Understanding Diode Saturation Current Temperature Dependence

The saturation current ($I_S$) of a semiconductor diode is highly dependent on temperature. For silicon diodes, a common rule of thumb used in electronics is that the saturation current approximately doubles for every $10^{\circ}C$ increase in temperature.

Calculating Saturation Current at Higher Temperature

We are given:

• Initial saturation current ($I_{S1}$) at $T_1 = 25^{\circ}C$ is $5 \ nA$.
• We need to find the saturation current ($I_{S2}$) at $T_2 = 95^{\circ}C$.

Step 1: Calculate the Temperature Difference

First, find the total change in temperature:

$ \Delta T = T_2 - T_1 $

$ \Delta T = 95^{\circ}C - 25^{\circ}C = 70^{\circ}C $

Step 2: Determine the Number of Doubling Periods

Using the rule of thumb that the current doubles every $10^{\circ}C$, we calculate how many times the current will double over the $70^{\circ}C$ increase:

$ N = \frac{\Delta T}{10^{\circ}C} = \frac{70^{\circ}C}{10^{\circ}C} = 7 $

This means the saturation current will double 7 times.

Step 3: Calculate the Final Saturation Current

The final saturation current ($I_{S2}$) can be calculated by multiplying the initial current ($I_{S1}$) by $2^N$:

$ I_{S2} \approx I_{S1} \times 2^N $

Substituting the values:

$ I_{S2} \approx 5 \ nA \times 2^7 $

$ I_{S2} \approx 5 \ nA \times 128 $

$ I_{S2} \approx 640 \ nA $

Conclusion

Based on the approximate doubling of saturation current for every $10^{\circ}C$ rise in temperature for a silicon diode, the saturation current at $95^{\circ}C$ is approximately $640 \ nA$. This calculation method provides a reasonable estimate commonly used in semiconductor device analysis.