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EE 5340 Semiconductor Device Theory Lecture 12 - Fall 2009

EE 5340 Semiconductor Device Theory Lecture 12 - Fall 2009. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc. Soln to Poisson’s Eq in the D.R. E x. W(V a - d V). W(V a ). x n. -x p. x. -x pc. x nc. -E max (V). -E max (V- d V). Effect of V  0. Junction C (cont.).

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EE 5340 Semiconductor Device Theory Lecture 12 - Fall 2009

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  1. EE 5340Semiconductor Device TheoryLecture 12 - Fall 2009 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

  2. Soln to Poisson’sEq in the D.R. Ex W(Va-dV) W(Va) xn -xp x -xpc xnc -Emax(V) -Emax(V-dV)

  3. Effect of V  0

  4. JunctionC (cont.) r +Qn’=qNdxn +qNd dQn’=qNddxn -xp x -xpc xn xnc Charge neutrality => Qp’ + Qn’ = 0, => Naxp = Ndxn -qNa dQp’=-qNadxp Qp’=-qNaxp

  5. JunctionCapacitance • The junction has +Q’n=qNdxn (exposed donors), and (exposed acceptors) Q’p=-qNaxp = -Q’n, forming a parallel sheet charge capacitor.

  6. JunctionC (cont.) • So this definition of the capacitance gives a parallel plate capacitor with charges dQ’n and dQ’p(=-dQ’n), separated by, L (=W), with an area A and the capacitance is then the ideal parallel plate capacitance. • Still non-linear and Q is not zero at Va=0.

  7. JunctionC (cont.) • The C-V relationship simplifies to

  8. Cj-2 Cj0-2 Va Vbi JunctionC (cont.) • If one plots [Cj]-2vs. Va Slope = -[(Cj0)2Vbi]-1 vertical axis intercept = [Cj0]-2 horizontal axis intercept = Vbi

  9. Junction Capacitance • Estimate CJO • Define y  Cj/CJO • Calculate y/(dy/dV) = {d[ln(y)]/dV}-1 • A plot of r  y/(dy/dV) vs. V has slope = -1/M, and intercept = VJ/M

  10. dy/dx - Numerical Differentiation

  11. Practical Junctions • Junctions are formed by diffusion or implantation into a uniform concentration wafer. The profile can be approximated by a step or linear function in the region of the junction. • If a step, then previous models OK. • If linear, let the local charge density r=qax in the region of the junction.

  12. Practical Jctns (cont.) Na(x) Shallow (steep) implant N N Na(x) Linear approx. Box or step junction approx. Nd Nd Uniform wafer con x (depth) x (depth) xj

  13. Linear gradedjunction • Let the net donor concentration, N(x) = Nd(x) - Na(x) = ax, so r =qax, -xp < x < xn = xp= xo, (chg neu) r = qa x r Q’n=qaxo2/2 -xo x xo Q’p=-qaxo2/2

  14. Linear gradedjunction (cont.) • Let Ex(-xo) = 0, since this is the edge of the DR (also true at +xo)

  15. Linear gradedjunction (cont.) Ex -xo xo x -Emax |area| = Vbi-Va

  16. Linear gradedjunction (cont.)

  17. Linear gradedjunction, etc.

  18. Doping Profile • If the net donor conc, N = N(x), then at x, the extra charge put into the DR when Va->Va+dVa is dQ’=-qN(x)dx • The increase in field, dEx =-(qN/e)dx, by Gauss’ Law (at x, but also all DR). • So dVa=-xddEx= (W/e) dQ’ • Further, since qN(x)dx, for both xn and xn, we have the dC/dx as ...

  19. Arbitrary dopingprofile (cont.)

  20. Arbitrary dopingprofile (cont.)

  21. Arbitrary dopingprofile (cont.)

  22. Arbitrary dopingprofile (cont.)

  23. Example • An assymetrical p+ n junction has a lightly doped concentration of 1E16 and with p+ = 1E18. What is W(V=0)? Vbi=0.816 V, Neff=9.9E15, W=0.33mm • What is C’j0? = 31.9 nFd/cm2 • What is LD? = 0.04 mm

  24. Reverse biasjunction breakdown • Avalanche breakdown • Electric field accelerates electrons to sufficient energy to initiate multiplication of impact ionization of valence bonding electrons • field dependence shown on next slide • Heavily doped narrow junction will allow tunneling - see Neamen*, p. 274 • Zener breakdown

  25. Effect of V  0

  26. Ecrit for reverse breakdown [M&K] Taken from p. 198, M&K**

  27. Reverse biasjunction breakdown

  28. Ecrit for reverse breakdown [M&K] Taken from p. 198, M&K** Casey Model for Ecrit

  29. Reverse biasjunction breakdown • Assume-Va = VR >> Vbi, so Vbi-Va-->VR • Since Emax~ 2VR/W = (2qN-VR/(e))1/2, and VR = BV when Emax = Ecrit (N- is doping of lightly doped side ~ Neff) • BV = e (Ecrit )2/(2qN-) • Remember, this is a 1-dim calculation

  30. Junction curvatureeffect on breakdown • The field due to a sphere, R, with charge, Q is Er = Q/(4per2) for (r > R) • V(R) = Q/(4peR), (V at the surface) • So, for constant potential, V, the field, Er(R) = V/R (E field at surface increases for smaller spheres) Note: corners of a jctn of depth xj are like 1/8 spheres of radius ~ xj

  31. BV for reverse breakdown (M&K**) Taken from Figure 4.13, p. 198, M&K** Breakdown voltage of a one-sided, plan, silicon step junction showing the effect of junction curvature.4,5

  32. References [M&K] Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, Wiley, New York, 1986. [2] Devices for Integrated Circuits: Silicon and III-V Compound Semiconductors, by H. Craig Casey, Jr., John Wiley & Sons, New York, 1999. Bipolar Semiconductor Devices, by David J. Roulston, McGraw-Hill, Inc., New York, 1990.

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