217k views
1 vote
In a p-type sample of GaAs, electrons are injected from a contact. If the minority carrier mobility is 4000 cm²/V.s at 300K. Calculate the diffusion length for the electrons.

User GISHuman
by
8.7k points

1 Answer

4 votes

Final answer:

The diffusion length for electrons in a p-type semiconductor can be calculated using the equation L = sqrt(Dτ), where L is the diffusion length, D is the diffusion coefficient, and τ is the minority carrier lifetime. The diffusion coefficient D can be calculated using the equation D = μkT/e, where μ is the mobility, k is Boltzmann's constant, T is the temperature in Kelvin, and e is the elementary charge. By substituting the given values into these equations, we can find the diffusion length for electrons in the p-type GaAs sample.

Step-by-step explanation:

The diffusion length for electrons in a p-type semiconductor can be calculated using the equation:

L = sqrt(Dτ)

Where L is the diffusion length, D is the diffusion coefficient, and τ is the minority carrier lifetime.

In this case, the minority carrier mobility is given, which is related to the diffusion coefficient D by the equation:

D = μkT/e

Where μ is the mobility, k is Boltzmann's constant (1.38 x 10^-23 J/K), T is the temperature in Kelvin, and e is the elementary charge (1.6 x 10^-19 C).

Substituting the given values into the equation for D, we have:

D = (4000 cm²/V.s)(1.38 x 10^-23 J/K)(300 K)/(1.6 x 10^-19 C)

Calculating D gives the diffusion coefficient in m²/s. Then, we can substitute the calculated D and the given minority carrier lifetime in the equation for L to find the diffusion length.