Essential Semiconductor Physics by Mark S Lundstrom;

Author:Mark S Lundstrom; [Mark Lundstrom]
Language: eng
Format: epub
Publisher: World Scientific Publishing Company
Published: 2026-06-15T00:00:00+00:00

The final results of solving the quadratic equations are shown above. For an N-type semiconductor, we solve a quadratic equation for nsubscript0 and then use to find psubscript0. For a P-type semiconductor, we solve a quadratic equation for psubscript0 and then use to find nsubscript0. Let’s see how this works by doing some examples.

The first example is silicon doped with moderate concentration of phosphorous or arsenic. We’ll also assume that the temperature is 300 K, so it’s safe to assume that the dopants are fully ionized. What are the electron and hole concentrations?

Remember that at 300 K, nsubscripti ≈ 10superscript10 per centimetercmsuperscript3. We can evaluate the expression, but you can see that for NsubscriptD ≫ nsubscripti and NsubscriptA = 0, the expression reduces to nsubscript0 = NsubscriptD.

Knowing the electron concentration, the hole concentration is readily found from .

Finally, note that this is an extrinsic semiconductor, NsubscriptD ≫ nsubscripti. For problems like this, we really don’t need to take the time to solve the quadratic equation because it is clear the nsubscript0 = NsubscriptD.

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