Derivation of The Ideal Diode EquationUNIVERSITY OF CALIFORNIA AT BERKELEYCollege of EngineeringDepartment of Electrical Engineering and Computer SciencesEE105 Monday DiscussionSeptember 10th, 20071 Derivation of The Ideal Diode Equation∆np(x′) =n2iNAeVFVT− 1e−x′Ln∆pn(x′′) =n2iNDeVFVT− 1 e−x′′Lp!11 DERIVATION OF THE IDEAL DIODE EQUATION 2Jn,diff= qDnddx′np,total(x′)Jp,diff= −qDpddx′′pn,total(x′′)np,total= ∆np+ np,opn,total= ∆pn+ pn,oddx′(np,total) =ddx′∆np(x′) + np,oddx′′(pn,total) =ddx′′∆pn(x′′) + pn,oddx′∆np(x′) + np,o=ddx′∆np(x′)ddx′′∆pn(x′′) + pn,o=ddx′′∆pn(x′′)Jn,diff|x′=0=−qDnn2iLnNAeVFVT− 1Jp,diff|x′′=0=qDpn2iLpNDeVFVT− 1Note here that our electron diffusion current is negative with respectto the x’ axis, and thus positive with respect to the x” axis. Tomatch up directions with the hole diffusio n current, we will negateour result for the electron diffusion current.Jtotal≈ Jn,diff+ Jp,diffJtotal=qDnn2iLnNAeVFVT− 1+qDpn2iLpNDeVFVT− 11 DERIVATION OF THE IDEAL DIODE EQUATION 3Jtotal= qn2iDnLnNA+DpLpNDeVFVT− 1Jtotal= JseVFVT− 1Is= JsAI = JtotalAI = IseVFVT−
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