Energy-gap change in silicon n-type inversion layers at low temperature

Abstract

Energy-gap changes in two-dimensional systems at low temperature are treated. The “pure” energy gap E c- E v is narrowed by three terms: the majority-carrier exchange energy, and the majority-carrier and minority-carrier correlation energies which are due to dynamic-screening processes. For the first time an expression for the minority-carrier correlation energy in such a two-dimensional system is derived. The expressions for the three bandgap narrowing terms are then applied to silicon n-type inversion layers. The correlation energies appear to be much higher than the corresponding ones in three dimensions. This may be explained by the enhancement of the collective excitations in two dimensions with respect to three dimensions. Furthermore, the minority-carrier correlation energy is found to be the dominant energy-gap narrowing term. On the other hand, an effective energy-gap widening occurs due to the upward shift of the electro-chemical potential into the conduction band (quantum-mechanical confinement). As a result the “effective” energy gap is found to be almost concentration-independent over a large electron-density range, and to increase at very high density values.