Physics and mechanisms of dielectric trap profiling by Multi-frequency Charge Pumping (MFCP) method

Multi-frequency Charge Pumping (MFCP) is a widely used technique to characterize bulk trap distribution, N_T(x, E), within the SiO_x/high-kappa dielectric. Thus far, the theoretical interpretation of MFCP has either been based on uncritical generalization of the classical CP theory of electron-hole recombination or has been interpreted as a dasiaquasi-geometricalpsila component of CP current. Moreover, the recent literature contains variants of the basic MFCP that attempts to rectify various perceived limitations of the dasiaotherpsila MFCP methods. Yet, without a comprehensive theoretical study supported by detailed numerical model of charging/discharging dynamics during the MFCP process, it is impossible to establish the relative merits of these techniques, let alone the accuracy of back-extracted N_T(x, E) by these methods. In this paper, we (i) present a physically-based numerical framework to establish that I_CP in long, medium and short channel (L_CH) transistors should be understood in a fundamentally different way-none of which can be interpreted by simple generalization of the classical CP theory, (ii) compare and contrast N_T(x, E), back-extracted from different variants of MFCP (e.g., amplitude-sweep, base-level sweep, etc.) for NMOS transistors, and (iii) show that, regardless of the combination of the chosen parameters of V_Pulse (e.g., frequency: f; hi/low voltage levels: V_H/V_L; high/low pulse duration: t_H/t_L; rise/fall time: t_r/t_f), the back-extracted N_T can only be attributed to certain patches within position-energy space, but not to unique x and/or E points. Therefore, other complementary methods must be used for a unique definition of N_T(x, E) within the modern gate dielectrics.