Nonlinear current-voltage characteristics of ion-implanted Si:As in the hopping transport regime

A new critical point in the non-linear conductivity due to variable-range hopping in Si

“…The phonon-phonon coupling between the phonons in the sensors and the heat sink at T B was given by Q = B(T 3.5 ph − T 3.5 B ) with B = 0.8 × 10 −4 W K −3.5 . Almost identical exponents were found in ion-implanted Si:As by van der Heijden et al [8].…”

“…In general R(E, T ) = R(0, T )G(E, T ), where G is some exponential function. Zhang et al [7] and van der Heijden et al [8] showed that, for sample parameters (principally T 0 ) in ion-implanted Si similar to those in the present experiments, the thermal model gave a better fit to the data than the electric field model. This is confirmed by the excellent fit to (2) which we find for the temperature-dependent electron-phonon coupling.…”

“…Alternatively, (2) may be regarded as a parametrization of the dependence of R on the input power. There is no doubt that it gives a very good account of the effects of a bias current in many VRH samples [7,8], including those studied here. The phonons then transfer the heat to the heat sink.…”

Numerical studies of variable-range hopping in one-dimensional systems

“…44,46 Interestingly, in systems that show conductivity jumps the Ohmic conductance shows a simple activation rather than VRH behavior. 43,45 It has become common 41,42,44,45,47,48,49,50,51,52 to attribute strong nonlinearity and S-shaped I-V to electron overheating. It is assumed that G is the function of the electron temperature T e , which can be much higher than the ambient temperature T .…”