Solid-State Electronic Devices: High-Frequency, High-Power and Nanoelectronic Devices [part 1]

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The diodes and transistors we have discussed thus far constitute the vast majority of semiconductor devices. However, there are a number of specialty devices that deserve our attention, and novel devices and materials can form the basis of future applications. In this section we describe two types of negative conductance devices, with applications in high-frequency circuits. Then we will discuss the semiconductor controlled rectifier (SCR), an important switching device which can handle large amounts of power. Finally we will consider new materials and device applications which depend on some very interesting extensions of the physics of materials we used in previous sections. These new materials and new applications of physics will likely form the basis for the electronics of the future.

GOALS:

1. Understand how tunneling, transit time effects, and electron transfer can lead to NDR

2. Understand SCRs

3. Describe how IGFETs switch power

4. Advances in a few nano-electronic logic and memory devices

1. Tunnel Diodes

The tunnel diode is a p-n junction device that operates in certain regions of its I-V characteristic by the quantum mechanical tunneling of electrons through the potential barrier of the junction. The tunneling process for reverse current is essentially the Zener effect, although negligible reverse bias is needed to initiate the process in tunnel diodes. As we shall see in this section, the tunnel diode (often called the Esaki diode after L. Esaki, who received the Nobel Prize in 1973 for his work on the effect) exhibits the important feature of negative resistance over a portion of its I-V characteristic.

1.1 Degenerate semiconductors

Thus far, we have discussed the properties of relatively pure semiconductors; any impurity doping represented a small fraction of the total atomic density of the material. Since the few impurity atoms were so widely spaced throughout the sample, we could be confident that no charge transport could take place within the donor or acceptor levels themselves. At high doping, the impurities are so close together that we can no longer consider the donor level as being composed of discrete, non-interacting energy states.

Instead, the donor states form a band, which may overlap the bottom of the conduction band. If the conduction-band electron concentration n exceeds the effective density of states Nc, the Fermi level is no longer within the band gap, but lies within the conduction band. When this occurs, the material is called degenerate n-type. The analogous case of degenerate p-type material occurs when the acceptor concentration is very high and the Fermi level lies in the valence band. We recall that the energy states below EF are mostly filled and states above EF are empty, except for a small distribution dictated by the Fermi statistics. Thus, in a degenerate n-type sample, the region between Ec and EF is for the most part filled with electrons, and in a degenerate p-type sample, the region between Ev and EF is almost completely filled with holes.

A p-n junction between two degenerate semiconductors is illustrated in terms of energy bands in FIG. 1a. This is the equilibrium condition, for which the Fermi level is constant throughout the junction. We notice that EFp lies below the valence-band edge on the p side, and EFn is above the conduction-band edge on the n side. Thus, the bands must overlap on the energy scale in order for EF to be constant. This overlapping of bands is very important; it means that, with a small forward or reverse bias, filled states and empty states appear opposite each other, separated by essentially the width of the depletion region. If the metallurgical junction is sharp, the depletion region will be very narrow for such high-doping concentrations, and the electric field at the junction will be quite large. Hence, the conditions for electron tunneling are met: filled and empty states separated by a narrow potential barrier of finite height. In FIG. 1, the bands are shown filled to the Fermi level for convenience of illustration, with the understanding that a distribution is implied.

Since the bands overlap under equilibrium conditions, a small reverse bias (FIG. 1b) allows electron tunneling from the filled valence-band states below EFp to the empty conduction-band states above EFn. This condition is similar to the Zener effect, except that no bias is required to create the condition of overlapping bands. As the reverse bias is increased, EFn continues to move down the energy scale with respect to EFp, placing more filled states on the p side opposite empty states on the n side. Thus, the tunneling of electrons from p to n increases with increasing reverse bias. The resulting conventional current is opposite to the electron flow-that is, from n to p.

At equilibrium (FIG. 1a), there is equal tunneling from n to p and from p to n, giving a zero net current.


FIG. 1 Tunnel diode band diagrams and I-V characteristics for various biasing conditions: (a) equilibrium (zero bias) condition, no net tunneling; (b) small reverse bias, electron tunneling from p to n; (c) small forward bias, electron tunneling from n to p; (d) increased forward bias, electron tunneling from n to p decreases as bands pass by each other.

When a small forward bias is applied (FIG. 1c), EFn moves up in energy with respect to E by the amount qV. Thus, electrons below E on the n side are placed opposite empty states above EFp on the p side.

Electron tunneling occurs from n to p as shown, with the resulting conventional current from p to n. This forward-tunneling current continues to increase with increased bias as more filled states are placed opposite empty states. However, as EFn continues to move up with respect to EFp, a point is reached at which the bands begin to pass by each other. When this occurs, the number of filled states opposite empty states decreases. The resulting decrease in tunneling current is illustrated in FIG. 1d. This region of the I-V characteristic is important in that the decrease in tunneling current with increased bias produces a region of negative slope; that is, the dynamic resistance dV/dI is negative. This negative-resistance region is useful in oscillators.


FIG. 2 Band diagram (a) and I-V characteristic (b) for the tunnel diode beyond the tunnel current region. In (b), the tunneling component of current is shown by the solid curve and the diffusion current component is dashed.

If the forward bias is increased beyond the negative-resistance region, the current begins to increase again (FIG. 2). Once the bands have passed each other, the characteristic resembles that of a conventional diode. The forward current is now dominated by the diffusion current-electrons surmounting their potential barrier from n to p and holes surmounting their potential barrier from p to n. Of course, the diffusion current is present in the forward tunneling region, but it is negligible compared with the tunneling current.


FIG. 3 Total tunnel diode characteristic.

The total tunnel diode characteristic (FIG. 3) has the general shape of an N (if a little imagination is applied); therefore, it is common to refer to this characteristic as exhibiting a type-N negative resistance. It is also called a voltage-controlled negative resistance, meaning that the current decreases rapidly at some critical voltage (in this case, the peak voltage Vp, taken at the point of maximum forward tunneling).

The values of peak tunneling current Ip and valley current Iv (FIG. 3) determine the magnitude of the negative-resistance slope for a diode of given material. For this reason, their ratio Ip / Iv is often used as a figure of merit for the tunnel diode. Similarly, the ratio V p/Vf is a measure of the volt age spread between the two positive-resistance regions.

The negative resistance of the tunnel diode can be used in a number of ways to achieve oscillation and other circuit functions. The fact that the tunneling process does not present the time delays of drift and diffusion makes the tunnel diode a natural choice for certain high-speed circuits. However, the tunnel diode has not achieved widespread application, because of its relatively low current operation and competition from other devices.

2. The IMPATT Diode

In this section, we describe a type of microwave negative-conductance device that operates by a combination of carrier injection and transit-time effects.

Diodes with simple p-n junction structure, or with variations on that structure, are biased to achieve tunneling or avalanche breakdown, with an a-c voltage superimposed on the d-c bias. The carriers generated by the injection process are swept through a drift region to the terminals of the device. We shall see that the a-c component of the resulting current can be approximately 180° out of phase with the applied voltage under proper conditions of bias and device configuration, giving rise to negative conductance and oscillation in a resonant circuit. Transit-time devices can convert d-c to micro wave a-c signals with high efficiency and are very useful in the generation of microwave power for many applications.


FIG. 4 The Read diode: (a) basic device configuration; (b) electric field distribution in the device under reverse bias.

The original suggestion for a microwave device employing transit-time effects was made by W. T. Read and involved an n+ - p - i - p+ structure such as that shown in FIG. 4. This device operates by injecting carriers into the drift region and is called an impact avalanche transit-time (IMPATT) diode.

Although IMPATT operation can be obtained in simpler structures, the Read diode is best suited for illustration of the basic principles. The device consists essentially of two regions: (1) the n+ - p region, at which avalanche multiplication occurs, and (2) the i (essentially intrinsic) region, through which generated holes must drift in moving to the p+ contact. Similar devices can be built in the p+ - n - i - n+ configuration, in which electrons resulting from avalanche multiplication drift through the i region, taking advantage of the higher mobility of electrons compared with holes.

Although detailed calculations of IMPATT operation are complicated and generally require computer solutions, the basic physical mechanism is simple. Essentially, the device operates in a negative-conductance mode when the a-c component of current is negative over a portion of the cycle during which the a-c voltage is positive, and vice versa. The negative conductance occurs because of two processes, causing the current to lag behind the voltage in time: (1) a delay due to the avalanche process and (2) a further delay due to the transit time of the carriers across the drift region. If the sum of these delay times is approximately one-half cycle of the operating frequency, negative conductance occurs and the device can be used for oscillation and amplification.

From another point of view, the a-c conductance is negative if the a-c component of carrier flow drifts opposite to the influence of the a-c electric field. For example, with a d-c reverse bias on the device of FIG. 4, holes drift from left to right (in the direction of the field), as expected. Now, if we superimpose an a-c voltage such that E decreases during the negative half-cycle, we would normally expect the drift of holes to decrease also.

However, in IMPATT operation, the drift of holes through the i region actually increases while the a-c field is decreasing. To see how this happens, let us consider the effects of avalanche and drift for various points in the cycle of applied voltage (FIG. 5).

To simplify the discussion, we shall assume that the p region is very narrow and that all the avalanche multiplication takes place in a thin region near the n+ - p junction. We shall approximate the field in the narrow p region by a uniform value. If the d-c bias is such that the critical field for avalanche Ea is just met in the n+ - p space charge region (FIG. 5a), avalanche multiplication begins at t = 0. Electrons generated in the avalanche move to the n+ region, and holes enter the i drift region. We assume that the device is mounted in a resonant microwave circuit so that an a-c signal can be maintained at a given frequency. As the applied a-c voltage goes positive, more and more holes are generated in the avalanche region. In fact, the pulse of holes (dotted line) generated by the multiplication process continues to grow as long as the electric field is above Ea (FIG. 5b). It can be shown that the particle current due to avalanche increases exponentially with time while the field is above the critical value. The important result of this growth is that the hole pulse reaches its peak value, not at p/2, when the voltage is maximum, but at p (FIG. 5c). Therefore, there is a phase delay of p/2 inherent in the avalanche process itself. A further delay is provided by the drift region. Once the avalanche multiplication stops (vt > p), the pulse of holes simply drifts toward the p+ contact (FIG. 5d). But during this period, the a-c terminal voltage is negative. Therefore, the dynamic conductance is negative, and energy is supplied to the a-c field.


FIG. 5 Time dependence of the growth and drift of holes during a cycle of applied voltage for the Read diode: (a) xt = 0; (b) xt = r/2; (c) xt = r (d) xt = 3r/2.

The hole pulse is sketched as a dotted line on the field diagram.

(In general, vd is a function of the local electric field. However, these devices are normally operated with fields in the i region sufficiently large that holes drift at their scattering-limited velocity. In this case, the drift velocity does not vary appreciably with the a-c variations in the field.)

If the length of the drift region is chosen properly, the pulse of holes is collected at the p+ contact just as the voltage cycle is completed, and the cycle then repeats itself. The pulse will drift through the length L of the i region during the negative half-cycle if we choose the transit time to be one-half the oscillation period; that is, (eqn. 1) where f is the operating frequency and vd is the drift velocity for holes.

Therefore, for a Read diode, the optimum frequency is one-half the inverse transit time vd/L of holes across the drift region. In choosing an appropriate resonant circuit for this device, the parameter L is critical. For example, taking vd = 10^7 cm/s for Si, the optimum operating frequency for a device with an i region length of 5 mm is f = 10^7 /2(5 * 10^-4 ) = 10^10 Hz. Negative resistance is exhibited by an IMPATT diode for frequencies somewhat above and below this optimum frequency for exact 180° phase delay. A careful analysis of the small-signal impedance shows that the minimum frequency for negative conductance varies as the square root of the d-c bias current for frequencies in the neighborhood of that described by Eq. (eqn. 1).

Although the Read diode of FIG. 4 displays most directly the operation of IMPATT devices, simpler structures can be used, and in some cases they may be more efficient. Negative conductance can be obtained in simple p-n junctions or in p-i-n devices. In the case of the p-i-n, most of the applied voltage occurs across the i region, which serves as a uniform avalanche region and also as a drift region. Therefore, the two processes of delay due to avalanche and drift, which were separate in the case of the Read diode, are distributed within the i region of the p-i-n. This means that both electrons and holes participate in the avalanche and drift processes.

3. The Gunn Diode

Microwave devices that operate by the transferred-electron mechanism are often called Gunn diodes, after J. B. Gunn, who first demonstrated one of the forms of oscillation. In the transferred-electron mechanism, the conduction electrons of some semiconductors are shifted from a state of high mobility to a state of low mobility by the influence of a strong electric field. Negative conductance operation can be achieved in a diode for which this mechanism applies, and the results are varied and useful in microwave circuits.

First, we shall describe the process of electron transfer and the resulting change in mobility. Then we shall consider some of the modes of operation for diodes using this mechanism.

3.1 The transferred-electron mechanism

Earlier, we discussed the non-linearity of mobility at high electric fields. In most semiconductors, the carriers reach a scattering-limited velocity, and the plot of velocity vs. field saturates at high fields. In some materials, however, the energy of electrons can be raised by an applied field to the point that they transfer from one region of the conduction band to another, higher-energy region. For some band structures, negative conductivity can result from this electron transfer. To visualize the process, let us recall the discussion of energy bands.

[These devices are called diodes, since they are two-terminal devices. No p-n junction is involved, however. Gunn effect and related devices utilize bulk instabilities, which do not require junctions.]


FIG. 6 Simplified band diagram for GaAs, illustrating the lower (G) and upper (L) valleys in the conduction band.

[We have shown only one satellite valley for convenience; there are other equivalent valleys for different directions in k-space. The effective mass ratio of 0.55 refers to the combined satellite valleys.]

A simplified E(k) band structure for GaAs is shown in FIG. 6 for reference; some of the detail has been omitted in this diagram to isolate the essential features of electron transfer between bands. In n-type GaAs, the valence band is filled and the central valley (or minimum) of the conduction band at G(k = 0) normally contains the conduction electrons. There is a set of subsidiary minima at L (sometimes called satellite valleys) at higher energy, but these minima are many kT above the central valley and are normally unoccupied. Therefore, the direct band gap at G and the energy bands centered at k = 0 are generally used to describe the conduction processes in GaAs. This was true, for example, of GaAs lasers, discussed earlier.

The presence of the satellite valleys at L is crucial to the Gunn effect, how ever. If the material is subjected to an electric field above some critical value (about 3000 V/cm), the electrons in the central G valley of FIG. 6 gain more energy than the 0.30 eV separating the valleys; therefore, there is considerable scattering of electrons into the higher-energy satellite valley at L.

Once the electrons have gained enough energy from the field to be transferred into the higher-energy valley, they remain there as long as the field is greater than the critical value. The explanation for this involves the fact that the combined effective density of states for the upper valleys is much greater than for the central valley (by a factor of about 24). Although we shall not prove it here, it seems reasonable that the probability of electron scattering between valleys should depend on the density of states available in each case and that scattering from a valley with many states into a valley with few states would be unlikely. As a result, once the field increases above the critical value, most conduction electrons in GaAs reside in the satellite valleys and exhibit properties typical of that region of the conduction band. In particular, the effective mass for electrons in the higher L valleys is almost eight times as great as in the central valley because of the smaller band curvature, and the electron mobility is much lower. This is an important result for the negative conductivity mechanism: As the electric field is increased, the electron velocity increases until a critical field is reached; then the electrons slow down with further increase in field. The electron transfer process allows electrons to gain energy at the expense of velocity over a range of values of the electric field. Taking the current density as qvdn, we see clearly that current also drops in this range of increasing field, giving rise to a negative differential conductivity dJ/dE.

A possible dependence of electron velocity vs. electric field for a material capable of electron transfer is shown in FIG. 7. For low values of field, the electrons reside in the lower (G) valley of the conduction band, and the mobility (mG = vd/E) is high and constant with field. For high values of field, electrons transfer to the satellite valleys, where their velocity is smaller and their mobility lower. Between these two states is a region of negative slope on the plot of vd vs. E, indicating a negative differential mobility dvd /dE = -o *.

The actual dependence of electron drift velocity on electric field for GaAs and InP is shown in FIG. 8. The negative resistance due to electron transfer occurs at a higher field for InP, and the electrons achieve a higher peak velocity before transfer from G to L occurs.

[This is a rather crude approximation, since o* is not a constant, but varies considerably with field; the negative dielectric relaxation time therefore changes with time as the domain grows.]

The existence of a drop in mobility with increasing electric field and the resultant possibility of negative conductance were predicted by Ridley and Watkins and by Hilsum several years before Gunn demonstrated the effect in GaAs. The mechanism of electron transfer is therefore often called the Ridley-Watkins-Hilsum mechanism. This negative conductivity effect depends only on the bulk properties of the semiconductor and not on junction or surface effects. It is therefore called a bulk negative differential conductivity (BNDC) effect.


FIG. 7 A possible characteristic of electron drift velocity vs. field for a semiconductor exhibiting the transferred-electron mechanism.

μΓ = Mobility in central (Γ) valley

μL = Mobility in satellite (L) valley

μ* = Average magnitude of negative differential mobility during transition


FIG. 8 Electron drift velocity vs. field for GaAs and InP.

3.2 Formation and Drift of Space Charge Domains

If a sample of GaAs is biased such that the field falls in the negative conductivity region, space charge instabilities result, and the device cannot be maintained in a d-c stable condition. To understand the formation of these instabilities, let us consider first the dissipation of space charge in the usual semiconductor. It can be shown from treatment of the continuity equation that a localized space charge dies out exponentially with time in a homogeneous sample with positive resistance (Ex. 3). If the initial space charge is Q0, the instantaneous charge is


(eqn. 2)

where td = g/s is called the dielectric relaxation time. Because of this process, random fluctuations in carrier concentration are quickly neutralized and space charge neutrality is a good approximation for most semiconductors in the usual range of conductivities. For example, the dielectric relaxation time for a 1.0 ohm - cm Si or GaAs sample is approximately 10^-12 s.

Equation (eqn. 2) gives a rather remarkable result for cases in which the conductivity is negative. For these cases, td is negative also and space charge fluctuations build up exponentially in time rather than dying out. This means that normal random fluctuations in the carrier distribution can grow into large space charge regions in the sample. Let us see how this occurs in a GaAs sample biased in the negative conductivity regime. The velocity-field diagram for n-type GaAs is illustrated in FIG. 9a. If we assume a small shift of electron concentration in some region of the device, a dipole layer can form as shown in FIG. 9b. Under normal conditions, this dipole would die out quickly. However, under conditions of negative conductivity, the charge within the dipole, and therefore the local electric field, builds up as shown in FIG. 9c. Of course, this buildup takes place in a stream of electrons drifting from the cathode to the anode, and the dipole (now called a domain) drifts along with the stream as it grows. Eventually, the drifting domain will reach the anode, where it gives up its energy as a pulse of cur rent in the external circuit.


FIG. 9 Buildup and drift of a space charge domain in GaAs: (a) velocity-field characteristic for n-type GaAs; (b) formation of a dipole; (c) growth and drift of a dipole for conditions of negative conductivity.

During the initial growth of the domain, an increasing fraction of the applied voltage appears across it, at the expense of electric field in the rest of the bar. As a result, it is unlikely that more than one domain will be present in the bar at a time; after the formation of one domain, the electric field in the rest of the bar quickly drops below the threshold value for negative conductivity. If the bias is d-c, the field outside the moving domain will stabilize at a positive conductivity point such as A in FIG. 9a, and the field inside the domain will stabilize at the high-field value B. A small dipole forms from a random noise fluctuation (or, more likely, at a permanent nucleation site such as a crystal defect, a doping inhomogeneity, or the cathode itself), and this dipole grows and drifts down the bar as a domain. The formation of stable domains is not the only mode of operation for transferred electron devices. Nor is it the most desirable mode for most applications, since the resulting short pulses of current are inefficient sources of microwave power. Removal of heat is a very serious problem in these devices. The power dissipation may be 10^7 W/cm^3 or greater (Prob. 10.5), giving rise to considerable heating of the sample. If the application does not require continuous operation, peak powers of hundreds of watts can be achieved in pulses of microwave oscillation.

4. The P-N-P-N Diode

One of the most common applications of electronic devices is in switching, which requires the device to change from an "off" or blocking state to an "on" or conducting state. We have discussed the use of transistors in this application, in which base current drives the device from cutoff to saturation. Similarly, diodes and other devices can be used to serve as certain types of switches. There are a number of important switching applications that require a device remain in the blocking state under forward bias until switched to the conducting state by an external signal. Several devices that fulfill this requirement have been developed, including the semiconductor controlled rectifier (SCR).

These devices are typified by a high impedance (the "off" condition) under forward bias until a switching signal is applied; after switching, they exhibit low impedance (the "on" condition). The signal required for switching can be varied externally; therefore, the devices can be used to block or pass currents at predetermined levels.

The SCR is a four-layer (p-n-p-n) structure that effectively blocks cur rent through two terminals until it is turned on by a small signal at a third terminal. We shall begin by investigating the current flow in a two-terminal p-n-p-n device and then extend the discussion to include triggering by a third terminal. We shall see that the p-n-p-n structure can be considered for many purposes as a combination of p-n-p and n-p-n transistors, and the analysis in Section 7 can be used as an aid in understanding its behavior.


FIG. 10 A two-terminal p-n-p-n device: (a) basic structure and common circuit symbol; (b) I-V characteristic.

4.1 Basic structure

First we consider a four-layer diode structure with an anode terminal A at the outside p region and with a cathode terminal K at the outside n region (FIG. 10a). We shall refer to the junction nearest the anode as j1, the center junction as j2, and the junction nearest the cathode as j3. When the anode is biased positively with respect to the cathode (v positive), the device is forward biased. However, as the I-V characteristic of FIG. 10b indicates, the forward-biased condition of this diode can be considered in two separate states: the high-impedance, or forward-blocking, state and the low- impedance, or forward-conducting, state. In the device illustrated here, the forward I-V characteristic switches from the blocking to the conducting state at a critical peak forward voltage V p.

[Since Si is the material commonly used for this device, it is often called a silicon-controlled rectifier.]

We can anticipate the discussion of conduction mechanisms that follows by noting that an initial positive voltage v places j1 and j3 under forward bias and the center junction j2 under reverse bias. As v is increased, most of the forward voltage in the blocking state must appear across the reverse-biased junction j2. After switching to the conducting state, the voltage from A to K is very small (less than 1 V), and we conclude that, in this condition, all three junctions must be forward biased. The mechanism by which j2 switches from reverse bias to forward bias is the subject of much of the discussion that follows.

In the reverse-blocking state (v negative), j1 and j3 are reverse biased and j2 is forward biased. Since the supply of electrons and holes to j2 is restricted by the reverse-biased junctions on either side, the device current is limited to a small saturation current arising from the thermal generation of electron-hole pairs (EHPs) near j1 and j3. The current remains small in the reverse-blocking condition until avalanche breakdown occurs at a large reverse bias. In a properly designed device, with guards against surface breakdown, the reverse breakdown voltage can be several thousand volts. We shall now consider the mechanism by which this device, often called a Shockley diode, switches from the forward-blocking state to the forward-conducting state.

4.2 The two-transistor analogy


FIG. 11 Two-transistor analogy of the p-n-p-n diode.

The four-layer configuration of FIG. 10a suggests that the p-n-p-n diode can be considered as two coupled transistors: j1 and j2 form the emitter and collector junctions, respectively, of a p-n-p transistor; similarly, j2 and j3 form the collector and emitter junctions of an n-p-n transistor. (Note that the emitter of the n-p-n is on the right, which is the reverse of what we usually draw.) In this analogy, the collector region of the n-p-n is in common with the base of the p-n-p, and the base of the n-p-n serves as the collector region of the p-n-p. The center junction j2 serves as the collector junction for both transistors.

This two-transistor analogy is illustrated in FIG. 11. The collector current iC1 of the p-n-p transistor drives the base of the n-p-n, and the base current iB1 of the p-n-p is dictated by the collector current iC2 of the n-p-n. If we associate an emitter-to-collector current transfer ratio a with each transistor, we can use the analysis in Section 7 to solve for the current i.

Using Eq. (7-37b) with c1 = cN for the p-n-p, c2 = cN for the n-p-n, and with IC01 and IC02 for the respective collector saturation currents, we have


(eqn. 3a)

(eqn. 3b)

But the sum of iC1 and iC2 is the total current through the device:

iC1 + iC2 = i (eqn. 4)

Taking this sum in Eq. (eqn. 3) we have


(eqn. 5)

As Eq. (eqn. 5) indicates, the current i through the devices is small (approximately the combined collector saturation currents of the two equivalent transistors) as long as the sum c1 + c2 is small compared with unity. As the sum of the alphas approaches unity, the current i increases rapidly. The current does not increase without limit as Eq. (eqn. 5) implies, however, because the derivation is no longer valid as c1 + c2 approaches unity. Since j2 becomes forward biased in the forward-conducting state, both transistors become saturated after switching. The two transistors remain in saturation in the forward-conducting state.

4.3 Variation of alpha with injection

Since the two-transistor analogy implies that switching involves an increase in the alphas to the point that c1 + c2 approaches unity, it may be helpful to review how alpha varies with injection for a transistor. The emitter-to-collector current transfer ratio c is given in Section 7.2 as the product of the emitter injection efficiency i and the base transport factor B. An increase in c with injection can be caused by increases in either of these factors or both. At very low currents (such as in the forward-blocking state of p-n-p-n diodes), i is usually dominated by recombination in the transition region of the emitter junction. As the current is increased, injection across the junction begins to dominate over recombination within the transition region, and g increases. There are several mechanisms by which the base transport factor B increases with injection, including the saturation of recombination centers as the excess carrier concentration becomes large.

Whichever mechanism dominates, the increase in c1 + c2 required for switching of the p-n-p-n diode is accomplished automatically. In general, no special design is required to maintain c1 + c2 smaller than unity during the forward-blocking state; this requirement is usually met at low currents by the dominance of recombination within the transition regions of j1 and j3.


FIG. 12 Three bias states of the p-n-p-n diode: (a) the forward blocking state; (b) the forward conducting state; (c) the reverse blocking state.

4.4 Forward-blocking state

When the device is biased in the forward-blocking state (FIG. 12a), the applied voltage v appears primarily across the reverse-biased junction j2.

Although j1 and j3 are forward biased, the current is small. The reason for this becomes clear if we consider the supply of electrons available to n1 and holes to p2. Focusing attention first upon j1, let us assume that a hole is injected from p1 into n1. If the hole recombines with an electron in n1 (or in the j1 transition region), that electron must be resupplied to the n1 region to maintain space charge neutrality. The supply of electrons in this case is severely restricted, however, by the fact that n1 is terminated in j2, a reverse-biased junction. In a normal p-n diode, the n region is terminated in an ohmic contact, so that the supply of electrons required to match recombination (and injection into p) is unlimited. In this case, however, the electron supply is restricted essentially to those electrons generated thermally within a dif fusion length of j2. As a result, the current passing through the j1 junction is approximately the same as the reverse saturation current of j2. A similar argument holds for the current through j3; holes required for injection into n2 and to feed recombination in p2 must originate in the saturation current of the center junction j2. The applied voltage v divides appropriately among the three junctions to accommodate this small current throughout the device.

In this discussion, we have tacitly assumed that the current crossing j2 is strictly the thermally generated saturation current. This implies that electrons injected by the forward-biased junction j3 do not diffuse across p2 in any substantial numbers, to be swept across the reverse-biased junction into n1 by transistor action. This is another way of saying that a2 (for the "n-p-n transistor") is small. Similarly, the supply of holes to p2 is primarily thermally generated, since few holes injected at j1 reach j2 without recombination (i.e., a1 is small for the "p-n-p"). Now we can see physically why Eq. (eqn. 5) implies a small current while c1 + c2 is small: Without the trans port of charge provided by transistor action, the thermal generation of carriers is the only significant source of electrons to n1 and holes to p2.

4.5 Conducting state

The charge transport mechanism changes dramatically when transistor action begins. As c1 + c2 approaches unity by one of the mechanisms described, many holes injected at j1 survive to be swept across j2 into p2. This helps to feed the recombination in p2 and to support the injection of holes into n2.

Similarly, the transistor action of electrons injected at j3 and collected at j2 supplies electrons for n1. Obviously, the current through the device can be much larger once this mechanism begins. The transfer of injected carriers across j2 is regenerative, in that a greater supply of electrons to n1 allows greater injection of holes at j1 while maintaining space charge neutrality; this greater injection of holes further feeds p2 by transistor action, and the process continues to repeat itself.

If c1 + c2 is large enough, so that many electrons are collected in n1 and many holes are collected in p2, the depletion region at j2 begins to decrease.

Finally, the reverse bias disappears across j2 and is replaced by a forward bias, in analogy with a transistor that is biased deep in saturation. When this occurs, the three small forward-bias voltages appear as shown in FIG. 12b. Two of these voltages essentially cancel in the overall v, so that the forward voltage drop of the device from anode to cathode in the conducting state is not much greater than that of a single p-n junction. For Si, this forward drop is less than 1 V, until ohmic losses become important at high current levels.

We have discussed the current transport mechanisms in the forward blocking and forward-conducting states, but we have not indicated how switching is initiated from one state to the other. Basically, the requirement is that the carrier injection at j1 and j2 must somehow be increased so that significant transport of injected carriers across j2 occurs. Once this transport begins, the regenerative nature of the process takes over and switching is completed.

4.6 Triggering mechanisms

The most common method of triggering a two-terminal p-n-p-n is simply to raise the bias voltage to the peak value Vp. This type of voltage triggering results in a breakdown (or significant leakage) of the reverse-biased junction j2; the accompanying increase in current provides the injection at j1 and j3, as well as the transport required for switching to the conducting state. The breakdown mechanism commonly occurs by the combination of base-width narrowing and avalanche multiplication.

When carrier multiplication occurs in j2, many electrons are swept into n1 and holes into p2. This process provides to these regions the majority carriers needed for increased injection by the emitter junctions. Because of transistor action, the full breakdown voltage of j2 need not be reached. As we showed in Eq. (7-52), breakdown occurs in the collector junction of a transistor with iB = 0 when Mc = 1. In the coupled-transistor case of the p-n-p-n diode, breakdown occurs at j2 when

Mpc1 + Mnc2 = 1 (eqn. 6)

where Mp is the hole multiplication factor and Mn is the multiplication factor for electrons.

As the bias v increases in the forward-blocking state, the depletion region about j2 spreads to accommodate the increased reverse bias on the center junction. This spreading means that the neutral base regions on either side (n1 and p2) become thinner. Since c1 and c2 increase as these base widths decrease, triggering can occur by the effect of base-width narrowing.

A true punch-through of the base regions is seldom required, since moderate narrowing of these regions can increase the alphas enough to cause switching. Furthermore, switching may be the result of a combination of avalanche multiplication and base-width narrowing, along with possible leakage current through j2 at high voltage. From Eq. (eqn. 6), it is clear that, with avalanche multiplication present, the sum c1 + c2 need not approach unity to initiate breakdown of j2. Once breakdown begins, the increased numbers of carriers in n1 and p2 drive the device to the forward-conducting state by the regenerative process of coupled transistor action. As switching proceeds, the reverse bias is lost across j2 and the junction breakdown mechanisms are no longer active. Therefore, base narrowing and avalanche multiplication serve only to start the switching process.

If a forward-bias voltage is applied rapidly to the device, switching can occur by a mechanism commonly called dv/dt triggering. Basically, this type of triggering occurs as the depletion region of j2 adjusts to accommodate the increasing voltage. As the depletion width of j2 increases, electrons are removed from the n1 side, and holes are removed from the p2 side, of the junction. For a slow increase in voltage, the resulting flow of electrons toward j1 and holes toward j3 does not constitute a significant current. If dv/dt is large, however, the rate of charge removal from each side of j2 can cause the current to increase significantly. In terms of the junction capacitance (Cj2) of the reverse-biased junction, the transient current is given by


(eqn. 7)

where vj2 is the instantaneous voltage across j2. This type of current flow is often called displacement current. The rate of change of Cj2 must be included in calculating current, since the capacitance varies with time as the depletion width changes.

The increase in current due to a rapid rise in voltage can cause switching well below the steady state triggering voltage VP. Therefore, a dv/dt rating is usually specified along with VP for p-n-p-n diodes. Obviously, dv/dt triggering can be a disadvantage in circuits subjected to unpredictable voltage transients.

The various triggering mechanisms discussed in this section apply to the two-terminal p-n-p-n diode. As we shall see in the next section, the SCR is triggered by an external signal applied to a third terminal.

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