Shockley Diode How to Calculate N and Is

The Shockley diode equation is fundamental in semiconductor physics. Calculating the ideality factor (n) and saturation current (Is) helps characterize diode behavior. This guide explains the process step-by-step with practical examples.

What is a Shockley Diode?

A Shockley diode is a p-n junction diode named after its inventor, William Shockley. The Shockley diode equation describes the current-voltage relationship of the diode:

Shockley Diode Equation:

I = Is (e^(qV/nkT) - 1)

Where:

I = Diode current
Is = Saturation current
q = Electron charge (1.602 × 10⁻¹⁹ C)
V = Applied voltage
n = Ideality factor
k = Boltzmann constant (1.381 × 10⁻²³ J/K)
T = Temperature in Kelvin

The equation shows that diode current depends exponentially on voltage, with the saturation current (Is) and ideality factor (n) as key parameters. Calculating these values is essential for diode characterization and circuit design.

Calculating the Ideality Factor (n)

The ideality factor (n) represents how closely the diode follows the ideal p-n junction behavior. It accounts for non-ideal effects like recombination currents and series resistance.

Ideality Factor Calculation:

n = q / (kT * d(ln(I))/dV)

Where:

d(ln(I))/dV = Slope of the ln(I) vs V curve in the forward bias region

To calculate n:

Measure current-voltage (I-V) data in the forward bias region
Plot ln(I) vs V to find the slope (d(ln(I))/dV)
Use the formula above to calculate n

Note: The ideality factor typically ranges from 1 to 2 for silicon diodes, with n=1 indicating ideal behavior and higher values indicating non-ideal effects.

Calculating the Saturation Current (Is)

The saturation current (Is) represents the reverse bias current when the diode is ideal. It's a key parameter for understanding diode behavior at low voltages.

Saturation Current Calculation:

Is = I / (e^(qV/nkT) - 1)

Where:

I = Measured current at a specific voltage
V = Applied voltage at which current is measured

To calculate Is:

Measure current at a specific forward voltage (typically 0.7V for silicon diodes)
Use the formula above to calculate Is

Note: Saturation current is temperature-dependent and typically ranges from 10⁻¹⁵ A to 10⁻⁶ A for silicon diodes.

Example Calculation

Let's calculate n and Is for a silicon diode with the following measurements:

Voltage (V)	Current (A)
0.6	1.0 × 10⁻⁵
0.7	1.0 × 10⁻⁴
0.8	1.0 × 10⁻³

Step 1: Calculate the slope (d(ln(I))/dV)

First, calculate ln(I) for each voltage:

ln(1.0 × 10⁻⁵) ≈ -11.51
ln(1.0 × 10⁻⁴) ≈ -9.21
ln(1.0 × 10⁻³) ≈ -6.91

Then calculate the slope between 0.7V and 0.8V:

Slope = (ln(I₂) - ln(I₁)) / (V₂ - V₁) = (-6.91 - (-9.21)) / (0.8 - 0.7) = 2.3 / 0.1 = 23

Step 2: Calculate the ideality factor (n)

Using the slope and known constants:

n = q / (kT * slope) = (1.602 × 10⁻¹⁹) / (1.381 × 10⁻²³ × 300 × 23) ≈ 1.1

Step 3: Calculate the saturation current (Is)

Using the current at 0.7V:

Is = I / (e^(qV/nkT) - 1) = 1.0 × 10⁻⁴ / (e^(1.602 × 10⁻¹⁹ × 0.7 / (1.1 × 1.381 × 10⁻²³ × 300)) - 1) ≈ 1.0 × 10⁻¹⁴ A

Result: For this example, the ideality factor n ≈ 1.1 and saturation current Is ≈ 1.0 × 10⁻¹⁴ A.

FAQ

What is the difference between n and Is?

The ideality factor (n) describes how closely the diode follows ideal behavior, while the saturation current (Is) represents the reverse bias current when the diode is ideal. Together, they fully characterize the Shockley diode equation.

How does temperature affect n and Is?

Both n and Is are temperature-dependent. The ideality factor typically increases slightly with temperature, while the saturation current increases exponentially with temperature.

What is a typical value for n?

For silicon diodes, n typically ranges from 1 to 2, with n=1 indicating ideal behavior. Higher values indicate non-ideal effects like recombination currents.

How accurate do the measurements need to be?

For precise results, measurements should be accurate to at least 1% for current and 0.1% for voltage. Use a high-quality multimeter and ensure stable operating conditions.