Semiconductor Conductivity Basics

The electrical conductivity ($\sigma$) of a semiconductor depends on the concentration of charge carriers and their mobility. For a p-type semiconductor, the majority charge carriers are holes.

Conductivity Formula for p-type Semiconductor

The conductivity ($\sigma$) is primarily determined by the hole concentration ($p$) and the hole mobility ($\mu_p$). The formula is:

$\sigma = p \cdot e \cdot \mu_p$

Where:

• $p$ is the concentration of holes.
• $e$ is the elementary charge (a constant value).
• $\mu_p$ is the mobility of holes.

Impact of Reduced Hole Mobility

The problem states that the mobility of holes ($\mu_p$) is reduced to half its original value, while other parameters ($p$ and $e$) remain constant. Let the original mobility be $\mu_p$ and the new mobility be $\mu_p'$.

New hole mobility: $\mu_p' = \frac{\mu_p}{2}$

The original conductivity was $\sigma = p \cdot e \cdot \mu_p$.

The new conductivity ($\sigma'$) is calculated using the new mobility:

$\sigma' = p \cdot e \cdot \mu_p'$

Substituting $\mu_p' = \frac{\mu_p}{2}$:

$\sigma' = p \cdot e \cdot \left(\frac{\mu_p}{2}\right)$

Rearranging the terms:

$\sigma' = \frac{1}{2} (p \cdot e \cdot \mu_p)$

Since $\sigma = p \cdot e \cdot \mu_p$, we have:

$\sigma' = \frac{1}{2} \sigma$

Conclusion on Conductivity

The calculation shows that the new conductivity ($\sigma'$) is exactly half of the original conductivity ($\sigma$). Therefore, the conductivity is reduced to half.