Non-Ideal Diode Equation (Saturation Current and Energy Gap)

Preamble

It can be shown that the reverse saturation current in a diode is given by the equation:

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Is= BT^(2/3) exp (-Eg/NkT)

where B is a constant that involves the physical properties, doping and geometry of the junction
T is the absolute temperature
Eg is the energy gap of the semiconductor in joules
k is the Boltzmann constant
N is the so-called ‘ideality factor’.

The ideality factor [or emission coefficient] of a diode is a measure of how closely the diode follows the ideal diode equation. N is a number usually in the range of 1 to 2; 1 representing the ideal diode. The ideality factor allows for certain second order effects not allowed for in the ideal diode equation and is used to modify the
ideal equation thus:

I = Is ( exp(eV/NkT)-1)

Question:

In an experiment to determine the temperature dependence of the reverse saturation current, IS of a selected diode was measured at different temperatures. The results are given in TABLE B. The diode (1N4001) has an ideality factor of N = 1.90.

Temperature degrees C [20 25 30 35 40 45]
Reverse current nA [16 26 33 53 73 106]

Determine the value of the energy gap, Eg, and hence state the likely type of semiconductor used to make the diode.

[Hint: taking natural logs in equation (1) gives:

ln(Is) = ln(BT^2/3) – Eg/NkT

Over the small temperature span of the experiment the term ln(BT^2/3) will not vary significantly and can be regarded as a constant.

Thus equation (2) is of the form y = mx + c. A graph of ln(Is) against (1/T) will give a straight line of gradient m=-Eg/Nk. Solution Preview
Please see attachments. First one with some explanation and solution, …

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