Semiconductor Electrical Field?

[Rome_Leader]

Homework Statement

The electron concentration in silicon at T = 300K is: n(x) = 10¹⁶e^(-x/18) cm^-3 where x is measured in μm and is limited to 0 ≤ x ≤ 25. The electron diffusion coefficient, D_n = 25 cm²/s and the electron mobility is μ_n = 960cm²/Vs. The total electron current density is constant and = J_n = -40^A/cm². The electron current has both diffusion and drift current components.

Determine the electric field as a function of x which must exist in the semiconductor.

Homework Equations

ε_x = (-kT/e)* d/dx (ln*Nd(x))

The Attempt at a Solution

Pretty lost here. My first instinct was to attempt a solution with the above equation by taking the derivative of n(x). Firstly, I was thrown off by the given range of x. Should I incorperate it somehow? Secondly, I'm not even sure if Nd(x) is the same quantity as the given n(x). How could I infer this from the question?

If anyone could put me on the right track at least with what equation to use, I would greatly appreciate it!

 

[mark726]

Hi there,

To find the electric field as a function of x, we can use the equation:

E(x) = (1/ε)* dV/dx

where ε is the permittivity of silicon and V is the potential.

To find the potential, we can use the Poisson's equation:

d^2V/dx^2 = -ρ/ε

where ρ is the charge density given by:

ρ = q*n(x)

where q is the charge of an electron and n(x) is the electron concentration given in the problem.

Using the given values for Dn, μn, and Jn, we can find the charge density ρ and then solve for the potential V. Once we have the potential, we can find the electric field using the first equation mentioned.

Hope this helps! Let me know if you have any further questions.