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Band‐Gap Narrowing in n‐Type Moderately Doped Silicon at 300 K
Author(s) -
Vancong H.
Publication year - 1983
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.2221170218
Subject(s) - doping , band gap , silicon , fermi level , condensed matter physics , quasi fermi level , physics , direct and indirect band gaps , atomic physics , chemistry , quantum mechanics , electron , optoelectronics
The band‐gap narrowing at 300 K in n‐type moderately doped silicon is investigated, basing on a second‐order Thomas‐Fermi model which was first developed by Friedel and recently by Van Cong et al. There are three contributions to band‐gap narrowing: (1) Δ g,opt (rigid‐band effect), (2) Γ n (non‐rigid band effect), and (3) Δ E g,FD (Fermi‐Dirac statistics effect), where Δ E g,FD is negligible because of large negative values of the Fermi energy. Δ E g,opt is a major contribution, while Γ n only takes an effect at sufficiently high donor concentrations; they increase with increasing doping. It is suggested that the numerical results of Δ E g, opt and Δ E g, elec ≈ (Δ E g, opt + Γ n ) are in good agreement with optical measurements of Balkanski et al., and with electrical measurements of Mertens et al., respectively. Finally, the present results of Δ E g,opt and Γ n are also compared with a recent theory of Lanyon and Tuft, and with that of Dhariwal and Ojha, respectively.