Quantization effects in hole inversion layers of tunnel MOS emitter transistors on Si (100) and (111) substrates at T=300K

The 2D consideration of the hole gas in the inversion layer is shown to be essential for a correct estimation of the currents flowing in the tunnel MO S structure on (100) n-Si and (111) n-Si substrates. The classical (3D) tre atment is found to lead to significant errors in the predicted distribution of the applied voltage, which results in incorrect evaluation of currents and makes the performance of a careful analysis of the energy relaxation of injected hot electrons impossible. A complete quantum treatment for an inv ersion should be based on the self-consistent solution of Poisson-Schroding er equations, as is done for MOSFETS. The hole tunnel current is to be calc ulated as a sum of currents from discrete levels. a simplified quantum appr oximation is also examined far the tunnel MOS structure. The quantization e ffects are shown to be important in almost all practically interesting oper ational modes, especially for high insulator bias and high doping concentra tion.