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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.

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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).

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