1 / 20

EE 5340 Semiconductor Device Theory Lecture 14 – Spring 2011

EE 5340 Semiconductor Device Theory Lecture 14 – Spring 2011. Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc. S-R-H net recom- bination rate, U. In the special case where t no = t po = t o = (N t v th s o ) -1 the net rec. rate, U is.

karl
Download Presentation

EE 5340 Semiconductor Device Theory Lecture 14 – Spring 2011

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. EE 5340Semiconductor Device TheoryLecture 14 – Spring 2011 Professor Ronald L. Carter ronc@uta.edu http://www.uta.edu/ronc

  2. S-R-H net recom-bination rate, U • In the special case where tno = tpo = to = (Ntvthso)-1 the net rec. rate, U is

  3. S-R-H “U” functioncharacteristics • The numerator, (np-ni2) simplifies in the case of extrinsic material at low level injection (for equil., nopo = ni2) • For n-type (no > dn = dp > po = ni2/no): (np-ni2) = (no+dn)(po+dp)-ni2 = nopo - ni2 + nodp + dnpo + dndp ~ nodp (largest term) • Similarly, for p-type, (np-ni2) ~ podn

  4. S-R-H rec forexcess min carr • For n-type low-level injection and net excess minority carriers, (i.e., no > dn = dp > po = ni2/no), U = dp/tp, (prop to exc min carr) • For p-type low-level injection and net excess minority carriers, (i.e., po > dn = dp > no = ni2/po), U = dn/tn, (prop to exc min carr)

  5. Minority hole lifetimes Mark E. Law, E. Solley, M. Liang, and Dorothea E. Burk, “Self-Consistent Model of Minority-Carrier Lifetime, Diffusion Length, and Mobility, IEEE ELECTRON DEVICE LETTERS, VOL. 12, NO. 8, AUGUST 1991 The parameters used in the fit are τo = 10 μs, Nref= 1×1017/cm2, and CA = 1.8×10-31cm6/s.

  6. Minority electron lifetimes Mark E. Law, E. Solley, M. Liang, and Dorothea E. Burk, “Self-Consistent Model of Minority-Carrier Lifetime, Diffusion Length, and Mobility, IEEE ELECTRON DEVICE LETTERS, VOL. 12, NO. 8, AUGUST 1991 The parameters used in the fit are τo = 30 μs, Nref= 1×1017/cm2, and CA = 8.3×10-32 cm6/s.

  7. Minority Carrier Lifetime, Diffusion Length and Mobility Models in Silicon A. [40%] Write a review of the model equations for minority carrier (both electrons in p-type and holes in n-type material) lifetime, mobility and diffusion length in silicon. Any references may be used. At a minimum the material given in the following references should be used. Based on the information in these resources, decide which model formulae and parameters are the most accurate for Dn and Ln for electrons in p-type material, and Dp and Lp holes in n-type material. B. [60%] This part of the assignment will be given by 10/12/09. Current-voltage data will be given for a diode, and the project will be to determine the material parameters (Nd, Na, charge-neutral region width, etc.) of the diode.

  8. References for Part A Device Electronics for Integrated Circuits, 3rd ed., by Richard S. Muller, Theodore I. Kamins, and Mansun Chan, John Wiley and Sons, New York, 2003. Mark E. Law, E. Solley, M. Liang, and Dorothea E. Burk, “Self-Consistent Model of Minority-Carrier Lifetime, Diffusion Length, and Mobility, IEEE ELECTRON DEVICE LETTERS, VOL. 12, NO. 8, AUGUST 1991. D.B.M. Klaassen; “A UNIFIED MOBILITY MODEL FOR DEVICE SIMULATION”, Electron Devices Meeting, 1990. Technical Digest., International 9-12 Dec. 1990 Page(s):357 – 360. David Roulston, Narain D. Arora, and Savvas G. Chamberlain “Modeling and Measurement of Minority-Carrier Lifetime versus Doping in Diffused Layers of n+-p Silicon Diodes”, IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-29, NO. 2, FEBRUARY 1982, pages 284-291. M. S. Tyagi and R. Van Overstraeten, “Minority Carrier Recombination in Heavily Doped Silicon”, Solid-State Electr. Vol. 26, pp. 577-597, 1983. Download a copy at Tyagi.pdf.

  9. S-R-H rec fordeficient min carr • If n < ni and p< pi, then the S-R-H net recomb rate becomes (p < po, n < no): U = R - G = - ni/(2t0cosh[(ET-Efi)/kT]) • And with the substitution that the gen lifetime, tg = 2t0cosh[(ET-Efi)/kT], and net gen rate U = R - G = - ni/tg • The intrinsic concentration drives the return to equilibrium

  10. The ContinuityEquation • The chain rule for the total time derivative dn/dt (the net generation rate of electrons) gives

  11. The ContinuityEquation (cont.)

  12. The ContinuityEquation (cont.)

  13. The ContinuityEquation (cont.)

  14. The ContinuityEquation (cont.)

  15. The ContinuityEquation (cont.)

  16. The ContinuityEquation (cont.)

  17. Review of depletion approximation Depletion Approx. • 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 0

  18. Review of D. A. (cont.) Ex -xp xn xnc -xpc x -Emax

  19. q(Vbi-Va) Imref, EFn Ec EFN qVa EFP EFi Imref, EFp Ev x -xpc -xp xn xnc 0 Forward Bias Energy Bands

  20. References 1 and M&KDevice Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 1986. See Semiconductor Device Fundamentals, by Pierret, Addison-Wesley, 1996, for another treatment of the m model. 2Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981. 3 and **Semiconductor Physics & Devices, 2nd ed., by Neamen, Irwin, Chicago, 1997. Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, 1989.

More Related