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Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002. Professor Ronald L. Carter [email protected] http://www.uta.edu/ronc/. Ideal Junction Theory. Assumptions E x = 0 in the chg neutral reg. (CNR) MB statistics are applicable Neglect gen/rec in depl reg (DR)

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semiconductor device modeling and characterization ee5342 lecture 7 spring 2002

Semiconductor Device Modeling and CharacterizationEE5342, Lecture 7-Spring 2002

Professor Ronald L. Carter

[email protected]

http://www.uta.edu/ronc/

ideal junction theory
Ideal JunctionTheory

Assumptions

  • Ex = 0 in the chg neutral reg. (CNR)
  • MB statistics are applicable
  • Neglect gen/rec in depl reg (DR)
  • Low level injections apply so that dnp < ppo for -xpc < x < -xp, and dpn < nno for xn < x < xnc
  • Steady State conditions
slide3

Ideal JunctionTheory (cont.)

Apply the Continuity Eqn in CNR

slide7

Forward Bias Energy Bands

q(Vbi-Va)

Imref, EFn

Ec

EF

qVa

EF

EFi

Imref, EFp

Ev

x

-xpc

-xp

xn

xnc

0

slide8

CarrierInjection

ln(carrier conc)

ln Na

ln Nd

ln ni

~Va/Vt

~Va/Vt

ln ni2/Nd

ln ni2/Na

x

xnc

-xpc

-xp

xn

0

ideal diode equation
Ideal diodeequation
  • Assumptions:
    • low-level injection
    • Maxwell Boltzman statistics
    • Depletion approximation
    • Neglect gen/rec effects in DR
    • Steady-state solution only
  • Current dens, Jx = Js expd(Va/Vt)
    • where expd(x) = [exp(x) -1]
ideal diode equation cont
Ideal diodeequation (cont.)
  • Js = Js,p + Js,n = hole curr + ele curr

Js,p = qni2Dp coth(Wn/Lp)/(NdLp) = qni2Dp/(NdWn), Wn << Lp, “short” = qni2Dp/(NdLp), Wn >> Lp, “long”

Js,n = qni2Dn coth(Wp/Ln)/(NaLn) = qni2Dn/(NaWp), Wp << Ln, “short” = qni2Dn/(NaLn), Wp >> Ln, “long”

Js,n << Js,p when Na >> Nd

slide14

Diffnt’l, one-sided diode conductance

ID

Static (steady-state) diode I-V characteristic

IQ

Va

VQ

slide16

Charge distr in a (1-sided) short diode

dpn

  • Assume Nd << Na
  • The sinh (see L12) excess minority carrier distribution becomes linear for Wn << Lp

dpn(xn)=pn0expd(Va/Vt)

  • Total chg = Q’p = Q’p = qdpn(xn)Wn/2

Wn = xnc- xn

dpn(xn)

Q’p

x

xn

xnc

slide17

Charge distr in a 1-sided short diode

dpn

  • Assume Quasi-static charge distributions
  • Q’p = Q’p = qdpn(xn)Wn/2
  • ddpn(xn) = (W/2)* {dpn(xn,Va+dV) - dpn(xn,Va)}

dpn(xn,Va+dV)

dpn(xn,Va)

dQ’p

Q’p

x

xnc

xn

effect of non zero e in the cnr
Effect of non-zero E in the CNR
  • This is usually not a factor in a short diode, but when E is finite -> resistor
  • In a long diode, there is an additional ohmic resistance (usually called the parasitic diode series resistance, Rs)
  • Rs = L/(nqmnA) for a p+n long diode.
  • L=Wn-Lp (so the current is diode-like for Lp and the resistive otherwise).
effect of carrier recombination in dr
Effect of carrierrecombination in DR
  • The S-R-H rate (tno = tpo = to) is
effect of carrier rec in dr cont
Effect of carrierrec. in DR (cont.)
  • For low Va ~ 10 Vt
  • In DR, n and p are still > ni
  • The net recombination rate, U, is still finite so there is net carrier recomb.
    • reduces the carriers available for the ideal diode current
    • adds an additional current component
references
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.

***Physics of Semiconductor Devices, Shur, Prentice-Hall, 1990.

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