EE 5340 Semiconductor Device Theory Lecture 14 - Fall 2003 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc L 14 Oct 9

Project Comments- Forward derivative A plot of r  dV/d[ln(C)] vs. V has slope = -1/M, and intercept = VJ/M Forward der. of data gives ri’ = dV/d(ln(C))=[Vi+1-Vi]/[ln(Ci+1)-ln(Ci)], at Vi’ = [Vi+1+Vi]/2 L 14 Oct 9

Project Comments- Central derivative A plot of r  dV/d[ln(C)] vs. V has slope = -1/M, and intercept = VJ/M Central der. of data gives ri’ = dV/d(ln(C))=[Vi+1-Vi-1]/[ln(Ci+1)-ln(Ci-1)], at Vi’ = [Vi+1-Vi-1]/2 (= Vi only if all DV are equal. L 14 Oct 9

Project Comments- Backward derivative A plot of r  dV/d[ln(C)] vs. V has slope = -1/M, and intercept = VJ/M Backward der. of data gives ri’ = dV/d(ln(C))=[Vi-Vi-1]/[ln(Ci)-ln(Ci-1)], at Vi’ = [Vi+Vi-1]/2 L 14 Oct 9

Choosing the data range for r vs. V L 14 Oct 9

Choosing the data range for r vs. V L 14 Oct 9

Minority hole lifetimes, taken from Shur** p. 101. L 14 Oct 9

Minority electron lifetimes, taken from Shur** p. 101. L 14 Oct 9

Lifetimes from data vs. that used in simulators Minority electron lifetimes, taken from Shur** p. 101. L 14 Oct 9

The Continuity Equation (cont.) L 14 Oct 9

Review of depletion approximation pp << ppo, -xp < x < 0 nn << nno, 0 < x < xn 0 > Ex > -2Vbi/W, in DR (-xp < x < xn) pp=ppo=Na & np=npo= ni2/Na, -xpc< x < -xp nn=nno=Nd & pn=pno= ni2/Nd, xn < x < xnc qVbi Ec EFp EFn EFi Ev x -xpc -xp xn xnc L 14 Oct 9

Review of D. A. (cont.) Ex -xpc -xp xn xnc x -Emax L 14 Oct 9

Forward Bias Energy Bands Ev Ec EFi xn xnc -xpc -xp q(Vbi-Va) EFP EFN qVa x Imref, EFn Imref, EFp L 14 Oct 9

Law of the junction: “Remember to follow the minority carriers” L 14 Oct 9

Law of the junction (cont.) L 14 Oct 9

Law of the junction (cont.) L 14 Oct 9

Injection Conditions L 14 Oct 9

Ideal Junction Theory Assumptions Ex = 0 in the chg neutral reg. (CNR) MB statistics are applicable Neglect gen/rec in depl reg (DR) Low level injections apply so that dnp < ppo for -xpc < x < -xp, and dpn < nno for xn < x < xnc Steady State conditions L 14 Oct 9

Apply the Continuity Eqn in CNR Ideal Junction Theory (cont.) Apply the Continuity Eqn in CNR L 14 Oct 9

Ideal Junction Theory (cont.) L 14 Oct 9

Ideal Junction Theory (cont.) L 14 Oct 9

Diffusion length model L = (Dt)1/2 Diffusion Coeff. is Pierret* model L 14 Oct 9

Excess minority carrier distr fctn L 14 Oct 9

Forward Bias Energy Bands Ev Ec EFi xn xnc -xpc -xp q(Vbi-Va) EFP EFN qVa x Imref, EFn Imref, EFp L 14 Oct 9

Carrier Injection ln(carrier conc) ln Na ln Nd ln ni ~Va/Vt ~Va/Vt ln ni2/Nd ln ni2/Na x -xpc -xp xnc xn L 14 Oct 9

References * Semiconductor Device Fundamentals, by Pierret, Addison-Wesley, 1996 ** Physics of Semiconductor Devices, M. Shur, Wiley. L 14 Oct 9