Distinction between the Poole-Frenkel and tunneling models of electric-field-stimulated carrier emission from deep levels in semiconductors

The enhancement of the emission rate of charge carriers from deep-level def ects in electric field is routinely used to determine the charge state of t he defects. However, only a limited number of defects can be satisfactorily described by the Poole-Frenkel theory. An electric field dependence differ ent from that expected fr om the Poole-Frenkel theory has been repeatedly r eported in the literature, and no unambiguous identification of the charge state of the defect could be made. In this article, the electric field depe ndencies of emission of carriers from DX centers in A1(x)Ga(1-x)As:Te, Cu p airs in silicon, and Ge:Hg have been studied applying static and terahertz electric fields, and analyzed by using the models of Poole-Frenkel and phon on assisted tunneling. It is shown that phonon assisted tunneling and Poole -Frenkel emission are two competitive mechanisms of enhancement of emission of carriers, and their relative contribution is determined by the charge s tate of the defect and by the electric-field strength. At high-electric fie ld strengths carrier emission is dominated by tunneling independently of th e charge state of the impurity. For neutral impurities, where Poole-Frenkel lowering of the emission barrier does not occur, the phonon assisted tunne ling model describes well the experimental data also in the low-field regio n. For charged impurities the transition from phonon assisted tunneling at high fields to Poole-Frenkel effect at low fields can be traced back. It is suggested that the Poole-Frenkel and tunneling models can be distinguished by plotting logarithm of the emission rate against the square root or agai nst the square of the electric field, respectively. This analysis enables o ne to unambiguously determine the charge state of a deep-level defect.