Determining energy gap of silicon and germanium semiconductors

Question

I need to determine the energy gaps of silicon and germanium transistors using a recorded temperature value range and changes in the reverse saturated current for this range.

The equation given is of the form:

Is = A exp (-Eg/kT)

Where:

• Is = reverse saturated current

• A = a constant

• Eg = energy gap of the semiconductor

• k - Boltzmann constant

• T = absolute temperature

I know I need to construct a graph using the Is and T values gathered, and then use the gradient of this graph, but I can't seem the rearrange the equation for Eg where this is possible. The constant 'A' seems to be causing the trouble.

For each transistor the reverse bias volatage was also noted.

Answer 1

If you take the logarithm of your equation, you get:

$$\log{I_s} = \log{A} - \frac{E_g}{kT}$$

So if you plot the logarithm of the current against $\frac{1}{kT}$, the slope of that function will give you the band gap energy. You need at least two points at different temperatures to do this - the more measurements you have, the better you will be able to determine that the relationship holds (and the more precise your estimation of $E_g$ will be).