| Contd... |
Using the depletion approximation, we can write depletion width  as a function of  as |
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where  is the substrate acceptor density, is dielectric constant of substrate and is the surface potential at substrate. |
| The depletion region grows with increased voltage across the capacitor until strong inversion is reached. After that, further increase in the voltage results in inversion rather than more depletion. Thus the maximum depletion width is: |
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| Also, | |
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| Therfore at |
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| But by Gauss's law, electrons must compensate for increasing Qs. |
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| So, |
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| where charge Qi is due to electrons in the inversion layer. |
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| Earlier due to low electric field, the electron-hole pairs formed below the oxide interface recombine. However, once the electric field increases, the electron-hole pairs formed are not able to recombine. So the free electron concentration increases. |
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By Kirchoff's law,  is given by:  |
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