn~~)

.

s I~1

i

i

30O

400

liiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii,;iiiii!iiiiiiiiil i !iiiiiiiiiiiiiiiiiiiiiiiiiii~iiiiiiiiiiiiiiiii!i!iiiiiii~i!i!!!iiiilili!ii1

COMPOSITION

tOaoA%~ .

.

1.0 (x)

Fig. 2. Phonon frequencies as a function of composition in AlxGat-xAs. The solid lines and filled squares are from [12], the filled circles are from [10], the open circles refer to the data from Fig. 1. The crosses, triangles and unfilled squares refer to samples 2WA, lWA and lWB discussed in the text and characterized with parameters shown in Table 1. data will be shown and is illustrated in Fig. 3(b) with sample parameters listed in Table 1. It is apparent from the figure that at high wavenumbers ('> 200 cm -t) the topmost epilayer has the dominant influence on

reflectivity, with the AlAs- and GaAs-like resonances plainly evident. At small wavenumbers ( < 200 em -1) the effect of the epilayers is much more subtle and the rising reflectivity in this region is due in fact to the interaction with free carriers in the moderately doped substrate. In the analysis of these structures some simplifying assumptions were made to reduce computation time. First, the buffer layer [see Fig. 3(a)] was similar enough to the substrate to warrant eliminating it as a separate entity in the reflectivity model. Second, in the confining ternary layers all of the parameters in equation (1), except coo, were allowed to vary and the lattice parameters were assumed to be equal in both regions Third, in the thin GaAs layer only carrier concentrations and mobility were permitted to vary while the other parameters were fixed at their bulk values. This was further checked by noting the insensitivity of the calculated spectra to variations in the fixed parameters. For these more complicated structures the calculated reflectivities agree, on the whole, quite well with the experimental data, an example of which is shown in Fig. 3(b) as the solid line. The divergence at either wavenumber extremum is due to measurement inaccuracies associated with the low background flux at these experimental situations. The parameters resulting from the fit are listed in Table 1 and are worth further comment.

310

INFRARED OPTICAL CHARACTERIZATION OF GaAs-AlxGal_xAs

First, consider the phonon frequencies obtained for the ternary layers which are also shown in Fig. 2. It is quite evident that the agreement between these values and the data for bulk material shown in Fig. 2 is very poor. Also shown in Fig. 3(b) as a dashed line is the calculated reflectivity obtained by using bulk phonon parameters. Because of the clear discrepancy, it is apparent that the results in Table 1 could not be an artifact because bulk parameters simply could not be used to match the large spectral shift evident in the data. Intuitively one would expect some frequency shift to take place because of the sharp discontinuity in ion masses at the interfaces between the ternary and binary alloys. Indeed, the replacement of an Al ion by a much heavier Ga ion in AlAs would give rise to gap modes, so the change induced by the presence of an extensive substitution is not unexpected. In fact, results similar to these have been reported in superlattices of these materials [19-21 ] but not in the comparatively simple structures studied here. At this time, the magnitude of these shifts is not accounted for by any theoretical model [22]. Next examine the carrier concentrations and mobilities in the quantum-size GaAs layers. In the case of the two single well samples (lWA and lWB) where the confining ternary alloy is heavily doped, a high concentration of free carriers is found from the fit whether or not the GaAs is doped initially. It is expected that the lower potential of the GaAs region traps carriers from the confining layers, spatially separating them from their donors. Thus a higher-than-expected concentration can be created with a large mobility because of the reduced impurity scattering. Similarly high mobilities have been observed in modulation doped samples in the GaAs-AlxGal_xAs system [23, 24]. The fact that the two well sample (2WA) is uniformly lightly doped and no such effects are observed tends to support these data and demonstrate that the convergence to the fit is not an artifact. In conclusion, the application of infrared and far infrared optical characterization to very thin heterostructures appears to be a viable alternative to traditional methods where these suffer difficulties and contactless techniques offer advantages. Phonon frequencies, carrier concentration, and mobility can be determined in multilayer semiconducting assemblies by utilizing this approach, but for the structures discussed here these preliminary results raise many questions concerning the physics of these devices and the limitations of the method. For example, there is an apparent "loss" of carriers implied by the optical results for the lWA sample which might be indicative of a breakdown in the optical approach, the invalidity of the simple two parameter characterization of the carrier effects, or true extreme charge rearrangement caused by the carrier

Vol. 40, No. 3

gradients and fields or inaccuracies in specifying the dopant profile. Further study to verify these data and explore their implications is underway. Acknowledgements - The authors wish to acknowledge many fruitful interactions with N. Holonyak, Jr., K. Hess, and G. Stillman. The quantum well samples were grown by P.D. Dapkus and R.D. Dupuis of Rockwell International and their generosity in loaning them for this study is greatly appreciated.

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19. 20. 21. 22. 23. 24.

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