# Ideal Junction Theory Assumptions Ex = 0 in the chg neutral reg. (CNR)

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Ideal Junction Theory 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 ©rlc L10-16Feb2011

Forward Bias Energy Bands
Ev Ec EFi xn xnc -xpc -xp q(Vbi-Va) EFP EFN qVa x Imref, EFn Imref, EFp ©rlc L10-16Feb2011

Law of the junction (follow the min. carr.)

Law of the junction (cont.)

Law of the junction (cont.)

Apply the Continuity Eqn in CNR
Ideal Junction Theory (cont.) Apply the Continuity Eqn in CNR ©rlc L10-16Feb2011

Ideal Junction Theory (cont.)

Ideal Junction Theory (cont.)

Excess minority carrier distr fctn

Carrier Injection ln(carrier conc) ln Na ln Nd ln ni ~Va/Vt ln ni2/Na
xn -xpc ln(carrier conc) ln Na ln Nd ln ni ln ni2/Nd ln ni2/Na xnc x ~Va/Vt -xp ©rlc L10-16Feb2011

Minority carrier currents

Evaluating the diode current

Special cases for the diode current

Ideal diode equation Assumptions: Current dens, Jx = Js expd(Va/Vt)
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] ©rlc L10-16Feb2011

Ideal diode equation (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 ©rlc L10-16Feb2011

Diffnt’l, one-sided diode conductance

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

Charge distr in a (1- sided) short diode
dpn Assume Nd << Na The sinh 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 ©rlc L10-16Feb2011

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 xn xnc

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

General time- constant

General time- constant (cont.)

General time- constant (cont.)

References *Fundamentals of Semiconductor Theory and Device Physics, by Shyh Wang, Prentice Hall, 1989. **Semiconductor Physics & Devices, by Donald A. Neamen, 2nd ed., Irwin, Chicago. M&K = Device Electronics for Integrated Circuits, 3rd ed., by Richard S. Muller, Theodore I. Kamins, and Mansun Chan, John Wiley and Sons, New York, 2003. 1Device Electronics for Integrated Circuits, 2 ed., by Muller and Kamins, Wiley, New York, 1986. 2Physics of Semiconductor Devices, by S. M. Sze, Wiley, New York, 1981. 3 Physics of Semiconductor Devices, Shur, Prentice-Hall, 1990. ©rlc L10-16Feb2011

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