Relaxation into tunnel induced nonequilibrium states in metal-oxide semiconductor structures

Abstract

The relaxation of a Metal Oxide Semiconductor structure from deep depletion towards a tunnel induced nonequilibrium stationary state is addressed in this work. A simple model was constructed, taking into account thermal generation, tunneling of both types of carriers and impact ionization. Experimental results obtained on p-and n-type Si substrates and oxides thinner than 6.5 nm are shown to be well fitted by the proposed model. A map describing the possible behavior patterns for a structure with given oxide thickness and effective generation velocity is presented.The transients in an Metal Oxide Semiconductor (MOS) structure relaxing from deep depletion towards equilibrium were previously investigated in connection with the characterization of the minority carriers generation mechanisms. It is assumed, for the methods to be applicable, that the transient ends in the thermal equilibrium state. The presence of tunneling currents alters this behavior, affecting the transient to yield a steady state different from thermal equilibrium [1][2][3][4][5].Very thin oxide samples exhibit similar transients for both p-and n-type substrates. This symmetry breaks down for oxide thicknesses above 3.5 nm. Three qualitatively different behavior patterns, depending of the oxide thickness, can be identified through current transient curves for the n-type substrate samples. From the analysis of the associated currents, the three patterns correspond to i) p-type substrate samples and very thin oxide n-samples for which minority carriers seem to dominate the tunneling current, ii) intermediate oxide thickness (3-6 nm) on n-substrates, for which the tunneling current is dominated by majority carriers but the whole current is limited by the generation of minority carriers, and iii) thicker oxides on n-substrates, for which the impact ionization mechanism removes the limit imposed to the current by supplying minority carriers.The problem of modeling the relaxation of a MOS structure from deep depletion into tunnel induced nonequilibrium states is addressed in this work.An exact formulation of this problem requires the coupling Poisson equation, continuity equations for holes and electrons, and complete expressions for the pair generation process, tunneling and impact ionization. An integral treatment for the continuity equations, as used in this work, leads to a unique differential equation describing the evolution towards equilibrium.The model was tested by reproducing experimental results in the three regimes, and was used to analyze the dependence of each type of behavior on the thickness and generation parameters.A map for the relationship between oxide thickness and thermal to obtain a given behavior pattern is given. TheoryThe measured current in the external circuit after applying a reverse voltage step to an n-MOS diode is given by [5]where J disp is the displacements current due to changes in the charge distribution within the semiconductor, and J t p and J tn are the conduction currents which in this case correspond to tunnel...