In a semiconductor material, the net charge is zero. This requires the density of positive charges to be equal to the density of negative charges. Both charge carriers (free electrons and holes) and ionized dopant atoms have a charge equal to the magnitude of one electronic charge. Therefore the charge neutrality equation (CNE) is:
where
no = equilibrium negative carrier density
po = equilibrium positive carrier density
= ionized acceptor density
= ionized donor density
The carrier product equation (CPE) states that as a semiconductor is doped, the product of the charge carrier densities remains constant:
The semiconductor material is n- or p-type depending on whether donor or acceptor doping is greater. Almost all dopant atoms are ionized at room temperature. If intrinsic silicon is doped:
Determine:
a. If this is an n- or p-type extrinsic semiconductor.
b. Which are the majority and which are the minority charge carriers.
c. The density of majority and minority carriers.
Analysis:
a) Each acceptor dopant atom introduces an additional positive charge carrier and a negative atomic ion. The ion is NOT a charge carrier. The density of positive carriers [holes] increases because of the doping so the material is extrinsic P type Silicon.
b) The majority carriers are the positive carriers or valence band holes; the minority carriers are the negative carriers or conduction band free electrons.
Note that because of the doping, the hole density is now about 100 times the electron density. The thermally produced carriers present in the intrinsic Silicon before doping has a small effect on the carrier densities in the extrinsic Silicon. At higher doping levels, the effect becomes negligible.
As temperature increases, the densities of the thermally produced carriers increase and their effect on the final carrier densities increase. At very high temperatures [about 175 C for Silicon] the thermally produced carriers primarily determine the final carrier densities and the doping has a negligible effect [ie, the semiconductor behaves as an intrinsic material]. This is why semiconductors cannot operate in high temperature environments.
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