UBC Theses and Dissertations
Hopping conductivity in lightly doped semiconductors Shegelski, Mark Raymond Alphonse
In lightly doped semiconductors (LDSs), electrons can exist in localized states around impurities and dc electronic conduction can occur by electrons hopping between localized states. Such hopping is the dominant mechanism for conduction if the temperature is so low that the contribution from band electrons is negligible. According to theories of hopping conduction, at low enough temperature T, the conductivity σ will be o=σ₀e⁻(T₀/T)¼ where T₀ is a temperature which depends on the material. Experimental work on doped semiconductors which exhibits this form of σ is scarce. Recently, however, conductivities which were clearly of this form were reported for lightly doped n-GaAs and lightly doped n-InP. The experimental results were surprising in that the temperature ranges were well above, and the T₀ values well below, the limits set by the theories. To understand these experimental results, hopping in LDSs is modelled in this dissertation using a resistor network. This dissertation is unique in that the conductivity of the unabridged resistor network is examined in a temperature range (called "the high temperature regime") where kT is comparable to the spread ∆ε in the energies of localized electrons. A numerical simulation is performed and an analytic theory based on percolation methods is presented. In this dissertation, an analytic approach is developed for the first time for studying how, in the high temperature regime, the conductivity of the unabridged resistor network depends on the density of localized states. It is found that, in either two or three dimensions, if the density of states is flat, σ is of the activated form o=σ₀e ⁻εa/kt. The activation energies are found to be εa=0.28∆ε in two dimensions and εa =0.20∆ε in three dimensions. These values are considerable improvements over the estimates of previous workers, who used the low temperature asymptotic form of the resistance in the high temperature regime. It is also revealed that σ can be o=µσ₀e ⁻(T₀/T)¼ in the high temperature regime if the density of states decreases with |ε⁻µ₀| for energy e far enough away from the zero temperature chemical potential µ₀, These results are in accord with the experimental results described above.
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