Consider what happens when silicon is doped with arsenic. Suppose that the extra, weakly bound electron from arsenic moves in the first Bohr orbit in a silicon atom. The first Bohr orbit has a radius of
Because of the effects of screening, it is necessary to replace ε0 with the electric permittivity , where is the dielectric constant ( = 11.7 for silicon).
(a) Compute the effective Bohr radius for this electron.
(b) Compare your result with the lattice spacing in silicon, about 0.235 nm, and comment on the result.
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