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sol3 - HOMEWORK No 3 SOLUTIONS ECE3040 Problem 4 JP = qp pE...

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HOMEWORK No. 3 SOLUTIONS ECE3040
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Problem 4. J P = p pE qD P dp dx =0 E = D P μ p 1 p dp dx = V T d ln p ( x ) dx V T = kT q V bi = Z x n - x p Edx = V T Z x n - x p d ln p ( x ) dx dx = V T ln " p ( x n ) p ( x p ) # p ( x n )= n 2 i N D p ( x p N A V bi = V T ln " n 2 i N A N D # = V T ln " N A N D n 2 i # Problem 5. Compute p ( x ) from the equation for the hole current density: J P = p pE P dp dx E = V T d ln p ( x ) dx dV dx = V T d ln p ( x ) dx Integrate: V ( x V T ln p ( x )+ c (1) Use boundary condition V ( x p ) = 0 to compute c : 0= V T ln p ( x p c c = V T ln p ( x p V T ln p p 0 Substitute into (1) and solve for p ( x ): V ( x V T ln p ( x ) V T ln p p 0 = V T ln " p ( x ) p p 0 # p ( x p p 0 e - V ( x ) /V T Compute n ( x ) from the equation for the electron current density: J N = n nE + N dn dx E = V T d ln n ( x ) dx dV dx = V T d ln n ( x ) dx
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Integrate: V ( x )= V T ln n ( x )+ c (2) Use boundary condition V ( x p ) = 0 to compute c : 0= V T ln n ( x p c c = V T ln n ( x p V T ln n p 0 Substitute into (2) and solve for
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sol3 - HOMEWORK No 3 SOLUTIONS ECE3040 Problem 4 JP = qp pE...

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