emiconductor technology is basically a series of
S physical and chemical processes aimed at constructing, within a single-crystal semiconductor, well MASS TRANSFER IN SEMICONDUCTOR TECHNOLOGY Andrew S. Grove
l h e unusual conditions encountered in manufacture of semiconductor materials appear, at first glance, t o lie outside the normal scope of chemical engineering practice. However the chemical engineer, as the author shows, has contributed a great deal to this unusual technology through his analysis of the fundamental processes involved. From this analysis, mass transfer across the gas-solid interfaces associated with semiconductor solids emerges as the critical variable
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defined regions in which certain impurities are concentrated. The combination of these regions constitutes a semiconductor device which performs a useful electrical function. The geometry of the various regions, the types of impurities contained within them, and the concentrations of these impurities are all determined by the desired electrical characteristics of the device. To indicate the size and concentration ranges involved in semiconductor devices, we note that their size is most conveniently expressed in microns. Consequently, we often encounter as many as 100,000 semiconductor devices per sq. cm. of semiconductor surface. The concentrations of the impurities contained in the various regions of the crystal are most conveniently measured in parts per million. These concentrations are to be achieved with accuracy of about 10%. A common feature of the various processes of semiconductor technology is the transport of a gaseous constituent to a solid surface. Once at the solid surface, the constituent will either react or it will be further transported to the interior of the solid by solid-state diffusion. We will first review the elements of modern semiconductor technology, the so-called planar technology, and then consider the reactions involved in the various steps of the planar technology. In particular, we will examine the available evidence regarding the role of the rate of mass transfer in determining the overall rate of these various steps.
The Planar Technology
We begin with a single-crystal silicon substrate such as that sketched in Figure 1. Silicon wafers are typically circular, with about a 1-inch diameter. In the example considered here, the substrate is doped with a high concentration of electron acceptor-type impurities. As a result, the silicon is highly conductive. Such silicon is referred to as being “P+ type.” In the first process step, a thin (-10-micron) film is grown on top of the silicon substrate by vapor phase deposition techniques. This film also contains acceptor-type impurities but in a much smaller concentration. The deposited film is called “P-.” The process is illustrated schematically in Figure 2. The conditions of growth are such that the integrity of the single crystal is maintained. Vapor phase deposition conducted in such a manner is referred to as epitaxial growth. In epitaxial growth (Figure 2) gas phase transport of a volatile compound of silicon, such as silicon tetrachloride, is involved. When this compound reaches the surface of the substrate, it reacts. As indicated in Figure 2 , a typical reaction might be that between silicon tetrachloride and hydrogen, resulting in crystalline silicon and hydrochloric acid. The gaseous product of this reaction, hydrochloric acid, is then transported away from the surface back into the gas. Thus, in epitaxial growth, three processes are combined in series; the slowest of the three will determine the overall rate of epitaxial growth. I n the second step, a thin (-1-micron) silicon dioxide layer is formed on top of the surface of the epitaxial
film. This step, oxidation, is illustrated in Figure 3. The silicon dioxide film is usually grown by exposing the silicon slice to an oxidizing ambient, such as oxygen or water vapor, at a high temperature. These ambients convert the surface of the silicon to an adherent silicon dioxide layer. In the oxidation step oxygen, for example, must first be transported to the surface of the oxide layer. It must then diffuse through the silicon dioxide layer already present, and, when it reaches the silicon, it must react to form more silicon dioxide. Again, three processes are combined in series. Once the oxide layer is formed, complex patterns can be delineated on it by photolithographic techniques. The oxide is first coated with a light-sensitive photographic emulsion, then the desired patterns are exposed, and the emulsion and the underlying oxide layer are removed at places of exposure. In this manner “windows” can be cut into the oxide layer exposing the silicon underneath. At this point the stage is set for the next major process step-the diffusion step. As illustrated in Figure 4, the silicon wafer, with the windows cut in its oxide layer, is placed in a gaseous ambient which contains a relatively high concentration of an electron donor-type impurity. Such impurities diffuse extremely slowly through the silicon dioxide layer which, therefore, acts as a mask against them. Only where the donor impurities can reach the silicon surface will they penetrate the silicon forming an N+-type plug. The interface between the N+ plug and the P--type film constitutes a P-N junction-the basic element of most semiconductor devices. The processes involved in the diffusion step are illustrated in Figure 4. The
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gas phase transport of the donor impunues TO me semiconductor surface is combined in series with the solidstate diffusion of these impurities into the body of the semiconductor where they will form the P-N junction. The highly idealized representations of the three major steps of the planar technology can be better appreciated by considering an end product. Figure 5 is a photomicrograph of a state-of-the-art silicon integrated circuit. This circuit, which can perform a certain set of logic functions in a digital computer, consists of 320 metal-oxide-silicon transistors all contained within an area which is 1 mm. square (5).
Andrew S. Grove is head of the Surface and Dcvicc Physics Section at the Research and Deucl@mmt Labmatmy, Fairchild Semiconductw, Palo Alto, Calif. This paper is based rm ths authw's presentation to the ACS Dinkion of Indushid and Engineering Chirtty Chrisbnos Symposium at Stanford UniucrSiry in December 1965. AUTHOR
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Exporimmhl Condiflonr
Most industrial reactors in use today are flow reactors, in which a gas containing the proper species streams past the silicon wafer. An interesting feature of the semiconductor industry is that the reactors used in the factory are not much different from those used in the laboratory in type or even in size. There are two kinds of reactors, cold-wall and hotwall reactors. In the cold-wall reactor the silicon sample itself is heated by a radio frequency induction coil while the glass walls remain cold. In contrast, the hot-wall reactor is surrounded by a furnace which heats the glaw walls as well as the silicon sample. The hot-wall reactor is less expensive but more prone to contamination. In epitaxial growth, minimizing contamination is important, and the cold-wall reactor is most widely w d . Figure 6a shows schematically the reactor used by one of the early workers in the field, Theuerer (71). In this vertical reactor, the silicon wafer rests on a pedestal, also made of silicon heated by induction. The
Figure 5. A state-of-the-art silicon integrated Circuit: 320 M-0-S transistors in an area 7-mm. square
gas stream, entering from top, hits the silicon wafer in a pattern reminiscent of stagnation flow (6). I n this type of reactor epitaxial film is grown only on one silicon wafer a t a time. I n more customary industrial practice, film is grown on many wafers simultaneously. Such a multiwafer epitaxial reactor is shown, schematically, in Figure Gb. I n this horizontal reactor the silicon wafers are placed on a pedestal parallel to the direction of the gas flow so that the flow pattern near the wafers is somewhat like that encountered in the flow of fluids past a flat plane. Heating is by radio frequency induction coils. The oxidation and diffusion steps are typically conducted in a hot-wall reactor such as that shown in Figure 7. The source of impurities (such as dopants in the diffusion step) can be a liquid through which a carrier gas is Ixibbled, or a solid compound of the desired
dopant held at a precisely controlled temperature upstream from the silicon wafers. Thus, by controlling the temperature of the solid source of the impurities, their concentration in the gas stream can be controlled over a wide range. I n most industrial reactors flow rates are very low. Thus, the Reynolds number R e = Ud/v, where U is the average flow velocity, d is the diameter of the reactor, and v is the kinematic viscosity, is typically between 10 and 100. This range is not often encountered in conventional chemical engineering practice. At first thought one might assume that a t such extremely low Reynolds numbers all processes would be limited by the rate of mass transfer. We shall now examine the available experimental evidence bearing on the relative rates of the gas phase mass transfer process and the reaction that takes place in series combination with it. VOL. 5 8
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RF
>WAFER
RF INDUCTION COILS
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Lo
i'
+
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6.
Figure 6. Reactors employed in the epitaxial growth of silicon.
VENT
( a ) Vertical reactor, ( 6 ) horizontal reactor
Oxidation
looooooooooooool
OXIDANT OR IMPURITY CARRIER GAS
+
00000000000000
PE-l Figure 7 . Hot-wall reactor used in the oxidation and diyusion steps
GAS
The basis for our discussion is the simple model of the thermal oxidation of silicon illustrated in Figure 8, which has been shown to be in excellent overall agreement with experimental findings ( 2 ) . As we have discussed earlier, the oxidizer is transported from the gas to the surface of the oxide film, where it diffuses through the oxide film already present, and finally reacts with the silicon. Each of these fluxes can be approximated as shown in Figure 8. I n particular, the gas phase mass transfer flux is proportional to the concentration difference of the oxidizer. The proportionality constant h is the mass transfer coefficient in terms of concentrations in the solid (12). Noting that in the steady state these three fluxes are equal, we can derive a general relationship for the thermal oxidation of silicon (2):
SILICON
xo2 f Ax0 =
where
Bt
B = 2 DeffC*/hT1
(1) (14
and
CI
Fa P-
Figure 8.
52
-kCI
The model of the oxidation process
INDUSTRIAL AND E N G I N E E R I N G C H E M I S T R Y
Equation 1 gives the thickness of the oxide film xo as a function of oxidation time t in terms of two coefficients related to the diffusivity of the oxidant in the oxide film Deff, the equilibrium concentration of the oxidant in the oxide film C*, the number of oxidant molecules incorporated into a cubic centimeter of the oxide film N 1 , the chemical reaction rate constant of the oxidation reaction k, and the mass transfer coefficient h. By measuring the thickness of the oxide film as a function of time under various oxidation conditions, we can determine the coefficients A and €3. I t is found that these coefficients depend on the diffusivities and the equilibrium concentrations of both pure oxygen and water vapor oxidants in the predicted manner. More relevantly to the present discussion, it is also found that the ratio B / A depends exponentially on temperature, as shown in Figure 9, for both oxidants. The activation
'
energy is approximately the same in both cases, about 45 Kcal./mole. Since, according to Equation 16, BIA depends primarily on the smaller of k or h, the obmved temperature dependence represents the temperature dependence of k or h, whichever is smaller (C' is practically independent of temperature in this range). Sice it in unlikely that the mags trader coefficient h should have an exponential temperature dependence, it is the reaction with the silicon and not the gas phase mass transfer which appears to control the overall rate of oxidation. This conclusion is made plausible by estimates of the mass transfer coefficient h based on boundary layer theory. Although the Reynolds number of the flow system is too low for boundary layer theory to hold accurately, one can nevertheless obtain an order-ofmagnitude estimate of the mass transfer coefficient from Pohlhausen's formula (7) for flow past a flat plane. Such an estimate turns out to be several orders ofmagnitude higher than the value of kh/(k h) obtained from measured values of B/A, further indicating that the gas phaze mass transfer is not the controlling step.
+
DMusion
As we have discussed earlier, in the diffusion step an impurity in transported from the gas to the silicon surface, where it continues to diffuse into the interior of the silicon. We now consider some experiments dealing with the complementary procars in which impurities diffuse outward from the silicon and escape into the gaseous ambient. The two proceases have many similar features; the difference is merely the direction of the motion ofthe impurities. The problem of the rate of escape of impurities froma silicon substrate, in which their concentration originally had been uniform, can be considered as a solid-state diffusion problem describing the impurity concentration profile within the silicon as a function of time, subject to the boundary condition imp& by the rate of the transport of the escaping impurity away from the surface into the flowing gas. As before, we approximate the rate of mass transfer away from the surface by the product of a mass transfer coefficient h and a concentration difference. Resulting calculations (70) of the impurity concentration profile are shown in Figure 10. Here the concentration C(x,t), normalized to the impurity concentration deep within the s i l i i n subatrate C,, is shown as a function of the distance x from the surface, normalized with the diffusion length of the impurity, 2 t / E The parameter ht/& characterizes the ratio of the rate of the gas phase mass transfer to the rate of the solid-state diffusion process. Note the two l i t ing c a w corresponding to very slow and very rapid gas phase m a s transfer: I n the first case the impurity distribution remains undisturbed; in the second it Xpproaches the well known error-function distribution. Experimental measurements (3) of the distribution of various acceptor type impurities in silicon obtained after exposing the originally uniformly doped silicon wafer to flowing hydrogen gas at elevated temperatures
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8 2.0
Figure 10. Th impuritp roncentrution pro@ m'thin thc silicon for , v m i a u VUIUCS of t i u p n r m t e r ht/t/E I .o
M/t/.\/a
= lo-'
0.8
0.6 J 3 0.4
0.2
0
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are shown in Figure 11. Since the measurements seem to follow the error-function distribution, it appears likely that the rate of the ~ a phase s mass transfer is much more rapid than the solid-state diffusion rate. Similar results were obtained for donor-type impurities also. Eplfaxlol Orowlh
Figwe 12. The @ect of gar flow rate on thc /ilm growth ratearfical reactor
0.11 0.625
I
I
0.65
0.675
I
I
0.70 0.725 rIlvturwl ( I O O O / I ~
I
0.75
Figure 13. Thc f l e d of tmperafwe on fhc rate of cp'tm'al film growth-hrizontal reactor
I n the cases of oxidation and diffusion it appears that, under conditions encountered in typical industrial practice, the m a s transfer process has little if any effect on the overall rates. That the situation might be otherwise in epitaxial growth is indicated by the fact that obtaining uniform epitaxial film growth over many wafers in a reactor is a much more difficult problem than the corresponding one in oxidation and diffusion. Theuerer's (77) experimental results, showing the effect of gas flow rate on the rate of epitaxial film growth in the vertical reactor, are indicated in Figure 12. It is evident that the film growth rate first increases with the gas flow rate, and then it reaches a plateau. In the plateau region Theuerer finds that the reaction rate depends exponentially on the temperature of the silicon wafer, with an activation energy of about 37 Kcal./niole. These experiments indicate two regions: At low gas velocities, the film growth rate is apparently determined by the rate of mam transfer; at high gas velocities, it is determined by the rate of chemical reaction at the surface of the wafer. Experimental results obtained in a horizontal reactor by Shepherd (8) are shown in Figure 13, whcre the deet of temperature of the water on the epitaxial film growth rate is shown. Again two regions can be distinguished: At low temperatures, the growth rate depends exponentially on temperature, with an activation energy of 44 Kcal./molenot too different from Theuerer's activation energy; at high temperatures, the growth rate is relatively insensitive to variations in temperature, as would be expcted if, in this region, the overall rate were determined by the m a s transfer rate. The solid lines in Figure 13 comespond to calculations based on a simple model of the epitaxial growth process. In this model the rate of gas phase mass transfer i: approximated by ha(C, Cs) where Cu and C, arc the concentrations of the silicon tetrachloride in thc bulk of the gas and next to the surface of the film, respec. tively, and ha is the mass transfer coefficientin terms ol concentrations in the gas. The rate of chemical reactior at the surface is approximated by ksCs where ks is the rate constant of the chemical reaction. Since in iteady state these two rates must be equal, we can eliminate Cs and arrive at an expression for the film growth rate V,
-
Figwc 74. Vortices in a hot-wall d#usion fulnacc. 54
I N D U S T R I A L AND ENGINEERING C H E M I S T R Y
where NIis the number of Si atoms/cc. of Si. A reasonable overall agreement is obtained between the curves calculated from Equation 2 and Shepherd's
data fork, = 107 (cm./sec.) exp [ (- 44 Kcal./mole)/RT] with ho between 5 and 10 cm./sec. Values of k s and hG of the same order of magnitude can be extracted from Theuerer’s data shown in Figure 12. While the above magnitude of hG is in agreement with an estimate based on mass transfer considerations, the two sets of experimental results contain an intriguing apparent discrepancy. While Theuerer’s data, obtained in the vertical reactor, show an increase of film growth rate with increasing flow rate in the mass transfer controlled region, Shepherd found only a very slight dependence of the film growth rate on the gas flow velocity in the horizontal reactor. One possible explanation for this apparent discrepancy might be through the relative importance of the natural and the forced convection processes in determining the rate of gas phase mass transfer. Evidence of the importance of natural convection in a hot-wall tube reactor is provided by the motion pictures of Smith and Donovan (9),which showed the existence of symmetrical vortices superimposed on the flow by photographing the motion of tracer particles. The appearance of such vortices, shown in Figure 14, indicates the presence of natural convection. In a cold-wall reactor, the entering gas stream is cold whereas the silicon wafer itself is kept at a very high temperature. As a consequence, temperature gradients of many hundreds of degrees centigrade per centimeter are encountered, further promoting the influence of natural convection. One can estimate that the Grashoff number Gr = (d3gpAT)/v2 in an epitaxial reactor is probably of the order of l o 3 to lo4. Thus, it appears reasonable that natural convection should have an important effect in determining the rate of gas phase mass transfer, in which case the gas phase mass transfer coefficient would be independent of the gas flow rate in the reactor. Why natural convection should dominate in the horizontal reactor and not in the vertical, we can only guess. In terms of a simplified picture, the mass transfer rate would depend on the velocity of the gas in the direction normal to the surface of the silicon wafer. In the case of the vertical reactor, the main flow itself is normal to the silicon surface, and the natural convection flow can only modify the main flow slightly. In the case of the horizontal reactor, the main flow is parallel to the surface of the wafer, and, therefore, the natural convection flow might have a larger influence in determining the flow velocity in the normal direction.
film is determined by the redistribution of the impurities originally contained within the substrate by solid-state diffusion alone. However, if such precautions are not taken, the impurity distribution may be much more gradual-“sloppy.” It has been suggested that the excess impurities originate from the backside of the heavily doped substrate (7). After escaping from the backside, these impurities are mixed into the gas stream and are then incorporated into the growing film. More recently, experiments with radioactive tracers verified this picture ( 4 ) . Details of this “autodoping” process must depend very critically on the gas flow pattern. However, this feature of the autodoping phenomenon has not yet been investigated. Conclusions
We have considered the role of gas phase mass transfer in the various process steps of the planar technology. In each case, mass transfer is combined in series with either a chemical reaction or a solid-state diffusion process. On the basis of the available information, it appears that under typical experimental conditions the gas phase mass transfer process has little or no influence on the rate of the oxidation and solid-state diffusion steps but that it may be the rate determining process in epitaxial growth and that it can be involved in determining the impurity distribution in epitaxial films. Little is known about the details of the gas phase mass transfer process in any of the above cases. Basic questions, such as the relative importance of natural us. forced convection or the role of various reactor geometries, are yet to be studied. As a result, gas phase deposition reactors, employed with increasing frequency in the growth of metals and insulators as well as of semiconductors, are designed empirically. Yet, reactions involving semiconductors have great advantages for basic studies of mass transfer processes. The reactions involved are relatively simple, and because the impurities involved are electrically active within the semiconductor, simple electronic measurements can be used to determine concentrations and concentration distributions with extreme accuracy. It is hoped that chemical engineers will make use of these advantages, with benefits to themselves and to semiconductor technology. REFERENCES
Autodoping
Another very interesting phenomenon which is connected intimately. with the gas phase mass transfer process involves the transport of impurities from one place within an epitaxial reactor to another resulting in an undesired impurity distribution in the epitaxial film. This process is called “autodoping.” I n epitaxial film growth it is frequently desired to grow a lightly doped film on a heavily doped substrate. If elaborate precautions are taken to eliminate contamination, it has been shown (3) that the impurity distribution in the
(1) Bassechest H., Tung, S. K., Manz, R. C., Thomas, C. O., Met. Semiconductor Mater. 15, 69 (1962). (2) Deal, B. E., Grove, A. S.,J . A.bpl. Phys. 36,3770 (1965). (3) Grove, A. S., Roder, A., Sah, C . T., Zbid., p. 802. ( 4 ) Joyce, B. A., Weaver, J. C., M a d e , D. J., J . Electrochem. Soc 112, 1100 (1965). (5) Moore, G. E., in “Microelectronics,” Chap V, McGraw-Hill, New York, 1963. (6) Schlichtinp H;,“Boundary Layer Theory,” Chap. V., 4th ed., McGraw-Hill, New York, 960 ( 7 ) Schlichting, H., Ibid., Chap. XIV; Bird, R. B., Stewart, W. E., Lightfoot, E. N., “Transport Phenomena,” p. 802, Wiley, New York, 1960. (8) Shepherd, W., J . Elcclrachem. Soc. 112,989 (1965). (9) Smith, A. M., Donovan, R. P., “Direct Dynamic Observation of Impurity Flow Patterns During Gas-Source Boron Diffusions of Silicon,” Electrochem. SOC.Fall Meeting, Washington, D. C., 1964. (10) Smits, F. M., Miller, R. C., Phys. Reu. 104,1242 (1956). 108,649 (1961). (11) Theuerer, H. C., J . Electrochem. SOC. (12) Treybal, R. E., “Mass Transfer Operations,” Chap. 5, McGraw-Hill, New York, 1955.
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