# From the Shockley Ideal Diode Equation derive...

1. Oct 3, 2016

### whatisreality

1. The problem statement, all variables and given/known data
The Shockley idea diode equation is

$I = I_0( e^{\frac{qV}{kT}}-1)$ (1)

Where $I_0$ is the reverse bias saturation current, $q$ is the charge of an electron, $T$ is temperature in Kelvin and $k$ is Boltzmann's constant. For large reverse voltages, $I$ is equal to $I_0$ and is the result of different contributions. Diffusion current varies as $n_i^2$ and generation current as $n_i$. We assume generation current can be neglected as the temperature is sufficiently high.

Then $I_0$ is solely due to minority carriers accelerated by the depletion zone field plus potential difference, and therefore it can be shown that

$I_0 = AT^{3 + \gamma/2}exp(-E_g(T)/kT)$ (2)

Where A is a constant and $E_g$ is the energy gap. Show how to get from (1) to (2).

2. Relevant equations

3. The attempt at a solution
I can't see at all how you would show that, because I don't see why the assumptions about temperature and where the current comes from affect the form of Equation 1 at all.

I haven't had any lecture series on semiconductor physics, so do I need some understanding of what's physically happening to answer this question?

Last edited by a moderator: Oct 3, 2016
2. Oct 8, 2016