doPhysics · Modern Physics
Diodes, Transistors and Logic Gates
Diodes built for special jobs, and the switches of digital circuits. Reverse breakdown and the Zener regulator, the photodiode, the LED and the solar cell, the transistor as a switch (beyond the Class 12 syllabus), and the logic gates, from NOT, AND and OR to the universal NAND and NOR.
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Why this chapter
Why this chapter exists
The last chapter built the p-n junction and the ordinary diode, a one-way valve for current. This chapter puts junctions to work. A diode driven into reverse breakdown holds a voltage steady, and it sits in every regulated supply. A junction that meets light becomes a detector, a lamp or a power station on a roof. A sandwich of two junctions, the transistor, becomes a switch. The fourth lesson, on the transistor, is beyond the Class 12 syllabus and is marked so. Switches that are either on or off give the logic gates, and a handful of gates can add numbers. Every phone, calculator and LED bulb in India rests on the ideas of this chapter.
You will learn
By the end of this chapter you will
- Explain reverse breakdown, and why a diode in breakdown holds its voltage fixed over a wide range of currents.
- Tell Zener breakdown from avalanche breakdown by doping, depletion width, mechanism, voltage and temperature coefficient.
- Find the series, load and Zener currents of a Zener regulator, decide when the Zener stops regulating, and choose the series resistance.
- Use \(\lambda = hc/E_g\) to link band gaps and colours, and explain the photodiode, the LED and the solar cell.
- Beyond the Class 12 syllabus: use \(I_E = I_B + I_C\) and \(\beta = I_C/I_B\), and explain cut-off and saturation of a transistor switch.
- Draw the symbols and write the truth tables and expressions of the basic gates, and build gates from diodes and a transistor.
- Build every gate from NAND or NOR alone, simplify with De Morgan's theorems, and read a gate's output from its input waveforms.
Before you begin
Before you begin
From the chapter on semiconductors and the p-n junction, you should know the energy bands and the band gap, electrons and holes, and doping. You should know the depletion layer, forward and reverse bias, and the diode's current-voltage curve. From the chapter on photons you should know that a photon of wavelength \(\lambda\) has energy \(hc/\lambda\), and the electron volt. Ohm's law and the current law at a junction are stated where they are first used.
Lessons
1
Reverse Breakdown: Zener and Avalanche
A reverse-biased diode passes almost no current until the breakdown voltage, where the current rises steeply while the voltage stays fixed. Two mechanisms cause it, the Zener effect in thin, heavily doped junctions and the avalanche in wide, lightly doped ones. They differ in voltage and in how heat changes them.
Reverse breakdownZener breakdown and avalanche breakdownWhich breakdown by voltage and temperature
2
The Zener Diode as a Voltage Regulator
A series resistor and a Zener diode across the load hold the output voltage steady while the input and the load change. The current law at the junction gives every current, and two limits fix the series resistance.
The zener regulator circuitCurrents in the regulatorChoosing the series resistance
3
Diodes and Light: Photodiode, LED, Solar Cell
A photon with at least the band-gap energy makes an electron-hole pair, and a pair that recombines can return a photon of the gap energy. The photodiode, the light-emitting diode and the solar cell use these two facts, in reverse bias, forward bias and no bias.
Band gap and colourThe photodiodeThe light emitting diodeThe solar cell
4
The Transistor as a Switch
Beyond the Class 12 syllabus. The n-p-n junction transistor, with its emitter, thin base and collector; the currents \(I_E = I_B + I_C\) and the gain \(\beta\); and the two states that make it a switch, cut-off and saturation.
The junction transistorTransistor currentsOn and off
5
Logic Gates: NOT, AND, OR
Digital circuits work with two levels, 0 and 1. The NOT, AND and OR gates, their symbols, truth tables and Boolean expressions, a few rules of Boolean algebra, and gates built from diodes and a transistor. Two gates together add two binary digits.
Binary levels and truth tablesNot and and or gatesGates built from diodes and a transistor
6
NAND, NOR and De Morgan
The NAND and NOR gates, and why each alone can build every other gate. De Morgan's two theorems, which turn an inverted AND into an OR and back, simplify gate circuits. Timing diagrams show a gate working on changing inputs.
Nand and nor gatesUniversal gatesDe morgans theoremsReading gate waveforms
Read in order. The small labels are the topics of each lesson. They take your colour as you answer the checks.
0%The Workbook
Questions to solve on paper, marked by you.
Glossary
The key words of this chapter, with the meaning this chapter gives them.
- AND gate
- A gate whose output is 1 only when all its inputs are 1, \(Y = A \cdot B\).
- avalanche breakdown
- Breakdown in a wide, lightly doped junction, where carriers multiply by impact ionisation, doubling at each generation. It occurs above about \(6\,\text{V}\), and its voltage rises with temperature.
- base
- The thin, lightly doped middle region of a transistor, through which nearly all the carriers from the emitter pass to the collector.
- binary
- The way of writing numbers with only the digits \(0\) and \(1\), each place worth twice the place to its right; 12 is 1100.
- Boolean algebra
- The algebra of the logic levels 0 and 1, with the operations NOT (a bar), AND (a dot) and OR (a plus). In it \(1 + 1 = 1\).
- breakdown voltage
- The reverse voltage at which reverse breakdown begins. For a Zener diode it is the Zener voltage \(V_Z\).
- collector
- The region of a transistor that gathers the carriers crossing the base; its junction with the base is reverse-biased in use.
- current gain
- The ratio of the collector current to the base current of a transistor, \(\beta = I_C/I_B\), typically about \(100\).
- cut-off
- The state of a transistor with no base current and so no collector current: an open switch.
- dark current
- The small reverse current of a photodiode when no light falls on it.
- De Morgan's theorems
- The two rules \(\overline{A + B} = \bar A \cdot \bar B\) and \(\overline{A \cdot B} = \bar A + \bar B\): to invert an expression, invert each part and swap + with ·.
- digital signal
- A signal that takes only two levels, low (0) and high (1), such as \(0\,\text{V}\) and \(5\,\text{V}\).
- emitter
- The heavily doped region of a transistor that supplies the charge carriers; its junction with the base is forward-biased in use.
- half adder
- A circuit that adds two binary digits, giving the sum from an XOR gate and the carry from an AND gate.
- impact ionisation
- The freeing of an electron from a bond by a collision with a fast carrier. The carrier has gained more than the band-gap energy from the field.
- junction transistor
- A three-layer semiconductor device, n-p-n or p-n-p, with an emitter, a thin base and a collector. A small base current controls a much larger collector current.
- light-emitting diode
- A forward-biased p-n junction, usually of a compound such as GaAs or GaN, in which recombining electrons and holes emit light of wavelength \(hc/E_g\). Short form LED.
- load
- The device or resistance that a supply or regulator feeds, such as a phone or a lamp; its current is the load current.
- logic gate
- A circuit with one or more inputs and one output, each at level 0 or 1, whose output follows a fixed logical rule.
- NAND gate
- An AND gate followed by a NOT, \(Y = \overline{A \cdot B}\); its output is 0 only when all inputs are 1.
- NOR gate
- An OR gate followed by a NOT, \(Y = \overline{A + B}\); its output is 1 only when all inputs are 0.
- NOT gate
- A one-input gate whose output is the opposite of its input, \(Y = \bar A\).
- open-circuit voltage
- The voltage of a solar cell when nothing is connected to it, at zero current. For a silicon cell it is about \(0.6\,\text{V}\) and depends only weakly on the light.
- OR gate
- A gate whose output is 1 when any of its inputs is 1, \(Y = A + B\).
- photodiode
- A reverse-biased p-n junction on which light falls. Photons with \(h\nu \ge E_g\) make electron-hole pairs, and the reverse current grows in proportion to the light.
- recombination
- The meeting of a free electron and a hole, in which both disappear. An energy of about the band gap is released, as light or as heat.
- reverse breakdown
- The sudden, steep rise of the reverse current of a p-n junction when the reverse voltage reaches the breakdown voltage. The voltage then stays almost constant while the current changes.
- saturation
- The state of a transistor carrying the largest collector current its circuit allows, \(V_{CC}/R_C\). It acts as a closed switch.
- series resistance
- In a Zener regulator, the resistor \(R_S\) between the input and the Zener. It carries the whole input current and takes the difference \(V_{in} - V_Z\).
- short-circuit current
- The current of a solar cell when its terminals are joined directly, at zero voltage. It is proportional to the light falling on the cell.
- solar cell
- A p-n junction of large area with no bias. Light makes electron-hole pairs, the built-in field separates them, and the cell drives a current through a load.
- temperature coefficient
- The fractional change of a quantity, such as a breakdown voltage, for each degree rise in temperature. It is negative for Zener breakdown and positive for avalanche breakdown.
- timing diagram
- A graph of the input and output levels of a logic circuit against time, drawn as pulses.
- truth table
- A table listing the output of a logic gate or circuit for every combination of its inputs; \(n\) inputs give \(2^n\) rows.
- universal gate
- A gate from which NOT, AND and OR, and so every logic circuit, can be built using that gate alone. NAND and NOR are universal.
- voltage regulator
- A circuit whose output voltage stays constant while its input voltage and its load change.
- XOR gate
- The exclusive OR gate, whose output is 1 when its two inputs differ, \(Y = A \oplus B = A \cdot \bar B + \bar A \cdot B\).
- Zener breakdown
- Breakdown in a thin, heavily doped junction, where the very strong field pulls electrons straight out of their bonds. It occurs below about \(5\,\text{V}\), and its voltage falls as the temperature rises.
- Zener diode
- A p-n junction diode made to work in reverse breakdown. Connected in reverse bias, it holds the voltage across it at \(V_Z\) over a wide range of currents.