# Calculate barrier height

1. Nov 25, 2008

### energymover

Hi,

Is this the correct place to post this? Perhaps it's more of a physics question. I'm trying to write a small program to design basic Schottky diodes. I'm using the following equation to calculate the current produced by a small applied voltage, far below Vt -->

I = A * Aast * T^2 * exp(-barrier/Vt) * exp(V/(n*Vt) - 1)

where barrier is the barrier height, A is the contact area, T is temp in kelvin, Vt is thermal voltage, V is applied voltage, n is ideality constant, and Aast is the Richardson constant -->

A = 4 * PI * q * m * k^2 / h^3

where m is the effective electron mass.

Everything seems fine except for my barrier height function, which is -->

if(ntype) {
barrier = F - Eea;
} else {
barrier = Eg - F + Eea;
}

Obviously something's missing, because there's no dopant density in the equations. An increase in dopant density will increase the current. I'm confident the current (I) equation is correct, so it must be the barrier height equation.

Any help is greatly appreciated,
Paul

2. Dec 17, 2008

### marcusl

I'll do my best to address this question, but take it with a grain of salt since I am not a semiconductor expert. You have a typo in your equation--the last term should read

$$\exp{\frac{V}{nV_t}}-1$$

The barrier height is

$$V_D=\frac{qN_d \lambda_0^2}{2\epsilon}$$

where Nd is the donor density and $$\lambda_0$$ is the barrier width (the point where the field drops to zero in the simple "abrupt junction" model). Henisch's book "Semiconductor Contacts" has a clear discussion of this material in Sections 2.1 to 2.2.4.

The equation you wrote, however, refers to the thermionic emission regime, where electron energy exceeds the junction barrier height. I wonder if this is inappropriate for your case where the forward applied voltage is "far below" the thermal voltage Vt. You probably want the diffusion-drift equation, which looks similar except for different (and temperature-independent) leading constants. See Henisch again, or you can check out this on-line reference