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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

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**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

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

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**Law of the junction (cont.)**

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**Law of the junction (cont.)**

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Injection Conditions ©rlc L10-16Feb2011

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**Apply the Continuity Eqn in CNR**

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

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**Ideal Junction Theory (cont.)**

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**Ideal Junction Theory (cont.)**

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**Excess minority carrier distr fctn**

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**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

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**Minority carrier currents**

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**Evaluating the diode current**

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**Special cases for the diode current**

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**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

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**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

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**Diffnt’l, one-sided diode conductance**

Static (steady-state) diode I-V characteristic IQ Va VQ ©rlc L10-16Feb2011

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

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**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

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**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

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

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**General time- constant**

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

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

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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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