2_1_p-n junction fbcurrent Lecture 16

2_1_p-n junction fbcurrent Lecture 16 - p n junction under...

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1 p n junction under forward bias : ii) Minority Carrier Diffusion and Current -
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2 We saw that under forward bias excess minority carriers are injected in the two neutral regions of the p n junction. The excess minority carriers will diffuse away from the junction. The behavior of the forward biased p n junction is gove - - - rned by the diffusion of minority carriers. p n junction under forward bias : minority carrier diffusion -
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3 ( 29 p p n0 p p The Continuity equation in the neutral n region is p p 1 d J t q dx Where p p p excess carrier lifetime. J hole current density. Assume no electric field is present. τ - ∂∆ = - - ∆ = - = =
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4 ( 29 ( 29 ( 29 p p p 2 p 2 p 2 2 2 2 2 2 p p p d p J qD qD x dx Substituting this in the continuity equation p p p D t x Under D.C. conditions, p is a function of d p p x only and hence x dx p and 0 t d p p Hence, dx D τ = - = - ∂∆ = - + ∂ ∆ = ∂∆ = =
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5 ( 29 ( 29 p p p 2 2 2 p n 2 2 2 p Define a parameter L D . We will give the physical interpretation later on. d p p dx L Let us now define a new variable x ' where x ' x x . The continuity equation written in terms of x ' , is d p p dx ' L τ = = = - =
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6 ( 29 ( 29 ( 29 ( 29 p p F x' x' L L qV kT 0 n0 n n n p 0 n p The solution is p Ae Be The Boundary conditions are a p x ' 0 p p e 1 b The second boundary condition at x ' W , is p x ' W 0 W x ' sinh L Applying these B.C.'s p p W sinh L - - ∆ = + = = ∆ = - ÷ = = = - ÷ ÷ ∆ = ∆ ÷ ÷
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7 ( 29 n p 0 n p 0 n p n p n p W x ' sinh L p p W sinh L Where p p x ' 0 The above is a general case solution without any W consideration to the ratio of L Let us distinguish two cases : Wide base: W L Narrow base : W L - ÷ ÷ ∆ = ∆ ÷ ÷ = ∆ = <<
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8 ( 29 ( 29 n n p p n p p n p n W W L L n W L n p x' L Wide Base Case W L If we evaluate p at x ' W , we get p x ' W Ae Be B e will be very large since W L Hence to satisfy the Boundary Condition, B has to be zero. p x ' Ae - - = = = + =
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9 ( 29 ( 29 p 0 0 x' L 0 By applying the boundary condition that p p at x ' 0, we get p p 0 A p x ' p e p decays exponentially with distance. What is the physical interpretation? A hole that is injected at x ' 0, diffuses to the right. As it travels in t - ∆ = ∆ = = ∆ = = ∆ = he n region, it recombines with an electron and is lost. -
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10 ( 29 Hence excess minority carrier density decreases with x '. We can now explain why it decreases exponentially. Let P x ' dx '
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2_1_p-n junction fbcurrent Lecture 16 - p n junction under...

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