# A pure Si material doped with donor atoms

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#### john andre

##### New Member
A pure Si material doped with donor atoms where ND = 9 ∙ 1014 cm-3 .
Compute the concentration of free electrons and holes in the material after doping.

How can I do this only knowing Nd?

#### Ratchit

##### Well-Known Member
A pure Si material doped with donor atoms where ND = 9 ∙ 1014 cm-3 .
Compute the concentration of free electrons and holes in the material after doping.

How can I do this only knowing Nd?
I think it is OK to give you the answer now because your homework is long past due. You need to know the intrinsic concentration (IC) of of holes and electrons of silicon at room temperature. Intrinsic means pure, with no dopants or contaminates. The ambient temperature causes a small fraction of silicon atoms to ionize, thereby losing an electron and gaining a hole. Ionization causes holes and free electrons to occur equally in pairs. At room temperature, the IC is 1E10 electrons or holes per cubic centimeter. At 540 K, the IC of silicon is 1E15. The IC for silicon at room temperatue can be found in any good text on semiconductors. You specified Nd in a confusing form, which I believe you meant 9E14. All dopant atoms are completely ionized at room temperature. A text on semiconductors will aver that if the dopant concentration is much greater than the IC, which it is in this case, and much greater than the acceptor dopant concentration, which is zero, then the concentration of electrons will be Nd = 9E14 and the hole concentration will be (IC^2)/Nd = 1E20/9E14 = 1.11E5 .

Ratch

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