Semiconductor Devices

16.1 Introduction

• A p-n junction diode acts as a switch: forward biased it is a closed switch and current flows; reverse biased it is an open switch and only a negligibly small current flows. This switching action is what makes it a rectifier.

• AC is generated and transmitted more cheaply than DC, so mains supply is AC — in India $230\ \text{V}$, $50\ \text{Hz}$, varying sinusoidally. Gadgets such as a TV or a mobile charger need DC, so the mains must be rectified.

• Block chain of a DC power supply, in order: AC mains $\rightarrow$ transformer $\rightarrow$ rectifier $\rightarrow$ filter $\rightarrow$ voltage regulator $\rightarrow$ load.

• Ripple: the AC component present in the DC output of a rectifier.

16.2 Rectifiers

• Rectification: the conversion of AC voltage into DC voltage. Rectifier: an electronic circuit which rectifies AC voltage.

• Two types: half wave rectifier (one diode) and full wave rectifier (two diodes, centre tapped transformer).

Half wave rectifier

• Secondary coil AB of the transformer is in series with a diode D and the load $R_L$.

• Positive half cycle: A is at higher potential than B, D is forward biased, it conducts, current flows through $R_L$.

• Negative half cycle: A is at lower potential than B, D is reverse biased, it does not conduct, no current flows.

• Output across $R_L$ is a set of alternate pulses in one direction only; the negative half cycles are lost. Output frequency $= 50\ \text{Hz}$ for a $50\ \text{Hz}$ input.

• Two advantages of using a transformer: it steps the AC input up or down as the circuit requires, and it isolates the rectifier from the mains, reducing the risk of electric shock.

Full wave rectifier

• Centre tapped transformer with diodes $D_1$ and $D_2$; they conduct alternately.

• Positive half cycle: A is at higher potential than B, $D_1$ conducts, current through $R_L$ follows the path APQRC.

• Negative half cycle: B is at higher potential than A, $D_2$ conducts, current through $R_L$ follows the path BPQRC.

• Current through $R_L$ is in the same direction in both half cycles, so the output is continuous pulses. Output frequency $= 100\ \text{Hz}$ for a $50\ \text{Hz}$ input.

• Advantages: rectification takes place in both half cycles of the AC input, and the ripple is less than in a half wave rectifier.

Distinguish: half wave and full wave rectifier

Ripple factor and filters

• Ripple factor $r = \dfrac{\text{rms value of AC component}}{\text{value of DC component}}$ in the rectifier output. A smaller ripple factor means a more effective rectifier.

• A filter circuit removes the AC component (the ripple) from the rectifier output and allows only the DC component through.

• Capacitor filter: the pulsating DC is applied across a capacitor in parallel with the load. As the rectifier voltage rises the capacitor charges up to the peak voltage $V_p$ at the end of the quarter cycle and supplies current to the load. When the rectifier voltage falls, the capacitor discharges through $R_L$ and the load voltage drops only slightly, because the next voltage peak recharges the capacitor immediately. Repeating this smooths the output.

• Capacitor filter is widely used because of its low cost, small size and light weight; it is preferred for small load currents and is common in battery eliminators.

• Unregulated power supply: one whose output voltage changes when a load is connected across it. Regulated power supply: one whose output remains steady even after a load is connected.

16.3 Special purpose junction diodes

Four studied: Zener diode, photodiode, solar cell, LED. The Zener works on junction breakdown; the other three make use of photosensitivity.

Zener diode

• A Zener diode is a heavily doped p-n junction diode designed to work in the breakdown region. Heavy doping makes the depletion layer very thin.

• Zener breakdown: increasing the reverse voltage raises the electric field across the junction; the field exerts a force on the bound electrons, covalent bonds break, electrons are freed and a large current flows. More voltage frees more electrons, so the current rises rapidly.

• Zener breakdown does not damage the diode; ordinary reverse breakdown of a normal diode does.

• Symbol in words: an ordinary diode symbol (triangle pointing at a bar) with the bar bent at both ends into the shape of the letter Z.

• Characteristic in words: in forward bias it behaves exactly like a normal diode (current rises sharply past the knee). In reverse bias almost no current flows until the reverse voltage reaches $V_Z$; there the current increases suddenly and steeply, while the voltage across the diode stays constant at $V_Z$ however large the current becomes.

• $V_Z$ depends on doping: heavier doping gives a thinner depletion layer and a lower breakdown voltage; lighter doping gives a higher breakdown voltage. Diodes below $6\ \text{V}$ operate mainly by Zener breakdown, those above $6\ \text{V}$ mainly by avalanche breakdown; both are called Zener diodes.

• As a regulator: $R_S$ in series limits the current; the Zener is in reverse bias across the load $R_L$, so $V_O = V_Z$. If $V_{in}$ rises, the extra voltage is dropped across $R_S$ and $V_Z$ is unchanged. If $R_L$ falls, $I_L$ rises and $I_Z$ falls by the same amount, again keeping $V_Z$ constant.

• Specifications on a datasheet: Zener V-I characteristic, Zener voltage $V_Z$, maximum Zener current $I_{ZM}$, power rating, Zener resistance (impedance) $R_Z$.

• Applications: voltage regulator, fixed reference voltage in transistor biasing, peak clipper or limiter in wave shaping, protection of meters against accidental fluctuations.

Photodiode

• A photodiode is a special p-n junction diode which converts light energy into electrical energy; also called a photodetector or photosensor. It is always operated in reverse bias, and only minority carrier current flows through it.

• Construction: the junction is placed inside a glass window so that only the junction is exposed to light; the rest of the diode is painted with an opaque colour or covered.

• Dark current: the reverse saturation current that flows even when the photodiode is not illuminated. It is due to minority carriers and depends only on their concentration, not on the applied voltage.

• On illumination with photons of energy greater than the band gap, electron-hole pairs are generated in the depletion region; the intrinsic field of the depletion region separates them, electrons going to the anode and holes to the cathode, so the reverse current increases.

• Reverse current depends on the intensity of the incident light; total current $=$ photocurrent $+$ dark current.

• Characteristic in words: a family of reverse-bias curves, one per light intensity, each nearly flat (current almost independent of reverse voltage) and each higher than the one below it. The reverse current first increases with intensity and then settles at a constant saturation current.

• Dark resistance $R_d = \dfrac{\text{maximum reverse voltage}}{\text{dark current}}$. Sensitivity improves when the dark current is minimised.

• Advantages: quick response to light; linear response (reverse current proportional to intensity); high speed of operation; light weight and compact; wide spectral response (silicon: $190\ \text{nm}$ to $1100\ \text{nm}$); relatively low cost.

• Disadvantages: properties are temperature dependent; low reverse current at low illumination.

• Applications: counters and switches, burglar alarms, detection of visible and invisible radiation, fast switching circuits, fibre optic communication, optocouplers, photo sensors for light intensity, fire and smoke detectors.

Solar cell (photovoltaic cell)

• A solar cell converts solar energy directly into electrical energy; it is a source of DC power.

• Structure: a p-n junction with the thin n-side facing the radiation and a relatively thick p-side at the back. Both sides are coated with conducting material — the front contact on the n-side, the back (rear) contact on the p-side. An antireflection coating on the n-side lets visible light through but reflects IR (heat) radiation, protecting the cell from temperature changes.

• Working, in four steps: (1) electron-hole pairs are generated in the depletion region; (2) electrons and holes are separated and collected at the cathode and the anode; (3) the accumulated carriers generate a voltage across the cell; (4) the power produced is dissipated in the load connected across the cell.

• The separation of carriers is possible because of the intrinsic electric field of the depletion region — otherwise the pairs would simply recombine and no current would be produced.

• Characteristic in words: the illuminated V-I curve is drawn in the fourth quadrant, because the cell supplies current to the load instead of drawing it. Its intercept on the current axis is the short circuit current $I_{sc}$ and its intercept on the voltage axis is the open circuit voltage $V_{oc}$. Power delivered is zero at both ends and is maximum at one point in between, the maximum power point.

• Criteria for the material: band gap between $1.0\ \text{eV}$ and $1.8\ \text{eV}$, high optical absorption, good electrical conductivity, easy availability.

• Uses: charging batteries during the day so they supply power at night; power at remote places, for calculators, satellites and space stations; traffic signals; communication stations; lux meters to measure light intensity.

Distinguish: photodiode and solar cell

Light Emitting Diode (LED)

• An LED is a diode which emits light when a large forward current passes through it.

• Symbol in words: the ordinary diode symbol with two small arrows pointing away from it, showing emitted light.

• Construction: the n-region is more heavily doped than the p-region; the junction is encased in a dome-shaped transparent case so that light is emitted uniformly in all directions and internal reflections are minimised; metal electrodes on either side act as contacts, the longer leg being the anode; the device is made so that the emitted light is not reabsorbed, with recombination occurring at the surface for maximum light output.

• Working: in forward bias, electrons from the conduction band recombine with holes in the valence band, releasing enough energy to produce photons of monochromatic light. Because the layer is thin, a good number of these photons escape the junction. Light output is directly proportional to the forward current.

• Characteristic in words: similar to the forward characteristic of an ordinary diode — negligible current until the cut-in voltage, then a steep rise — except that the forward drop is much larger, $1.5\ \text{V}$ to $3.5\ \text{V}$.

• Colour depends on the compound semiconductor used: AlGaAs gives infrared, GaAsP red or yellow, AlGaP red or green, ZnSe blue.

• Advantages: energy efficient (up to $135$ lumens/watt), long lifetime ($50\,000$ hours or more), rugged solid state light with no filament, almost no warm-up (emits in nanoseconds), excellent colour rendering, environment friendly (no mercury), controllable brightness and colour.

• Disadvantages: hazardous blue light quality, temperature dependence, voltage sensitivity, high initial cost.

• Applications: burglar alarms, counters, optical communication, indicator lamps, cell phone displays, LED television, vehicle head lamps, decorative illumination, street lighting, seven segment displays.

• White LED: made by wavelength conversion — a blue LED excites a yellow phosphor, and the mixture of blue and yellow light appears white. The blue LED was invented by Shuji Nakamura (Nobel Prize in Physics, 2014).

16.4 Bipolar Junction Transistor (BJT)

• A junction transistor is a semiconductor device with two junctions and three terminals. The current is carried by both electrons and holes, so it is called bipolar.

• Two types: n-p-n (a thin p-type base between two n-type layers) and p-n-p (a thin n-type base between two p-type layers).

• Symbols in words: three leads meeting at a vertical bar (the base); the emitter lead carries an arrow. For n-p-n, the arrow points away from the base, out of the emitter. For p-n-p, the arrow points from the emitter towards the base. The arrow always shows the direction of conventional current.

• Two-diode analogy: a transistor behaves like two junction diodes connected back to back. It cannot, however, be made by joining two diodes.

• Biasing for normal (active) operation: emitter-base junction forward biased, collector-base junction reverse biased. The E-B junction then has low resistance and the C-B junction high resistance.

• Working of an n-p-n transistor: electrons are the majority carriers in the emitter. When $V_{BE}$ exceeds the barrier potential ($0.6$ to $0.7\ \text{V}$ for silicon), electrons are injected into the base. A few recombine in the base and form $I_B$ (about $5\%$ of $I_E$); the rest diffuse across the thin base into the collector-base depletion region and are swept into the collector by its field, forming $I_C$ (about $95\%$ of $I_E$). A p-n-p transistor works exactly the same way with holes as the carriers.

• $I_E = I_B + I_C$, and since $I_B$ is small, $I_C \approx I_E$.

• Three configurations: common emitter (CE), common base (CB), common collector (CC). The CE amplifier gives the highest current gain and power gain of the three, because the input impedance is low (forward biased junction) and the output impedance is high (reverse biased junction).

CE characteristics

• Input characteristic: variation of $I_B$ with $V_{BE}$, keeping $V_{CE}$ fixed. In words: current is very small until the barrier potential is overcome, after which the curve looks like that of a forward biased diode. Slope gives $r_i = \Delta V_{BE} / \Delta I_B$.

• Output characteristic: variation of $I_C$ with $V_{CE}$, keeping $I_B$ constant. In words: $I_C$ rises steeply for very small $V_{CE}$ and then becomes almost flat — $I_C$ is independent of $V_{CE}$ as long as the collector-emitter junction stays reverse biased. Each higher fixed $I_B$ gives a higher flat curve. Slope of the flat part gives $r_o = \Delta V_{CE} / \Delta I_C$.

Transistor as an amplifier (CE)

• An amplifier increases the amplitude of an alternating signal (voltage, current or power).

• Circuit in words: an n-p-n transistor in CE configuration; a DC bias $V_{BB}$ with $R_B$ in the base circuit, a supply $V_{CC}$ with the load resistance $R_L$ in the collector circuit, a small sinusoidal signal $v_i$ superimposed on the DC bias at the input, and a capacitor in the output to block the DC component so that only the amplified AC appears across the output.

• Working: the AC signal changes $V_{BE}$, hence $I_B$, hence $I_C$. Since $V_{CC} = V_{CE} + I_C R_L$ with $V_{CC}$ fixed, a change in $I_C$ forces an opposite change in $V_{CE}$, and this change is the amplified output.

• $A_v = -\dfrac{\beta_{AC} R_L}{r_i}$, negative sign meaning input and output are out of phase; $A_p = \beta_{AC} \times A_v$ in magnitude.

• A transistor amplifies power but does not generate power — the extra power comes from the DC supply $V_{CC}$, not from nothing.

16.5 Logic gates

• Analog signal: a continuously varying voltage or current, e.g. a sine wave. Digital signal: one that can take only two discrete values, e.g. a square wave. In a digital circuit these are low ($0\ \text{V}$) and high ($+5\ \text{V}$).

• Logic gate: a digital circuit with one or more inputs but only one output, which follows a certain logical relationship between input and output voltages. They are called gates because they control the flow of signal or information.

• Truth table: a table showing all possible combinations of the inputs with the corresponding outputs. It defines the function of the gate.

• Boolean expression: the mathematical statement giving the relationship between the input and output of a logic gate.

• Symbols in words: NOT is a triangle with a small circle (bubble) at its tip. AND is a D-shape, flat at the input side and round at the output. OR is a curved shield shape, concave at the input side and pointed at the output. NAND is the AND shape with a bubble at the output. NOR is the OR shape with a bubble at the output. X-OR is the OR shape with one extra curved line across the inputs.

• NAND and NOR are called universal gates because any gate can be implemented using only NAND gates or only NOR gates.

• The NOT gate is also known as an inverter, because it produces a negated version of the input at its output.

Traps that cost marks

• Half wave output frequency is $50\ \text{Hz}$, not $100\ \text{Hz}$. Only the full wave rectifier doubles the frequency. Many students swap the two.

• A full wave rectifier needs a centre tapped transformer. Leaving the centre tap out of the diagram loses marks even if the working is written correctly.

• Half wave efficiency $40.6\%$, full wave $81.2\%$ — full wave is twice half wave, not four times.

• A Zener diode is always used in reverse bias when regulating. Drawing it forward biased is a straight loss of marks.

• Never omit the series resistance $R_S$ in a Zener regulator circuit. Its job is to limit the Zener current and protect the diode; the load $R_L$ is in parallel with the Zener, not in series.

• Zener breakdown does not damage the diode. Ordinary reverse breakdown of a normal diode does. State the difference explicitly when asked how a Zener differs from an ordinary diode.

• A photodiode is reverse biased, a solar cell is unbiased. Do not describe a photodiode as forward biased.

• Dark current is not zero and is not caused by light — it flows because of minority carriers even in complete darkness.

• LED forward drop is $1.5$ to $3.5\ \text{V}$, not $0.7\ \text{V}$, and an LED must have a series resistance because its current rating is only a few tens of milliampere.

• In an LED it is the n-region that is more heavily doped, and the light comes from electron-hole recombination, not from heating of the junction.

• Base is thin and lightly doped — write both, not just one. That is what makes most carriers reach the collector instead of recombining in the base.

• In a transistor, $I_E$ is the largest current, not $I_C$. And $I_E = I_B + I_C$, so $I_B = I_E - I_C$ — the commonest slip in the numericals is subtracting the wrong pair.

• $\alpha_{DC} = I_C/I_E$ is always less than 1; $\beta_{DC} = I_C/I_B$ is large. Getting these two the wrong way round makes every gain calculation wrong.

• The negative sign in $A_v$ is physics, not an error: it records the $180^\circ$ phase difference between input and output. Drop it only when quoting a magnitude for the power gain.

• In the output characteristic, $I_B$ is held constant; in the input characteristic, $V_{CE}$ is held constant. Stating the wrong constant loses the mark.

• Write the truth table with all four input combinations in order, even if the question asks only for the Boolean expression — and remember the NAND output is high in three rows out of four, not one.

• NAND and NOR are universal, not AND and OR.