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Concepts Of Physics MCQ Edition [Volume 2]PhysicsSemiconductors and Semiconductor Devices

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 an expression for the diode's dynamic resistance as a function of V in the region V > V₀ (where V₀ is the voltage at which e^ eV/kT = 100 , allowing the term 1 in the current expression to be neglected).

Options

  1. Ae i₀ kT e^ eV/kT
  2. BkT e i₀ e^ -eV/kT
  3. CkT e i₀ e^ eV/kT
  4. De i₀ kT e^ -eV/kT

Correct answer

B. kT e i₀ e^ -eV/kT

Step-by-step solution

The current-voltage characteristic of the diode is given by i = i₀ (e^ eV/kT - 1) . For V > V₀ , the term e^ eV/kT 100 , so 1 can be neglected compared to e^ eV/kT . The expression for current becomes i i₀ e^ eV/kT . The dynamic resistance r_d of a diode is defined as r_d = dV di . Differentiating the current with respect to voltage V , we get: di dV = d dV (i₀ e^ eV/kT ) = e i₀ kT e^ eV/kT Therefore, the dynamic resistance is: r_d = 1 di dV = kT e i₀ e^ -eV/kT

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