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Heavy Doping Effects on the Energy Band Structure of n‐Type Crystals
Author(s) -
van Cong H.,
Charar S.,
Brunet S.,
Averous M.,
Birman J. L.
Publication year - 1982
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2221130242
Subject(s) - quasi fermi level , band gap , condensed matter physics , doping , polaron , semimetal , fermi level , physics , fermi–dirac statistics , fermi energy , electronic band structure , direct and indirect band gaps , materials science , electron , quantum mechanics
The density of states, ϱ( E ), the penetration of the Fermi level into parabolic conduction bands, E n , relative respectively to optical and electrical conduction band edges E c and E ′ c , the band‐gap narrowing for the optical energy gap, Δ E g, opt ., the physical band‐gap narrowing (Δ E g, elec .), and the effective band‐gap narrowing (Δ E g, eff .) for the electrical energy gap, the “apparent” band‐gap narrowing due to the Fermi‐Dirac statistics effect, Δ E g, F.D ., the band‐gap narrowing due to the changes in ϱ( E ), Γ n 0+ Γ p 0 , are investigated for n‐type heavily doped crystals at an arbitrary temperature T , basing on a second‐order Thomas‐Fermi model and on a polaron model. It is suggested, in the n‐type heavily doped silicon at 300 K, that (i) while E n is larger than the penetration of Fermi level into the unperturbed conduction band, E n 0 , for 5 × 10 25 m −3 ≦ n 0 ≦ 10 26 m −3 , E n is found to be smaller than E n 0 , for n 0 ≧ 2 × 10 26 m −3 , (ii) Δ E g, elec , is significantly larger than Δ E g, opt . because of important band edge shifts caused by the polaron effect, (iii) Δ E g, FD < 0 is much more important than (Γ n 0+ Γ n 0 ), and (iv) Δ E g, eff . is thus smaller than Δ E g, elec ., The results of band‐gap narrowings are in good accordance with some existing experimental results, and also compared with those obtained by other theories.