Bandgap narrowing in moderately to heavily doped silicon
- 1 July 1979
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Electron Devices
- Vol. 26 (7) , 1014-1018
- https://doi.org/10.1109/t-ed.1979.19538
Abstract
A model of bandgap reduction in silicon through the stored electrostatic energy of majority-minority carrier pairs is developed and compared with experimental results in the doping range from 3 × 1017to 1.5 × 1020/cm3at room temperature. An analytic expression for the bandgap reduction in nondegenerate material is obtained\delta\epsilon _{g} = 3q^{2}/(16\pi \epsilon) \cdot (q^{2}n/\epsilonkT)1/2having a square-root dependence on the majority carrier concentration. At room temperature this becomes\delta\epsilon _{g} = 22.5 (n/10^{18})^{1/2}meV. In degenerate material, the bandgap reduction is independent of temperature, following the relationship\delta \epsilon _{g} = 162 (n/10^{20})^{1/6}meV. The experimental data at room temperature are in excellent agreement with this theory. Plots of bandgap narrowing as a function of doping level are presented for a number of temperatures.Keywords
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