Shubnikov-de Haas Effect Under Stress: A New Tool for Determining Deformation Potentials and Band-Structure Information

Abstract

We report the first direct experimental evidence for the inversion-asymmetry splitting of the conduction band of InSb. Band-structure information and deformation potentials are obtained from Shubnikov-de Haas measurements by comparison with a theoretical model.In this Letter we show that a study of the Shubnikov-de Haas (SdH) effect under uniaxial stress is an extremely valuable tool for determining band-structure information and deformation potentials of semiconductors. The significance of this technique is demonstrated by the analysis of experiments on n-type InSb.Previous SdH and de Haas-van Alphen studies 1 " 8 of w-InSb have shown no indications of beating effects, even though the theoretical existence of the inversion-asymmetry splitting is well known. 9 " 11 Previously, a beat frequency in the SdH oscillations has only been seen in the semiconductors HgSe 12 " 15 and GaSb. 16 ' 17 The studies on these materials enabled values of the inversion-asymmetry splitting of the conduction bands to be estimated. In this work we report the observation of stress-induced beating effects in the SdH oscillations of tt-type InSb that are caused by the conduction-band inversion-asymmetry splitting. By comparing the beating-effect data with the E-versus-^ theories containing the effects of uniaxial stress, we find the first values of the inversionasymmetry splitting for the conduction band in InSb.The theoretical work of Bir and Pikus 18 showed that the conduction band of InSb-type semiconductors should become anisotropic under the application of uniaxial stress. However, until the present time, no direct experimental proof for this anisotropy has been given for any semiconductor. In this paper unambiguous evidence is presented that the conduction band of InSb becomes anisotropic with the application of uniaxial stress. This anisotropy was investigated by using the SdH frequencies to monitor the changes with stress in the extremal cross-sectional areas of the Fermi surfaces. In addition, the anisotropy of the conduction band is shown to be directly related to the valence-band deformation potentials b and d, thus permitting their direct extraction from the data.The SdH measurements were carried out on a sample having an electron concentration of ~2 xlO 17 cm" 3 . Magnetic field modulation and phasesensitive detection techniques were used to observe the oscillatory magnetoresistance. Figure 1 shows data which illustrate the emergence of the beating effects for BII [001] as compressive uniaxial stress is applied along a [110] crystallographic direction. Beating effects are also observable for Bll[lTl], but at higher stress values than for B II [001], No beating effects could be observed up to 4 kbar for B ll[lT0]. The interpretation of these beating effects is discussed below.10 B(kG) FIG. 1. Reproduction of x-y recorder traces of the SdH oscillations taken at 1.3 K while detecting at the second harmonic of the modulation frequency and for BII [001]. The stress a is given in units of kilobars. The arrows show the approximate...

Band parameters for III–V compound semiconductors and their alloys

“…There appears to be a consensus on values for the shear deformation potentials in InSb: bϭϪ2.0 and dϭϪ4.7. 1,[285][286][287] All of the recommended band structure parameters for InSb are given in Table IX.…”

The Shubnikov–de Haas Effect in Semiconductors: A Comprehensive Review of Experimental Aspects

“…The SdH effect has also been shown to be a valuable tool in studying the strain or uniaxial stress dependence of the band structure and Fermi surface of n-InSb (Seiler and Hathcox 1972a, Seiler 1974. Band-structure parameters and deformation potentials can be determined as shown in section 5.3.…”

“…21. This anisotropy was investigated by using the average SdH frequencies to monitor the changes in the extremal cross-sectional areas of the Fermi surfaces with stress (Seiler and Hathcox 1972a, Seiler 1974. The effects of stress are quite drastic.…”

“…The following semiconductors have been studied: Bi 2 Te 3 (Kohler 1977) Bi^Sb* (Brandt et al 1979(Brandt et al , 1980c(Brandt et al , 1981 GaSb (Sherwood 1970, Bhattacharjee and Rodriguez 1973 HgSe Hathcox 1972b, 1974) InSb (Seiler and Hathcox 1972a, Seiler 1974 The SdH effect has been used to study the strain or uniaxial-stress dependence of the inversion-asymmetry splitting of the conduction band and the Fermi-surface anisotropy induced in InSb by stress (Seiler and Hathcox 1972a, Seiler 1974. These studies have shown that stress is an important additional tool.…”