Thermally activated diffusion of impurities along a semiconductor layer

The dynamics of impurities that walk along a semiconductor layer assisted by thermal noise strength and quartic potential is explored analytically and numerically. Applying two cold spots in the vicinity of the quartic potential forces the system to undergo a phase transition from a single-well to a double-well effective potential. This also implies that the impurities (the positively charged particles) trapped by the quartic potential diffuses away from the central region and assemble around two peripheral regions (around local minima) of the semiconductor layer once the two cold spots are applied. The electrons, on the other hand, stay around the potential maxima where they occupy before cold spots are applied. The resulting charge distribution forms series of N-P-N junctions, indicating that our theoretical work gives a clue on how to fabricate artificial semiconductor layers. Moreover, the dynamics of these impurities as a function of model parameters is explored both analytically and with Monte Carlo simulation methods. In this work, not only we propose the ways of mobilizing (eradicating) unwanted dopants along the semiconductor layer but also we study the stochastic resonance for the impurity dynamics in the presence of a time-varying signal. Via Monte Carlo simulation approaches, we study how the signal-to-noise ratio as well as the spectral amplification depends on the model parameters.