Relaxation of post-illumination electric fields in strongly biased high-resistance structures with a single deep impurity level

Abstract

This paper examines how an electric field relaxes when a discontinuous large carrier-depleting voltage applied to high-resistance symmetric metal-semiconductor-metal (MSM) and metal-insulator-semiconductor-insulator-metal (MISIM) structures having a single impurity level, and how its energy level ɛt=Ec−Et and the tunneling transparency Tn,p of the metal-semiconductor or metal-insulator boundary affect the relaxation. It is shown that the relaxation of the field and the form of its steady-state distribution depend on the ratio of the time constant tp in the majority-carrier (hole) region to the ionization time τt−1=αn(n*+n1)+αp(p*+p1) of a deep trap in the bulk. This ratio determines the relative contributions of free ρp,n and bound charge dnsities ρt (where αn,p is the coefficient for capture by an impurity, and p*, n*, p1, n1 are equilibrium concentrations and Shockley-Read constants in the bulk). For τt≈(τt)max≫tp,ρt≫ it is found that ρp,n and ρt≫ρp,n, which corresponds to a trap energy close to \(\varepsilon _t = {{E_g } \mathord{\left/ {\vphantom {{E_g } 2}} \right. \kern-\nulldelimiterspace} 2} + kT\ln \sqrt {{{N_c \alpha _n } \mathord{\left/ {\vphantom {{N_c \alpha _n } {(N_\upsilon \alpha _p )}}} \right. \kern-\nulldelimiterspace} {(N_\upsilon \alpha _p )}}} \), independent of the value of Tn,p, decaying oscillations arise in the concentration distribution, bulk charge, and field appear in the bulk. The amplitude of these oscillations reaches a maximum at time t≈0.4τt. Decreasing the ratio αp/αn causes τt to deviate from (τt)max. When this happens, the field no longer oscillates; instead, it increases with positive curvature in the cathode portion of the bulk. The quantity Tn,p determines the behavior of the field in the neighborhood of the anode. The value of (dE/dx)0 is positive for MSM structures (Tn,p≈1), and negative for MISIM structures (Tn,p≈0). For transparencies close to a critical value Tn,p0, the field in the structure remains almost uniform over an impurity ionization time.