Statistical approach to the process of tunnel ionisation of impurity centres near the heterointerface

Abstract

To date, the processes of tunnel ionisation of impurities near the interface between two different semiconductors have been comprehensively studied. The most important parameters of the contact electron states of impurities have been determined. However, the calculated expressions for these parameters have been of local nature, as applied to individual impurities. Meanwhile, it is easy to understand that a number of processes, such as the flow of charge carriers and their diffusion through a heterojunction, are clearly statistical in nature. The same applies to the processes of tunnel ionisation of shallow and/or deep impurities near the interface. A statistical approach to the calculation of the parameters of tunnel ionisation of impurities broadens the opportunities for obtaining fundamental information regarding surface electronstates.The aim of this work was to use a statistical approach to study the effect of the heterointerface on the energy spectrum of shallow and deep centres. For this purpose, the expansion of the reflected quasi-classical wave function within the complete system of spherical harmonics and the subsequent extraction of the zero harmonic amplitude (s-component) was used to estimate the minimum distance from the impurity to the heterobarrier and to specify the limitations of the applicability of the results obtained in other works. The article analyses the conditions of the quasi-classical approximation which are used to estimate the order of the value for the minimum height of the potential barrier (pit).This work (with due consideration given to the minimum distance estimate) presents averaged formulas obtained for the energy shift of the ground state and the lifetime of the quasi-stationary state depending on the distance from the heterobarrier. Some qualitatively new considerations can also be found in the article. The distribution of impurity centres near the heterobarrier is assumed to be uniform. The article discusses the role of electron transitions in causing the buffer field effect for both shallow and deep centres. The focus of the article is on the estimates of various physical parameters characterising electron transitions near the heterobarrier.