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**Tip 1: Problems based on calculating number of charge carriers:**

Some important points to be kept in mind while solving such problems:

- At thermal equilibrium, $n_{e}×n_{h}=n_{i}_{2}$ in all cases: be it intrinsic or extrinsic. This is law of mass action.
- The material always possesses an overall charge neutrality.

Usually, the density of dopant is given as $xppm$ (parts per million) for given number of intrinsic semiconductor atoms per $m_{3}$, i.e.

$x$ atoms of dopant are there for every one million ($10_{6}$) atoms of intrinsic semiconductor in one $m_{3}$ of volume.

We calculate the number of dopants ($n_{d}$ or $n_{a}$)as

$10_{6}x ×n_{intrinsic}m_{−3}$

When the semiconductor is doped, we assume the thermally generated electrons and holes to be negligibly small as compared to those produced by doping, i.e.,

- $n_{e}≈n_{d}$ if doped with donor atoms (pentavalent impurities)
- $n_{h}≈n_{a}$ if doped with acceptor atoms (trivalent impurities)