Semiconductor device modeling and characterization ee5342 lecture 7 spring 2002
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Semiconductor Device Modeling and Characterization EE5342, Lecture 7-Spring 2002. Professor Ronald L. Carter ronc@uta.edu 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

ronc@uta.edu

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


Semiconductor device modeling and characterization ee5342 lecture 7 spring 2002

Ideal JunctionTheory (cont.)

Apply the Continuity Eqn in CNR


Semiconductor device modeling and characterization ee5342 lecture 7 spring 2002

Ideal JunctionTheory (cont.)


Semiconductor device modeling and characterization ee5342 lecture 7 spring 2002

Ideal JunctionTheory (cont.)


Excess minority carrier distr fctn
Excess minoritycarrier distr fctn


Semiconductor device modeling and characterization ee5342 lecture 7 spring 2002

Forward Bias Energy Bands

q(Vbi-Va)

Imref, EFn

Ec

EF

qVa

EF

EFi

Imref, EFp

Ev

x

-xpc

-xp

xn

xnc

0


Semiconductor device modeling and characterization ee5342 lecture 7 spring 2002

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



Semiconductor device modeling and characterization ee5342 lecture 7 spring 2002

Evaluating thediode current


Semiconductor device modeling and characterization ee5342 lecture 7 spring 2002

Special cases forthe diode current


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


Semiconductor device modeling and characterization ee5342 lecture 7 spring 2002

Diffnt’l, one-sided diode conductance

ID

Static (steady-state) diode I-V characteristic

IQ

Va

VQ


Diffnt l one sided diode cond cont
Diffnt’l, one-sided diode cond. (cont.)


Semiconductor device modeling and characterization ee5342 lecture 7 spring 2002

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


Semiconductor device modeling and characterization ee5342 lecture 7 spring 2002

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


Cap of a 1 sided short diode cont
Cap. of a (1-sided) short diode (cont.)


General time constant
General time-constant


General time constant cont
General time-constant (cont.)


General time constant cont1
General time-constant (cont.)


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.