Fowler-Nordheim current modeling of metal/ultra-thin oxide/semiconductor structures in the inversion mode, defects characterization

In this paper, we present a simple model of Fowler-Nordheim (FN) current of metal/ultra-thin oxide/semiconductor (MOS) structures biased in the inversion mode ($V_{g }> 0$) (injection of electrons from the semiconductor). The oxide thickness varies from 45 Å to 110 Å, the gate is in chrome and the semiconductor is of P type. From the general models of the conduction by FN effect and by assuming a continuum energy in the inversion layer, we have shown by using the Wentzel-Kramers-Brillouin (WKB) approximation that the modeling of the FN current, cannot be made by using the classical model generally used in the case of electrons injection from the metal ($V_{g }< 0$). However, it requires to introduce in the classical model a corrective term due to the effects of the temperature, the oxide/semiconductor interface degeneracy (the Fermi energy is localized in the semiconductor conduction band) and the Schottky effect. The results obtained from the numerical simulation show that these effects, at the ambient temperature, on the potential barrier at the oxide/semiconductor interface is lower than 4% and the conduction pre-exponential value (K1) is higher than that obtained in the classical model ($K_1^o =10^{-6}$ A/V2) [J. Appl. Phys. 40, 278 (1969)]. These results are validated experimentally by modeling the current-voltage characteristics of MOS structures where the oxide thickness is 109 Å. For oxide thickness lower than 100 Å, we have found that the results of simulation disagree with those experimental. We have attributed this disagreement to the degradation of the conduction parameters by the presence of leakage current before stressing the MOS structure (LCBS). This leakage current is attributed to defects localized in the oxide layer. We have shown that the leakage current is of FN type and deduced the effective barrier of defects. By taking account of this barrier value and the corrective term due to the temperature, the oxide/semiconductor interface degeneracy and the Schottky effects (TDSEs), we have determined the defects effective area. From the comparison between these results and those obtained in the case of electrons injection from the metal ($V_{g} < 0$) [Eur. Phys. J. Appl. Phys. 9, 239 (2000)], we have concluded that the defects depth in the oxide layer is identical to the oxide thickness.