Shri Sant Gajanan Maharaj College of Engineering Department

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Shri Sant Gajanan Maharaj College of Engineering Department of Electronics & Telecommunications Engineering Electronic

Shri Sant Gajanan Maharaj College of Engineering Department of Electronics & Telecommunications Engineering Electronic Devices & Components Unit – IV Ordinary Diode & Zener Diode Proof of junction width proportional to square root of potential barrier of a PN Junction Diode

Relation between Junction Width and Barrier Potential Space Charge Region in PN Junction Figure

Relation between Junction Width and Barrier Potential Space Charge Region in PN Junction Figure 1

Relation between Junction Width and Barrier Potential and PN Junction Figure 2

Relation between Junction Width and Barrier Potential and PN Junction Figure 2

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W • The PN Junction is assumed as abruptly doped and space charge distribution is as shown in Figure 1. Also see Figure 2 and note X 1, V 1, X 2, V 2 • Let ρ represent space charge. It is uniform on either side of depletion region. If q is charge on an electron and NA and ND are acceptor and donor impurity concentrations, then ρ = -q NA 0>x> X 1 ρ = q ND ρ=0 X 2 >x>0 elsewhere

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W • If V is barrier potential, εo is permittivity of free space and εr is dielectric constant of silicon/Germanium, then Poisson’s Equation is given as • This equation is applied to P region Equation 1

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W • Integrate Equation 1 with respect to ‘x’ Equation 2 Where C is constant of integration • Integrate Equation 2 with respect to ‘x’ Equation 3 Where D is constant of integration

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W • For finding value of ‘D’, apply the condition at x-=0, V=0 to Equation 3 The value of D is found to be 0 • For finding value of ‘C’, apply condition (d. V/dx) = 0 at x=X 1 to Equation 2

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W • Hence we get value of ‘C’ as • Now substitute this value of C and also D=0 in Equation 3 Hence

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W • Previous equation can be rearranged as Equation 4 • At x=X 1, we have V=V 1. Substitute this in equation 4 Equation 5 • Whatever steps have been evaluated so far, the same steps if applied to N side gives Equation 6

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W • Barrier potential Vo = V 2 – V 1 • Hence subtract Equation 5 from Equation 6 Equation 7 • Positive charge on N side must be equal to negative charge on P side. Hence NAX 1 = -NDX 2 • Hence substitute this condition in Equation 7 and rearrange the terms

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W • Similarly, expression can be written for X 2 • Total depletion width W = X 1 - X 2 • Square both sides Equation 8

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W

Relation between Junction Width and Barrier Potential Derivation of Expression for Junction Width W • Hence, final expression for W can be evaluated by substituting expressions for X 1 and X 2 in Equation 8 • The only variable term on RHS is barrier potential Vo • Hence, W is proportional to square root of Vo