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. Determine Thermal Voltage The thermal voltage ($V_T$) can be calculated using the formula:

$$ V_T = \frac{k \cdot T}{q} $$

Where:

• $k$ = Boltzmann’s constant = $1.38 \times 10^{-23} , \text{J/K}$
• $T$ = Absolute temperature in Kelvin
• $q$ = Charge of an electron = $1.6 \times 10^{-19} , \text{C}$

First, convert the temperature from Celsius to Kelvin:

$$ T = 20°C + 273.15 = 293.15 , \text{K} $$

Now calculate $V_T$:

$$ V_T = \frac{(1.38 \times 10^{-23}) \cdot (293.15)}{(1.6 \times 10^{-19})} $$

2. Convert Units and Perform the Calculation Substituting the values, we compute:

$$ V_T = \frac{4.036 \times 10^{-21}}{1.6 \times 10^{-19}} = 0.0252 , \text{V} , (\text{or } 25.2, \text{mV}) $$

3. Calculate the Diode Current Next, use the diode equation to find the diode current ($I_D$):

$$ I_D = I_S \left( e^{\frac{V}{n V_T}} - 1 \right) $$

Where:

• $I_S = 40 , \text{nA} = 40 \times 10^{-9} , \text{A}$
• $n = 2$ (ideality factor)
• $V = 0.5 , \text{V}$ (applied bias voltage)

Plug in the values into the equation:

$$ I_D = 40 \times 10^{-9} \left( e^{\frac{0.5}{2 \cdot 0.0252}} - 1 \right) $$

4. Perform the Exponential Calculation Calculate the exponent:

$$ \frac{0.5}{2 \cdot 0.0252} = \frac{0.5}{0.0504} \approx 9.92 $$

Thus,

$$ e^{9.92} \approx 13901.14 $$

So now substitute back to find $I_D$:

$$ I_D = 40 \times 10^{-9} \left( 13901.14 - 1 \right) \approx 40 \times 10^{-9} \cdot 13900 \approx 0.000556 , \text{A} = 556 , \mu \text{A} $$