PIEZOREFLECTANCE OF GERMANIUM FROM 1.9 TO 2.8 EV

The dependence of the imaginary part of the dielectric function, ε2(ω), on a small-amplitude ac stress in the energy range from 1.9 to 2.8 eV for germanium is analyzed. The dependence of the differential δε2 on polarization and stress direction is described in terms of three symmetry-adapted response functions: W1(ω), W3(ω), and W5(ω). The function W1(ω) characterizes the response to hydrostatic stress. [001] uniaxial stress generates W1(ω) and W3(ω) while [111] stress generates W1(ω) and W5(ω). The Wj(ω) contain contributions Wjshift(ω) from energy-band shifts, and also Wjmvar(ω) due to optical-matrix-element variation. We find W3shift(ω)=0, which implies that the critical points near 2.1 and 2.3 eV lie in the [111] direction (Λ) or at the L point, in agreement with previous work. W1(ω) contains almost purely energy-shift effects, which leads to the derivative of the unstrained ε2(ω) function, since hydrostatic shifts lead to very little wave-function mixing. W1(ω) and W3(ω) give very distinct line shapes which are characteristic of energy-band shifts and matrix-element variation, respectively. Here W5(ω) can be represented as a linear combination of W1(ω) and W3(ω). We can account for the observed line shapes quantitatively on the assumption that ε2(ω) consists of two distinct contributions ε2+(ω) and ε2-(ω) from each spin-orbit-split band, which are identical except for an energy shift equal to the spin-orbit splitting. This analysis yields four deformation potential constants: D11, D15, D33 and D35. The quantities D11 and D15 agree with previous measurements by Zallen and Paul and by Gerhardt. D33 agrees with the value determined by Pollak and Cardona using a dc stress method, while D35 differs by a factor of 4. The origin of this discrepancy is not presently understood, but recent calculations by Saravia and Brust tend to support this value. © 1969 The American Physical Society.