Quantum Effects in Ge and Si. I

Abstract

Experimental quantum effect spectra have been observed in germanium and silicon at liquid helium temperatures and a frequency of 136 kMc/sec. Detailed spectra are presented for the applied magnetic field in the [100], [111], and [110] directions. Anisotropy data of some of the more intense lines are also presented. Using the theory of Luttinger and Kohn with the assumption of thermal equilibrium, effective masses and line intensities were computed for an applied magnetic field in the [111] direction. By adjusting the parameters of the theory, good agreement was obtained between the theoretical and experimental spectra. The experimentally determined parameters are: Yl 72 73 * Ge 13.2 4.10 5.62 3.29 Si 4.22 0.50 1.35 -0.39 These lead to parameters A =* 13.2, | B \ = 8.2, and | C | = 13.3 for germanium and A = 4.22, | B | = 1.0, and | C\ =4.34 for silicon. (See note added in proof.)

Temperature dependence of silicon carrier effective masses with application to femtosecond reflectivity measurements

“…Experimentally, the curvature parameters have been inferred from cyclotron resonance and quantum spectra measurements. [18][19][20]35,36 Table 1 lists four sets of experimentally determined values of A, ͉B͉, and ͉C͉. The first two sets are from cyclotron resonance measurements from two independent groups of researchers 35,36 ; the third set, from Stickler et al, is from quantum spectra 18 ; and the fourth set was obtained by Balslev and Lawaetz 20 from cyclotron resonance measurements on uniaxially stressed Si.…”

“…Here we use an orthogonal, three-center model that includes up to third-neighbor interactions, 14 which we have extended to explicitly include the spinorbit interaction. 15 In our calculations we start with three previously derived sets of three-center interaction parameters 14,16,17 that are slightly modified to exactly reproduce experimental valence-band curvature parameters [18][19][20] (which describe the shapes of the three valence bands near their band maxima 21 ), thus ensuring accurate low-temperature values of m h (T). We then use our calculated values of m e (T) and m h (T) to calculate the temperature-dependent optical effective mass m opt (T).…”

Cyclotron Resonance of Holes in Si

“…The solution of the eigenvalue problem for the case of B pointing in the [ I l l ] direction is very simple and referring to [l], [2], and [3] we shall omit it here.…”

“…and some of the results are listed below: Stickler It is seen that there is a certain disagreement between the values of y3 and especially between the values of yz. The parameters from [ 2 ] are obtained from a theo-retical fit to experimental cyclotron-resonance data as we are doing but in [ 2 ] the fit is only made for B =+ [ l l l ] . The parameters from 171 are obtained by measuring on uniaxially stressed Si.…”

Nonlinear terahertz transmission spectroscopy on Ga-doped germanium in high magnetic fields

“…Nonlinear processes in hole-doped germanium (p-Ge) have been investigated to advance the development of lasers [23,24] and THz technology [25][26][27][28]. Despite the fact that p-Ge has been widely studied, also in high magnetic fields [29][30][31], several outstanding issues still remain, which are mostly related to the nonparabolic band structure of the valence band, the appearance of nonequidistant LLs [32][33][34], and the lack of a clear under-standing of the light-induced ionization of the dopant atoms [35][36][37][38][39]. Figure 1 shows schematically the band structure of Ge:Ga near the bottom of the valence band.…”