positively charged holes move in the direction of the field as the negatively charged electrons move in the opposite di- rection. If the semiconductor is attached to metal wires on either side, as in Figure 32.26, free electrons travel into the semiconductor from the right (eliminating holes that reach the right edge) and travel out of the semiconductor on the left (producing holes on the left edge). Electrons thus flow from right to left, making holes travel in the opposite direc- tion. Unlike the electrons, however, the holes never leave the semiconductor.
Doped semiconductors are classified according to the nature of the dopant. In a p-type semiconductor, the dopant has fewer valence electrons than the host atoms, contribut- ing positively charged holes as the free charge carriers (thus the p in the name). In an n-type semiconductor, the dopant has more valence electrons than the host atoms, contribut- ing negatively charged electrons as the free charge carriers (thus the n in the name). Substituting as few as ten dopant atoms per million silicon atoms produces conductivities ap- propriate for most electronic devices.
32.5 Is a piece of n-type silicon positively charged, nega- tively charged, or neutral?
32.4 Diodes, transistors, and logic gates
Although tailoring the conductivity of a single piece of semiconductor can be a useful procedure, the most versatile semiconductor devices combine doped layers that have dif- ferent types of charge carriers. The simplest such device is a diode, made by bringing a piece of p-type silicon into con- tact with a piece of n-type silicon (Figure 32.27a). Near the junction where the two pieces meet, free electrons from the n-type silicon wander into the p-type material, where they end up filling holes. This recombination process turns free electrons into bound electrons (that is, electrons not free to roam around in the material) and eliminates the holes. Like- wise, some of the holes in the p-type silicon wander into the n-type silicon, where they recombine with free electrons.
As recombination events take place, a thin region con- taining no free charge carriers (neither free electrons nor holes), called the depletion zone, develops at the junction.
Although there are no free charge carriers in this zone, the trapping of electrons on the p-side of the junction causes negative charge carriers that are nonmobile to accumulate there. Similarly, positive nonmobile charge carriers accumu- late on the n-side of the junction. As a result, the depletion zone consists of a negatively charged region and a positively
Figure 32.27 How a diode transmits current in one direction but blocks it in the other. If the battery is connected as shown in part d and produces a sufficiently strong electric field to compensate for the field of the depletion zone, there is a steady flow of both electrons and holes. (Remember, though: The holes never leave the semiconductor. Only the electrons enter and leave the semiconductor.)
(a) Pieces of p- and n-type doped silicon
p-type n-type
electrically neutral electrically neutral
ESbatt
ESdepl
(c) Battery connected so as to produce electric field in same direction as electric field in depletion zone; diode blocks current
Electric field due to battery broadens depletion zone, so diode blocks current.
electrically neutral electrically neutral ESdepl
(b) When the two are put in contact, a diode is formed
electron and hole recombine electric field due to recombination in depletion zone
depletion zone: insulator
electrically neutral electrically neutral
ESbatt
Electric field due to battery eliminates depletion zone, so diode conducts current.
(d) Battery connected with the opposite polarity; diode conducts current
electrons in electrons out
CONCEPTS
An ideal diode acts like a short circuit for current in the permitted direction and like an open circuit for current in the opposite direction. (That is not exactly how a diode be- haves, but it’s pretty close.)
32.7 Suppose a sinusoidally varying potential difference is applied across a diode connected in series with a resistor. Sketch the potential difference across the diode as a function of time, and then, on the same graph, sketch the current in the resistor as a function of time.
Example 32.4 Rectifier
Consider the arrangement of ideal diodes shown in Figure 32.29. This arrangement, called a rectifier, converts alternating cur- rent (AC) to direct current (DC). Sketch a graph showing, for a sinusoidally alternating source, the current in the resistor in the direction from b to c as a function of time.
charged region, and an electric field points across the deple- tion zone from the n-side to the p-side (Figure 32.27b).
As this electric field in the depletion zone of the diode increases, it becomes more difficult for free electrons and holes to cross the junction and recombine because the elec- tric field pushes free electrons back into the n-type silicon and pushes holes back into the p-type silicon. Consequent- ly, the depletion zone stops growing. Typically this region is less than a micrometer wide. Because of the lack of free charge carriers in it,
the depletion zone acts as an electrical insulator.
If we now connect the n-side of this diode to the positive terminal of a battery and the p-side to the negative terminal, the battery produces across the diode an electric field that points in the same direction as the electric field in the deple- tion zone (Figure 32.27c). The electric field of the battery pulls free electrons in the n-type silicon toward the posi- tive terminal and pulls holes in the p-type silicon toward the negative terminal, broadening the (nonconducting) deple- tion zone. Connecting the battery in this manner therefore causes no flow of charge carriers in the diode.
When the battery is connected in the opposite direction, however, the depletion zone narrows as the battery’s electric field pushes free electrons and holes toward the junction (Figure 32.27d). When the magnitude of the applied electric field created by the battery equals that of the electric field across the depletion zone, both types of free charge carriers can reach the junction, resulting in a current in the device carried both by free electrons and by holes.
As Figure 32.27 shows, a diode conducts current in one direction only: from the p-type side to the n-type side. The symbol for a diode is shown in Figure 32.28a; the triangle points in the direction in which the diode conducts current (from the p-side to the n-side).
32.6 In the diode of Figure 32.28a, which way do holes travel? Which way do electrons travel?
Figure 32.28 (a) Circuit symbol for a diode. (b) Schematic of a diode made using integrated-circuit technology.
p-type n-type (a)
(b) aluminum pads
p-n junction insulating layer
(SiO2)
p n diode
Figure 32.29 Example 32.4.
ℰ R
a
d b c
1 2
4 3
Figure 32.30
❶ GettinG Started Because the source is alternating, the cur- rent in the circuit periodically reverses direction. During part of the cycle the charge carriers creating the current flow clockwise through the source, and during another part of the cycle they flow counterclockwise. The diodes, however, conduct current in one direction only. I begin by making a sketch of the current between a and d, taking the direction from a to d to be positive (Figure 32.30a).
❷ deviSe plan In an ideal diode, the charge carriers can flow only in the direction in which the triangle in the diode symbol points. I shall determine which diodes allow charge carriers to
CONCEPTS 32.4 diodes, trAnsistors, And logic gAtes 871 left p-n junction merges with the depletion zone formed at the right p-n junction. The merged depletion zones form one wide depletion zone.
When a potential difference is applied across such a tran- sistor (Figure 32.32a), the depletion zone across junction 1 disappears, but that across junction 2 grows, shifting the depleted region toward the positive terminal of the battery.
While charge carriers can now cross junction 1 where the depletion zone has disappeared, the (shifted) depletion zone that still exists prohibits their movement, which means no current in the transistor. For historical reasons, the n-type region connected to the negative terminal is called the emit- ter, the n-type region connected to the positive terminal is called the collector, and the p-type layer is called the base. If the direction of the applied potential difference is reversed, the roles of the emitter and the collector are also reversed, and there is still no current in the transistor.
flow when the current direction is clockwise and when it is coun- terclockwise. I can then determine in each case which way the charge carriers flow through the resistor.
❸ execute plan When the current in the circuit is clock- wise, only diodes 1 and 3 are conducting, so the current direc- tion is abcd. When the current in the circuit is counterclockwise (iad60), only diodes 2 and 4 are conducting, so the current di- rection is dbca. At all instants, the current in the resistor points in the same direction: from b to c. This means that ibc is positive regardless of whether iad is positive or negative. Whenever iad is negative, the diodes reverse the direction of the current in the resistor, so ibc is always positive and my graph is as shown in Fig- ure 32.30b. ✔
❹ evaluate reSult The arrangement of diodes keeps the cur- rent from b to c always in the same direction, even though the current from a to d alternates in direction. It makes sense, then, that this arrangement of diodes is called a rectifier.
Figure 32.28b shows how a diode may be constructed as part of an integrated circuit (a computer chip, for example).
An aluminum pad (part of the metal wire connecting the diode to the rest of the circuit) is in contact with a small p-type region of silicon, which is surrounded by a larger n- type region that is in contact with a second aluminum pad.
The p-n junction forms at the interface between the p- and n-type regions. A thin layer of silicon oxide (SiO2) insulates the aluminum from the underlying silicon except where electrical contact is needed. On a modern computer chip, the entire device is only a few micrometers wide.
Another important circuit element in modern electron- ics is the transistor, a device that allows current control that is more precise than the on/off control of a diode. A transis- tor consists of a thin layer of one type of doped semicon- ductor sandwiched between two layers of the opposite type of doped semiconductor. Figure 32.31, for example, shows an npn-type bipolar transistor—a thin layer of p-type silicon sandwiched between two thicker regions of n-type silicon.*
If the p-type layer is thin, the depletion zone formed at the
* Transistors in which a thin layer of n-type silicon is sandwiched between pieces of p-type silicon, called pnp-type bipolar transistors, are also used.
Figure 32.31 Schematic of an npn-type bipolar transistor, showing charge distribution and depletion zones for both p-n junctions.
ESdepl ESdepl
p-type
n-type n-type
two merged depletion zones, one from each p-n junction
electrically neutral electrically neutral
Figure 32.32 How an npn-type bipolar transistor works.
(b) Potential difference also applied from base to emitter
Ic Ib
Ie
junction 2: Electric field due to battery broadens depletion zone. Current blocked.
electrically neutral electrically neutral junction 1: Depletion
zone eliminated.
flow of electrons base current
collector current Depletion zone narrow; electrons have
enough kinetic energy to pass through it.
1 2
1 2
(a) Potential difference applied from collector to emitter only
emitter
(n-type) base
(p-type) collector (n-type) ES
CONCEPTS
and so the collector current (and therefore the current in the device) is zero. When switch S is closed, the small cur- rent from base to emitter causes a large current from collec- tor to emitter that turns on the motor.
32.8 In a bipolar transistor, what relationship, if any, exists among Ib, Ic, and the emitter current Ie?
Figure 32.35 shows how an npn-type bipolar transis- tor can be fabricated. A drawback of this type of transis- tor, however, is that a continuous small current through the base is required to make the transistor conducting. For this reason, another type of transistor, called the field-effect tran- sistor, is used much more frequently. Figure 32.36a shows the configuration of one. Two n-type wells are made in a piece of p-type material. The p-type material between the two wells is covered with a nonconducting oxide layer (typically SiO2) and then with a metal layer called the gate. The two n-type wells are called the source and the drain (the n-type well that is kept at a higher potential is the drain).
Because of the depletion zones between the p-type and n-type materials, no charge carriers can flow from the source to the drain (or vice versa). The nonconducting layer between the gate and the p-type material prevents charge carriers from traveling between the gate and the rest of the device.
If the gate is given a positive charge, as in Figure 32.36b, the (positively charged) holes just underneath the gate are pushed away, forming underneath the gate an additional depletion zone that connects the depletion zones around the two n-p junctions. If the positive charge is made large enough, electrons from the source and from the drain are pulled underneath the gate, forming an n-type channel be- low the gate (Figure 32.36c). This channel allows charge carriers to flow between the source and the drain. The gate thus controls the current between the source and the drain, just as the base in an npn-type bipolar transistor controls the current between the emitter and the collector. (The dif- ference is that there is no current in the gate in a field-effect transistor.) Applying a positive charge to the gate is often referred to as putting a positive bias on the gate.
Figure 32.37a shows the circuit symbol for a field-effect transistor, and Figure 32.37b shows how this type of tran- sistor can be realized in an integrated circuit. This type of transistor has two advantages over the bipolar transistor The situation changes drastically when, in addition to
the potential difference between the emitter and the col- lector, a small potential difference is applied between the emitter and the base (Figure 32.32b). Adding this potential difference, called a bias or bias potential difference, makes the depletion zone much thinner than it is in Figure 32.32a because the formerly negatively charged region of this zone is brought to a positive potential, restoring mobile holes to that region. Because the emitter-base junction is conduct- ing (remember, the depletion zone at junction 1 has disap- peared), electrons now start flowing from the emitter to- ward the base. Once in the base, three things happen: (1) a small fraction of the electrons recombine with holes in the base, (2) electrons are attracted by the positive charge on the collector and have sufficient kinetic energy to pass straight through the very thin depletion zone, producing a collector current Ic, and (3) electrons diffuse through the base toward the positively charged end of the base, causing a small base current Ib. In a typical bipolar transistor, the collector cur- rent is 10 to 1000 times greater than the base current.
The circuit symbol for an npn-type bipolar transistor is shown in Figure 32.33.
Transistors are ubiquitous in modern electronics. In most applications, the transistor functions as either a switch or a current amplifier. If we consider Ib to be the input cur- rent and Ic the output current, the transistor acts as a switch in which Ib turns on and controls Ic. As a current amplifier, a small current Ib produces a much larger current Ic.
For electrical devices that draw large currents, it is useful to switch the device on and off with a mechanical switch wired in parallel with the device, rather than in series, so that the current in the device does not have to pass through the switch. Figure 32.34 shows a circuit that utilizes such switching. When switch S is open, the base current is zero,
Figure 32.33 Circuit symbol for an npn-type bipolar transistor.
npn-type bipolar transistor
collector
base
emitter
Figure 32.34 Circuit in which a bipolar transistor is used to turn a motor on and off.
R S
Ib = 0
Ic = 0
Ie motor
transistor ℰ
Figure 32.35 Schematic of an npn-type bipolar transistor made using integrated-circuit technology.
collector emitter base
n p-type
n-type insulating layer
(SiO2)
CONCEPTS 32.4 diodes, trAnsistors, And logic gAtes 873
when both inputs are at positive potential with respect to ground. In an OR gate, the output potential is nonzero when either input potential is positive. The symbols used for these gates in circuit diagrams are shown in Figure 32.38; the inputs are on the left, and the output is on the right. In analyzing these circuits, we’ll make the simplifying assump- tion that a transistor is just a switch that is open (off) when the potential of the gate is either at ground or negative with respect to ground and is closed (on) when the gate is at a positive potential.
shown in Figure 32.35. First, all the terminals in the field- effect transistor are on the same side of the chip, making fabrication in integrated circuits much easier. Second, the current between the source and the drain is controlled by the charge on the gate, allowing a potential difference rather than a current to be used to control the source-drain cur- rent. Because no current is leaving the gate, no energy is re- quired to keep current flowing from the source to the drain.
Field-effect transistors are widely used in devices called logic gates, which are the building blocks of computer pro- cessors and memory. A logic gate takes two input signals and provides an output after performing a logic operation on the input signals. For example, in a so-called AND gate, the output potential is nonzero with respect to ground only
Figure 32.36 How a field-effect transistor works.
n-type channel (a) Field-effect transistor with uncharged gate
(b) Small positive charge on gate attracts electrons to gate and extends depletion zone below gate
(c) Large positive charge on gate attracts more electrons to gate and causes n-type channel, which connects source and drain
insulating layer source
(n-type well) drain
(n-type well) gate (uncharged)
p-type depletion
zone
Uncharged gate: Separate depletion zones at p-n junctions.
Small gate charge causes depletion zone to extend beneath gate.
Strong gate charge pushes depletion zone away; conducting n-type channel now connnects source and drain.
Figure 32.37 (a) Circuit symbol for a field-effect transistor. (b) Sche- matic of a field-effect transistor made using integrated-circuit technology.
drain
gate source
insulating layer (SiO2)
p-type
n-type n-type
source gate drain
(a)
(b)
field-effect transistor
Figure 32.38 Circuit symbols for AND and OR logic gates.
A B
A
AND A B B OR A B
32.9 Circuit diagrams for two logic gates are shown in Figure 32.39. Which is the AND gate, and which is the OR gate?
Explain briefly how each one works.
Figure 32.39 Checkpoint 32.9
(a) (b)
transistor 1
transistor 2 output +5 V
A
B
transistor 1
output +5 V
A
B transistor 2
self-quiz
1. At the instant shown in Figure 32.40, the potential differ- ence across the capacitor is half its maximum value and the charge on the plates is increasing. Draw the direction of the current and sketch the magnetic field at this instant. Is the magnitude of current increasing or decreasing?
2. Construct a phasor diagram representing the current and potential difference in Figure 32.10 at t=T>4, T>2, and 3T>4.
3. Figure 32.41 shows the time-varying potential difference and current for the circuit of Figure 32.8. At the instant labeled ta, what are the charge on the capacitor plates and the direction of the current?
Self-quiz
Figure 32.40
E
Figure 32.41
T ta t
i vC
Figure 32.42
p-type n-type
aluminum SiO2
Figure 32.43
4. Is there any current in a diode connected as shown in Figure 32.42?
Answers:
1. Your sketch should show the current directed counterclockwise. The magnetic field in the center of the coil points up the page according to the right-hand dipole rule (assuming we are looking down on the top of the coil in Figure 32.40). Because the current is zero when the capacitor has maximum charge, the magnitude of the current is decreasing at the instant shown in Figure 32.40.
2. See Figure 32.43. At t=T>4 the potential difference phasor VC points along the positive y axis because the potential difference reaches its maximum positive value at this instant, and the current phasor I points along the negative x axis because it leads the current by 90°. Each quarter cycle both phasors rotate 90° counterclockwise.
3. Because the potential difference across the capacitor is zero at instant ta, the charge on the plates must be zero.
The current is a maximum at this instant and is directed clockwise.
4. Yes. The holes in the p-type material move away from the positive terminal, and the electrons move toward it.
According to Figure 32.27d, this flow shrinks the depletion zone, the charge carriers can flow, and so there is a current.