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

Abstract

A new critical point and a non-equilibrium phase transition in the non-linear conductivity in doped silicon have been observed in the variable-range hopping regime, due to a negative differential resistance with a dc bias current . We show this critical behaviour is intrinsic in a thermal model, and for a resistance - temperature characteristic given by the Efros - Shklovskii law we find a critical temperature , independent of and the electron - phonon coupling strength. Below this gives circuit-limited oscillations with a frequency .

Non-Ohmic hopping transport ina−YSi: From isotropic to directed percolation

“…On the experimental side, I-V non linearities were investigated both in amorphous materials [26]- [34] and in doped crystalline semiconductors [35]- [47]. In most of these works, the authors focussed either on very high fields or on intermediate fields.…”

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

“…The high-field nonlinearities in this second group are much stronger. In the extreme cases, the I-V characteristic was determined to be S-shaped, 43,44 which led to hysteretic conductivity jumps by orders of magnitude 43,45 and circuit oscillations. 44,46 Interestingly, in systems that show conductivity jumps the Ohmic conductance shows a simple activation rather than VRH behavior.…”

“…In the extreme cases, the I-V characteristic was determined to be S-shaped, 43,44 which led to hysteretic conductivity jumps by orders of magnitude 43,45 and circuit oscillations. 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.…”

“…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 .…”

“…Equation (44) predicts that P (u) decays as a Gaussian at u M < u < u I and as an exponential of the exponential at u > u I . In between, it exhibits a narrow peak of width δu ∼ ln(u 2 M /u I ) near the non-Ohmic threshold u = u I .…”