Answer:
5.6 × 10⁻²[1 + 4.643 × 10⁻⁷exp (x/18)] V/cm
Explanation:
The total current density, J = drift current density, J' + diffusion current density, J"
J = J' + J"
J' = nμeE where n = electron concentration = 10¹⁶ exp (-x/18) cm³, μ = electron mobility = 960 cm²/V-s, e = electron charge = 1.602 × 10⁻⁹ C and E = electric field
J" = eDdn/dx where e = electron charge = 1.602 × 10⁻¹⁹ C, D = diffusion coefficient = 25 cm²/s and dn/dx = concentration gradient = d10¹⁶ exp (-x/18) cm³/dx = (-10¹⁶/18)exp (-x/18) cm³
So,
J = J' + J"
J = nμeE + eDdn/dx
E = (J - eDdn/dx)/nμe
Since J = 40 A/cm², substituting the values of the variables into the equation, we have
E = (J - eDdn/dx)/nμe
E = [40 A/cm² - 1.602 × 10⁻⁹ C × 960 cm/V-s × (-10¹⁶/18)exp (-x/18) cm²] ÷ (10¹⁶exp (-x/18) cm³ × 960 cm²/V-s × 1.602 × 10⁻⁹ C)
E = [40 A/cm² - 1537.92 × 10⁻⁹ C-cm/V-s × (-10¹⁶/18)exp (-x/18) cm²] ÷ (10¹⁶exp (-x/18) cm² × 1537.92 × 10⁻⁹ C-cm³/V-s)
E = [40 A/cm² + 85.44 × 10⁷ C-cm/V-s exp (-x/18) cm²] ÷ (exp (-x/18) cm² × 1537.92 × 10⁷ C-cm³/V-s)
E = [40 A/cm² ÷ (exp (-x/18) cm² × 1537.92 × 10⁷ C-cm³/V-s)] + [85.44 × 10⁷ C-cm/V-s exp (-x/18) cm² ÷ (exp (-x/18) × 1537.92 × 10⁷ C-cm²/V-s]
E = [0.026 × 10⁻⁷ A/cm²exp (x/18) V-s/C-cm³] + 0.0056]
E = [0.026 × 10⁻⁷exp (x/18) V/cm] + 0.0056]
E = 0.056[0.026 × 10⁻⁷exp (x/18) V/cm]/0.056 + 1]
E = 0.056[4.643 × 10⁻⁷exp (x/18) V/cm] + 1]
E = 5.6 × 10⁻²[1 + 4.643 × 10⁻⁷exp (x/18)] V/cm
