Acta Technica 80. (1975)
1-2. szám - Vörös, T.: Frequency-Dependent Complex Dielectric Function for Semiconductors
Acta Technica Academiae Scientiarum Hungaricae, Tomus 80 (1—2), pp. 273 —279 (1975) FREQUENCY-DEPENDENT COMPLEX DIELECTRIC FUNCTION FOR SEMICONDUCTORS T. VÖRÖS* CAND. OF PHYS. SC. [Manuscript received October 14, 1974] The real and imaginary parts of the frequency-dependent complex dielectric constant are derived on the basis of the isotropic three-dimensional nearly-freeelectron model. 1. Introduction On the basis of the isotropic three-dimensional nearly-free-electron model expressions for the frequency-dependent complex dielectric function are derived in paper [1]. Application and comparison with experimental values [2] is given for Ge. The present paper shortly looks over the derivation of the complex e(q —0, a>) on the basis of paper [1]. Then an application for Si is given and the results are discussed. 2. Theory of noninteracting electrons For the optical (long-wavelength) limit only the umklapp, interband transitions out of normal and umklapp transitions of the nearly-free-electron model give contribution to e(q—>■ 0, со). These transitions are induced by the external field component This produces the interaction Hamiltonian: Uxt(g) = J d3r {cpWp*(r) + ср+к4’р*(г) }vqe‘4 T{cp' Wp'(r) + Ср-+Кур(г)} = p,p' (1st B. Z.) * T. Vörös, Gogol u. 36., 1133 Budapest, Hungary. v',,r = vq 2 p (1st B. Z.) 1 bp+Kp 77 + CpCP+K VI + (.*pTV1 + 7Í)2 l + %pXl; flT(a- )2 fl + («F)2J (T + (<_„)2 yi + ку T cpcp—q T" cp+Kc(p —Iq)+K U) Acta Technica Academiae Scientiarum Hungaricae 80, 1975