In the context of electronic circuit theory, the word bias refers to a de volt ge (or current) that is maintained in a device by some externally connected sour: We will discuss the concept of bias and its practical applications in considerable in Chapter 3. For now suffice it to say that a PN junction can be biased by connecting a de voltage source across its P and N sides
Recall that the internal electric field established by the space charge across a junction acts as a barrier to the flow of diffusion current. When an external de source IS connected across a PN junction, the polarity of the connection can be such that it either opposes or reinforces the barrier. Suppose a voltage source V is connected as shown in Figure 2-10, with its positive terminal attached to the P side of a’PN junction and its negative terminal attached to the N side. With the polarity of the connections shown in the figure. the external source creates an electric field component across the junction whose direction opposes the internal field established by the space charge. In other words, the barrier is reduced, so diffusion current is enhanced. Therefore, current flows with relative ease through the junction, its direction being that of conventional current, from P to N, as shown in Figure 2-10. With the polarity of the connections shown in the figure, the junction is said to be forward biased. (It is easy to remember that a junction is forward biased when the Positive terminal of the external source is connected to the P side, and the Negative terminal to the N side )
When the PN junction is forward biased, electrons are forced into the N region by the external source, and holes are forced into the P region. As free electrons move toward the junction through the N material, a corresponding number of holes progresses through the P material. Thus, current in each region is the result of majority carrier flow. Electrons diffuse through the depletion region and recombine with holes in the P material. For each hole ~h~t recombines with an electron, an electron from a covalent bond leaves the P region and enters the positive terminal of the external source thus maintaining the equality of current entering and leaving the source.
Since there is a reduction in the electric field barrier at the forward-biased junction. there is a corresponding reduction in the quantity of ionized accept or and donor atoms required to maintain the field. As a result, the depletion region narrows under forward bias. It might be supposed q~al the forward-biasing voltage V could be increased to the point that the barrier Held would be completely overcome. and .in fact reversed in direction. This is not, however, the case. As the forward-biasing voltage is increased, the corresponding increase in current causes a Jarger voltage drop across the P and N material outside the depletion region, and the barrier field can never shrink to O.
Recall that the unbiased PN junction has a component of drift current consisting of minority carriers that cross the junction from the P to the N side. We discussed the fact that this reverse current is the direct result of the. electric field across the depletion region. Since a reverse-biasing voltage increases the magnitude of that field. we can expect the reverse current to increase correspondingly. This is indeed the case. However. since the current is due to the flow of minority carriers only. its magnitude is very much smaller than the current that flows under forward bias (the forward current).
It is this distinction between the ways a PN junction reacts to bias voltage-very little current flow when it is reverse biased ard substantial current flow when it is forward biased-that makes it a very useful device in ·many circuit applications. In one of the most common applications, a single PN junction is fitted with a suitable enclosure, through which conducting terminals are brought out so that electrical connections can be made to the P and N sides. This device is called a (discrete) diode. The P side of the diode is called its anode and the N side is called its cathode. Figure 2-13(a) shows the standard symbol for a PN junction diode. Figure 2-13(b) shows the diode connected to an external source for forward biasing, and 2-13( c) shows reverse biasing. Diode circuits will be studied in detail in Chapter 3.
Returning to our discussion of the reverse-biased junction. we should mention that it is conventional to regard reverse voltage and reverse current as negative quantities. When this convention is’observed, equation 2-13, repeated here. can be used to compute reverse current due to a reverse-biasing voltage
From the standpoint of plotting the I-versus- V relationship in a PN junction, the sign convention makes further good sense. If forward current is treated as positive (upward), then reverse current should appear below the horizontal axis, i.e., downward, or negative. Similarly, forward voltage is plotted to the right of 0 and reverse voltage is plotted to the left of 0, i.e., in a negative direction. Figure 2-14 shows a plot of I versus V in which this convention is observed. Note that the current scale is exaggerated in the negative direction, since the magnitude of the reverse current is so very much smaller than that of the forward current.
When V is a few tenths of a volt negative in equation 2-14, the magnitude of the term e ~/~VT is negligible compared to 1. For example, if V = -0.5, then e “/~VT = 4.5 X lO-s• Of course, as V is made even more negative” the value of eV/~VT becomes even smaller. As a consequence, when the junction is reverse biased beyond a few tenths of a volt:
Equation 2-15 shows that the reverse current in the junction under these conditions is essentially equal to In the saturation current. This result accounts for the name saturation current: The reverse current predicted by the equation never exceeds the magnitude of .
Equation 2-14 is called the ideal diode equation. In real diodes, the reverse current can, in fact, exceed the magnitude of Is. One reason for this deviation from theory is the existence of leakage current, current that flows along the surface of the diode and that obeys an Ohm’s law relationship, not accounted for in equation 2-14. In a typical silicon diode having Is = 10″14 A, the leakage current may be as t great as 10-9 A, or 100,000 times the theoretical saturation value.
The reverse current also deviates from that predicted by the ideal diode equation if tbe reverse-biasing voltage is allowed to approach a certain value called the reverse breakdown voltage, VBR• When the reverse voltage approaches this value, asubstantial reverse current flows. Furthermore, a very small increase in the reversebias
voltage in the vicinity of VBR results in a very large increase in reverse current. In other words, the diode no longer exhibits its normal characteristic of maintaining a very small, essentially constant reverse current with increasing reverse voltage. Figure 2-15 shows how the current-voltage plot is modified to reflect breakdown. Note that the reverse current follows ‘an essentially vertical line as the reverse
voltage approaches This part of the plot conveys the fact that large increases’ in reverse current result from very small increases in reverse voltage in the vicinity of
In ordinary diodes, the breakdown phenomenon occurs because the high electric field in the depletion region imparts high kinetic energy (large velocities) ‘0 the carriers crossing the region. and when these carriers collide with other atoms they atom bonds. The large number of carriers that are freed in this way accounts for the increase in reverse current through the junction. The process is called avalanching. The magnitude of the reverse current that flows when V approaches VI/II can be predicted from the following experimentally determined relation:
where II is a constant determined by experiment and has a value between 2 and 6. Certain special kinds of diodes, called zener diodes. arc designed for Lise in the breakdown region. The essentially vertical characteristic in the breakdown region means that the voltage across the diode remains constant in that region, independent of the (reverse) current that flows through it. This property is useful in many applications where the zener diode serves as avorage reference. similar to an ideal voltage source. Zener diodes arc more heavily doped than ordinary diodes, and they have narrower depletion regions and smaller breakdown voltages, The breakdown mechanism in zener diodes having breakdown voltages less than about 5 V.differs from the avalanching process described earlier. In these cases. the very high electric field intensity across the narrow depletion region directly forces carriers out of their bonds. i.e .. strips them loose. Breakdown occurs by avalanching in zener diodes having. breakdown voltages greater than about 8 V. and it occurs by a cobination of the two mechanisms when the breakdown voltage is between 5 V and H V. The characteristics and special properties of zener diodes arc discussed, in detail in Chapter 17.
Despite the name breakdown, nothing about the phenomenon is inherently damaging to a diode. On the other hand. a diode. like any other electronic device. is susceptible to damage caused by overheating. Unless there is sufficient currentlimIting resistance connected in series with a di~)tle. the large reverse current that would result if the reverse voltage were allowed to approach breakdown could cause excessive heating. Remember that the power dissipation of any device is
where V is the voltage across the device and I is the current through it. At the onset of breakdown, both V (a value near VII/I) and I (the reverse current) are liable to be large, so the power computed by equation 2-17 may weJI exceed the device’s ability to dissipate heat. The value of the breakdown voltage depends on doping and other physical characteristics that are controlled in manufacturing. Depending on these factors, ordinary diodes may have breakdown voltages ranging from 10 or 20 V to hundreds of volts.
The ideal diode equation shows that both forward- and reverse-current magnitudes depend on temperature, through the thermal voltage term VT (see equations 2-11 and 2-13). It is also true that.the saturation current, Is in equation 2-13, depends on temperature. In fact, the value of Is is more sensitive to temperature variations than.is VI’, so it can have a pronounced effect on the temperature dependence of diode current. A commonly used rule of thumb is that 1.1 doubles for every 10 c rise in temperature. The following example illustrates the effect of a rather wide temperature variation on the current in a typical diode
Example 2-6 illustrates that forward current in a ‘diode increases with temperature when the forward voltage is held constant. This result is evident when the I-V characteristic of a diode is plotted at two different temperatures, as shown in Figure 2-16. At voltage VI in the figure, the current can be. seen to increase from II to 12 as the temperature changes from 20°C to 100°C. (Follow the vertical line drawn upward from VI-the line of constant voltage VI’) Note that the effect of increasing temperature is to shift the 1- V plot toward the left. Note also that when the current is held constant, the voltage decreases with increasing temperature. At the constant current 12 in the figure, the voltage can be seen to decrease from ‘V2 to VI as
temperature increases from 20°C to 100°C. (Follow the horizontal line drawn through 12-the line of constant current 12,) As a rule of thumb, the forward voltage decreases 2.5 mV for each 1°C rise in temperature when the current is held constant. , Of course, temperature also affects the value of reverse current in a diode.since the ideal diode equation (and its temperature-sensitive factors) applies to the reverse- HS well as forward-biased condition. In many practical applications, the increase in reverse current due to increasing temperature is a more severe limitation on the’ usefulness of a diode than is the increase in forward current. This is particuIarly the case for germanium diodes, which have values of I,that are typically much larger than those of silicon. In a germanium diode, the value of I, may be as great as or greater than the reverse leakage current across the surface. Since I, doubles for every lOoC rise in temperature, the total reverse current through a germanium junction can become quite large with a relatively small increase in temperature. For this reason; germanium devices are not. so widely used as their silicon counterparts. Also, germanium devices can withstand temperatures up to only about H)()OC, , while silicon devices can be used up to 200°C
Use SPICE to obtain a plot of diode current versus diode voltage for a forward- SPICE biasing voltage that ranges from 0.6 V through 0.7 V in 5-mV steps. The diode has saturatiori current 0.01 pA and emission coefficient 1.0.
Solution. Figure 2-17(a) shows a diode circuit that can be used by SPICE to perform a :DC analysis and generate the required plot. Note that VDUM is a dummy voltage source used as an ammeter to determine diode current. The polarity of VDUM is such that positive current values. ](VDUM), will be plotted. (If we plotted J(V 1). current values would be negative.) Although the .MODEL statement
specifics the saturation current, IS, and emission coefficient, N, the values used arc the same as the default values so these could have been omitted from the statement. The .DC statement causes VI to be stepped from 0.6 V through 0.7 V in 5-mV increments.
Figure 2-17(b) shows the resulting plot. (Portions of the complete printout produced by SPICE have been omitted to conserve space.) The plot has values of diode current, I(VDUM), scaled along the horizontal axis, and diode voltage, VI, along the vertical axis, By rotating the plot 90° counterclockwise, we see the conventional portrayal of current versus voltage, similar to that in Figure 2-11. Note that the forword current ranges from 0.1188 mA to 5.676 mA as the forward voltage ranges from fl.6 V to 0.7 V.
This input file is written in lowercase letters for illustrative purposes but PSpice unlike the original Berkeley SPICE, does not distinguish between Icwercase and uppercase letters. so either (or both) could have been used.