A SUMMARY OF SEMICONDUCTOR AND TRANSISTOR THEORY ROBERT A. LEFEVER Massachusetts Institute of Technology, Cambridge, Massachusetts
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value of the transistor to the electronics industry has encouraged a large volume of research hearing on EMPTY ZONE EMPTY ZONE the physics of metals. The electron theory of metals has tndergone considerable modification and elaboration as a result of these studies, but it still remains the ----- occuplED most adeauate basis for the inter~retation of the IMPURITY LEVELS UNOCCUPIED o o 0 0 o o 0 0 accumulated data. The fundamental principles underIMPURITY lying the theory were outlined in a previous article.' LEVELS Although electrical conductivity was already discussed to some extent, a few points require emphasis before considering semiconductor theory. Accordina- to the electron theory of metals, the ern , t ht u, ,", neressary condition for electrical conductivity is partly ,FFe a. SBmiconductor Energy (b) -Type filled energy bands. This allows the high-energy electrons to further illcrease ill energy as is required. On wave-frollt scatterillg rather t,han .actual collision of application of a potential to a metal, the high-energy . . . mdlvldual electrons with lattice points. A perfectly electrons are accelerated in the direction of the field uniform lattice presents resistance, thus accoulltillg until a limiting value is reached. Above about 100°K. for high conductivit,y at low temperatures. As this resistance to continued acceleration is a linear the t,emperature increases, lattice points undergo function of the absolute tem~ewture,as illustrated in causing imperfect,ions that, Figure 1. In the neighborhood of O°K. the resistance is the front, Lattice imperfectious caused by impurities also result in resistance to current flow. The resistance of an alloy in which atoms are randomly distributed often decreases appreciably when the alloy is heat-treated t o bring about ordering. This derrease in resist,a.ncewith an inrrease in ordering is sometimes useful in following the course of heat treabment. Several interesting problems in the conductivity of .2 metals find solution in the electron theory. Although the alkaline earth metals have two valence elect,ronsper atom, their relative condurtirities, rompared under conditions of equal lattice vibrations, are less than those of the alkali metals. The first Brillouin zone of the alkali metals is only half full, however, and t,he high0 increase in~ energy~ as reT ~ ~ D ~ energy~ electrons ~ can easily ~ ~ quired for conductivity. On the other hand, the alkaFigure I. Redstanoe of s M n t d a.* Function of Tempe~ntura line earth metals have an almost full first zone and an almost empty second zone as a result of zone overlap. The proportional to T 5a~ld,as the temperature is further re- high-energy electrons in the first zone can only increase duced, it approaches zero for a perfect lattice. This i,, energy by a small amoullt, ~ ~ h ithe l e second zone conbehavior can be explained in terms of the mean free tains only a relatively small numher of electrons to conpath but to do so it is necessary to assume a value of tribute to conductivity. Although electrons a t the top about atomic a t room temperature. of the first zone can he accelerated into the second zone, firthermo% as the temperature decreases, the mean the t~ransitionis accompanied by a scattering that also free path increases until it approaches infinity in the contributes to resistance. The 11et result is a resistance vicinity of absolute zero. I n view of these facts, it is higher than would otherlvise he expected for the alkanecessary to assume that resistance is the result of a lille earth metals. Normally, the resistance of a condurtor inrreases on melting because of breakdown in ' LEFEVER.R.A,, J. CHEM.EDUC..30, 486 (1953).
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lattice structure. Bismuth, however, affords an interesting exception to this behavior. As a result of an extremely small zone overlap, resistance of the metal is relatively high. When melting occurs, the zone strncture is destroved and the resistance decreases. SEMICONDUCTOR THEORY
Two interesting properties serve to characterize semiconductors. Contrary to the behavior of normal metals, over certain temperature ranges semiconductor resistance decreases with an increase in temperature. Furthermore, the presence of impurities in small concentration has a marked effect on resistance. The behavior of semiconductors may best be explained b dividine them into two proups: (1) intrinsic semiconcluctors and (2) extrinsic semiconductors. The intrinsic semiconductor results from a very narrow forbidden region between a completely filled zone and a completely empty one. As the temperature of the semiconductor increases, an increasing - number of electrons receive elloup$ e n e r-~ h to cross the forbidden region, becoming conductors. Pure graphite, silicon, and germanium exhibit this behavior. Extrinsic semiconducton, on the other hand, owe their unique properties to the presenke of impurity atoms. These impurities create narrow energy levels in the forbidden region. Extrinsic semiconductors may be divided into two groups depending upon the nature of these energy levels. In n-type material the levels contain electron* while in p-type they are available for electron ocrupation. The energy diagrams of n- and p-type semiconductors are given in Figures 2a and 2b respectively. 4 s the temperature of an n-type semiconductor illrreases, electrons in the impurity levels are excited into the unfilled zone and become conductors. A temperature increase in the case of p-type material resuks in the excitation of electrons from the filled zone into the available energy states. Resistance is thereby decreased since electrons can be accelerated -into the--vmancim created a t the top of the zone. Germanium and silicon afford interesting examples of extrinsic semiconductors. At room temperature, the (ohm-cm.)-I. The conductivity of silicon is 4 X addition of one boron atom per million silicon atoms increases the conductivity to 0.8 (ohm-cm.)-'. The resulting material is p-type because boron has one less valence electron per atom than does silicon. This elect,rondeficiency disturbs the basic silicon lattice, in which each atom is covalently bonded to four other atoms. In the vicinity of each boron atom only seven electroils are available for bond formation and the effect of this one electron deficiency is to introduce an energy level available for occupation just above the filled Brillouin zone. The introduction of phosphorus or arsenic impurity atoms into a silicon lattice results in n-type material, since each of these atoms adds an extra electron over that required for bond formation. The resulting energy levels appear just under the empty zone and are occupied by electrons. The required amount of impurity atoms is normally added to the host lattice
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after the latter has been obtained in the highest possible degree of purity. The extremely low impurity content required for optimum extrinsic properties has resulted in difficult problems relating to purification, analysis, and control. Whether a material conducts by movement of electrons or holes may be determined by the nature of the Hall effect, illustrated in Figure 3. The application of a
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potential to the ends of a thin strip of a conductor causes no difference in potential between opposite edges perpendicular to the current direction. If, however, a magnetic field is applied a t right angles to the plane of the strip, the current vector, i, will shift to j or k depending upon whether electrons or holes are the conductors. As a result, one connection of the galvanometer. G, must be moved in one direction or the other along the edge of the strip to retain a reading of zero. If, for example, conduction by electrons shifts the vector to j, then conduction by holes will shift it to k and, correspondingly, galvanometer lead B must be moved to C @ rD, .respectively .4%:is n a t m r e a a r y -twmwe~%hs galvanometer lead, however, as the nature of the conduction mechanism may be determined by observing the sign of the potential difference between the opposite edges. While this illustration serves to outline the principles of the Hall effect, in practice the situation is usually more complicated. Nevertheless, under certain conditions the Hall effect may be utilized to quantitatively determine semiconductor impurity content. -1s the temperature of an extrinsic semiconductor increases above absolute zero, the resistance decreases until a minimum value is reached. This decrease is a result of an increasing number of electrons being excited into the conduction zone. Counteract,ing this effect, however, is the tendency for an increase in resistance caused by thermal vibration.' As the latter factor hecomes predominant, the material begins to increase in resistance. Further temperature increase eventually results in another resistance decrease as a result of the hitherto subordinate intrinsic character. In this temperature range electrons are exdted directly across the forbidden region and the effect of impurities is lost.
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Above the temperature a t which this effect begins to manifest itself, the resistance is largely independent of impurity concentration, while below this temperature it is highly dependent. This intrinsic phenomenon is aided by the fact that the forbidden energy region is temperature-dependent, decreasing in size as the temperature increases. TRANSISTOR THEORY
they interact and cancel one another. This cancellation does not result in a current decrease, since both holes and electrons are continuously supplied at the terminals. If the junction bias is reversed, as shown in Figure 4b, electrons and holes are withdrawn from the contact region. I n this vicinity the material assumes its basic intrinsic character because energy levels in the forbidden region have been removed. As a result, the resistance of this region increases. Thus, the resistance
Current research in the transistor field is extensive and rapidly expanding. This interest is a result of the many advantages transistors have over the vacuum P TYPE N TYPE P TYPE tubes they are rapidly replacing. Small sine and low power requirements are of great importance in promising reduced size and rveight in complex electronic equipment. In additioq they have proved to be rugged and to have long lives. Since they require no warm-up period, equipment in which they are utilized can be brought into immediate operation. Among the many problems that remain to be solved are low powerhandling capacity, high inherent noise characteristics, and a large thermal coefficient of resistance. Transistors result from the combination of semicon- of the junction depends upon the sign of the applied ductors with metals and with each other. The first of potential and the device becomes a rectifier, capable of these devices was reported in 1948,%and since then a allowing more current to flow in one direction than in number of important types have been developed. The the other. p-n junction, resulting from contact between p- and nOf the three-component transistors useful for amtype semiconductors, is best adapted for an explanation plification, the p-n-p type illustrated in Figure 5 is the of the basic theory, however. most common. If biased as illustrated, electrons and If the junction between p- and n-type semiconductors holes continuously cross the junction at D. On the is biased as illustrated in Figure 4a, holes in the p-type other hand, junction E is biased inversely and has, therefore, a high resistance. Some of the holes that migrate into the n-type material from the left manage to reach and pass through the harrier a t E (under influence of the potential between B and C). The resistance of this barrier is very sensitive to the concentration of holes and the number of holes that reach this P-TYPE N-TYPE region is highly dependent upon the magnitude of the potential between A and B. Thus, a signal introduced a t X to alter the potential between A and B will be reproduced in amplified form a t Y. It should be understood that many complications normally encountered in the experimental work have been omitted from the above discussion to avoid confusion. Some idea of the problems encountered in material migrate across the junction toward the nega- transistor research and production may be obtained by tive side while electrons in the n-type material migrate consulting current literature, while a more detailed and across the junction toward the positive side. Some in- quantitative description of the basic theory may be terpenetration of holes and electrons takes place before found in a recent book on the s u b j e ~ t . ~ ' BARDEEN, J., AND W. H. BRAWAIN, P h p . Rev., 74, 230 a SSHCKLEY, W.,"Electrons and Holes in Semiconduotors," D. {1(118).
Van Nostrxnd Co., Inc., New York, 1950.
