EE 5340 Semiconductor Device Theory Lecture 13  Fall 2009 Professor Ronald L. Carter [email protected] http://www.uta.edu/ronc Reverse bias junction breakdown E crit for reverse breakdown (M&K**) Taken from p. 198, M&K** Casey Model for E crit Reverse bias junction breakdown
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Professor Ronald L. Carter
http://www.uta.edu/ronc
Reverse biasjunction breakdown
Reverse biasjunction breakdown
Note: corners of a jctn of depth xj are like 1/8 spheres of radius ~ xj
Table 4.1 (M&K* p. 186) Nomograph for silicon uniformly doped, onesided, step junctions (300 K).(See Figure 4.15 to correct for junction curvature.) (Courtesy Bell Laboratories).
E doped, onesided, step junctions (300 K).


Ec
Ec
Ef
Efi
gen
rec
Ev
Ev
+
+
k
Direct carriergen/recomb(Excitation can be by light)
n = no + dn and p = po + dp, where nopo=ni2
and for dn and dp > 0, the recombination rates increase to R’n and R’p
ShockleyRead doped, onesided, step junctions (300 K).Hall Recomb
E
Indirect, like Si, so intermediate state
Ec
Ec
ET
Ef
Efi
Ev
Ev
k
Nt (trap conc.),
vth (thermal vel of the carriers),
sn (capture cross sect for electrons),
sp (capture cross sect for holes), with
tno = (Ntvthsn)1, and
tpo = (Ntvthsp)1, where sn,p~p(rBohr,n.p)2
(npni2) = (no+dn)(po+dp)ni2 = nopo  ni2 + nodp + dnpo + dndp ~ nodp (largest term)
U = dp/tp, (prop to exc min carr)
U = dn/tn, (prop to exc min carr)
Mark E. Law, E. Solley, M. Liang, and Dorothea E. Burk, “SelfConsistent Model of MinorityCarrier 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 = 1.8×1031cm6/s.
Mark E. Law, E. Solley, M. Liang, and Dorothea E. Burk, “SelfConsistent Model of MinorityCarrier 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 = 8.3×1032 cm6/s.
A. [40%] Write a review of the model equations for minority carrier (both electrons in ptype and holes in ntype 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 ptype material, and Dp and Lp holes in ntype material.
B. [60%] This part of the assignment will be given by 10/12/09. Currentvoltage data will be given for a diode, and the project will be to determine the material parameters (Nd, Na, chargeneutral region width, etc.) of the diode.
References for Part A Models in Silicon
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, “SelfConsistent Model of MinorityCarrier 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 912 Dec. 1990 Page(s):357 – 360.
David Roulston, Narain D. Arora, and Savvas G. Chamberlain “Modeling and Measurement of MinorityCarrier Lifetime versus Doping in Diffused Layers of n+p Silicon Diodes”, IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED29, NO. 2, FEBRUARY 1982, pages 284291.
M. S. Tyagi and R. Van Overstraeten, “Minority Carrier Recombination in Heavily Doped Silicon”, SolidState Electr. Vol. 26, pp. 577597, 1983. Download a copy at Tyagi.pdf.
U = R  G =  ni/(2t0cosh[(ETEfi)/kT])
The Continuity Models in SiliconEquation (cont.)
The Continuity Models in SiliconEquation (cont.)
The Continuity Models in SiliconEquation (cont.)
The Continuity Models in SiliconEquation (cont.)
The Continuity Models in SiliconEquation (cont.)
[M&K] Device Electronics for Integrated Circuits, 2nd ed., by Muller and Kamins, Wiley, New York, 1986.
[2] Devices for Integrated Circuits: Silicon and IIIV Compound Semiconductors, by H. Craig Casey, Jr., John Wiley & Sons, New York, 1999.
Bipolar Semiconductor Devices, by David J. Roulston, McGrawHill, Inc., New York, 1990.