Question

a) The reverse-saturation current of a pn junction diode is IS = 10−11 A. Determine the diode voltage to produce currents of (i) 10 µA, 100 µA, 1 mA, and (ii) −5 × 10−12 A. (b) Repeat part (a) for IS = 10−13 A and part (a) (ii) for −10−14 A.

Answer 1

Answer:

a) i) Vd = 358 mV , Vd = 417.5 mV, Vd = 477.2 mV

   ii) Vd = -17.9 mV

b) Vd = 477.2 mV, Vd = 536.8 mV, Vd = 596.5 mV

   Vd = 161 mV

Explanation:

We will use the ideal diode equation:

$I_{D} = I_{s} (e^{\frac{qv_{d} }{nkT} }-1)$

Where Id = Diode current

           Is = Reverse Saturation Current

           Vd = Diode Voltage

           q = charge of electron

           n = ideality factor

           k = Boltzmann constant

           T = Temperature in Kelvin

(a) We are given:

     Is = 10⁻¹¹ A

i) Id = 10 μA

Ideally, kT/q = 25.9mV and n=1. So,

q/nkT = 38.6

Id = Is e^(38.6Vd) -1

Id/Is + 1 = e^(38.6Vd)

ln(Id/Is + 1) = 38.6Vd

Vd = ln(Id/Is + 1)/38.6

     = ln [(10*10⁻⁶)/10⁻¹¹ + 1] / 38.6

     = 13.815/38.6

Vd = 0.3579

Vd = 358 mV

Id = 100 µA

Vd = ln(Id/Is + 1)/38.6

     = ln [(100*10⁻⁶)/10⁻¹¹ + 1] / 38.6

     = 16.118/38.6

Vd = 0.4175

Vd = 417.5 mV

Id = 1 mA

Vd = ln(Id/Is + 1)/38.6

     = ln [(1*10⁻³)/10⁻¹¹ + 1] / 38.6

    = 18.420/38.6

Vd = 0.4772

Vd = 477.2 mV

ii) Id = -5 x 10⁻¹² A

   Vd = ln(Id/Is + 1)/38.6

         = ln [(-5 x 10⁻¹²)/10⁻¹¹ + 1] / 38.6

         = -0.693/38.6

   Vd = -0.0179 V

   Vd = -17.9 mV

(b) Is = 10⁻¹³ A

i) Id = 10 µA

Vd = ln(Id/Is + 1)/38.6

     = ln [(10 x 10⁻⁶)/10⁻¹³ + 1] / 38.6

     = 18.42/38.6

Vd = 0.4772 V

Vd = 477.2 mV

Id = 100 µA

Vd = ln(Id/Is + 1)/38.6

     = ln [(100 x 10⁻⁶)/10⁻¹³ + 1] / 38.6

     = 20.723/38.6

     = 0.5368 V

Vd = 536.8 mV

Id = 1 mA

Vd = ln(Id/Is + 1)/38.6

     = ln [(1 x 10⁻³)/10⁻¹³ + 1] / 38.6

     = 23.025/38.6

     = 0.5965

Vd = 596.5 mV

ii) Id = -5 x 10⁻¹² A

   Vd = ln(Id/Is + 1)/38.6

         = ln [(-5 x 10⁻¹²)/10⁻¹³ + 1] / 38.6

         = ln (-49) / 38.6

     Not possible.

Is = -10⁻¹⁴

Id = -5 x 10⁻¹² A

Vd = ln(Id/Is + 1)/38.6

         = ln [(-5 x 10⁻¹²)/-10⁻¹⁴ + 1] / 38.6

         = 6.216/38.6

Vd = 0.161 V

Vd = 161 mV