Intrinsic Carrier Concentration

1 Zulfiqar Ali EEE1321 Intrinsic Carrier Intrinsic semiconductor: A semiconductor material with no dopants. It electrical characteristics such as Concentration of charge carriers, depend only on pure crystal. derive Carrier Concentration in thermal equilibrium condition that is in a steady state condition at a given temperature without any external an Intrinsic semiconductor is one that contains relatively small amount of Ali EEE1322 Intrinsic Carrier obtain the electron density (number of electron per unit volume) in Intrinsic semiconductor , we must evaluate the electron density in an incremental energy range n(E) is given by product of density states N(E) and a probability of occupying energy range F(E). the electron density is given by: ==ETOPETOPdEEFENdEEnn00)()()(Zulfiqar Ali EEE1323 Intrinsic Carrier ConcentrationWhere n is in cm-3and N(E) is in (cm3-eV) probability that an electron occupies and electronic state with energy E is given by Fermi-Dirac is Boltzman constant, t is temperature( K), EFis Fermi )(11)( +=Zulfiqar Ali EEE1324 Intrinsic SemiconductorzThe Fermi energy is the energy at which the probability of occupation by an electron is exactly on Ali EEE1325 Figure distribution function F(E) versus (E EF) for various Ali EEE1326 Figure semiconductor.

2 (a) Schematic band diagram. (b) density of states . (c) Fermi distribution function. (d) Carrier Ali EEE1327 Intrinsic Carrier ConcentrationzThere are large number of allowed states in the conduction there will not be many electrons in the conduction the possibility for the electron to be in region is very we refer to the bottom of the conduction band the electron density is equivalent to Zulfiqar Ali EEE1328 Intrinsic semiconductorzElectron density in the conduction X 1019cm-3for silicon and X 1017cm-3for gallium X 1019cm-3for silicon and 7 X 1018cm-3for gallium arsenide])(exp[kTEENnFCC =])(exp[kTEENpVFV =Zulfiqar Ali EEE1329 Intrinsic SemiconductorzIn Intrinsic semiconductor the number of electron per unit volume is equal to number of hole per unit volume in the valence band. zThe larger the band gap the smaller Intrinsic Carrier Ali EEE13210 Nondegenerated Semiconductor zFor shallow donors in silicon there usually enough energy to ionize all donor impurities at room condition is called complete n = NDzEC-EF= kT ln (NC/ND)zSame case applies to Ali EEE13211 Figure n-Type semiconductor.

3 (a) Schematic band diagram. (b) density of states . (c) Fermi distribution function (d) Carrier Concentration . Note that np= Ali EEE13212zReading assignment read on the Degenerated SemiconductorZulfiqar Ali EEE13213 Carrier Transport Phenomena ( Carrier Drift)MobilityzElectrons move in all different small electric field E is applied to the semiconductor electron will experience force. electron will accelerated along the field. In opposite component is called a drift velocity. Zulfiqar Ali EEE13214 MobilityzThe momentum applied to an electron is momentum drift velocity depend on the applied electric field. == nCnnncmqvvmqZulfiqar Ali EEE13215 MobilityzThe proportionality factor is called electron mobilityzIs important parameter in Carrier transport because it describes how strongly the motion of electron in influenced by applied electric Zulfiqar Ali EEE13216 MobilityzDrift velocityzHole flows in the same direction as electric mobility is influenced by impurity scattering and lattice scattering.

4 Ppnnvv= =Zulfiqar Ali EEE13217 CurrentzThe transport carriers under the influence of an electric field produce drift Ali EEE13218 Figure conduction in a uniformly doped semiconductor bar with length Land cross-sectional Ali EEE13219 ResistivityzSample semiconductor of length L and cross section of A and an electron Concentration of n we apply an electric field to the sample the electron current density Jnflowing in the sample should be product of charge (-q) on electron time the electron =Zulfiqar Ali EEE13220 ResistivityzCurrent densityzConductivityzResistivity )(pqpnqnJJJpn+=+=)(pnpnq += 1=