Impurity-band density of states in heavily doped semiconductors: Numerical results

Abstract

The "band-tail" density of states p(E) available to electrons in a field of randomly distributed, attractive impurities developed in previous work is extended to higher energy E. Numerical values of p(E) are also presented (1) for comparison with p(E) developed by other methods and (2) for calculation of optical and other properties of heavily doped semicoflductors depending on p(E).

Description of low temperature bandtail states in two-dimensional semiconductors using path integral approach

“…WðXðsÞ À XðrÞÞ ¼ ð dx VðXðsÞ À xÞ VðXðrÞ À xÞ: (2) An electron moving in a field of random impurities can be described by the action 1…”

Effects of Donor Size and Heavy Doping on Optical, Electrical and Thermoelectric Properties of Various Degenerate Donor-Silicon Systems at Low Temperatures

“…(B.5): Δr ≫ 0 as → −0. Finally, we also remark that, in the full ground-state case and deep-tail approximation, the exponential conduction-band tail, obtained by Sa-yakamit et al [23], was also equal to a constant at = −0, being not correct.…”

“…Therefore, the density of states, the optical absorption coefficient and the electrical conductivity, being proportional to our result (20), vanished at the conduction-band edge = 0, as given in Eqs. (23,26). Those results were also compared with other theoretical results, obtained at − = 0, in the small time approximation [21,29,30] and in the full ground-state case and deep-tail approximation [21], which were found to be constant, being not correct, as discussed also in Eq.…”

“…(iii) Finally, for ≤ 0 , they went to zero as → −0 and − ∞ and presented the maxima, being found to be in good accordance with an asymptotic form for the exponential conduction-band tail, obtained by Halperin and Lax [19], using the minimum counting methods. Hence, the problem posed in the past for those exponential tails [14,17,19,21,23,25,29,30,37] should now be solved.…”

“…In the present paper, the degenerate d-Si system is considered, noting that all the optical, electrical, and thermoelectric properties given in the degenerate a-Si system can also be investigated by a same treatment. So, in the degenerate d-Si system, a good knowledge of: (i) energy-band structure parameters such as: the reduced band gap [7][8][9][10][11][12], N [11,12] and effective donor ionization energy [13], (ii) exponential conduction-band tails [14][15][16][17][18][19][20][21][22][23][24][25] and Fermi energy [26][27][28], and finally (iii) optical [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], electrical , and thermoelectric [58,61,68,…”