Determine thermal voltage for the diode at a temperature of 20°C. Also find diode current if reverse saturation current is 40 nA, ideality factor is 2, and applied bias voltage is... Determine thermal voltage for the diode at a temperature of 20°C. Also find diode current if reverse saturation current is 40 nA, ideality factor is 2, and applied bias voltage is 0.5 V. Read more

Steps to Solve

1. Calculate Thermal Voltage

The thermal voltage ($V_t$) can be calculated using the formula: $$ V_t = \frac{k \cdot T}{q} $$ where:

• $k$ is the Boltzmann constant ($8.617 \times 10^{-5} , \text{eV/K}$),
• $T$ is the temperature in Kelvin, and
• $q$ is the charge of an electron ($1.602 \times 10^{-19} , \text{C}$).

First, convert the temperature from Celsius to Kelvin: $$ T = 20^\circ C + 273.15 = 293.15 , K $$

Now substitute the values into the equation: $$ V_t = \frac{8.617 \times 10^{-5} \times 293.15}{1.602 \times 10^{-19}} $$

2. Find Diode Current

The diode current ($I_D$) can be calculated using the diode equation: $$ I_D = I_s \left( e^{\frac{V}{n V_t}} - 1 \right) $$ where:

• $I_s$ is the reverse saturation current (given as $40 , nA = 40 \times 10^{-9} , A$),
• $V$ is the applied bias voltage (given as $0.5 , V$),
• $n$ is the ideality factor (given as $2$), and
• $V_t$ is the thermal voltage calculated in step 1.

Substituting the known values: $$ I_D = 40 \times 10^{-9} \left( e^{\frac{0.5}{2 V_t}} - 1 \right) $$

3. Plug in the value of Thermal Voltage

Calculate $V_t$ and then substitute it back into the equation for $I_D$:

• Find the value of $V_t$ from step 1.
• Replace $V_t$ in the diode current equation.

4. Calculate Current

Evaluate the expression to find the value of $I_D$.