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)) at a temperature ((T)) can be calculated using the formula:

$$ V_T = \frac{kT}{q} $$

Where:

• (k) (Boltzmann constant) = (1.38 \times 10^{-23} , \text{J/K})
• (q) (elementary charge) = (1.6 \times 10^{-19} , \text{C})

Convert temperature from Celsius to Kelvin:

$$ T(K) = 20 + 273.15 = 293.15 , K $$

Now calculate (V_T):

$$ V_T = \frac{(1.38 \times 10^{-23} , \text{J/K})(293.15 , K)}{1.6 \times 10^{-19} , \text{C}} \approx 0.0259 , \text{V} $$

2. Calculate Diode Current

The diode current ((I)) can be calculated using the Shockley diode equation:

$$ I = I_0 \left( e^{\frac{qV}{nV_T}} - 1 \right) $$

Where:

• (I_0) = Reverse saturation current = (40 , nA = 40 \times 10^{-9} , A)
• (n) = Ideality factor = 2
• (V) = Applied bias voltage = (0.5 , V)

Substituting the values into the equation and using the previously calculated (V_T):

$$ I = 40 \times 10^{-9} \left( e^{\frac{(1.6 \times 10^{-19})(0.5)}{(2)(0.0259)}} - 1 \right) $$

First, calculate the exponent:

$$ \frac{(1.6 \times 10^{-19})(0.5)}{(2)(0.0259)} \approx 1.549 $$

Now, compute:

$$ I \approx 40 \times 10^{-9} \left( e^{1.549} - 1 \right) $$

Calculating (e^{1.549}):

$$ e^{1.549} \approx 4.705 $$

Finally substitute back:

$$ I \approx 40 \times 10^{-9} \left( 4.705 - 1 \right) \approx 40 \times 10^{-9} \times 3.705 \approx 148.2 \times 10^{-9} , A = 148.2 , nA $$