Anomalously high ``mobility'' in GaAsC. M. Wolfe, G. E. Stillman, D. L. Spears, D. E. Hill, and F. V. Williams Citation: Journal of Applied Physics 44, 732 (1973); doi: 10.1063/1.1662253 View online: http://dx.doi.org/10.1063/1.1662253 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/44/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Anomalous temperature dependence of the Hall mobility in undoped bulk GaAs J. Appl. Phys. 82, 3832 (1997); 10.1063/1.365747 Anomalous mobility enhancement in heavily carbondoped GaAs J. Appl. Phys. 75, 5453 (1994); 10.1063/1.355706 Anomalous magnetization of GaAs J. Appl. Phys. 61, 3555 (1987); 10.1063/1.338722 Mobility enhancement in highly doped GaAs quantum wells J. Appl. Phys. 61, 1643 (1987); 10.1063/1.338051 Electron Mobility in HighPurity GaAs J. Appl. Phys. 41, 3088 (1970); 10.1063/1.1659368

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Anomalously high "mobility" in GaAst c. M. Wolfe, G. E. Stillman, and D. L. Spears

Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02173

D. E. Hill and F. V. Williams

Monsanto Company, St,Louis, Missouri 63166 (Received 22 September 1972)

A high-purity GaAs sample with a measured room-temperature mobility of 15200 cm'/V sec is examined in detail. Resistivity and Hall measurements are in reasonable agreement with a previously developed model which shows that conducting inhomogeneities can result in anomalously high measured mobilities. A sizeable number of precipitates (probably gallium) are observed in the sample.

INTRODUCTION

Although mobility values are commonly used as an indi­cation of the quality of a material, mobilities which are apparently anomalously high have been observed in GaAs and other semiconductors. In an effort to explain these results we have theoretically and experimentally dem­onstrated1• 2 by the use of a simple model that conducting inhomogeneities in a Hall sample can result in calculated mobilities which are too high by as much as several or­ders of magnitude. From this model several criteria were obtained which should be applicable for determin­ing if the measured mobility in a "real" sample is gen­uine or anomalously high. In this paper the authors ex­amine the properties of a GaAs sample with an anoma­lously high measured mobility and examine the extent to which the predictions of the model can be applied to this "real" sample.

CONDUCTING INHOMOGENEITY MODEL

Briefly, the model consists of a cylindrically symmetric van der Pauw3 measurement sample with a conducting inhomogeneity in the center. Neglecting effects due to sample geometry, the resistivity (measured in zero magnetic field) is an average value for the sample and the inhomogeneity. The Hall constant measured in the low-magnetic-field limit is also an average value for the sample and the inhomogeneity. However, as the magnetic field is increased, the Hall constant begins to increase because of the magnetic-field-induced interac­tions between the boundary conditions at the sample-in­homogeneity interface. 4 As a result of these interac­tions, in the high-magnetic-field limit there is no cur­rent flow into the inhomogeneity and the measured Hall constant is the Hall constant of the homogeneous part of the sample.

From this model one would suspect an anomalously high measured mobility for a sample if any of the following are observed2 : (i) Conducting inhomogeneities of any kind are detected. (ii) High mobility values are not very re­producible. (iii) Mobility values exceed theoretical es­tim ate s . (iv) Resistivity and Hall measurements indicate that the sample is less compensated than is normally observed. (v) The Hall constant does not change with the expected magnetic field dependence of the Hall factor.

HIGH-MOBILITY SAMPLE

To test the applicability of these criteria the properties

732 J. Appl. Phys., Vol. 44, No.2, February 1973

of a high-purity GaAs sample with a measured room­temperature mobility of 15200 cm2 Iv sec were examined in detail. This sample was a 20-!Lm-thick epitaxial layer which was grown on a (lOO)-oriented semi-insulating GaAs substrate and ultrasonically cut into a cross­shaped van der Pauw measurement configuration. The parts of the epitaxial layer remaining after the cross was cut were also measured and they exhibited normal mobility values. Thus, the value of 15200 cm2 Iv sec was not characteristic of the entire epitaxial layer and was not very reproducible. Also, the mobility of the cross­shaped sample exceeds recent theoretical estimates of the room-temperature lattice-limited mobility in GaAs 5

by a factor of about 2. It should be emphaSized that the measurement of 15200 cm2 Iv sec is an accurate exper­imental value and there is no possibility for a factor of 2 experimental error.

Anomalous

14 -3 No= 7.79 x 10 em

NA

" 1 .44 x 1014 cm-3

ED" 4.90meV

B = 5kG

NO = 7.76 x 10/4

em-3

NA = f .86 x 1014

em-3

Eo= 4.28meV

FIG. 1. Temperature dependence of the Hall constant (RH)

measured at 5 kG for the anomalous sample (solid circles) and a normal sample (open circles) selected to have similar values for ND and NA from analyses (curves) of the data.

Copyright © 1973 American Institute of Physics 732

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733 Wolfe et al.: Anomalous "mobility" in GaAs

104

t03

t02

E .., I c: Q.. t0

1

FIG. 2. Temperature dependence of the resistivity (p) for the anomalous and normal samples.

HOMOGENEITY DETERMINATION

The sample homogeneity was first examined by looking for macroscopic variations in conductivity. For this purpose the photoconductivity was monitored while the sample was scanned6 with a 2-mil square optical beam. The entire thickness was measured by selecting the wavelength of the exciting radiation to give about 20% transmission through the sample. The results of this measurement indicated that to within the resolution of the optical probe the lateral conductivity of the sample did not vary by more than about 10%. Since the quan­titative features2 of the theoretical model indicate that a conductivity variation this small could not account for the measured mobility of the sample, it was next ex­amined for inhomogeneities smaller than the 2-mil resolution of the scanning photoconductivity technique.

Infrared microscopy with transmitted light revealed the presence of a rather high density (-109 cm-3 ) of preci­pitates randomly dispersed throughout the epitaxial lay­er. Although these precipitates were too small « 10 /J.m) to be easily indentified by analytical methods, they were apparently of su'fficient size and density to cause considerable strain in the epitaxial layer. This strain was evident in far-infrared photoconductivity measure­ments at liquid-helium temperatures of the shallow­donor levels. 7 Although not a conventional method for measuring strain, these spectra clearly showed evi­dence for an anisotropic compressive strain in the sam­pIe. This anisotropic compressive strain is consistent with the precipitates being gallium, since gallium would

J. Appl. Phys., Vol. 44, No.2, February 1973

733

be expected to expand by about 3% upon freezing, leav­ing the sample in compreSSion. Also, from previous mass spectrographic analyses of high-purity GaAs 8 it is doubtful that any residual impurity could account for the size and denSity of precipitates in this sample. There­fore, it seems most likely that the anomalously high mobility in this sample is due to gallium precipitates.

HAll AND RESISTIVITY MEASUREMENTS

Detailed Hall and reSistivity measurements were per­formed on the sample. Figure 1 shows the temperature dependence of the Hall constant (RH ) measured at 5 kG. The solid circles are the experimental data and the cor­responding curve is a least-squares analysis of the data using the usual Single-donor statistics. Values for the shallow-donor concentration (N D)' the total compensa­ing acceptor concentration (NA ), and the donor thermal binding energy (ED) obtained from this analysis are also shown in the figure. The open circles and curve marked "normal" are for an epitaxial GaAs sample with appar­ently normal properties which was selected to have val­ues for N D and N A as close as possible to those obtained for the anomalous sample. Although the method of anal­ysis was identical for the two samples, it should be noted that the values for ED are markedly different. The concentration dependence of the donor thermal binding energy has been examined in detail. 9-12 From this de­pendence13 it can be seen that the ND and ED for the nor­mal sample are in good agreement, whereas the ND and ED for the anomalous sample do not agree. This indi­cates that the analysis of the Hall data for the anomalous sample does not give appropriate values for ND, ED' and (because of the nature of the analysis) NA •

The temperature dependence of the reSistivity (P) for the anomalous and normal samples is shown in Fig. 2. It can be seen that p for the anomalous sample is about a factor of 2 lower than p for the normal sample in the temperature range from 300 to aQout 20 OK, even though

B = 5kG

Anomatous

T (OK)

FIG. 3. Temperature dependence of the mobility calculated from RH/p for the anomalous and normal samples.

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734 Wolfe et al.: Anomalous "mobility" in GaAs

1.20

T= 295°K

f.f5 Normal

!.f0

:I: Q:: 1.05 CD c:

1.00

B (kG)

FIG. 4. Magnetic field dependence of the Hall factor deter­mined from neRH for the anomalous and normal samples. The lower solid curve without data points is the qualitative depend­ence expected from the conducting inhomogeneity model.

1 I eRH from Fig. 1 is fairly close for the two samples in the same temperature range. At lower temperatures this factor of 2 changes due to different freeze-out properties of the two samples. This change cannot be resolved since ND , NA , and ED are not known for the anomalous sample. However, if the carrier concentra­tion (n) determined from 11eRH is almost correct in the high-temperature region, as will be shown below, then the difference in p for the two samples is qualitatively what would be expected from the conducting inhomogene­ity model.

Figure 3 shows the temperature dependence of the mo­bility calculated from RHlp for the two samples. As can be seen the anomalous sample has a higher calculated mobility than the normal sample over the entire tem­perature range. Also of interest is the fact that the normal sample has a change in slope in the temperature range from about 20 to 10 OK, whereas the anomalous sample does not have a change in slope. This change in slope reflects the compensation of the material (the ratio of NAto N D); that is, the more pronounced the change in slope, the lower the compensation, and vice versa. This is because ionized impurity scattering is dominant in this temperature range. 5.9014 Thus, if NA is substantially smaller than N D , there will be a signi­ficant change in the number of ionized impurities and the mobility as the ionized donors are neutralized by carrier freeze out. This change in mobility should be apparent even though the mobility is too high. Since the anomalous sample shows no such change in slope, it must be more compensated than the normal sample, in contrast to what the analyses of the Hall data indicate.

The magnetic-field (B)-dependence of the Hall factor determined from neRH at room temperature is given in

J. Appl. Phys., Vol. 44, No.2, February 1973

734

Fig. 4. The carrier concentration (n) for both samples was obtained from the highest magnetic field measure­ment of RH • The lower curve shows the qualitative de­pendence expected from the conducting inhomogeneity model. The magnetic field dependence shown for the normal sample is in reasonable agreement with recent calculated values for the Hall factor. 15 Although neRH for the anomalous sample does not increase monotoni­cally with magnetic field as predicted by the model, it does demonstrate unusual behavior. This behavior probably reflects a combination of Hall factor and in­homogeneity effects. Also, the change in neRH for the anomalous sample is small which indicates that n as determined from 1/ eRH at low fields is probably fairly accurate.

CONCLUSIONS

In conclUSion, precipitates (probably gallium precipi­tates) are the main inhomogeneity observed in the GaAs sample with the anomalously high measured mobility. These preCipitates apparently have a sizeable effect on the electrical properties of the sample, most of which are in qualitative agreement with the predictions of the conducting inhomogeneity model. The carrier concen­tration determined from 1/ eRH at low magnetic fieldS appears to be about right, whereas the sample is more heavily compensated than the Hall constant analysis or the mobility indicate. Also, the magnetic field de­pendence of the Hall constant is anomalous in agreement with the model.

tWork sponsored by the Department of the Air Force. Ie. M. Wolfe and G. E. Stillman, Appl. Phys. Lett. 18, 205 (1971). 2C. M. Wolfe, G. E. Stillman, and J. A. Rossi, J. Electrochem. Soc.

119, 250 (1972). 3L. J. van der Pauw, Philips Res. Rep. 13, I (1958). 4C. Herring, J. Appl. Phys. 31, 1939 (1960). 50. L. Rode and S. Knight, Phys. Rev. B 3, 2534 (1971). 60. L. Spears and R. Bray, J. Appl. Phys. 39, 5093 (1968). 7G. E. Stillman, C. M. Wolfe, and 1. O. Oimmock, Solid State

Commun. 7,921 (1969). 8C. M. Wolfe, G. E. Stillman, and E. B. Owens, J. Electrochem. Soc.

117, 129 (1970). 90. E. Bolger, J. Franks, J. Gordon, and J. Whitaker, Proceedings of

the 1st International Symposium GaAs (Institute of Physics and Physics Society, London, 1967), p. 16.

100. V. Eddolls, Phys. Status Solidi 17, 67 (1966). llM. Maruyama, S. Kikuchi, and O. Mizuno, J. Electrochem. Soc.

116,413 (1969). 12G. E. Stillman, C. M. Wolfe, and J. O. Oimmock, Proceedings of the

3rd Photoconductivity Conference (Pergamon, New York, 1971), p. 265.

l3e. M. Wolfe and G. E. Stillman, Proceedings of the 3rd International Symposium GaAs (Institute of Physics, London, 1971), p. 3.

14C. M. Wolfe, G. E. Stillman, and W. T. Lindley, J. Appl. Phys. 41, 3088 (1970).

150. L. Rode (private communication).

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