An ideal p - n junction diode has a current-voltage characteristic described by i = i₀ ! (e^ eV/kT - 1 ) , in which the drift current i₀ is 10 A . The temperature T is taken as 300 K . Determine the voltage V₀ such that e^ eV/kT = 100 . (The term 1 may be neglected for voltages exceeding this value.)

Step-by-step solution

Given the condition: e^ eV₀/kT = 100 Taking natural logarithm on both sides: eV₀ kT = (100) eV₀ kT = 2.303 ₁₀(100) = 2.303 2 = 4.606 Rearranging for V₀ : V₀ = 4.606 kT e Substituting the standard values k = 1.38 10⁻²³ J/K , T = 300 K , and e = 1.6 10⁻¹⁹ C : V₀ = 4.606 1.38 10⁻²³ 300 1.6 10⁻¹⁹ V₀ = 4.606 0.025875 V V₀ 0.119 V 0.12 V