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I am studying semiconductors and I have a very basic question on the definition of a hole. Why do we add up the contributions of holes and electrons when calculating the current density ( J = (n.q.un + p.q.up).E )? Aren't they equivalent? I mean, if the hole is the absence of an electron, what is the reason this equation holds? Wouldn't we be calculating a value of J that is above its real value?

Thank you

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  • \$\begingroup\$ because that's the amount the charges we can move? I don't see how the equation would add up if we didn't count the holes? \$\endgroup\$ – Marcus Müller May 16 '18 at 18:51
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The electron current is due to movement of free electrons in the conduction band (CB) and the hole current is due to the movement of holes/electrons in the valence band (VB). Hence the mobility of holes in VB and electrons in CB are different as well. Hence the respective current densities are different too. Since both contribute to the net current flow in a semiconductor, we add them up.

$$J = J_p + J_n = e(nu_n + pu_p) $$

Where n, p are electron and hole concentrations.

\$u_p\$ and \$u_n\$ are respective mobilities.

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