Charge-Carrier Mobility in Polycrystalline Semiconducting Films Based on Bulk Single-Crystal Theory

The temperature and thickness dependence of charge‐carrier mobility in vacuum‐deposited germanium films can be represented by the relation $${\text{1/μ}}_e{\text{=1/μ}}_L{\text{+1/μ}}_I{\text{+1/μ}}_d{\text{+1/μ}}_F,$$ where the first three terms represent the lattice, impurity, and dislocation scattering in bulk material. The term μ_F is a function of the surface scattering of the carriers as well as of grain‐boundary effects. Thus film‐size effects are represented in a large part by the fourth term which satisfies the empirical relation $${\text{1/μ}}_F\mathrm{=A\hspace{0.17em}}\log \mathrm{(\delta /a).}$$ For the films studied, this is the dominant term for polycrystalline films less than 5000 Å in thickness or single‐crystal films less than 1800 Å in thickness. The measured value of the coefficient A was 0.0219 V·sec·cm⁻² for our polycrystalline films and 0.0176 for the single‐crystal films of Sloope and Tiller. The characteristic thickness, δ, was found to be dependent upon grain‐boundary scattering, having a value of 8000 Å for polycrystalline films as compared to 2000 Å for the single‐crystal films.