ECE340_L16_S14_Distribution

# 2 evaluate nx at the center of each segment consider

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Unformatted text preview: ative Slope: Net particle motion in positive direction ༉ - Negative charge, negative current Diﬀusion: Net Mo\on &amp; Slope Positive Slope: Net particle motion in negative direction ༉ Diﬀusion: Net Current Positive Slope: Net particle motion in negative direction ༉ Positive charge, negative current + Diﬀusion: Net Current Positive Slope: Net particle motion in negative direction ༉ Negative charge, positive current - Diﬀusion Current 1) Divide distribution in segments l wide. 2 ) Evaluate n(x) at the center of each segment. Consider the motion in a mean free time t where half move into each adjacent section. The net number of electrons passing from left to right ( → ) in time t is: 1 1 Net particle (electron) flow = n1 l A − n2 l A 2 2 l A rate of electron flow can be defined: φn ( xo ) = ( n1 − n2 ) 2t ( )( ) Note: 1) l is the mean free path between collisions 2) t is the mean free time for half the population to move one mean free path away 13 Diﬀusion Current Since l is small: ( n1 − n2 ) = n( x ) − n( x + Δx ) l Δx 2 l ⎛ n( x ) − n( x + Δx ) ⎞ −l dn( x ) In the limit of small Δx: φn ( x ) = lim ⎜ ⎟= ⎠ 2t dx Δx 2t Δx→0 ⎝ l2 The term is the electron diffusion coefficient Dn with units cm 2 / s 2t l2 2t A similar relation can be derived for hole motion. So: dn( x ) φn ( x ) = − Dn dx dp( x ) φ p ( x ) = − Dp dx Electron and hole flux can be expressed as current: dn( x ) dn( x ) J n (diff .) = − Dn × (− q ) = qDn dx dx dp( x ) dp( x ) J p (diff .) = − D p × (+ q ) = − qD p dx dx Dn = dn( x ) dp( x ) J n ( x ) = qDn and J p ( x ) = − qD p dx dx 14 Dris in a Semiconductor Combined Current J x,total = q(nµn + pµ p )Ex = σ Ex σ = q(nµn + pµ p ) + - R= ρL ρL 1 L 1 L = = = A wt σ wt nµn + pµ p wt ( ) Recall: ve = − µn Ex ; v p = µ p Ex J n (drift ) = (− q )n ve = qnµn Ex J p (drift ) = (q ) p v p = qpµ p Ex Assume uniform distribution of carriers: no diffusion 16 Par\cle Flux and Current Density Derivative is negative 17 Total Current: Dris and Diﬀusion J n ( x ) = J n (drift ) + J n (diff ) dn( x ) J n ( x ) = qn( x )µnE ( x ) + qDn dx J p ( x ) = J p (drift ) + J p (diff ) dp( x ) J p ( x ) = qp( x )µ pE ( x ) − qD p dx J (x) = Jn (x) + J p (x) dn( x ) dp( x ) J ( x ) = qn( x )µnE ( x ) + qDn + qp( x )µ pE ( x ) − qD p dx dx...
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