Asksia AI LOGO

Sia

pighead's Question
Physics E&M
Posted 9 months ago

Question 3
10 points
Sanved
A p-n junction forms a p-n diode has a reverse saturation current at 300∘K300^{\circ} \mathrm{K} of 10−16 A10-16 \mathrm{~A}. If the forward diode current is 8 mA8 \mathrm{~mA}, what is the forward bias voltage in volts?

Note: Do not add the units to your answer and use three decimal places.
0.832
Sign in to unlock the answer
Answer from Sia
Posted 9 months ago
Sure, Pighead! Let's solve the problem step by step.

 Problem Statement:
A p-n junction forms a p-n diode with a reverse saturation current at 300∘K300^{\circ} \mathrm{K} of 10−16 A10^{-16} \mathrm{~A}. If the forward diode current is 8 mA8 \mathrm{~mA}, what is the forward bias voltage in volts?

 Solution:
Solution
a
Given Data: - Reverse saturation current, Is=10−16 AI_s = 10^{-16} \mathrm{~A} - Forward diode current, If=8 mA=8×10−3 AI_f = 8 \mathrm{~mA} = 8 \times 10^{-3} \mathrm{~A} - Temperature, T=300 KT = 300 \mathrm{~K}
b
Diode Equation: The current through a diode is given by the Shockley diode equation: If=Is(eVfnVT−1) I_f = I_s \left( e^{\frac{V_f}{nV_T}} - 1 \right) where: - IfI_f is the forward current - IsI_s is the reverse saturation current - VfV_f is the forward bias voltage - nn is the ideality factor (typically assumed to be 1 for simplicity) - VTV_T is the thermal voltage, given by VT=kTqV_T = \frac{kT}{q} For T=300 KT = 300 \mathrm{~K}, VT≈26 mV=0.026 VV_T \approx 26 \mathrm{~mV} = 0.026 \mathrm{~V}
c
Solving for $V_f$: Rearrange the Shockley diode equation to solve for VfV_f: 8×10−3=10−16(eVf0.026−1) 8 \times 10^{-3} = 10^{-16} \left( e^{\frac{V_f}{0.026}} - 1 \right) Since If≫IsI_f \gg I_s, we can approximate: 8×10−3≈10−16eVf0.026 8 \times 10^{-3} \approx 10^{-16} e^{\frac{V_f}{0.026}} Taking the natural logarithm on both sides: ln⁡(8×10−3)=ln⁡(10−16)+Vf0.026 \ln(8 \times 10^{-3}) = \ln(10^{-16}) + \frac{V_f}{0.026} ln⁡(8×10−3)=−4.8283 \ln(8 \times 10^{-3}) = -4.8283 ln⁡(10−16)=−36.8414 \ln(10^{-16}) = -36.8414 −4.8283=−36.8414+Vf0.026 -4.8283 = -36.8414 + \frac{V_f}{0.026} Vf0.026=32.0131 \frac{V_f}{0.026} = 32.0131 Vf=32.0131×0.026 V_f = 32.0131 \times 0.026 Vf≈0.832 V V_f \approx 0.832 \mathrm{~V}
Answer
0.832


 Key Concept
Key Concept
Shockley diode equation


 Explanation
Explanation
The Shockley diode equation relates the forward current through a diode to the forward bias voltage, reverse saturation current, and thermal voltage. By solving this equation, we can determine the forward bias voltage given the forward current and reverse saturation current.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Unlock Smarter Learning with AskSia Super!

Join Super, our all-in-one AI solution that can greatly improve your learning efficiency.

30% higher accuracy than GPT-4o
Entire learning journey support
The most student-friendly features
Study Other Question