Barrier Potential: Explaining the Contradiction

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    Barrier Potential
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The barrier potential equation indicates that it is directly proportional to temperature, suggesting an increase in barrier potential with rising temperatures. However, it contradicts the observation that increased temperature generates more minority charge carriers, which leads to a decrease in barrier potential. This results in equilibrium being achieved at a lower barrier potential, approximately decreasing by 2 mV per degree Celsius. The discussion highlights that multiple factors are influencing the barrier potential, particularly the role of minority carrier concentrations. Understanding this contradiction requires a comprehensive analysis of both the barrier potential equation and the effects of temperature on carrier dynamics.
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The equation for the barrier potential is as follows:

Vb = Vt loge(Na*Nd/square(n)) mV
where Vt=KT/e

This equation shows that the barrier potential is directly proportional to the temperature. So as temperature increases the barrier potential should increase.

But in contradiction to this, I have found the following statement:

" With increase in temperature, more minority charge carriers are produced, leading to their increased drift across the junction. As a result, equilibrium occurs at a lower barrier potential. It is found that the Vb decreases by about 2 mV/0C

Please explain...
 
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There is more than one effect happening here.
Presumably the equation for the barrier potential did not take into account the minority carrier concentrations.
Where are you reading this?
 
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