Slide 1S-R-H net recom- bination rate, US-R-H “U” function characteristicsS-R-H rec for excess min carrMinority hole lifetimesMinority electron lifetimesSlide 7Slide 8S-R-H rec for deficient min carrThe Continuity EquationThe Continuity Equation (cont.)Slide 12Slide 13Slide 14Slide 15Slide 16Review of depletion approximationReview of D. A. (cont.)Slide 19Law of the junction: “Remember to follow the minority carriers”Law of the junction (cont.)Slide 22Slide 23Ideal Junction TheorySlide 25Slide 26Slide 27Slide 28Excess minority carrier distr fctnSlide 30Slide 31Minority carrier currentsSlide 33Slide 34Ideal diode equationIdeal diode equation (cont.)Slide 37Diffnt’l, one-sided diode cond. (cont.)Slide 39Slide 40Cap. of a (1-sided) short diode (cont.)ReferencesEE 5340Semiconductor Device TheoryLecture 14 – Spring 2011Professor Ronald L. [email protected]://www.uta.edu/ronc©rlc L14-08Mar20112S-R-H net recom-bination rate, U•In the special case where tno = tpo = to = (Ntvthso)-1 the net rec. rate, U is )pn( ,ppp and ,nnn wherekTEfEcoshn2npnpnUdtpddtndGRUoooTi2i©rlc L14-08Mar20113S-R-H “U” functioncharacteristics•The numerator, (np-ni2) simplifes 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©rlc L14-08Mar20114S-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)Minority hole lifetimesMark 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 1991The parameters used in the ft are τo = 10 μs, Nref = 1×1017/cm2, and CA = 1.8×10-31cm6/s.2DAorefDopNCNN1 τττ©rlc L14-08Mar20115Minority electron lifetimesMark 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 1991The parameters used in the ft are τo = 30 μs, Nref = 1×1017/cm2, and CA = 8.3×10-32 cm6/s.2DAorefDonNCNN1 τττ©rlc L14-08Mar20116Minority Carrier Lifetime, Diffusion Length and Mobility Models in SiliconA. [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.MB. [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.©rlc L14-08Mar20117References for Part ADevice 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.©rlc L14-08Mar20118©rlc L14-08Mar20119S-R-H rec fordefcient 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-Ef)/kT])•And with the substitution that the gen lifetime, tg = 2t0cosh[(ET-Ef)/kT], and net gen rate U = R - G = - ni/tg•The intrinsic concentration drives the return to equilibrium©rlc L14-08Mar201110The ContinuityEquation•The chain rule for the total time derivative dn/dt (the net generation rate of electrons) givesn,kzjyixnis gradient the of defnition The .dtdzzndtdyyndtdxxntndtdn©rlc L14-08Mar201111The ContinuityEquation (cont.)--vntndtdn then ,BABABABA Since .kdtdzjdtdyidtdxvis velocity vector the of defnition Thezzyyxx©rlc L14-08Mar201112The ContinuityEquation (cont.)etc. ,0xxdtddtdxx since ,0dtdzzdtdyydtdxxv RHS, the on term second the gConsiderin .vnvnvn as ddistribute be can operator gradient The----©rlc L14-08Mar201113The ContinuityEquation (cont.).Equations" Continuity" the are Jq1tpdtdp and ,Jq1tndtdnSo .Jq1tnvntndtdnhave we ,vqnJ since ly,Consequentpnnn----©rlc L14-08Mar201114The ContinuityEquation (cont.)z).y,(x,at por n of Change of Rate Local explicit"" theis , RHS, on the first term Thez).y,(x, spacein point particular aat por n of Rate GenerationNet therepresents Eq. Continuity theof -U,or LHS, Thetportndtdpdtdn--©rlc L14-08Mar201115The ContinuityEquation (cont.)q).( holes and (-q) electrons for signsin difference the Note z).y,(x, point the of" out" flowing ionsconcentrat p or n of rate local the is Jq1 orJq1 RHS, the on term second Thepn--©rlc L14-08Mar201116The ContinuityEquation (cont.)inflowof rate rate generation net changeof rate Local :as dinterprete be can Which nUdtdn