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High rate evaporation from graphite crucibles
Thin Solid Films, 148 (1987) 293-300 PREPARATION AND CHARACTERIZATION
293
H I G H RATE E V A P O R A T I O N F R O M G R A P H I T E CRUCIBLES J. RICHARDS Electronics Research Laboratory, Defence Science and Technology Organisation, Department of Defence, GPO Box 2151, Adelaide, South Australia 5001 (Australia) (Received May 1, 1986; revised September 1, 1986; accepted September 16, 1986)
A technique has been found that eliminates the ejection of small droplets of evaporant during high rate vacuum evaporation of tin and germanium from heated graphite crucibles. A model is presented in which it is proposed that the energy causing the ejection comes from the release of surface energy that occurs when condensed droplets coalesce on the crucible walls.
1. INTRODUCTION In a study of the properties of vacuum-deposited thin films a need arose for a neutral source capable of high rates of deposition, able to hold a large quantity of evaporant and capable of evaporating many different materials. A problem encountered in meeting this need was the rapid corrosion by the evaporant of many crucible materials, such as tungsten, tantalum and molybdenum, at the elevated temperatures needed for reasonable rates of deposition. In an attempt to overcome this problem, graphite crucibles were used and were found to exhibit low rates of corrosion. However, the use of graphite caused another problem that was absent with metal crucibles, namely the occurrence of small molten lumps of evaporant in the vapour stream emerging from the crucible. At rates of deposition exceeding 1 n m s - 1 these lumps or spits easily reached and stuck to substrates positioned many centimetres above the crucible. Films grown under these conditions possessed very rough surfaces and were unusable. In this paper a method that eliminates spitting from graphite crucibles is reported, and a probable mechanism causing the ejection of lumps of evaporant is proposed. 2. EXPERIMENTALMETHOD A schematic diagram of the apparatus used in this study is shown in Fig. 1. The evaporant is contained in a graphite crucible, which is heated by a defocused electron beam drawn from a ring filament. A feature of this source is that the position of the filament with respect to the crucible can be altered. Since the emitted electrons tend to travel to those areas of the crucible closest to the filament, changing the 0040-6090/87/$3.50
© ElsevierSequoia/Printedin The Netherlands
294
J. RICHARDS
Insulator
Graphite Collimator
Microscope _ slide Upper filamer position L o w e r filamer position
Heat shield Filament . Graphite crucible . Tantalum platform
Filament - supports
_Supports
Fig. 1. Schematic diagram of apparatus used.
position of the emitter will alter the distribution of power onto the crucible and will thus alter the temperature distribution of the crucible. Two positions of the filament are used; in one the filament is situated adjacent to the bottom of the crucible and in the other it is placed near the top. In the low position the top of the crucible is typically 200 °C cooler than the melt and in the high position it is typically 25 °C hotter than the melt. By making the top of the crucible hotter or cooler than the evaporant, it is possible to control the rate of condensation of evaporant on the crucible walls and in fact to inhibit condensation altogether. The significance of this will be discussed below. The substrate is mounted on a temperature-controlled holder located 80 mm above the source and is inclined at 45 ° to the direction of the vapour stream. Rates of deposition are inferred by weighing the samples before and after deposition. An approximately constant rate is obtained during a deposition by maintaining at a fixed value the temperature of the platform that supports the crucible. The apparatus is evacuated to a pressure below 10-3 Pa by a liquid-nitrogen-trapped diffusion pump. 3. RESULTS With the filament in the low position, evaporation of tin produced significant ejection of lumps at rates of deposition over about 1 nm s- 1. Spitting was detected either by viewing the substrates after the deposition had ceased, to see whether any lumps were present on the surface of the deposit, or by observing directly spits flying
HIGH RATE EVAPORATION FROM GRAPHITE CRUCIBLES
295
in the space between the collimator and the substrate during deposition. This was feasible in the case of the larger spits because they could be readily seen in the bright light coming from the vapour source. The spitting rate was observed to increase considerably with increasing rate of evaporation. Inspection of the crucible after the deposition had been completed showed that tin spheres, ranging in size from 0.5 mm down to the submicrometre range, had formed in the cooler upper areas of the crucible. Very similar results were observed when evaporating germanium. The height reached by ejected lumps was also examined visually and typically varied from very low values to as high as 0.3 m, with the great majority reaching only a few centimetres. The relationship between the rate of spitting and the condition of the graphite was also investigated and it was observed that highly outgassed crucibles produced fewer spits t h a n those not loutgassed, other factors being the same. Crucibles that were given a cleaning treatment in which the graphite was heated to about 1000 °C and then dropped into distilled water produced less spitting than crucibles not so treated. Pyrolytic graphite crucibles were found to spit less than coarsegrained graphite crucibles. However, when the filament was in the low position all graphite crucibles produced too many lumps on the substrate to enable useful films to be grown at high rates of deposition. With the filament in the high position, entirely different results were observed. Evaporation of both tin and germanium showed no evidence of any ejection of lumps at any rate of deposition, the highest rate tested being 20 nm s- 1. Apart from the achievement of a far greater range of rates of deposition, there was no need to apply any special heat treatment to the graphite, and no special type of graphite was required. Further, there was no sign of any condensed material on the exposed surfaces of the crucible above the melt. Thus the performance of the source was greatly improved in every respect by the repositioning of the filament. These results indicate an association between spitting and the temperature distribution of the crucible and perhaps a relationship between spitting and the formation of condensed evaporant on the crucible walls. To investigate the relationship between spitting and droplet formation more fully a graphite disc made of the same material as the crucible was placed on one of the substrate holders and heated to 360 °C, the maximum temperature that the holder could reach. A glass microscope slide was positioned as shown in Fig. 1 so that it could only intercept objects emanating from the graphite disc. A tin deposit of mean thickness 6 Ixm was then built up on the graphite at a rate of 10 nm s- 1 from the source operated in the spit-free mode. The graphite and microscope slide were then carefully examined by scanning electron microscopy. A scanning electron micrograph of an area of the microscope slide is shown in Fig. 2. The photograph reveals the presence on the glass slide of small, mainly spherical, lumps of tin that range in size from a maximum diameter of 25 I.tm down to 0.15 I.tm. These sizes agree reasonably well with the size of spits emanating from a spitting graphite crucible. From the geometry of the apparatus it is clear that these lumps could not have come from any region other than the graphite surface. Further confirmation of this fact comes from two other observations. First, when the graphite disc was replaced by a cool copper substrate the film grown on it did not
296
J. RICHARDS
possess any lumps of tin, indicating that the vapour source did not generate spits and could not be the source of the lumps observed on the microscope slide. Secondly, the larger lumps on the microscope slide are rather similar to the lumps on the graphite surface. This can be seen by comparison of Figs. 2 and 3, which shows that the larger lumps of tin, both on the microscope slide and on the graphite, have small spheres attached to them.
I
I
51ma Fig. 2. Scanning electron micrograph of lumps of tin collected on the microscope slide. Fig. 3. Scanning electron micrograph of spheres of tin formed on a graphite substrate.
I
I
20 Inn
The angular distribution of spits ejected from the graphite was determined by measuring the spatial distribution of spits on the microscope slide and using the known geometry of the apparatus. The result is shown in Fig. 4 for spits exceeding about 1 p.m in diameter. Angular errors arise because of the large size of the emitting area and the influence of gravitational forces acting on the spits after ejection. Errors in counting the number of spits arise because of difficulties in detecting very small spits and the possibility that not all spits stick to the microscope slide. The broken curve shown in Fig. 4 is a distribution calculated assuming that all directions of ejection are equally probable. This curve has been normalized to give the same total yield as is observed experimentally; comparison of the curves shows that the ejection of spits in directions close to the normal is preferred. A comparison of the size distribution of lumps collected on the microscope slide and the size distribution of condensed spheres on the graphite surface does not reveal a significant difference for spheres greater than approximately 1 p.m in diameter. There were far fewer spheres of submicrometre size on the microscope slide than on the graphite. The total number of spits ejected from the graphite surface can also be estimated by counting the spits collected on the microscope slide. Assuming that the sticking probability of ejected lumps is unity, then from a mere 1.4 mg of tin deposited onto graphite at 360 °C some 25000_+ 3000 lumps are ejected with diameters exceeding 1 p.m. The large number of lumps ejected from a small quantity
HIGH RATE EVAPORATION FROM GRAPHITE CRUCIBLES
297
1.O
0.8
co
:~
0.6
0.4
0.2
00 20 40 60 80 Angle between trajectory and surface normal 0 (degrees)
Fig. 4. Angular distribution of ejected lumps (---, calculated distribution assuming that all directions of ejection are equally probable).
of material indicates how troublesome spitting can be. For example, in a graphite crucible containing 5 g of evaporant the amount condensing on the crucible walls could be as much as 2-3 g, indicating that more than 10 7 spits could be generated. It is obvious that appreciable contamination would occur if only a small fraction of these end up on the substrate. 4. DISCUSSION These results show that spitting is associated with the growth of liquid droplets on a graphite surface. Several studies of the growth of many materials on amorphous surfaces have been made 1-3 and the results depend strongly on whether condensation occurs as a liquid or a solid. In these experiments condensation as liquid occurs because the substrate temperature is well above the melting point, although even this is not necessary since Komnik 2 has found that condensation as a liquid occurs in many materials down to substrate temperatures as low as two-thirds of the bulk melting point. In the initial stages of growth under these conditions extremely small nuclei develop that contain small numbers of atoms. These nuclei grow by intercepting atoms from the vapour stream and by absorbing mobile adatoms that have condensed elsewhere on the substrate surface. On amorphous surfaces or those where little wetting of the surface occurs by the condensate these nuclei will be almost spherical in shape. If adjacent spheres touch during growth they may coalesce to form a single larger sphere. Coalescence of spheres will continue irrespective of the size of the spheres and will only cease when the arrival of vapour on the surface stops. This model can explain most of the features visible in Fig. 3. Of the processes mentioned above, the coalescence of spheres on the graphite
298
J. RICHARDS
surface could be responsible for ejection of lumps. During coalescence there is a release of surface energy, as has been shown by Pocza 3. He proposed that the released energy causes the temperature of the coalescing objects to rise; however, it is possible that the released energy causes mechanical movement as well. For coalescing spheres of radii r and xr, the surface energy released is given by E = 47tar2{(1 + x 2) - (1 + x3) 2/3 }
(1)
where a is the surface tension of the evaporant. Equation (1) indicates that energy is released for all values of x, since (1 + x z) is always greater than (1 + x3) 2/3. If it is assumed that all the energy released is transferred to kinetic energy of the coalescing objects it is simple to show that the maximum velocity of the ejected lump is given by
V=[6a{l + x2--(l + x3)2/3}ll/2 ~-1- + x 5
(2)
where p is the density Of the evaporant. For coalescing tin spheres 10 ~m in radius, eqn. (2) gives a velocity of 2.98 m s- 1, sufficient to reach a height of 0.45 m if the sphere is ejected vertically. This is larger than ejection heights observed from spitting crucibles; hence we do not require 100~o conversion of released surface energy into mechanical energy to explain the spit velocities observed. Equation (1) can be used to evaluate the optimum value of x that leads to the release or ejection of the coalescing spheres from the surface. Presumably the probability of release will be proportional to the energy available and inversely proportional to the bond strength between spheres and substrate. The probability P of ejection is therefore given by a{ l+x2 } P oc ~ (1 + xa) 2/3 1 (3) where k is the bond strength per unit area of contact. Equation (3) shows that the probability of ejection is independent of r, supporting the experimental observation that the size distribution of spits collected on the microscope slide is similar to the size distribution observed on the graphite substrate. Analysis of eqn. (3) reveals that P is maximum when x = 1, i.e. when spheres of equal size coalesce. When the ratio of sizes is 2: 1, P drops to 60~ of its peak value, indicating that it is unlikely that the coalescence of spheres with very different sizes will lead to ejection. Although it has been shown that sufficient energy is released during coalescence to explain observed spit velocities, a mechanism is still required to explain how the energy released causes mechanical motion. It is probable that, on coalescing, two spheres will form a highly deformed object that will subsequently oscillate about its equilibrium spherical shape. It is possible that this oscillation will stress the bonds between the object and the substrate and may lead to the object's escape from the surface. With this assumption the maximum velocity Vmaxand acceleration Ama~ of the surface of the spheroid can be found by also assuming that the surface executes simple harmonic motion. If the period of vibration is T and the ampitude yr, then Vm*-
2rtyr T
(4)
H I G H RATE EVAPORATION FROM G R A P H I T E CRUCIBLES
299
and A,=ax =
yr
(5)
where r is the radius of the sphere formed after coalescence. According to Rayleigh a the period of oscillation of spherical liquid drops of radius r is
f pr3"~l/2
T= n~-a )
(6)
where p is the density and tr the surface tension of the liquid. Assuming that th'~s expression is valid for oscillations of large amplitude, the amplitude required to account for the maximum observed height of ejection for tin (0.3 m) is 30~ of the radius for a sphere 10 ~tm in radius and 10~ of the radius for a sphere 1 lam in radius. The corresponding accelerations are 1.9 x 106 m s-2 and 6.0 x 107 m s-2; assuming an area of contact between sphere and substrate of half the cross-sectional area of the sphere, the stresses imposed on the surface bond are some 3.6 MPa and 11.6 MPa respectively. The amplitudes of these oscillations, although large, are not unreasonable and since the stress on the surface could easily break weak adhesion forces it does indicate that ejection through this mechanism is feasible. The observed dependence between ejection of lumps from graphite crucibles and the treatment or type of graphite used could be accounted for by a dependence between the treatment or type of graphite and the surface adhesion forces operating on weakly trapped lumps of evaporant. Any variation in the strength of adhesion forces would cause a variation in the probability of ejection of coalescing spheres. The observation of a preference for normal ejection can be accounted for by noting that ejection is most likely for coalescing spheres of equal size and that the resulting deformed body should have little momentum in a direction parallel to the surface. However, a complicating factor is the possibility that material ejected at low angles to the surface could collide with the larger spheres on the surface and hence be prevented from leaving the surface, thereby biasing the observed distribution. In fact it is possible that the many smaller spheres apparently stuck to the larger ones are the result of such collisions. Predictions of the model that can be tested include the relationship between size and velocity given by eqn. (2). Such a test would require an elaborate experimental arrangement and might not lead to a definitive conclusion since surface adhesion forces and other mechanisms of energy loss may also be size dependent. Perhaps the most convincing test would be the direct observation of the coalescence of two spheres; however, the need for submicrometre resolving power and frame times of 1 las would severely test any imaging system. 5. A P P L I C A T I O N TO OTHER TECHNIQUES OF EVAPORATION
The ejection of lumps of evaporant is a reasonably common occurrence when high rates of evaporation are used during vacuum evaporation from amorphous crucibles. In many cases liquid droplets can form on some area of the source and it is very likely that in such cases spitting occurs via the mechanisms described here. The
300
J. RICHARDS
only reliable method of suppressing this behaviour is to prevent the formation of the liquid droplets. In general this can be achieved in two ways. The first is by cooling the areas likely to develop droplets to a temperature at which condensation occurs as a solid and not as a liquid. The second method is the one reported here, namely raising the temperature of the whole source above the condensation temperature so that no deposit can grow. The choice of method will depend on the type of evaporation source used. 6. CONCLUSION The ejection of lumps of evaporant during high rate evaporation from graphite crucibles has been shown to be associated with the formation of condensed droplets on the crucible walls. A model in which ejection is caused by the release of surface energy as droplets coalesce has been proposed and this explains most of the observed properties of the ejected lumps. By using a special heating technique that prevents the formation of droplets on the crucible walls, intense spit-free vapour sources of tin and germanium have been demonstrated; the technique's application to other materials is probably straightforward. ACKNOWLEDGMENTS The author would like to acknowledge the assistance given by Mr. E. H. Hirsch in the preparation of this report and the help given by Mr. I. K. Varga in many useful discussions during the course of this work. REFERENCES 1 K.L. Chopra, Thin Film Phenomena, McGraw-Hill,New York, 1969,Chapter 4. 2 Yu. F. Komnik, Soy. Phys.-Solid State, 6 (10) (1965)2309. 3 J.F. Pocza, in E. Hahn (ed.), Proc. 2nd Colloq. on Thin Films, Budapest, 1967, Vandenhoeckand Ruprecht, G6ttingen, 1968,p, 93. 4 Lord Rayleigh,Proc. R. Soc. London, 29 (1879)71.
293
H I G H RATE E V A P O R A T I O N F R O M G R A P H I T E CRUCIBLES J. RICHARDS Electronics Research Laboratory, Defence Science and Technology Organisation, Department of Defence, GPO Box 2151, Adelaide, South Australia 5001 (Australia) (Received May 1, 1986; revised September 1, 1986; accepted September 16, 1986)
A technique has been found that eliminates the ejection of small droplets of evaporant during high rate vacuum evaporation of tin and germanium from heated graphite crucibles. A model is presented in which it is proposed that the energy causing the ejection comes from the release of surface energy that occurs when condensed droplets coalesce on the crucible walls.
1. INTRODUCTION In a study of the properties of vacuum-deposited thin films a need arose for a neutral source capable of high rates of deposition, able to hold a large quantity of evaporant and capable of evaporating many different materials. A problem encountered in meeting this need was the rapid corrosion by the evaporant of many crucible materials, such as tungsten, tantalum and molybdenum, at the elevated temperatures needed for reasonable rates of deposition. In an attempt to overcome this problem, graphite crucibles were used and were found to exhibit low rates of corrosion. However, the use of graphite caused another problem that was absent with metal crucibles, namely the occurrence of small molten lumps of evaporant in the vapour stream emerging from the crucible. At rates of deposition exceeding 1 n m s - 1 these lumps or spits easily reached and stuck to substrates positioned many centimetres above the crucible. Films grown under these conditions possessed very rough surfaces and were unusable. In this paper a method that eliminates spitting from graphite crucibles is reported, and a probable mechanism causing the ejection of lumps of evaporant is proposed. 2. EXPERIMENTALMETHOD A schematic diagram of the apparatus used in this study is shown in Fig. 1. The evaporant is contained in a graphite crucible, which is heated by a defocused electron beam drawn from a ring filament. A feature of this source is that the position of the filament with respect to the crucible can be altered. Since the emitted electrons tend to travel to those areas of the crucible closest to the filament, changing the 0040-6090/87/$3.50
© ElsevierSequoia/Printedin The Netherlands
294
J. RICHARDS
Insulator
Graphite Collimator
Microscope _ slide Upper filamer position L o w e r filamer position
Heat shield Filament . Graphite crucible . Tantalum platform
Filament - supports
_Supports
Fig. 1. Schematic diagram of apparatus used.
position of the emitter will alter the distribution of power onto the crucible and will thus alter the temperature distribution of the crucible. Two positions of the filament are used; in one the filament is situated adjacent to the bottom of the crucible and in the other it is placed near the top. In the low position the top of the crucible is typically 200 °C cooler than the melt and in the high position it is typically 25 °C hotter than the melt. By making the top of the crucible hotter or cooler than the evaporant, it is possible to control the rate of condensation of evaporant on the crucible walls and in fact to inhibit condensation altogether. The significance of this will be discussed below. The substrate is mounted on a temperature-controlled holder located 80 mm above the source and is inclined at 45 ° to the direction of the vapour stream. Rates of deposition are inferred by weighing the samples before and after deposition. An approximately constant rate is obtained during a deposition by maintaining at a fixed value the temperature of the platform that supports the crucible. The apparatus is evacuated to a pressure below 10-3 Pa by a liquid-nitrogen-trapped diffusion pump. 3. RESULTS With the filament in the low position, evaporation of tin produced significant ejection of lumps at rates of deposition over about 1 nm s- 1. Spitting was detected either by viewing the substrates after the deposition had ceased, to see whether any lumps were present on the surface of the deposit, or by observing directly spits flying
HIGH RATE EVAPORATION FROM GRAPHITE CRUCIBLES
295
in the space between the collimator and the substrate during deposition. This was feasible in the case of the larger spits because they could be readily seen in the bright light coming from the vapour source. The spitting rate was observed to increase considerably with increasing rate of evaporation. Inspection of the crucible after the deposition had been completed showed that tin spheres, ranging in size from 0.5 mm down to the submicrometre range, had formed in the cooler upper areas of the crucible. Very similar results were observed when evaporating germanium. The height reached by ejected lumps was also examined visually and typically varied from very low values to as high as 0.3 m, with the great majority reaching only a few centimetres. The relationship between the rate of spitting and the condition of the graphite was also investigated and it was observed that highly outgassed crucibles produced fewer spits t h a n those not loutgassed, other factors being the same. Crucibles that were given a cleaning treatment in which the graphite was heated to about 1000 °C and then dropped into distilled water produced less spitting than crucibles not so treated. Pyrolytic graphite crucibles were found to spit less than coarsegrained graphite crucibles. However, when the filament was in the low position all graphite crucibles produced too many lumps on the substrate to enable useful films to be grown at high rates of deposition. With the filament in the high position, entirely different results were observed. Evaporation of both tin and germanium showed no evidence of any ejection of lumps at any rate of deposition, the highest rate tested being 20 nm s- 1. Apart from the achievement of a far greater range of rates of deposition, there was no need to apply any special heat treatment to the graphite, and no special type of graphite was required. Further, there was no sign of any condensed material on the exposed surfaces of the crucible above the melt. Thus the performance of the source was greatly improved in every respect by the repositioning of the filament. These results indicate an association between spitting and the temperature distribution of the crucible and perhaps a relationship between spitting and the formation of condensed evaporant on the crucible walls. To investigate the relationship between spitting and droplet formation more fully a graphite disc made of the same material as the crucible was placed on one of the substrate holders and heated to 360 °C, the maximum temperature that the holder could reach. A glass microscope slide was positioned as shown in Fig. 1 so that it could only intercept objects emanating from the graphite disc. A tin deposit of mean thickness 6 Ixm was then built up on the graphite at a rate of 10 nm s- 1 from the source operated in the spit-free mode. The graphite and microscope slide were then carefully examined by scanning electron microscopy. A scanning electron micrograph of an area of the microscope slide is shown in Fig. 2. The photograph reveals the presence on the glass slide of small, mainly spherical, lumps of tin that range in size from a maximum diameter of 25 I.tm down to 0.15 I.tm. These sizes agree reasonably well with the size of spits emanating from a spitting graphite crucible. From the geometry of the apparatus it is clear that these lumps could not have come from any region other than the graphite surface. Further confirmation of this fact comes from two other observations. First, when the graphite disc was replaced by a cool copper substrate the film grown on it did not
296
J. RICHARDS
possess any lumps of tin, indicating that the vapour source did not generate spits and could not be the source of the lumps observed on the microscope slide. Secondly, the larger lumps on the microscope slide are rather similar to the lumps on the graphite surface. This can be seen by comparison of Figs. 2 and 3, which shows that the larger lumps of tin, both on the microscope slide and on the graphite, have small spheres attached to them.
I
I
51ma Fig. 2. Scanning electron micrograph of lumps of tin collected on the microscope slide. Fig. 3. Scanning electron micrograph of spheres of tin formed on a graphite substrate.
I
I
20 Inn
The angular distribution of spits ejected from the graphite was determined by measuring the spatial distribution of spits on the microscope slide and using the known geometry of the apparatus. The result is shown in Fig. 4 for spits exceeding about 1 p.m in diameter. Angular errors arise because of the large size of the emitting area and the influence of gravitational forces acting on the spits after ejection. Errors in counting the number of spits arise because of difficulties in detecting very small spits and the possibility that not all spits stick to the microscope slide. The broken curve shown in Fig. 4 is a distribution calculated assuming that all directions of ejection are equally probable. This curve has been normalized to give the same total yield as is observed experimentally; comparison of the curves shows that the ejection of spits in directions close to the normal is preferred. A comparison of the size distribution of lumps collected on the microscope slide and the size distribution of condensed spheres on the graphite surface does not reveal a significant difference for spheres greater than approximately 1 p.m in diameter. There were far fewer spheres of submicrometre size on the microscope slide than on the graphite. The total number of spits ejected from the graphite surface can also be estimated by counting the spits collected on the microscope slide. Assuming that the sticking probability of ejected lumps is unity, then from a mere 1.4 mg of tin deposited onto graphite at 360 °C some 25000_+ 3000 lumps are ejected with diameters exceeding 1 p.m. The large number of lumps ejected from a small quantity
HIGH RATE EVAPORATION FROM GRAPHITE CRUCIBLES
297
1.O
0.8
co
:~
0.6
0.4
0.2
00 20 40 60 80 Angle between trajectory and surface normal 0 (degrees)
Fig. 4. Angular distribution of ejected lumps (---, calculated distribution assuming that all directions of ejection are equally probable).
of material indicates how troublesome spitting can be. For example, in a graphite crucible containing 5 g of evaporant the amount condensing on the crucible walls could be as much as 2-3 g, indicating that more than 10 7 spits could be generated. It is obvious that appreciable contamination would occur if only a small fraction of these end up on the substrate. 4. DISCUSSION These results show that spitting is associated with the growth of liquid droplets on a graphite surface. Several studies of the growth of many materials on amorphous surfaces have been made 1-3 and the results depend strongly on whether condensation occurs as a liquid or a solid. In these experiments condensation as liquid occurs because the substrate temperature is well above the melting point, although even this is not necessary since Komnik 2 has found that condensation as a liquid occurs in many materials down to substrate temperatures as low as two-thirds of the bulk melting point. In the initial stages of growth under these conditions extremely small nuclei develop that contain small numbers of atoms. These nuclei grow by intercepting atoms from the vapour stream and by absorbing mobile adatoms that have condensed elsewhere on the substrate surface. On amorphous surfaces or those where little wetting of the surface occurs by the condensate these nuclei will be almost spherical in shape. If adjacent spheres touch during growth they may coalesce to form a single larger sphere. Coalescence of spheres will continue irrespective of the size of the spheres and will only cease when the arrival of vapour on the surface stops. This model can explain most of the features visible in Fig. 3. Of the processes mentioned above, the coalescence of spheres on the graphite
298
J. RICHARDS
surface could be responsible for ejection of lumps. During coalescence there is a release of surface energy, as has been shown by Pocza 3. He proposed that the released energy causes the temperature of the coalescing objects to rise; however, it is possible that the released energy causes mechanical movement as well. For coalescing spheres of radii r and xr, the surface energy released is given by E = 47tar2{(1 + x 2) - (1 + x3) 2/3 }
(1)
where a is the surface tension of the evaporant. Equation (1) indicates that energy is released for all values of x, since (1 + x z) is always greater than (1 + x3) 2/3. If it is assumed that all the energy released is transferred to kinetic energy of the coalescing objects it is simple to show that the maximum velocity of the ejected lump is given by
V=[6a{l + x2--(l + x3)2/3}ll/2 ~-1- + x 5
(2)
where p is the density Of the evaporant. For coalescing tin spheres 10 ~m in radius, eqn. (2) gives a velocity of 2.98 m s- 1, sufficient to reach a height of 0.45 m if the sphere is ejected vertically. This is larger than ejection heights observed from spitting crucibles; hence we do not require 100~o conversion of released surface energy into mechanical energy to explain the spit velocities observed. Equation (1) can be used to evaluate the optimum value of x that leads to the release or ejection of the coalescing spheres from the surface. Presumably the probability of release will be proportional to the energy available and inversely proportional to the bond strength between spheres and substrate. The probability P of ejection is therefore given by a{ l+x2 } P oc ~ (1 + xa) 2/3 1 (3) where k is the bond strength per unit area of contact. Equation (3) shows that the probability of ejection is independent of r, supporting the experimental observation that the size distribution of spits collected on the microscope slide is similar to the size distribution observed on the graphite substrate. Analysis of eqn. (3) reveals that P is maximum when x = 1, i.e. when spheres of equal size coalesce. When the ratio of sizes is 2: 1, P drops to 60~ of its peak value, indicating that it is unlikely that the coalescence of spheres with very different sizes will lead to ejection. Although it has been shown that sufficient energy is released during coalescence to explain observed spit velocities, a mechanism is still required to explain how the energy released causes mechanical motion. It is probable that, on coalescing, two spheres will form a highly deformed object that will subsequently oscillate about its equilibrium spherical shape. It is possible that this oscillation will stress the bonds between the object and the substrate and may lead to the object's escape from the surface. With this assumption the maximum velocity Vmaxand acceleration Ama~ of the surface of the spheroid can be found by also assuming that the surface executes simple harmonic motion. If the period of vibration is T and the ampitude yr, then Vm*-
2rtyr T
(4)
H I G H RATE EVAPORATION FROM G R A P H I T E CRUCIBLES
299
and A,=ax =
yr
(5)
where r is the radius of the sphere formed after coalescence. According to Rayleigh a the period of oscillation of spherical liquid drops of radius r is
f pr3"~l/2
T= n~-a )
(6)
where p is the density and tr the surface tension of the liquid. Assuming that th'~s expression is valid for oscillations of large amplitude, the amplitude required to account for the maximum observed height of ejection for tin (0.3 m) is 30~ of the radius for a sphere 10 ~tm in radius and 10~ of the radius for a sphere 1 lam in radius. The corresponding accelerations are 1.9 x 106 m s-2 and 6.0 x 107 m s-2; assuming an area of contact between sphere and substrate of half the cross-sectional area of the sphere, the stresses imposed on the surface bond are some 3.6 MPa and 11.6 MPa respectively. The amplitudes of these oscillations, although large, are not unreasonable and since the stress on the surface could easily break weak adhesion forces it does indicate that ejection through this mechanism is feasible. The observed dependence between ejection of lumps from graphite crucibles and the treatment or type of graphite used could be accounted for by a dependence between the treatment or type of graphite and the surface adhesion forces operating on weakly trapped lumps of evaporant. Any variation in the strength of adhesion forces would cause a variation in the probability of ejection of coalescing spheres. The observation of a preference for normal ejection can be accounted for by noting that ejection is most likely for coalescing spheres of equal size and that the resulting deformed body should have little momentum in a direction parallel to the surface. However, a complicating factor is the possibility that material ejected at low angles to the surface could collide with the larger spheres on the surface and hence be prevented from leaving the surface, thereby biasing the observed distribution. In fact it is possible that the many smaller spheres apparently stuck to the larger ones are the result of such collisions. Predictions of the model that can be tested include the relationship between size and velocity given by eqn. (2). Such a test would require an elaborate experimental arrangement and might not lead to a definitive conclusion since surface adhesion forces and other mechanisms of energy loss may also be size dependent. Perhaps the most convincing test would be the direct observation of the coalescence of two spheres; however, the need for submicrometre resolving power and frame times of 1 las would severely test any imaging system. 5. A P P L I C A T I O N TO OTHER TECHNIQUES OF EVAPORATION
The ejection of lumps of evaporant is a reasonably common occurrence when high rates of evaporation are used during vacuum evaporation from amorphous crucibles. In many cases liquid droplets can form on some area of the source and it is very likely that in such cases spitting occurs via the mechanisms described here. The
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only reliable method of suppressing this behaviour is to prevent the formation of the liquid droplets. In general this can be achieved in two ways. The first is by cooling the areas likely to develop droplets to a temperature at which condensation occurs as a solid and not as a liquid. The second method is the one reported here, namely raising the temperature of the whole source above the condensation temperature so that no deposit can grow. The choice of method will depend on the type of evaporation source used. 6. CONCLUSION The ejection of lumps of evaporant during high rate evaporation from graphite crucibles has been shown to be associated with the formation of condensed droplets on the crucible walls. A model in which ejection is caused by the release of surface energy as droplets coalesce has been proposed and this explains most of the observed properties of the ejected lumps. By using a special heating technique that prevents the formation of droplets on the crucible walls, intense spit-free vapour sources of tin and germanium have been demonstrated; the technique's application to other materials is probably straightforward. ACKNOWLEDGMENTS The author would like to acknowledge the assistance given by Mr. E. H. Hirsch in the preparation of this report and the help given by Mr. I. K. Varga in many useful discussions during the course of this work. REFERENCES 1 K.L. Chopra, Thin Film Phenomena, McGraw-Hill,New York, 1969,Chapter 4. 2 Yu. F. Komnik, Soy. Phys.-Solid State, 6 (10) (1965)2309. 3 J.F. Pocza, in E. Hahn (ed.), Proc. 2nd Colloq. on Thin Films, Budapest, 1967, Vandenhoeckand Ruprecht, G6ttingen, 1968,p, 93. 4 Lord Rayleigh,Proc. R. Soc. London, 29 (1879)71.