ee 5340 semiconductor device theory lecture 13 fall 2009
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EE 5340 Semiconductor Device Theory Lecture 13 - Fall 2009

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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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slide3

Ecrit for reverse breakdown (M&K**)

Taken from p. 198, M&K**

Casey Model for Ecrit

slide4

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
junction curvature effect on breakdown
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

slide6

Table 4.1 (M&K* p. 186) Nomograph for silicon uniformly doped, one-sided, step junctions (300 K).(See Figure 4.15 to correct for junction curvature.) (Courtesy Bell Laboratories).

direct carrier gen recomb

E

-

-

Ec

Ec

Ef

Efi

gen

rec

Ev

Ev

+

+

k

Direct carriergen/recomb

(Excitation can be by light)

direct gen rec of excess carriers
Direct gen/recof excess carriers
  • Generation rates, Gn0 = Gp0
  • Recombination rates, Rn0 = Rp0
  • In equilibrium: Gn0 = Gp0 = Rn0 = Rp0
  • In non-equilibrium condition:

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

direct rec for low level injection
Direct rec forlow-level injection
  • Define low-level injection as dn = dp < no, for n-type, and dn = dp < po, for p-type
  • The recombination rates then are R’n = R’p = dn(t)/tn0, for p-type, and R’n = R’p = dp(t)/tp0, for n-type
  • Where tn0 and tp0 are the minority-carrier lifetimes
slide10

Shockley-Read-Hall Recomb

E

Indirect, like Si, so intermediate state

Ec

Ec

ET

Ef

Efi

Ev

Ev

k

s r h trap characteristics
S-R-H trapcharacteristics*
  • The Shockley-Read-Hall Theory requires an intermediate “trap” site in order to conserve both E and p
  • If trap neutral when orbited (filled) by an excess electron - “donor-like”
  • Gives up electron with energy Ec - ET
  • “Donor-like” trap which has given up the extra electron is +q and “empty”
s r h trap char cont
S-R-H trapchar. (cont.)
  • If trap neutral when orbited (filled) by an excess hole - “acceptor-like”
  • Gives up hole with energy ET - Ev
  • “Acceptor-like” trap which has given up the extra hole is -q and “empty”
  • Balance of 4 processes of electron capture/emission and hole capture/ emission gives the recomb rates
s r h recombination
S-R-H recombination
  • Recombination rate determined by:

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

s r h net recom bination rate u
S-R-H net recom-bination rate, U
  • In the special case where tno = tpo = to = (Ntvthso)-1 the net rec. rate, U is
s r h u function characteristics
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
s r h rec for excess min carr
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)

minority hole lifetimes
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.

minority electron lifetimes
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.

minority carrier lifetime diffusion length and mobility models in silicon
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.

slide20

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.

s r h rec for deficient min carr
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
the continuity equation
The ContinuityEquation
  • The chain rule for the total time derivative dn/dt (the net generation rate of electrons) gives
references
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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