A sample of Si is doped with 10¹⁷ donor atoms/cm³. Considering electron mobility in the doped Si 700 cm²/V-sec, the approximate resistivity of the doped Si is

Concept

For a semiconductor slab doped with excess carriers and placed in an electric field, the current equation is given by:-

J = σ E

Where J = Current Density

σ = Conductivity of the semiconductor defined as:

σ = qnμn + qpμp

n = excess electrons contributing to the current conduction.

p = excess holes contributing to the current conduction.

Also, the Resistivity is defined as the reciprocal of conductivity.

i.e. 

Calculation:

Since the intrinsic carrier concentration of Germanium is of the order of 1013, and the given donor density is of the order of 1020, we can write:

n0 = Nd = 1017 atoms/cm3

μn = 700 cm2/V-sec

Since there is no acceptor impurity, p0 << n0 and can be easily neglected and the resistivity becomes:

ρ = 0.089 Ω-cm  ≈ 0.1 Ω-cm