Physics of Electronics: Semiconductor Devices Problem sheet 3
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Physics of Electronics: Semiconductor Devices
Problem sheet 3
This problem sheet covers the material covered in Part 3 of the notes. The margins of the notes are also marked with relevant problems in Sedra and Smith (found at the end of each chapter), which you can also do for further practice.
Q.1 Breakdown
A Zener diode is made from a pn junction, and is rated at 1 mA for a forward bias of 0.7 V. Deduce the value of the saturation current IS .
The Zener voltage of the diode is VZ = 3.2 V. Sketch the full IV charac- teristic, marking the values of all known quantities.
The Zener diode is rated with a maximum power of 0.5 W, and is used in the circuit shown below (Q1). Evaluate the power dissipated in the diode for the following values of the applied voltage V : i) 2 V, 3 V, 4 V, 5 V. What is the maximum voltage which could safely be applied in this circuit without damaging the diode?
(Q1)
5 kΩ
0 V
(Q2)
430 Ω
V
0 V
Q.2 Forward bias and iterative method
You have a supply of pn junction diodes rated at 1 mA for 0.7 V forward bias. You place one such diode between the two terminals in the circuit above (Q2) so that it is forward biased. Calculate the voltage V across the diode to three significant figures, using the exponential diode model and the iterative method.
Suggest what you should place between the two terminals so that the voltage V is 0.700 V, bearing in mind you only have the supply of diodes mentioned above.
What would geometric parameter would you change in the diodes that you have (e.g. if you were fabricating them again) so that you could achieve the same voltage using just one diode.
Q.3 A PN junction diode and a current source
A diode rated at 1 mA for 0.7 V forward bias is placed in the circuit below, with a constant current source of 10 mA. The aim of this question is to calculate the voltage V across the diode.
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2 kΩ |
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Write down an equation for the voltage V , in terms of the current through the diode, I .
Write down an equation for the voltage across the resistor (which is the same as the voltage across the diode) as a function of the current through the diode.
Use an iterative method to solve for V and I, correct to 3 significant figures.
What value of V and I do you get using the constant-voltage-drop method? What value of V and I do you get using the ideal diode model?
Draw an equivalent circuit assuming i) the constant-voltage-drop method, and ii) the ideal diode method.
Q.4 Voltage limiter
Examine the circuit below and, using the constant-voltage-drop model, plot the output voltage Vo as a function of the input voltage Vi , for the range -2 V < Vi < +2 V
1 kΩ
Vi
0 V
Still using the constant-voltage-drop model, sketch the output waveform for the following input waveforms:
a. Vi (t) = 0.5 cos(100πt) Volts
b. Vi (t) = 1 cos(100πt) Volts
c. Vi (t) = 0.5 + 0.5 cos(100πt) Volts
Q.5 LEDs
The bandgap of the semiconductor alloy Alx Ga1 −x As can be expressed in terms of the aluminium content, x, as:
1.42 eV + x1.25 eV
Deduce the fraction of aluminium needed to make an AlGaAs LED with an output wavelength of 650 nm.
Q.6 Solar cells
A solar cell is made from a 10 × 10 cm piece of p-type silicon, with [B] = 1016 cm−3 , implanted with donors to create a shallow n-type region at the surface [P] = 1019 cm−3 . This solar cell design gives a short-circuit current of 28 mA/cm2 under optimal solar illumination (with an incident optical power density of 1kW/m2 ), and has a reversed-biased dark current of 1.4 nA
a. Calculate the value of the short circuit current Isc for this solar cell
b. Calculate the value of the open circuit voltage Voc for this solar cell
c. Estimate the maximum power extracted from this solar cell
d. Compare this to the optical power incident on the solar cell, and deduce the nominal efficiency
e. Estimate the optimum load for this solar cell to extract the maximum power
2022-03-11