EE 5340 Semiconductor Device Theory Lecture 17 Fall 2003

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EE 5340Semiconductor Device TheoryLecture 17 -
Fall 2003

• Professor Ronald L. Carter
• ronc_at_uta.edu
• http//www.uta.edu/ronc

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Summary of Va gt 0 current density eqns.

• Ideal diode, Jsexpd(Va/(hVt))
• ideality factor, h
• Recombination, Js,recexp(Va/(2hVt))
• appears in parallel with ideal term
• High-level injection, (JsJKF)1/2exp(Va/(2hVt
  ))
• SPICE model by modulating ideal Js term
• Va Vext - JARs Vext - IdiodeRs

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Plot of typical Va gt 0 current density equations
ln(J)
data
Effect of Rs
Vext
VKF
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For Va lt 0 carrierrecombination in DR

• The S-R-H rate (tno tpo to) is

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Reverse bias (Valt0)gt carrier gen in DR

• Consequently U -ni/2t0
• t0 mean min. carr. g/r lifetime

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Reverse bias (Valt 0),carr gen in DR (cont.)
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Ecrit for reverse breakdown (MK)
Taken from p. 198, MK
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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

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Reverse biasjunction breakdown

• Assume -Va VR gtgt Vbi, so Vbi-Va--gtVR
• 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

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Junction curvatureeffect on breakdown

• The field due to a sphere, R, with charge, Q is
  Er Q/(4per2) for (r gt 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

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BV for reverse breakdown (MK)
Taken from Figure 4.13, p. 198, MK Breakdown
voltage of a one-sided, plan, silicon step
junction showing the effect of junction
curvature.4,5
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Diode equivalentcircuit (small sig)
ID
h is the practical ideality factor
IQ
VD
VQ
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Small-signal eqcircuit
Cdiff and Cdepl are both charged by Va VQ
Va
Cdepl
rdiff
Cdiff
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Diode Switching

• Consider the charging and discharging of a Pn
  diode
• (Na gt Nd)
• Wn ltlt Lp
• For t lt 0, apply the Thevenin pair VF and RF, so
  that in steady state
• IF (VF - Va)/RF, VF gtgt Va , so current source
• For t gt 0, apply VR and RR
• IR (VR Va)/RR, VR gtgt Va, so current source

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Diode switching(cont.)
VF,VR gtgt Va
F t lt 0
Sw
RF
R t gt 0
VF

RR
D
VR

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Diode chargefor t lt 0
pn
pno
x
xn
xnc
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Diode charge fort gtgtgt 0 (long times)
pn
pno
x
xn
xnc
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Equationsummary
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Snapshot for tbarely gt 0
pn
Total charge removed, QdisIRt
pno
x
xn
xnc
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I(t) for diodeswitching
ID
IF
ts
tstrr
t
- 0.1 IR
-IR
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Ideal diode equation for EgN EgN

• Js Js,p Js,n hole curr ele curr
• Js,p qni2Dp coth(Wn/Lp)/(NdLp), cath.
  qni2Dp/(NdWn), Wn ltlt Lp, short
  qni2Dp/(NdLp), Wn gtgt Lp, long
• Js,n qni2Dn coth(Wp/Ln)/(NaLn), anode
  qni2Dn/(NaWp), Wp ltlt Ln, short
  qni2Dn/(NaLn), Wp gtgt Ln, long
• Js,nltltJs,p when NagtgtNd , Wn Wp cnr wdth

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Ideal diode equationfor heterojunction

• Js Js,p Js,n hole curr ele curr
• Js,p qniN2Dp/NdLptanh(WN/Lp), cath.
  qniN2Dp/NdWN, WN ltlt Lp, short
  qniN2Dp/(NdLp), WN gtgt Lp, long
• Js,n qniP2Dn/NaLntanh(WP/Ln), anode
  qniP2Dn/(NaWp), Wp ltlt Ln, short
  qniP2Dn/(NaLn), Wp gtgt Ln, long
• Js,p/Js,n niN2/niP2 expEgP-EgN/kT

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Bipolar junctiontransistor (BJT)

• The BJT is a Si sandwich Pnp (Pp,pp-)
  or Npn (Nn, nn-)
• BJT action npn Forward Active when VBE gt 0 and
  VBC lt 0

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npn BJT topology
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BJT boundary andinjection cond (npn)
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BJT boundary andinjection cond (npn)
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IC npn BJT(Fig 9.2a)
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References

• Semiconductor Physics and Devices, 2nd ed., by
  Neamen, Irwin, Boston, 1997.
• Device Electronics for Integrated Circuits, 2nd
  ed., by Muller and Kamins, John Wiley, New York,
  1986.