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q1_review - disclaimer use this sheet at your own risk i.e...

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disclaimer: use this sheet at your own risk; i.e. there may be errors on this, make sure you know when to use the formulas, don’t use this as substitute for studying, blah blah blah…) Semiconductor Physics mass-action law * *under T.E. (or quasi-equilibrium) 2 i o o n p n = where at 300K -3 20 2 cm 10 = i n n-type: & d o N n d i o N n p 2 p-type: & a o N p a i o N n n 2 drift velocity * *for v < v sat only ( v sat = 10 7 cm/s) E v n dn µ = (electron) E v p dp µ = (hole) current density (drift + diffusion) dx dn qD E qn J J J n n diff n dr n n + = + = µ (electron) dx dp qD E qp J J J p p diff p dr p p = + = µ (hole) Einstein Relation q kT D p p = µ and q kT D n n = µ “thermal voltage” : mV q kT V th 26 = = Electrostatics Gauss’ Law / Electrostatic Potential ε ρ = dx dE dx d x E φ = ) ( Poisson Equation : ε ρ φ ) ( ) ( 2 2 x dx x dE dx d = = Permittivity in vacuum: cm F o / 10 85 . 8 14 × = ε in silicon: o s ε ε 7 . 11 = in SiO 2 : o ox ε ε 9 . 3 = Boltzmann relations* (requires J no = J po = 0) kT x q i o o e n x n / ) ( ) ( φ = kT x q i o o e n x p / ) ( ) ( φ =
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