(a) A forward-bias voltage of 15.0 mV produces a positive current of 9.25 mA through a p-n junction at 300 K. What does the positive current become if the forward-bias voltage is reduced to 10.0 mV?

Verified step by step guidance

1. Understand that the problem involves a p-n junction diode, which follows the Shockley diode equation: \( I = I_0 (e^{\frac{qV}{kT}} - 1) \), where \( I \) is the current, \( I_0 \) is the reverse saturation current, \( q \) is the charge of an electron, \( V \) is the voltage, \( k \) is Boltzmann's constant, and \( T \) is the temperature in Kelvin.
2. Identify the given values: the initial forward-bias voltage \( V_1 = 15.0 \) mV, the initial current \( I_1 = 9.25 \) mA, and the temperature \( T = 300 \) K. The task is to find the current \( I_2 \) when the forward-bias voltage is reduced to \( V_2 = 10.0 \) mV.
3. Use the Shockley diode equation to express the initial current: \( I_1 = I_0 (e^{\frac{qV_1}{kT}} - 1) \). Rearrange this equation to solve for \( I_0 \), the reverse saturation current.
4. Substitute \( I_0 \) back into the Shockley diode equation for the new voltage \( V_2 \): \( I_2 = I_0 (e^{\frac{qV_2}{kT}} - 1) \). This will allow you to find the new current \( I_2 \).
5. Calculate the exponential terms using the given voltages and constants, and solve for \( I_2 \) using the expression derived in the previous step. This will give you the new current through the diode at the reduced forward-bias voltage.

Key Concepts

p-n Junction

A p-n junction is a boundary or interface between p-type and n-type semiconductor materials, crucial in diodes. It allows current to flow more easily in one direction than the other, forming the basis of rectification. In forward bias, the p-side is connected to the positive terminal, reducing the barrier and allowing current to flow.

Diode Equation

The diode equation describes the current-voltage (I-V) characteristics of a diode. It is given by I = I_s (e^(qV/kT) - 1), where I is the current, I_s is the saturation current, V is the voltage across the diode, q is the charge of an electron, k is Boltzmann's constant, and T is the temperature in Kelvin. This equation helps predict how current changes with voltage.

Thermal Voltage

Thermal voltage (V_T) is a parameter in semiconductor physics, defined as V_T = kT/q, where k is Boltzmann's constant, T is the absolute temperature, and q is the charge of an electron. At room temperature (300 K), V_T is approximately 25.85 mV. It is a key factor in the diode equation, influencing how current responds to changes in voltage.