On the minority-carrier quasi-Fermi level in metal-oxide-semiconductor tunnel structures

Abstract

This paper presents a theoretical study on the behaviors of the minority-carrier quasi-Fermi level (EFP) in the ultra thin (10–60 Å) MOS tunnel structures under reverse bias. Considering the transport of carriers across the oxide layer and the electrostatic potential distribution in these diodes, the quantitative details of the energy difference between EFP and the metalFermi level (EFM), ΔE, at the semiconductor-oxide interface are reported and analyzed. Besides, the effects of ΔE on the electrical properties of MOS tunnel diodes are discussed. It is shown that ΔE is a measure of the driving force for the minority-carrier tunnel currents. For a given oxide thickness ( d), ΔE, increases with the reverse bias ( VA), approaching a saturation value when VA is greater than a critical voltage. This critical voltage refers to an electrical characteristics transition from the tunnel-limited mode to the semiconductor-limited mode, which increases with the oxide thickness. For a given bias, ΔE decreases with decreasing the oxide thickness. It is found that, for d ≤ 10 A ̊ , EFP is pinned to EFM; for d ≥ 60 A ̊ , EFP is pinned to EFN (the majority-carrier quasi-Fermi level in the semiconductor); for d ≤ 36 A ̊ and without external minority-carrier injection, the semiconductor surface can not reach strong inversion condition even when the reverse bias is sufficient high. For a given bias and oxide thickness, ΔE increases linearly with the logarithm of the external minority-carrier injection current. It is also shown that, for 20 ≤ d ≤ 50 A ̊ , the presence of interface states at the O-S interface causes a drastic reduction in ΔE; while for other oxide thickness, the interface states have little influence on ΔE. The quantitative results presented in this article are of considerable importance in understanding the behaviors of the minority-carrier quasi-Fermi level in the MOS tunnel structures.