Diode Current Equation

The diode current equation shows the relationship between the current flowing through the diode as a function of applied voltage. The mathematical expression of the diode current is given below.

diode current equation

I = current flowing through the diode 
Io = reverse saturation current
q = the charge of the electron
V = the voltage applied across the diode
η = the exponential ideality factor of the diode
K = the Boltzmann constant and K = 1.38 x 10-23   J/K
T is the absolute temperature in Kelvin

The current flowing through the diode does not vary linearly with an increase in applied voltage. The V-I characteristics of the diode have an exponential relationship. The diode resistance varies with an increase in the temperature. As a result, the current does not vary linearly with voltage. The diode is a non-ohmic and nonlinear semiconductor device.

Let us understand what factors the diode current depends on.

Reverse Saturation Current:

The current flowing through the p-n junction diode when it is reversed-biased is called reverse saturation current. The minority carriers are responsible for this current. In a PN junction diode, the reverse saturation current is due to the diffusive flow of minority electrons from the p-side to the n-side and the minority holes from the n-side to the p-side. The reverse saturation current of the diode is in the range of μA to nA. The reverse saturation current gets doubled for every 10-degree centigrade rise in temperature.

η, the (exponential) Ideality Factor

Ideality factor is a way of measuring how accurately the diode follows the ideal diode equation. If the diode under consideration behaves precisely like an ideal diode, then η will be 1. Its value increases from 1 as the difference between the behaviors of the ideal diode and the diode under consideration increases. The greater the deviation, the greater the value of η. The value of η is 1 for germanium diodes and 2 for silicon diodes. The ideality factor depends on the following parameters of the diode.

  • Electron Drift
  • Diffusion
  • Carrier Combination in the depletion region
  • Doping Level
  • Manufacturing Process
  • Purity of the material

The value of ideality factor η generally lies between 1 and 2.

Diode Equation in Forward Biased Condition

When the diode is in a biased condition, the large forward current flows through the diode, the value of the exponent term is more significant, and the diode equation becomes

diode current equation in forward bias condition

Diode Equation in Reverse Biased Condition

When the diode is reverse-biased, the exponential term becomes negligible, and the diode current is equal to the reverse saturation current.

I = – Io

Diode Equation at Room Temperature

Let the room temperature be 27°C. 
Temperature in Kelvin = 27 +273 =300 K
K =1.38 x 10-23  JK-1
q =1.6 x 10-19  C

diode current equation solved problem

The ratio KT/q is called the thermal voltage of the diode.

η, the (exponential) Ideality Factor

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