Question

At a temperature of 290 290 K, a certain p−np-n junction has a saturation current IS=0.500I_S = 0.500 mA. Find the current at this temperature when the voltage is (i) 1.001.00 mV, (ii) −1.00-1.00 mV, (iii) 100100 mV, and (iv) −100-100 mV.

Accepted Answer

Step 1: Understand the problem. The current through a p-n junction diode can be calculated using the diode equation: $$ I = I_S (e^{\frac{qV}{kT}} - 1) $$, where $$ I  is $$the current, $$ I_S  is $$the saturation current, $$ q  is $$the charge of an electron ($$ 1.6 	imes 10^{-19}  C$$), $$ V  is $$the applied voltage, $$ k  is $$Boltzmann's constant ($$ 1.38 	imes 10^{-23}  J/K$$), and $$ T  is $$the temperature in Kelvin. Step 2: Substitute the given values into the equation. The temperature $$ T  is 290 K$$, and the saturation current $$ I_S  is 0.500 mA (or$$ $$ 0.500 	imes 10^{-3}  A). $$For each voltage $$ V  (1.00 mV$$, -1.00 mV, 100 mV, -100 mV), substitute $$ V $$ into the equation. Step 3: Convert the voltage $$ V $$ into volts for consistency. For example, 1.00 mV = $$ 1.00 	imes 10^{-3}  V$$, -1.00 mV = $$ -1.00 	imes 10^{-3}  V$$, 100 mV = $$ 100 	imes 10^{-3}  V$$, and -100 mV = $$ -100 	imes 10^{-3}  V. $$Step 4: Calculate the exponential term $$ e^{\frac{qV}{kT}} $$ for each voltage. Use $$ q = 1.6 	imes 10^{-19}  C$$, $$ k = 1.38 	imes 10^{-23}  J/K$$, and $$ T = 290  K. $$For example, for $$ V = 1.00 	imes 10^{-3}  V$$, calculate $$ \frac{qV}{kT} $$ and then find $$ e^{\frac{qV}{kT}} . $$Repeat this for each voltage. Step 5: Use the diode equation to calculate the current $$ I $$ for each voltage. For example, for $$ V = 1.00 	imes 10^{-3}  V$$, substitute $$ I_S $$, $$ e^{\frac{qV}{kT}} $$, and $$ -1 $$ into the equation $$ I = I_S (e^{\frac{qV}{kT}} - 1) . $$Repeat this process for $$ V = -1.00 	imes 10^{-3}  V$$, $$ V = 100 	imes 10^{-3}  V$$, and $$ V = -100 	imes 10^{-3}  V.$$

At a temperature of $290$ K, a certain $p - n$ junction has a saturation current $I sub S equals 0.500$ mA. Find the current at this temperature when the voltage is (i) $1.00$ mV, (ii) $negative 1.00$ mV, (iii) $100$ mV, and (iv) $negative 100$ mV.

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Concetti chiave

p-n Junction

Saturation Current (IS)

Diode Equation