J>-u JL'\CTI().\S l.\ SKMICOXDICroKS 4SI 



where the eigenvalues jJ^ are determined by the boundary condition 



l3iu' tan iSrcH' = sb/D = x- 



We use dt = iSrw for brevity later, liecause of the symmetry of the boundary 

 conditions it is not necessary to include sine functions in the sum. The value 

 of a,j is given by 



a.j = (1 + iu>T,j)'/iDT,if 



where r,/ is the lifetime of a hole in the eigenfunction cos jSyy cos /3;S; i.e. 

 Tij is the lifetime which makes 



p = exp {-I /Tij) cos (3iy cos jSys, 



a function which satishes the surface boundary conditions, a solution of the 

 equation 



dp/dl = DV-p - p/t = -Difi + l^'j)p - p/t 



where to simplify the subsequent expressions we have omitted the subscript 

 p from r. This equation leads to 



Tij T 



The coefficients an are readily found since the cos ji,y functions form an 

 orthogonal set (as may be veritied by integrating by parts and using the 

 boundary conditions). The values are 



an/pK = 4[sin 0, sin dA'9>ej[l + (1/26,) sin 2d,\-[l + {l/2dj) sin 26,] 



The current corresponding to this solution is 



/i = -qD j I (dp'dx) dydz 



integrated over the cross section at .v = 0. This gives 



/i = qDpice"^ Z aij{a,j/pioj{-i-d\ '6fij) sin 6i sin 6; 



Substituting for a,; and inserting pu) = p,^qv\ kT, we obtain an exjiression 

 for the admittance -1^ = /i/l'i exp(/a)/): 



o 4 sin- 6i sin- dj 



where the sum plays the role formerly taken by (I + iuil)^''/y/DT in equation 

 (4.12); the factor Aiv is the area of the junction. 



We shall analyze the formula for the case in which recombination on the 



