Question

The hole concentration in an intrinsic semiconductor is 5 × 10⁸ m⁻³. When it is doped with certain impurity, the electron concentration becomes 4 × 10¹² m⁻³. Find the new value of the hole concentration. Also, identify the type of new semiconductor formed after doping.

Answer 1

Given: Intrinsic carrier concentration n_i = 5 × 10⁸ m⁻³    ...[since intrinsic n_h = n_i]

New electron concentration after doping n_e = 4 × 10¹² m⁻³

New hole concentration (n_h) = `(n_i^2)/n_e`

= `((5 xx 10^8)^2)/(4 xx 10^12)`

= `(25 xx 10^16)/(4 xx 10^12)`

= `6.25 xx 10^(16 - 12)` 

= 6.25 × 10⁴ m⁻³

Comparing the concentrations:

n_e = 4 × 10¹² m⁻³

n_h = 6.25 × 10⁴ m⁻³

Since n_e > n_h, electrons are the majority charge carriers. Therefore, the semiconductor is an n-type semiconductor.

∴ The new hole concentration is 6.25 × 10⁴ m⁻³ and the semiconductor formed is n-type.