An n‑type silicon wafer has a donor concentration $N_{D} = 3 \times 1 0^{15}, cm^{- 3}$ and electron mobility $μ_{n} = 1400, cm^{2} V^{- 1} s^{- 1}$ . Assuming holes are negligible, calculate the resistivity $ρ$ of the wafer in $Ω! \cdot! cm$ . (Take $q = 1.6 \times 1 0^{- 19}, C$ )

hard 4 marks Class 12 · Physics · Semiconductor Electronics Materials Devices and Simple Circuits

Answer

1.49, Ω! \cdot! cm

The correct answer is $1.49, Ω! \cdot! cm$ — Round to two significant figures: $1.49, Ω! \cdot! cm$ .

Step-by-step solution

Use the relation for resistivity: $ρ = \frac{1}{q m u _{n} N _{D}}$ .
Compute the denominator: $q m u_{n} N_{D} = 1.6 \times 1 0^{- 19} \times 1400 \times 3 \times 1 0^{15} = 0.672$ .
Take the reciprocal to get $ρ = 1/0.672 = 1.488; Ω! \cdot! cm$ .
Round to two significant figures: $1.49, Ω! \cdot! cm$ .

Common mistake: Using

σ

instead of

ρ

or forgetting the factor

q

Concept tested: Resistivity of doped silicon