Method for controlling the solidification of a liquid-solid system and a device for the application of the method

The growth of a solid obtained by cooling a liquid solution is observed and controlled by measuring the variation in volume of the solid-liquid system at the time of solidification. The method is applicable to the control of oriented crystallization from an initial crystal seed or epitaxial growth on a substrate having a suitable crystal orientation. The rate of crystallization can be controlled by means of a furnace provided with means for producing regulated thermal gradients, temperature-measuring means, a chamber filled with an inert liquid, an open-topped container filled with the liquid to be solidified and immersed in the inert liquid, the container being suspended from one arm of the beam of an electrobalance.

This invention relates to a method for controlling the solidification of a 
liquid-solid system and especially a method for controlling the growth of 
a single-crystal layer in liquid phase. The invention is also concerned 
with a device for the practical application of the method in accordance 
with the invention. 
As is already known, accurate measurement and control of liquid-solid 
transformation is necessary in order to obtain from the liquid state 
crystalline substances which have a high degree of structural perfection, 
that is, which have no defects such as twinning, crystal impurities or 
microprecipitates. Techniques of the prior art achieve these objectives 
only to a very partial extent since the phenomenon of crystallization is 
controlled only by means of approximate measurement of the range of 
temperatures within the sample (in a furnace of the Bridgman type, for 
example). Control of the liquid-solid transformation process can really be 
ensured only on the basis of measurement and control of an extensive 
quantity which is characteristic of said transformation or in other words 
directly related to the quantity of liquid which has solidified or 
crystallized in the course of time. 
The direct observation of the limit between the liquid phase and the solid 
phase which can be performed by optical means satisfies the condition 
stated above but can clearly be employed only for transparent elements. 
Similarly, gravimetric methods based on direct weighing of the solid 
immersed in the nutrient liquid phase or mother medium of different 
density, such methods having been described in the article by S. H. Smith 
and D. Elwell, Journal of Crystal Growth (3,4) (1968), page 471 which 
forms part of the description, result in extensive measurements; however, 
it has been possible by means of these methods to obtain only imprecise 
observations since there are a number of sources of error which affect the 
results of the measurements: 
the real density of the displaced liquid is unknown since it remains a 
function of the concentration gradients, 
it is not possible to orient the crystal growth, which consequently gives 
rise to multidirectional growth with variable rates according to the 
crystal orientation of the interfaces, 
there remains the difficulty of eliminating the disturbances introduced by 
convection currents in the liquid. 
The method in accordance with the invention overcomes the disadvantages 
discussed in the foregoing and makes it possible to measure an extensive 
quantity related to the liquid-solid transformation and applies to the 
oriented solidification of an extremely wide range of material, whether 
such material is of the congruent-fusion type or not. 
The method according to the invention further permits of real and 
continuous control of the transformation process by either manual or 
automatic action. 
More precisely, the method for controlling the solidification of a 
liquid-solid system in accordance with the invention essentially consists 
in observing the growth of the solid obtained by cooling a liquid solution 
by measuring the variation in volume of the solid-liquid system at the 
time of solidification. 
One preferential application of the method according to the invention is 
the control of oriented crystallization in liquid phase which is carried 
out from an initial crystal seed or by epitaxial growth on a substrate 
having a suitable crystal orientation. 
The method for controlling the crystal growth for example utilizes the 
continuous measurement of variations in volume of the liquid-solid system 
during the transformation process. These variations in volume are 
primarily due to the difference between the specific volume of the same 
substances in the solid state and in the liquid state: this is the molar 
volume of fusion .DELTA.V.sub.F in the case of pure substances or the 
difference in integral molar volumes in the case of mixtures. 
Thus the quantitative determination of the crystallized (or solidified) 
mass as a function of time is possible when the molar volume of 
transformation of the material is known. Moreover, even if this quantity 
.DELTA.V.sub.F is unknown, the method in accordance with the invention 
makes it possible to show and thus to control any possible variations in 
the growth rate which are the cause of many structural defects of the 
crystallized solid. 
The method in accordance with the invention also makes it possible to 
regulate the rate of crystallization by producing action on the 
temperature of the furnace in which the crystallization takes place as 
well as on the thermal gradients which exist within said furnace, as a 
function of the measurement of the growth rate of the solid in the liquid 
phase. 
The advantages of the method of control arise from the very nature of the 
parameter being measured which is a characteristic extensive quantity of 
the phenomenon and therefore representative of the quantities transformed. 
The measurement of the liquid volumes can be obtained with a high degree of 
accuracy by making use of conventional dilatometric techniques which are 
adapted to the experimental conditions of solidification. The sensitivity 
of these types of measurements makes it possible to detect 
micro-variations in speed of transformation or alternatively to control 
the thickness of a thin-film deposit in the case of deposition by 
epitaxial growth. The method in accordance with the invention is 
applicable both to the solidification of either pure or low-alloyed 
substances and to the solidification of binary or more complex 
concentrated mixtures. 
In the two cases just mentioned, it is known that the variations in 
transformation volume are only slightly influenced by the progressive 
variation of concentrations in each of the two phases in the vicinity of 
the interface. On the contrary, the transformation temperature is an 
unknown factor since it is largely dependent on the measurement of the 
solidification rate, on the nature and concentration of the components in 
the vicinity of the interface. This phenomenon thus accounts for a further 
advantage of the method in accordance with the invention. 
Similarly, the influence of the mean solidification rate which is laid down 
as a result of experience and modifies to a considerable extent the 
temperature of transformation by the phenomenon of kinetic undercooling 
remains imperceptible in regard to the molar volume of fusion. 
Measurement of the variation in solid-liquid volume can be carried out in a 
preferential embodiment of the invention by immersing the solid-liquid 
system in an inert liquid and by measuring the variations in Archimedean 
thrust on the solid-liquid system, this variation in thrust being related 
to the variations in volume of said liquid-solid system. There is employed 
in this case an inert liquid having a lower density than that of the 
liquid to be crystallized. 
In an alternative embodiment of the method according to the invention and 
in order to guard against parasitic variations in the volume of the 
solid-liquid system and of the enclosure containing said system which are 
essentially dependent on the temperature of the liquid melting bath, a 
preliminary calibration of said variations in volume is accordingly 
carried out. This preliminary calibration is performed under conditions 
which are as closely related as possible to those of the real 
solidification. Thus the variation in parasitic volume which is not 
related to a liquid-solid transformation can be associated with each value 
of the temperature and of a temperature gradient. Accordingly, said 
calibration or preliminary calibration makes it possible in respect of any 
temperature condition of the liquid bath to be crystallized to determine 
the variations in parasitic volume which can accordingly be deducted from 
the variations in volume to be observed so as to permit of accurate 
determination of the variations in real volume which relate to the 
solid-liquid transformation. 
In more general terms, the method under consideration which is designated 
as a simulated differential method consists in measuring an elementary 
parameter on which the system depends and in interpreting said parameter 
independently of the transformation which takes place therein. Measurement 
of this elementary parameter (temperature, temperature gradient and so 
forth) is converted to an electrical quantity such that this latter can be 
set up in opposition at each instant to the voltage delivered by the 
volume-variation detector. The resultant signal is thus entirely freed 
from variations and parasitic fluctuations induced in the system by those 
of the parameter which is chosen. The elementary parameter or parameters 
are usually the temperature of the liquid bath or the temperature and 
gradient of the liquid bath to be solidified but can also be a vapor 
pressure, solubility, electrical or optical properties of the bath and so 
forth. 
In the event that a number of parameters are observed, it is possible to 
study the action of each parameter independently, to check the corrections 
to be made in each of these parameters and, at the time of measurement of 
the variation in volume as a function of the different values of said 
parameters, to correct the variations in volume as measured by means of 
the different variations in parasitic volume in order to obtain the 
variations in real volume. 
In the case of crystallization, the simulated differential method which 
eliminates the parasitic variations in volume of the sample makes it 
possible to measure small quantities of the transformation volume alone 
with the high degree of accuracy obtained by means of conventional 
dilatometric detectors, this being achieved without entailing any 
excessive increase in complexity of the equipment. 
Two particularly important applications of the method of control are 
concerned in one case with massive monocrystallization from the liquid 
phase and in the other case with monocrystallization obtained by thin-film 
epitaxial growth from a saturated liquid phase.

The thermal portion of the massive crystallization device as shown in FIG. 
1 makes it possible to obtain from a liquid solution 2 a crystal 4 which 
is crystallized from a seed deposited at the bottom of the container 6. 
The open-topped container 6 is immersed in an inert liquid 8 contained in a 
vessel 10. 
The container 6 which is totally immersed in the liquid 8 is connected by 
means of the wire 12 to the end of one arm of the beam of an 
electrobalance which is shown in FIG. 2. 
A circulation of gas through the ducts 14 and 16 makes it possible to renew 
the atmosphere which is present above the bath 8 of inert liquid. 
The vessel 10 is placed within a tubular furnace of the Bridgman type; this 
vertical tubular furnace delivers a centripetal thermal flux; the axial 
thermal gradient is increased by means of a winding 18, the intended 
function of which is to overheat the upper portion of the immersion bath 
which is filled with inert fluid 8. The heat sink is constituted by a 
cooled probe 20 which is placed in the axis of the furnace at the lower 
end of this latter. The arrangement of the vessel 10 which contains the 
inert liquid 8 makes it possible to minimize the volume of fluid 2 in the 
liquid state in which the solid sample 4 is immersed while eliminating 
surface-active effects produced by the walls on the suspension wire 12 and 
the container 6. 
The bottom portion of the reservoir in the shape of a glove finger makes it 
possible to increase the radial and axial thermal flux within the 
solid-liquid sample. 
The temperature is measured by means of the thermocouple 22 in a zone which 
is close to the medium of the container 6. The thermocouple 22 is 
protected from external thermal influences by means of an inert mass 24 of 
refractory material. The thermocouple 22 is connected to a correcting unit 
56 which is shown in greater detail in FIG. 2. 
The thermal gradient which is continuously measured within the inert fluid 
8 is maintained constant during the experiment by automatic regulation, 
this being performed by means of a regulator of known type fitted with a 
linear programmer 26 which controls the power in the hot region of the 
Bridgman furnace and which is well known to those versed in the art. Said 
programmer 26 controls a thermal regulator 29 which in turn controls the 
power source 41. A second regulator 28 associated with the differential 
comparator 27 for collecting the indications of the regulating 
thermocouples 33 and 35 produces action on the position of the cooling 
unit 20 in order to stabilize the value of the thermal gradient at a 
predetermined value. 
A system of horizontal screens 30 has the effect of reducing the convective 
movements of the atmosphere around the vessel 10. 
Measurement of the variations in volume of the two-phase solid-liquid 
system 2-4 which is present within the container 6 is carried out by 
gravimetry by converting the variations in volume to variations in 
Archimedean thrust on the container. 
In the furnace of the Bridgman type shown in FIG. 1, the value of the 
thermal gradient and the power programming are adjusted so as to carry out 
solidification of the sample at different cooling rates. 
The possibility of carrying out good measurement of the variations in 
volume of the liquid-solid system calls for very high hydrodynamic 
stability of the fluids 2 and 8 and also for cancellation by electrical 
opposition of the factors which influence the response of the balance 
other than that which results from liquid-solid transformation. 
The first condition makes it necessary to establish values of thermal and 
mass flow which stabilize the fluid masses. 
This condition which is undoubtedly favorable to monocrystallization in the 
Bridgman technique is satisfied by the application of the principle of the 
thermal core described in the article by Messrs. H. S. Carslaw and J. C. 
Jaeger, Conduction of Heat in Solids, The Clarendon Press, Oxford, 1967, 
this article being an integral part of the description. Thus a centripetal 
horizontal thermal flux and a downwardly oriented vertical axial flux are 
so applied that the condition of Rayleigh stability is maintained at all 
points of the fluid media. 
The second condition is satisfied by adopting the simulated differential 
method. 
The response of the balance during a crystallization operation is 
influenced by a certain number of phenomena : it is necessary to take 
account not only of the effects which are directly related to the 
existence of a transformation volume but also of major parasitic effects 
which are related to variations in density of the liquid, solid and even 
gaseous masses including the sample and the surrounding bath such as those 
produced by variations as a function of the temperature, positions and 
dimensions of the container and the suspension wire and also of surface 
tension forces. 
This combination of parasitic factors is essentially dependent on the 
ranges of temperature within the device and on its variations. 
A comparison of a measurement of temperature which is representative of the 
thermal state of the system at each instant with the indication supplied 
by the balance in the absence of any liquid-solid transformation shows the 
linearity and reversibility of the relation existing between these two 
quantities within the temperature range selected. 
It will therefore be necessary only to convert the voltage delivered by the 
reference thermocouple 22 to another voltage which can be directly set up 
in opposition to that delivered by the electrobalance. 
The use of the device for the practical application of the method according 
to the invention makes it possible to measure the variation and also to 
control the crystal growth rate (this factor governs the crystalline 
quality of the solid) by having recourse to methods of automatic control. 
The method according to the invention offers the possibility of measuring 
the solidification rate as a function of time and also serves to control 
the thermal parameters in dependence on optimum fixed values in respect of 
the rate of solidification in solution. 
A further possibility of use of the simulated differential method in 
accordance with the invention lies in the direct comparison of the growth 
rates of a sample with the growth rate of a standard reference. For 
example, it is possible to measure the effect of addition elements on the 
rate of growth of a sample. 
The immersion bath must meet the known requirements of the methods of 
unidirectional crystallization, among which can be mentioned : 
total relative insolubility of the liquid 8 and of the sample formed in the 
liquid 2 and the solid 4, 
density of the inert liquid 8 which is lower than that of the general 
container sample, 
high chemical inertia with respect to these elements in contact and high 
chemical purity, 
excellent wetting properties, 
low melting point and low vapor pressure, 
molten salt baths of the alkali metal chlorides in a eutectic composition, 
for example, are wholly suitable for metallic solid-liquid samples. Baths 
having a base of boric oxide can also be employed. 
In FIG. 2, there is shown the electronic diagram in connection with the 
thermal-gradient furnace for controlling the crystallization of a 
solid-liquid system. The same elements in FIGS. 1 and 2 are designated by 
identical reference numerals. 
The arm 50 of the beam of the electrobalance 52 is connected by means of 
the wire 12 to the container 6 in which the solid-liquid system is 
present. Measurement of the force applied to the wire 12 is obtained by 
compensation on the solenoid 54 of the other arm of the beam of the 
electrobalance 52. 
The unit 56 comprises a function module 60, an opposition source 61, an 
amplifier 62 having a gain G and a differential connection unit 63. In 
this example of construction, a temperature measurement is performed by 
means of the thermocouple at 22 in the vicinity of the container 6. After 
amplification, the signal which has been processed by the function module 
acts in opposition to the signal produced by the electrobalance via 
channel 54. The signal on channel 66 at the output of the unit 56 is 
recorded in the recording unit 67 and the same applies to the signal 
obtained from a thermocouple 23 which is placed next to the thermocouple 
22. After calibration, the signal on channel 66 measures the real growth 
of the solid 4 and can be employed for transmission into the unit 29 for 
regulating the growth rate as a result of regulation of the furnace 
temperatures. 
The electrobalance 52 is a conventional "zero" instrument which delivers a 
voltage which is proportional to the variations in thrust. The signal 
obtained from the thermocouple 23 may simply be recorded in the unit 67. 
The complete assembly consisting of container and liquid-solid sample must 
be in equilibrium with the immersion bath prior to commencement of any 
transformation process. This assembly must also be freed as far as 
possible of gas bubbles which adhere to the surfaces by capillary tension 
prior to establishment of a base line representing the variations in 
parasitic volume in the absence of an actual liquid-solid transition. In 
the case of seedless growth, the entirely liquid immersed sample as well 
as the bath are first placed in a vacuum in order to permit removal of the 
occluded gases. Under the initial conditions of the synthesis to be 
performed, a temperature stage is then maintained for the period of time 
which is necessary in order to establish equilibrium. The progressive 
variation of the system is followed by dilatometry and equilibrium is 
attained when the signal delivered by the detecting unit (52 and 56) to 
the channel 66 and recorded in the recording unit 67 no longer varies. 
At the end of said temperature stage, the programmed cooling of the furnace 
obtained by the regulator 29 is resumed without thereby initiating the 
transformation of the sample. The opposition circuit 61 which is 
incorporated in the unit 56 is calibrated so as to ensure that the base 
line is retained. Crystallization proper can then begin and is indicated 
by a corresponding progressive variation in the electrical output signal 
on channel 66 which is recorded in the recording unit 67. 
A different method can also be adopted for establishing the base line; this 
method consists in carrying out adjustments during melting of the samples 
or dissolving of the solute. Any subsequent deviation from this line which 
may be observed during the reverse operation corresponds to an abnormality 
in the growth rate, this being due either to the mechanisms of attachment 
in the stationary state or to the various transient states which may in 
some cases occur. 
Example of process of crystal growth of an indiumantimony intermetallic 
compound : 
a. Physical characteristics of the compound 
melting temperature : T.sub.f = 530 .+-. 5.degree. C 
density of the solid : .rho..sub.S = 5.765 [1 - 1.643.times.10.sup. -5 (T - 
530.degree.)] 
density of the liquid : 
This latter can be linearly related to the temperature by postulating a 
correlation factor which is equal to 0.995. 
EQU .rho..sub.1 = 6.470 [1 - 1.0267 .times. 10.sup.-4 (T - 530)] 
relative variation in volume at the time of fusion : 
(.DELTA.V.sub.f /V.sub.L ) = 12.3%. 
b. Operating conditions 
container : tubular crucible of transparent quartz which contains the 
sample. This sample is constituted by a single-crystal seed which is 
attached mechanically to the base of the crucible and by a polycrystalline 
charge which is placed above the seed. 
section : 1 cm.sup.2 - height : 10 cm 
immersion bath : purified mixture of Li Cl - K Cl having the eutectic 
composition : 
Melting point : 355.degree. C 
Density of the liquid : .rho..sub.e = 1.70 [1 - 3.105 .times. 10 .sup.-4 
(T-355)] 
Suspension wire : 10% rhodium-platinum alloy having a diamter of 0.2 mm. 
The thermal conditions have been defined in connection with two cases of 
synthesis. The first case corresponds to congruent solidification of the 
compound In Sb : 
Mean temperature of the sample : 600.degree. C 
Mean thermal gradient : 20.degree.C/cm 
Rate of programmed cooling : 15.degree.C/hour. 
The second case relates to the crystallization of the stoichiometric 
compound from a solution containing 64% by weight of indium, the 
liquid-solid equilibrium temperature of which is 500.degree. C. 
Mean temperature of the sample : 570.degree. C 
Mean thermal gradient : 20.degree. C 
Rate of programmed cooling : 0.6.degree. C/hour. 
c. Measurements 
Detection : the electrobalance employed offers a sensitivity of 0.121 mV/mg 
under these operating conditions. 
Base line : the signal of the reference thermocouple is amplified with a 
gain of 2.330. 
Drift of the base line is observed but remains constant and equal to 50 
.mu.V/hour. The variations observed do not exceed .+-. 2 .mu.V. 
Under these conditions of measurement, it has been possible to follow the 
liquid-solid transformations in both cases with a sensitivity of 10 .mu.V, 
which corresponds to a thickness of 5 .mu. of formed solid InSb. 
In the simple case in which there is observed experimentally by calibration 
on the sample in the liquid state a linear variation in thrust as a 
function of temperature, the mathematical function which serves to modify 
the thermocouple signal is of the form : E = A + B S.sub.TC, where E is 
the correction potential and S.sub.TC is the temperature signal delivered 
by the thermocouple 22. 
There is then employed as shown in FIG. 2 an adjustable electric opposition 
source 61 for measuring the coefficient A and a variable-gain 
direct-current voltage amplifier 62 for obtaining the coefficient B of the 
formula given above. 
In cases in which there is observed a non-linear variation in temperature 
caused by liquid alloys having a density which does not vary linearly with 
temperature (this being the case with tellurium-base alloys such as 
In.sub.2 Te.sub.3, Ga.sub.2 Te.sub.3, for example), processing of the 
thermocouple signal accordingly utilizes a mathematical function which is 
better adapted (polynominal, logarithmic function and so forth). This type 
of treatment of the signal clearly forms part of the device in accordance 
with the invention (function module of FIG. 2). 
FIG. 3 shows at 200 the curve, recorded as a function of time, of the 
signal obtained on channel 26 of the diagram of FIG. 2 comprising the base 
line 202 and the corrected signal of resultant force .DELTA.F 204 
corresponding to solidification in the case of an InSb alloy. 
Solidification takes place between the points 206 and 208. The temperature 
curve 205 T(t) measured by means of the thermocouple 23 is also recorded 
as a function of time. 
FIG. 4a shows an epitaxial growth cell and FIGS. 4b, 4c, 4d, 4e and 4f show 
the different stages of operation for the deposition of a layer by 
epitaxial growth on a substrate 70. The epitaxial-growth cell showed in 
FIG. 4a is employed for the formation of thin films by the method of 
horizontal epitaxy. The epitaxial-growth cell 4a is provided with sliding 
elements which permits chronological performance of the stages of 
operation shown in FIGS. 4b, 4c, 4d, 4e and 4f which will hereinafter be 
described. The epitaxial-growth cell 72 of the drawer type has been 
modified so as to conform to the conditions of detection of variations in 
volume. The cell 72 can be constructed of graphite or of any other 
chemically inert material which is both heat-resistant and capable of 
being machined with precision. The epitaxial-growth cell which is 
generally designated by the reference 72 has a parallelepipedal shape and 
consists of two main elements. One of these latter is a stationary element 
74 which constitutes the cell body and in which two recesses are formed, 
the single-crystal substrate 70 being intended to be placed in one recess 
and a sample 76 employed as a source for saturating the solution 78 is 
placed in the other recess. 
A moving system referred-to as a drawer is made up of three sections : 
a main section 80 comprises the cavity which serves as a reservoir for the 
solution 78 and can be positioned with respect to the cell body. The 
capacity of said reservoir is accurately adjusted by displacing a dead 
space 84, this displacement being controlled from the exterior of the 
furnace 100. Three thermocouples 82 are placed within said dead space 
which is immersed in the solution during the epitaxial-growth stage. One 
of these thermocouples serves to regulate the furnace 100 which surrounds 
the epitaxial-growth cell. The second thermocouple serves to measure the 
mean temperature of the bath and the third thermocouple constitutes the 
reference element for the system of the simulated differential method. 
the top portion of the drawer is a sliding plate 86 constituting a cover 
for the reservoir on which is fixed the capillary tube 88 of transparent 
quartz. An end-stop 90 permits the displacement of the plate 86. 
Detection of the position of the meniscus within the capillary tube is 
obtained by means of an optical system constituted by a source 92, a first 
lens 94, a lens 96 and a system 98 for measuring the illumination produced 
by the lens 96 such as the sensitive surface of a photodetector, for 
example. The optical system forms the image of the meniscus located within 
the capillary tube 88 on the sensitive surface of the photoelectric cell 
98. In order to prevent variations in the image as a result of convection 
currents of the furnace atmosphere which surrounds the cell, this optical 
sighting operation can be carried out through a transparent solid medium 
such as a quartz rod (not shown in the figure). The electrical signal at 
the output of the cell 98 is a function of all the factors which influence 
the position of the meniscus within the capillary tube 88. The simulated 
differential method consists in the case of deposition by epitaxy in 
generating in opposition to the signal A delviered by the photoelectric 
cell 98 another electrical signal B delivered by the reference 
thermocouple 82, this signal being proportional to the displacement of the 
meniscus independently of the liquid-solid transformation by epitaxial 
growth. 
Thus in the absence of variations in volume resulting from the phase 
transformation, the two signals A and B remain equal and opposite during 
the recording which has been defined as the base line. When transformation 
takes place, namely either crystallization or dissolution, a difference 
appears which is proportional to the mass transformed. 
The operating procedure is represented by the different stages in FIGS. 4b, 
4c, 4d, 4e and 4f. FIG. 4b shows the degassing stage during which the cell 
filled with the single-crystal substrate of the saturation source and with 
the bath of predetermined composition containing if necessary a doping 
solute is placed in the vacuum-degassing position. 
Adjustment of the base line shown at 202 in FIG. 3 is carried out in the 
position shown in FIG. 4c, namely the position of the drawer obtained 
after having adjusted the capacity of the reservoir 78 in order to bring 
the meniscus contained in the capillary tube 88 into its initial position. 
This adjustment takes place under a number of different 
temperature-variation regimes. 
In the stage shown in FIG. 4d, the bath is brought to the initial 
temperature which was chosen and contacted with the solution 76 which is a 
source for the saturation of the solution 78. Contact between the solution 
78 and the substrate 76 is maintained until a physico-chemical equilibrium 
between the solid and the liquid is established, this equilibrium being 
clearly observed by means of the system for detecting variations in 
volume. Homogeneity of the doping agent is obtained in the same liquid. 
FIG. 4e shows the stage of deposition by epitaxy. The bath 78 which is 
saturated at the suitable initial temperature is placed in contact with 
the single-crystal substrate 70. 
If necessary, a re-adjustment of the physico-chemical equilibrium can be 
carried out before initiating the program of cooling of the furnace 100 
which surrounds the cell. When crystallization begins, an optical signal 
appears and this latter is automatically converted to a signal which is 
proportional to the thickness of the deposit on the substrate 70. 
The end of the epitaxial growth operation is shown in FIG. 4f. Thus, when 
the thickness of the layer deposited on the substrate 70 attains a 
predetermined value, the drawer 86 is brought into the position shown in 
FIG. 4f in a movement of translation which causes sweeping of the surface 
of the layer deposited on the substrate 70, thus removing any excess 
quantity of solution. The complete drawer-type cell is then cooled to room 
temperature. In one example of execution, namely crystallization of the 
In-Sb compound in a thin film, deposition of a film is carried out from a 
solution containing 64% by weight of indium on a substrate having a 
surface area of 100 mm.sup.2. 
The cross-sectional area of the capillary tube 88 is 1 mm.sup.2 and the 
unit for detecting the displacement of the meniscus permits measurement of 
a level difference of 10.sup.-2 mm, namely a minimum volume variation of 
10.sup.-2 mm.sup.3. Taking into account the value of the melting volume of 
the compound, this corresponds to a value of 8 .times. 10.sup.-2 mm.sup.3 
of solid formed at the surface of the substrate, namely a deposit having a 
theoretical thickness equal to 0.8 micron. 
In the alternative embodiment which has just been described, the inert 
liquid in which the container is immersed sets temperature limitations 
which may prove objectionable and entails the need for chemical 
compatibilities between the elements in mutual contact and the elements 
used as contaminants for the crystal which is being formed. Furthermore, 
the container for the liquid-solid system is entirely supported by the 
beam of the electrobalance; the variations in Archimedean thrust thus 
relate to the entire weight of the container and this is liable to affect 
the sensitivity of the balance since this latter is subjected to a fairly 
substantial weight. 
In another alternative embodiment which will now be described, the 
disadvantages mentioned in the foregoing are overcome by dispensing with 
the inert liquid and concurrently increasing the accuracy of the 
measurement. 
In the second alternative embodiment, control of the solidification of a 
two-phase liquid-solid system essentially consists in determining the 
variation in volume related to the solid-liquid transformation by 
partially immersing in the liquid phase a plunger which is maintained in a 
substantially stationary position, in then measuring the variations in 
Archimedean thrust on said stationary plunger with respect to the 
container which is also stationary; the variations in Archimedean thrust 
are due to the variations during solidification in the level of the liquid 
which is present above the crystal; these variations in level of the 
liquid result from the differences between the specific weights of the 
liquid and of the solid which are transformed one into the other during 
crystallization. 
The plunger employed has a regular shape and especially a cylindrical shape 
with calibrated dimensions, a density which is higher than the density of 
the liquid undergoing crystallization and is supported by a wire attached 
to one of the arms of the beam of an electrobalance. It is readily 
apparent that the weight of the plunger is independent of the quantity of 
crystal to be formed, which was not the case in the embodiment described 
in the main patent. Thus only the resultant weight in relation to the 
depth of an immersion of the plunger and therefore to the quantity of 
crystal formed is recorded by the electrobalance. 
The method which relates to the device in accordance with this second 
alternative embodiment applies to all methods of solidification of a 
mixture (growth of homogeneous crystals) wherein the stationary container 
in which the solid-liquid system is present during crystallization is 
placed within a furnace which is maintained at a constant temperature 
gradient by regulating means or any other suitable means and which is 
programmed so as to permit of controlled cooling. 
In FIG. 5, the container 102 is filled with a liquid 104 which crystallizes 
so as to form the crystal 106 under the influence of a temperature 
gradient (not shown) which is obtained in a conventional manner under the 
influence of heating means 108, said heating means being programmed 
electrically so as to produce a variation in the falling temperatures as a 
function of time. A heat-resistant casing 110 surrounds the 
temperature-gradient furnace together with its electrical heating means 
108 and isolates said furnace from the exterior. A plunger 112 is 
partially immersed in the liquid bath 104 which is the bath of liquid to 
be crystallized; the plunger is suspended by means of the wire 114 on the 
beam 116 of an electrobalance 118. 
The plunger 112 and the container 102 are maintained in a stationary 
position by means which are related to the principle of operation of the 
electrobalance (zero instrument). After preliminary adjustment and 
balancing of the current within the electrobalance in respect of a 
predetermined position of the plunger, a measurement is taken of the 
variations in Archimedean thrust caused by the variations .DELTA.L.sub.m 
in the level of the surface of the liquid within the container during 
crystallization. This measurement of Archimedean thrust makes it possible 
to follow the growth of the crystallization process. As in the first 
alternative embodiments, the parasitic forces (capillary tension, 
variation in thrust due to the variation in mean density of the liquid, 
variation in dimensions of the plunger and of the container and so forth) 
are eliminated by the use of the differential method. 
The respective cross-sections of the crucible and of the plunger can be 
chosen in order to produce a predetermined amplitude of the measured 
Archimedean thrust and therefore to achieve enhanced accuracy. This 
advantage can be shown by the following simplified formula : 
.DELTA.L.sub.m = (.DELTA. V/S-s ) which indicates that, in the case of a 
variation in volume of the sample .DELTA.V resulting from modification of 
part of the liquid, the variation in thrust which is directly proportional 
to the variation in measured depth of immersion .DELTA.L.sub.m will be 
greater as the cross-section s of the plunger comes closer to that of the 
crucible S. 
As mentioned in the foregoing, the load applied to the beam of the 
electrobalance is essentially the weight of the plunger 112 reduced by the 
Archimedean thrust over the immersed depth and not, as in the device shown 
in FIG. 1, the weight of the solid-liquid container assembly reduced by 
the Archimedean thrust exerted by the inert liquid which surrounds said 
assembly.