Reverse current, in the context of a p-n junction diode, is primarily determined by the reverse saturation current (I₀) and influenced by the applied reverse voltage and temperature. The actual calculation depends on the level of reverse voltage.
Here's a breakdown of how to calculate reverse current:
Understanding Reverse Current in a Diode
When a diode is reverse biased (meaning the p-side is connected to a negative voltage and the n-side to a positive voltage), ideally, no current should flow. However, a small amount of current, called the reverse current or reverse saturation current (I₀), always exists due to minority carriers. These minority carriers (electrons in the p-side and holes in the n-side) are swept across the junction by the electric field in the depletion region.
Calculating Reverse Current
The diode current equation, sometimes referred to as the Shockley diode equation, generally describes the current (I) through a diode based on the voltage (V) across it, and it's crucial for understanding reverse current. The equation is:
*I = I₀ (exp(eV / (nkT)) - 1)**
Where:
- I is the diode current.
- I₀ is the reverse saturation current. This is the current that flows under a large reverse bias. It's temperature dependent and intrinsic to the diode's construction.
- e is the elementary charge (approximately 1.602 x 10⁻¹⁹ Coulombs).
- V is the voltage across the diode (positive for forward bias, negative for reverse bias).
- n is the ideality factor (typically between 1 and 2, depending on the diode).
- k is the Boltzmann constant (approximately 1.38 x 10⁻²³ J/K or 8.617 x 10⁻⁵ eV/K).
- T is the absolute temperature in Kelvin.
Cases of Reverse Bias
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Small Reverse Bias:
When the reverse voltage (V) is significantly negative (e.g., V << 0), the term exp(eV / (nkT)) approaches zero. Therefore, the equation simplifies to:
*I ≈ I₀ (0 - 1) = -I₀**
In this scenario, the reverse current is approximately equal to the negative of the reverse saturation current. This holds true for most practical reverse bias voltages, below the breakdown voltage. The current will be very close to -I₀, and almost constant.
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Reverse Breakdown Voltage:
If the reverse voltage increases to the breakdown voltage (Vbr), a very large reverse current begins to flow. The diode equation does not accurately describe the current under breakdown conditions. Breakdown is due to avalanche or Zener effects. In practice, the diode will likely be damaged if operated in breakdown for any significant amount of time, unless it is designed to be a Zener diode.
Determining Reverse Saturation Current (I₀)
I₀ is highly temperature-dependent. It approximately doubles for every 10°C increase in temperature. Its value can be found:
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From the diode's datasheet: Manufacturers often specify I₀ at a particular temperature.
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Experimentally: By measuring the reverse current at a known reverse voltage (well below the breakdown voltage) and temperature.
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Estimation: Without specific data, one can estimate I₀, but this is not recommended for precise calculations.
Example
Suppose a silicon diode has a reverse saturation current (I₀) of 1 nA at 25°C (298 K) and is reverse biased with -5V. Assuming an ideality factor (n) of 2:
I ≈ 1 nA (exp((1.602 x 10⁻¹⁹ C -5 V) / (2 1.38 x 10⁻²³ J/K 298 K)) - 1)
Since the exponential term becomes very small, I ≈ -1 nA.
Important Considerations
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Temperature: As mentioned, temperature significantly affects I₀. A diode datasheet will often give you the value of I₀ at room temperature and the temperature coefficient so that you can extrapolate for other temperatures.
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Surface Leakage: Surface leakage can also contribute to the reverse current, especially in older diodes. This leakage is often voltage-dependent.
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Real Diodes: The Shockley diode equation is an idealization. Real diodes exhibit more complex behavior, particularly at high currents or near breakdown.
In summary, calculating reverse current typically involves using the Shockley diode equation, with a focus on the reverse saturation current (I₀). For most reverse bias voltages (well below the breakdown voltage), the reverse current is approximately equal to -I₀. Remember to consider temperature effects, as I₀ is highly temperature-dependent.
