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A battery of emf 2 V is applied across the block of a semiconductor of length 0.1 m and the area of cross-section 1xx10^(-4)m^(2). If the block is of intrinsic silicon at 300K, find the magnitude of tatal current. What will be the order of magnitude of total current if germanium is used instead of silicon? Given that for silicon ay 300K, electron mobility, mu_(e)=0.135m^(2) V^(-1)s^(-1), hole mobility mu_(h)=0.048m^(2)V^(-1)s_(-1), instrisic carrier concentration, n_(i)=1.5xx10^(16)m^(-3). For germanium at 300K, electron mibility mu_(e_(2))=0.39m^(2)V^(-1)s^(-1), hole mobility, mu_(h)=0.19m^(2)V^(-1)s_(-1), instric carrier concentration is 2.4xx10^(19)m^(-3). |
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Answer» Solution :For silicon Total current, `I=EA(n_(e)v_(e)+n_(h)v_(h))` or `I_(s)=eA(n_(e)E mu_(e)+n_(h)Emu_(h))` `=eA(n_(e)mu_(e)+n_(h)mu_(h))E` `=eA (e_(e)mu_(e)+n_(h)mu_(h))V/I` `=(1.6xx10^(19))xx(1xx10^(4))[(1.5xx10^(16))xx(0.135)+(1.5xx10^(16))xx0.048]xx2/0.1` `=8.7xx10^(-7)A` For Germanium `I_(G)=(1.6xx10^(-19))xx(1xx10^(-4))[(2.4xx10^(19))xx0.39+(2.4xx10^(19))xx0.19]xx2/0.1` `=4.46xx10^(-3)A` `I_(G)/I_(s)=(4.46xx10^(-3))/(8.7xx10^(-7))~~0.512xx10^(4)~~10^(4)` THEREFORE, the total current in germanium is about four orders of the total current in silicon. |
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