A silicon wafer is n‑type with 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 $q = 1.6 \times 1 0^{- 19} C$ )

easy 1 mark Class 12 · Physics · Semiconductor Electronics Materials Devices and Simple Circuits

Answer

ρ

= 1.49\,

Ω

\cdot

cm

The correct answer is $ρ$ = 1.49\, $Ω$ \! $\cdot$ \! $cm$ — Thus $ρ = 1/0.672 = 1.488 Ω \cdot cm \approx 1.49 Ω \cdot cm$ .

Step-by-step solution

Calculate the conductivity using $σ = q N_{D} μ_{n}$ .
Substitute the numbers: $σ = (1.6 \times 1 0^{- 19}) (3 \times 1 0^{15}) (1400) = 0.672 S cm^{- 1}$ .
Resistivity is the reciprocal of conductivity: $ρ = 1/ σ$ .
Thus $ρ = 1/0.672 = 1.488 Ω \cdot cm \approx 1.49 Ω \cdot cm$ .

Common mistake: Using

ρ = q N_{D} μ_{n}

instead of

ρ = 1/ (q N_{D} μ_{n})

Concept tested: Resistivity and conductivity