Investigation of Thermo-Electrical Instabilities in a Semiconductor as 2D Dynamical Systems

Abstract

A semiconducting sample placed in cryogenic media with applied electric field generates low frequency oscillations of electric current and sample temperature and known to be thermo-electrical instabilities. Although observation of current oscillations on oscilloscope is possible, change of sample temperature cannot be detected experimentally. Description of the phenomenon through mathematical equations helps to understand relationship of the two variables as well as their connection to deep trap behavior that are involved in supporting the instability. Mathematical model for thermo-electrical instabilities in an n type semiconductor based on the two deep trap level model with non-degenerate electron statistics has been introduced in order to investigate the unique relationship between the change in time of both electric current flowing through a semiconductor sample and the sample temperature. The 3D dynamical system of nonlinear inhomogeneous ordinary differential equations has been investigated as component 2D dynamical systems (n,T), (n,n<sub>t</sub>) and (n<sub>t</sub>,T) for local behavior at isolated equilibrium and at points on individual trajectories, where n, n<sub>t</sub> and T are free electron concentration at conduction band, electron concentration at deep traps and temperature of a semiconductor sample accordingly. Each of the planar systems is expressed in canonical form and investigated as a Cauchy problem with a set of appropriate initial values. This paper presents investigation results of phase trajectories of the planar systems depending on a single parameter – the temperature of cooling media T<sub>0</sub>. Based on obtained calculation results of time sequences of the three variables n, n<sub>t</sub> and T, phase differences among these variables have been determined for different values of T<sub>0</sub>. It has been established that the change in sample temperature lags behind change in current and this lag increases with T<sub>0</sub>. Clearly defined correlations among systems (n,T), (n,n<sub>t</sub>) and (n<sub>t</sub>,T) are seen, being the result of balance between field aided and thermal ionization mechanisms for charge carrier generation and recombination processes. Thermal and field assisted generation mechanisms compete with one another in achieving steady non equilibrium state in the system depending on temperature of cooling media T<sub>0</sub>.