CN103774214A - Method for growing large-size oxide crystal - Google Patents
Method for growing large-size oxide crystal Download PDFInfo
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Abstract
The invention discloses a method for growing a large-size oxide crystal. The method comprises the following steps: establishing a set of stable temperature field according to crystal growing principles in combination with theories of melt growth process characteristics, driving force of crystallization process, material transfer, segregation and solute distribution, thermal transmission, convection and temperature distribution, interface stability and component overcooling, growing the crystal in a seed crystal planting mode, and after the seed crystal planting is finished, naturally forming a solid-liquid interface by using the crystal and the melt, controlling the movement of the solid-liquid interface by using growth parameters so as to complete crystal growth, wherein the crystal growth process specifically comprises the following steps: starting crystal growth, dissociating to stop growth, and annealing to release the residual stress in the crystal. The method for growing large-size oxide crystal combines the advantages of various conventional crystal growth processes, the growth parameters are changed according to the characteristics of growth of various crystals, and the crystal defects are reduced, so that the purpose of optimizing the crystal quality is reached, and the target of industrialization is further reached.
Description
Technical field
The present invention relates to the growth method of large size oxide crystal, be specifically related to grow oxide crystal from melt, the different various methods of growing crystal from melt in the past.
Background technology
At present, from melt growing crystal be prepare crystal the most frequently used with a kind of most important method.The needed monocrystal material in the modern technologies such as electronics, optics application Shen, major part is standby by melt growth legal system.The halogen compounds of some alkali and alkaline earth metal ions etc., many crystal enter the suitability for industrialized production of different scales already.
In melt, the method for growing crystal is varied, for example crystal pulling method, first be in melt, to introduce seed crystal to form a monocrystalline core, then, on the boundary of nucleus melt, constantly carry out rearranging of atom or molecule, the array of piling up directly changes oldered array into and forms crystal, and this is the most general the most frequently used method.Also has warm terraced method, utilize thermograde that melt in earthenware snail is solidified into crystal gradually, wherein can be with or without seed crystal, also can keep temperature-resistant and make degradation under crucible, kyropoulos (Kyropoulos method) seed crystals that use more, be immersed in and in melt, control temperature and adopt growth, wherein can slow circumvolve be lifted or rotary pulling not.Also has the top-seeded solution growth of flux method and improvement thereof, zone melting method, melting zone method (float-zone method), flame melt method etc.
But above-mentioned middle finger goes out the method for growing crystal, understand the characteristic because of different crystal growth, thereby cause the generation of lattice defect, can not reach the object of optimizing crystal mass.
Summary of the invention
The technical problem that the present invention mainly solves is to provide a kind of growth method of large size oxide crystal, as basis by crystal growing principle, in conjunction with melt growth Track character, the motivating force of crystallisation process, mass transfer, fractional condensation and solute distribution, hot transmission, convection current and temperature distribution, the theoretical model of interface stability and constitutional supercooling forms a kind of oxide crystalgrowth technology.The present invention need set up a set of stable warm field condition, the mode growing crystal that adopts seed crystal to sow, crystal and solid-liquid interface of melt self-assembling formation after completing seed crystal and sowing, the movement of recycling growth parameter(s) control solid-liquid interface completes the technique of crystal growth, combine the advantage of various conventional crystal growth, feature with different crystal growth changes growth parameter(s), reduces the generation of lattice defect and reaches the object of optimizing crystal mass, further reaches the target of industrialization.
For solving the problems of the technologies described above, the technical scheme that the present invention adopts is: the growth method that a kind of large size oxide crystal is provided, according to crystal growing principle in conjunction with melt growth Track character, the motivating force of crystallisation process, mass transfer, fractional condensation and solute distribution, heat transmission, convection current and temperature distribution, the theory of interface stability and constitutional supercooling is set up a set of stable temperature, the mode growing crystal that adopts seed crystal to sow, crystal and solid-liquid interface of melt self-assembling formation after completing seed crystal and sowing, utilize the movement of growth parameter(s) control solid-liquid interface to complete crystal growth, the process of growth of its crystal specifically comprises the following steps:
A, the growth of beginning crystal: in temperature field, be warming up to 1500-2500 ℃, seed crystal declines until 3-5mm under the melt liquid level that submerges, if the trend of the diameter zero growth of seed crystal start crystal growth after 5-10min, according to growing crystal characteristic, design different growth velocitys, and the actual observation of utilizing crystal weight to increase, feedback crystal growth equipment operating device output growth parameter(s);
B, pull finish growth: after crystal weight no longer increases, increase pull rate, make crystal depart from crucible completely and stop growing;
C, annealing discharge residual stress in crystal: comprise high temperature section, middle-temperature section and low-temperature zone, high temperature section setting declines with 5-60 ℃/h, and middle-temperature section setting declines with 10-80 ℃/h, and low-temperature zone setting declines with 10-50 ℃/h.
In a preferred embodiment of the present invention, the thermoscreen that make for metallic substance described temperature field, wherein, described metallic substance is tungsten, molybdenum, platinum or stainless steel.
In a preferred embodiment of the present invention, the thermoscreen that make for metallic substance described temperature field, wherein, described metallic substance is tungsten, molybdenum, platinum or stainless steel.
In a preferred embodiment of the present invention, the insulation layer that make for insulating material described temperature field, wherein, described insulating material is zirconium white, aluminum oxide or asbestos.
In a preferred embodiment of the present invention, described temperature also comprises crystal growth atmosphere, and described crystal growth atmosphere is vacuum, shielding gas or air, and wherein, described shielding gas is nitrogen, argon gas, helium or hydrogen.
In a preferred embodiment of the present invention, pulling rate, rotating speed, weight, power, shield gas flow rate, cooling water flow and water temperature that described growth parameter(s) comprises crystal growth equipment operating device.
In a preferred embodiment of the present invention, described pulling rate is at different growth phases, and the scope of pulling rate is between 0-10mm/h; Rotating speed is at different growth phases, and the scope of rotating speed is between 0-100rpm; Weight is at different growth phases, and the scope of weight rate of increase changes span of control corresponding between 0-3kg/h between 0-5Kw/h for rate; Shield gas flow rate scope is between 0-10KL/h; Cooling water flow is variable at equipment different positions, and cooling-water flowing weight range is situated between between 0-5KL/h.
In a preferred embodiment of the present invention, described crystal is LT, LN, YAG, GGG, YVO4, LSO, LYSO, YSO or Sapphire crystal.
The invention has the beneficial effects as follows: the growth method of large size oxide crystal of the present invention, as basis by crystal growing principle, in conjunction with melt growth Track character, the motivating force of crystallisation process, mass transfer, fractional condensation and solute distribution, hot transmission, convection current and temperature distribution, the theoretical model of interface stability and constitutional supercooling forms a kind of oxide crystalgrowth technology.The present invention need set up a set of stable warm field condition, the mode growing crystal that adopts seed crystal to sow, crystal and solid-liquid interface of melt self-assembling formation after completing seed crystal and sowing, the movement of recycling growth parameter(s) control solid-liquid interface completes the technique of crystal growth, combine the advantage of various conventional crystal growth, feature with different crystal growth changes growth parameter(s), reduces the generation of lattice defect and reaches the object of optimizing crystal mass, further reaches the target of industrialization.
Accompanying drawing explanation
In order to be illustrated more clearly in the technical scheme in the embodiment of the present invention, below the accompanying drawing of required use during embodiment is described is briefly described, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skills, do not paying under the prerequisite of creative work, can also obtain according to these accompanying drawings other accompanying drawing, wherein:
Fig. 1 is the schema of the process of growth of crystal of the present invention;
Fig. 2 is the schematic diagram of the G-T of solid liquid system;
Fig. 3 is the fusing point of pure element and the graph of a relation of zero pour;
Fig. 4 is its fusing point of compound of congruent melting and the graph of a relation of zero pour;
Fig. 5 is the graph of a relation of equilibrium temperature and material composition in impure material system;
Fig. 6 is the graph of a relation of the solid-liquid line of solute-solvent systems;
Fig. 7 is the graph of a relation of the solid-liquid line of another solute-solvent systems;
Fig. 8 is near the equilibrium state graph of a relation of solute concentration solid-liquid interface;
Fig. 9 is near the stable growth state relation figure of solute concentration solid-liquid interface;
Figure 10 is the hot-fluid graph of a relation in crystal and melt;
Figure 11 is the temperature profile of crystal while not rotating;
Temperature profile when Figure 12 is Crystal Rotation;
Figure 13 is crystal low-rotate speed or minor diameter structural representation;
Figure 14 is the low-rotate speed surface liquid stream in water or aqueous glycerol model;
Figure 15 is crystal medium speed or middle diameter structure schematic diagram;
Figure 16 be in water or aqueous glycerol model among rotating speed surface liquid stream;
Figure 17 is the fast rotating speed of crystal or major diameter structural representation;
Figure 18 is the fast rotating speed surface liquid stream in water or aqueous glycerol model;
Figure 19 is the temperature distribution for the near interface of pure melt;
Figure 20 is the solute distribution for the near interface of impure melt;
Figure 21 is the temperature distribution for the near interface of impure melt;
Figure 22 is the schematic diagram that cell structure row becomes process.
Embodiment
To the technical scheme in the embodiment of the present invention be clearly and completely described below, obviously, described embodiment is only a part of embodiment of the present invention, rather than whole embodiment.Based on the embodiment in the present invention, those of ordinary skills, not making all other embodiment that obtain under creative work prerequisite, belong to the scope of protection of the invention.
A kind of growth method of large size oxide crystal, according to crystal growing principle in conjunction with melt growth Track character, the motivating force of crystallisation process, mass transfer, fractional condensation and solute distribution, heat transmission, convection current and temperature distribution, the theory of interface stability and constitutional supercooling is set up a set of stable temperature, the mode growing crystal that adopts seed crystal to sow, crystal and solid-liquid interface of melt self-assembling formation after completing seed crystal and sowing, utilize the movement of growth parameter(s) control solid-liquid interface to complete crystal growth, as shown in Figure 1, the process of growth of its crystal specifically comprises the following steps:
A, the growth of beginning crystal: in temperature field, be warming up to 1500-2500 ℃, seed crystal declines until 3-5mm under the melt liquid level that submerges, if the trend of the diameter zero growth of seed crystal start crystal growth after 5-10min, according to growing crystal characteristic, design different growth velocitys, and the actual observation of utilizing crystal weight to increase, feedback crystal growth equipment operating device output growth parameter(s);
B, pull finish growth: after crystal weight no longer increases, increase pull rate, make crystal depart from crucible completely and stop growing;
C, annealing discharge residual stress in crystal: comprise high temperature section, middle-temperature section and low-temperature zone, high temperature section setting declines with 5-60 ℃/h, and middle-temperature section setting declines with 10-80 ℃/h, and low-temperature zone setting declines with 10-50 ℃/h.
In above-mentioned, the thermal field that the thermoscreen that make for metallic substance described temperature field, the insulation layer that insulating material is made or thermoscreen and insulation layer collocation form, wherein, described metallic substance is tungsten, molybdenum, platinum or stainless steel; Described insulating material is zirconium white, aluminum oxide or asbestos.Described temperature also comprises crystal growth atmosphere, and described crystal growth atmosphere is vacuum, shielding gas or air, and wherein, described shielding gas is nitrogen, argon gas, helium or hydrogen.
Wherein, described growth parameter(s) comprises crystal growth equipment operating device pulling rate, rotating speed, weight, power, shield gas flow rate, cooling water flow and water temperature.Wherein, described pulling rate is at different growth phases, and the scope of pulling rate is between 0-10mm/h; Rotating speed is at different growth phases, and the scope of rotating speed is between 0-100rpm; Weight is at different growth phases, and the scope of weight rate of increase changes span of control corresponding between 0-3kg/h between 0-5Kw/h for rate; The weight control of the object of power control in the time guaranteeing crystal growth, weight control is at different growth phases; Shield gas flow rate scope is between 0-10KL/h; Cooling water flow is variable at equipment different positions, and cooling-water flowing weight range is situated between between 0-5KL/h.
In the present invention, described crystal is LT, LN, YAG, GGG, YVO4, LSO, LYSO, YSO or Sapphire crystal, can certainly be other crystal.
The growth method of large size oxide crystal of the present invention, as basis by crystal growing principle, in conjunction with melt growth Track character, the motivating force of crystallisation process, mass transfer, fractional condensation and solute distribution, hot transmission, convection current and temperature distribution, the theoretical model of interface stability and constitutional supercooling forms a kind of oxide crystalgrowth technology.
One, melt growth Track character:
Conventionally,, when the temperature of a crystalline solid is during higher than fusing point, solid is just molten into melt; When the temperature of melt is during lower than zero pour, melt is just frozen into solid (polycrystalline often).Therefore, melt growth process only relates to solid-liquid phase change process, and this is the directional freeze process of melt under in check condition.In this process, the random array of piling up of atom or molecule directly changes oldered array into, this from not being a group effect without symmetry structure to the transformation that has symmetric figure structure, but complete gradually by the movement of solid-liquid interface.
The object of melt growth is in order to obtain high-quality single crystal, for this reason, first in melt, form a monocrystalline core (introduce seed crystal or sporadic nucleation), then, on the interface of monocrystalline and melt, constantly carry out atom and rearranging of molecule and form single crystal.While only having near the melt temperature nucleus lower than zero pour, nucleus could continue to develop.The interface of therefore, growing must be in supercooled state.But, for fear of occurring new nucleus and the unstable (this unstable will cause the structural disorder of crystal with chemical unordered) of avoiding growth interface, cross within cold-zone must concentrate on the narrow and small scope of near interface, remaining part of melt is in superheat state.In this case, the latent heat discharging in crystallisation process can not be led away by melt, and must lead away by the crystal of growing.Conventionally, make the crystal of growing among colder environment, lead away heat by conduction and the surface emissivity of crystal.Along with interface is developed to melt, the condensate depression of near interface will level off to zero gradually, in order to keep certain condensate depression, growth interface must constantly leave towards low temperature direction the isothermal surface of zero pour, just only in this way process of growth can be proceeded down.On the other hand, the temperature of melt, conventionally far above room temperature, in order to make melt keep suitable temperature, must constantly be supplied heat by well heater.Above-mentioned heat transfer process is set up certain temperature (forming in other words a series of isothermal surface) in growing system, and has determined the type shape of solid-liquid interface.Therefore,, in the process of melt growth, the transmission problem of heat will play a part domination.In addition,, for compound those admixtures or non-same composition fusing, on interface, there will be the problems of segregation of solute.Problems of segregation is arranged by the molten matter concentration of near interface, and the latter is depended on the diffusion of solute in melt and to stream transmission procedure.Therefore, the transmission problem of solute is also a major issue in melt growth process.
From melt, growing crystal generally has following two types:
Crystal has identical composition with melt.Pure element and the compound (having peak melting point) melting with composition belong to this class, and this class material is actually unit system.In process of growth, it is constant that the composition of crystal and melt all keeps, and fusing point does not also change, and this class material easily obtains high-quality crystal (for example Si, Ge, Al2O3, YAG etc.), also allows higher growth rate.
The crystal of growth is different from bath composition.The compound of the element of doping or compound and non-same composition fusing belongs to this class.This class material is actually binary and multicomponent system.In process of growth, the composition of crystal and melt all constantly changes, and fusing point also says the variation of composition and change, and fusing point and zero pour are no longer a definite numerical value, but have a solidus and a liquid represented.It is just much more difficult that this class material will obtain uniform single crystal.This class material can form continuous Solid solution, but most material only has limited Solid solution, once exceed admittedly molten limit, by two throw outs that there will be, even occurs eutectic or Peritectic Reaction, and the growth of monocrystalline is damaged.
In addition, the solid-liquid equilibrium problem not only existing in melt growth process, also exists solid vapour balance and liquid vapor equilibrium.The material that those vapour pressures and dissociation pressure are higher, the at high temperature volatilization of certain component will make melt depart from needed composition, and other superfluous components will become harmful impurity.The crystal of this class of growing will increase technical difficulty.
Moreover, after crystal growth is complete, must be down to room temperature by high temperature, some material has solid-state phase changes (comprising de-molten precipitation and eutectoid reaction) in this temperature range, and also to crystal, growth brings very large difficulty for this.
Therefore, only have those there is no destructive phase transformation, the compound again with the same composition fusing of lower vapour pressure and dissociation pressure is only (comprising pure element) ideal material of melt growth.Can obtain easily the high quality single crystal of this class material by melt growth method.
Two, the motivating force of crystallisation process:
The item key that crystalline solid is different from other melts is the symmetry that the former has structure.The crystal lattice of the regularly arranged formation of one or more atoms, the symmetry of dot matrix has determined the mean place of each atom, the bonding force between atom pairs makes crystal become rigid solid.Make crystalline solid change melt into, need to provide energy to weaken this bonding force, make atom depart from the mean place that determines of dot matrix and stochastic distribution.Conventionally, adopt the way of heating to make solid complete this transformation at its melting temperature, the heat applying is exactly the latent heat of fusion (L).In the time of melt solidifying, this part latent heat is released again, and to reduce the free energy of system, while only having free energy to reduce, crystal could be grown.Therefore, d/d free energy, between solid, liquid two-phase, the poor matter Δ G of free energy is the motivating force of crystallisation process.
Gibbs free energy can be expressed as: G=H-TS, and wherein, H is enthalpy, and S is entropy, and T is absolute temperature.
At solid-liquid equilibrium temperature T e, between two-phase, the poor matter of free energy is zero,
ΔG＝(?H
s－T
eS
s?)－(?H
l－T
eS
l?)=0 …(1)
So, T
e(S
l-S
s)=(H
l-H
s)
ΔS＝ΔH?/?T
e …(2)
Subscript s, l represent respectively solid phase and liquid phase, the variation (melting entropy) of entropy when Δ S is thawing, the variation (latent heat) of enthalpy when Δ H is thawing.
In the time that temperature is not equilibrium temperature (the actual temperature T of system is not equal to equilibrium temperature Te), poor matter Δ G is
ΔG=ΔH－TΔS …(3)
(2) formula is brought in (3) formula and can be obtained
ΔG＝
…(4)
When melt solidifying, specific heat at constant pressure c
pchange, thereby affect the variation of enthalpy, the Precise Representation of free energy change is:
ΔG＝(ΔH－
Δc
pΔT)
…(5)
Δ c in formula
pthe difference of solid, liquid two-phase specific heat, Δ T=T
e-T
eit is condensate depression.
In the ordinary course of things, a crystal melt system, can be for melting or solidifying.If a kind of material is can exist mutually with two kinds of phases a time, less one of free energy is stable phase mutually, that is to say, the future development that system always reduces towards free energy, so Δ G should be a negative value.For thaw process, so because system absorb heat Δ H be on the occasion of, so according to equation (4), only have the T of working as
ewhen being negative value ,-T just can make Δ G be less than 0, i.e. T
e< T is the prerequisite of melting.Equally for process of setting, so because system release of heat Δ H is negative value, therefore only have the T of working as
e> T just can make Δ G be less than 0, i.e. T
e> T is the prerequisite from melt growth crystal, as shown in Figure 2.
Can be write as for crystallisation process equation (4)
ΔG＝－(
)ΔT …(6)
In formula, L is latent heat, and Δ T is condensate depression.
Discussion is above in supposition system, originally just to have a solid-liquid interface, and does not consider to form the impact of solid-liquid interface on system free energy.If originally there is not solid-liquid interface (or solid-liquid interface constantly expands) in system, the formation at new interface needs energy, the surface energy that the potential Partial Conversion that now crystallisation process disengages is interface, i.e. and the motivating force of crystallization has reduced.Under certain situation, form the needed energy in new interface may close to (
) Δ T, at this moment, actual crystallization driving force is by vanishing, under this situation, although the temperature of melt is lower than zero pour, but solid phase can not form, so only have the Δ of increasing T could increase crystallization driving force, therefore must provide very large condensate depression for sporadic nucleation system at the initial period of crystallization.
In addition, in the time that the crystal lattices of seed crystal and growth does not match, the free energy part of release the becomes strain energy, and the motivating force of crystallization is declined.If when crystal and young Jingjing lattice mismatch, the numerical value that the free energy that discharged so reduces is
(
)
2, V in formula
mbe mole volume, Y is yang type modulus, ν
0be Poisson's ratio, Δ a is that the pressure of lattice constant a changes.Along with the growth of crystal, Δ a has reduced, and increases (increasing with the growth of crystal) but shearing strain reduces with Δ a.This just makes the above formula that relates to initial mismatch increase a factor 1+
(L is growth thickness, and R is seed crystal radius, and L≤R).Therefore, in the time that crystal grows to a certain thickness, total strain energy just may equal the free energy discharging, and at this thickness, crystal stops growing, and with said the same, only has the Δ of increasing T above, could continued growth.
The latent heat discharging in crystallisation process, also must lead away from solid-liquid interface, if this part energy can not all be led away, the temperature of near interface will raise, then Δ T reduce, thereby reduced crystallization driving force.Work as T
e=T, when Δ G=0, at this moment crystal stops growing.
Three, mass transfer, fractional condensation and solute distribution:
Except pure material (pure element and the compound with composition fusing), the crystal of melt and wherein growth has different compositions conventionally, and this shows to exist the problem of component fractional condensation in process of setting.For convenience's sake, certain component of the admixture in material or material is all called to solute, and all the other components (or main ingredient) of material are become to solvent, we just can go wrong with the fractional condensation that the concentration of solute is described in process of setting like this.Certainly said solute and solvent and solution growth are different here, and for melt growth, solute and solvent are the integral part of crystalline solid.
(1) fusing point, zero pour and equilibrium temperature: the material of supposing certain composition can exist and do not decompose and distil with the form of melt, the temperature of the solid-state material that so slowly raises, when reaching a certain temperature T
mso time material start melt T
mbe called the fusing point of this solid-state material; After the solid-state material of this composition melts completely, slowly by the temperature of its melt, when reaching a certain temperature T
ftime solvent start to solidify, so T
fbe called the zero pour of this melt.Fusing point and zero pour are all the equilibrium temperatures between solid, liquid two-phase, the temperature of fusing point is the biphase equilibrium temperature in thaw process, the temperature of zero pour is the temperature of biphase equilibrium in process of setting, and they are the functions (representing with solidus G and liquidus Y respectively) of the composition of material.
As pure element with the fusing compound (C in Fig. 4) of composition, obviously, be the unique equilibrium temperature of solid-liquid two-phase for pure material (as the A in Fig. 3 or B).In fusing and process of setting, the temperature of the constant biphase equilibrium of cost of material does not also change, and crystal and solvent thereof are of identical composition in this case, does not naturally also just have so-called problems of segregation.At this moment the factor that affects equilibrium temperature is the shape of solid-liquid interface.
The equilibrium temperature of supposing flat solid-liquid interface is T
e, interface is radius while being the curved surface of R, its equilibrium temperature T
e(song),
T
e(song)=T
e+
(7)
In formula, σ is surface tension, is the L latent heat of fusion.
If interface is protruding to melt (center of curvature is in solid one side),
be a negative value (R is a negative value), therefore protruding interface has reduced equilibrium temperature.The situation at recessed interface (center of curvature is in melt one side) is just in time contrary.In the time that the stability of crystal microscopic growth rate is discussed, should consider that the variation of interface shape is on the impact of equilibrium temperature, under normal conditions, the impact of above-mentioned factor can be ignored because it is too faint, and this point is also suitable for for pure material not.
For impure material, equilibrium temperature changes the variation of the composition with material.Contrary with pure material, the zero pour of the fusing point of solid and the melt of same composition no longer overlaps, and having the solid of identical component and melt can not be in equilibrium state, and the solid in equilibrium state and melt right and wrong are with composition in other words.By finding out in Fig. 5, solid phase (C
2) fusing point be T
2, liquid phase (C
2) zero pour be T
1, solid phase (C
2) and liquid phase (C
3) in balance, (equilibrium temperature is T
2), and liquid phase (C
2) and solid phase (C
1) in balance, (equilibrium temperature is T
1).
Since crystal and melt are off-congruents under equilibrium state, this just means in process of setting will there is problems of segregation, the problem that fractional condensation of solute and solute distribute along the characteristic of crystal.
(2) segregation coefficient: the balance between crystalline solid and its melt, can represent with two lines (solidus and liquidus) on the binary phase diagram of solute-solvent system.Fig. 6 and 7 is parts of phasor, and ordinate represents temperature (T), and abscissa represents solute concentration (c).Liquidus is the relation curve of melt solidifying point and solute concentration, and the melt more than liquidus is stable phase.Solidus is the fusing point of solid and the relation curve of solute concentration, and is the stable phase of solid below solidus.Article two, between line, be two-phase coexistent district.Use equilibrium segregation coefficient k
0can explain easily the feature of solid-liquid plane.K
0definition be: when solid-liquid two-phase is during in balance, the solute concentration c in solid
swith the solute concentration c in melt
lratio, i.e. k
0=
, wherein k
0depend on the characteristic of material system, for definite system, except the very low situation of solute concentration, k conventionally
0to change with concentration.
For Fig. 6, k
0=
be less than 1, solid rejects solute, and along with the increase of molten matter concentration, the equilibrium temperature of system reduces in addition.For Fig. 7, because of k
0=
be greater than 1, solid rejects solvent, and along with the increase of molten matter concentration, the equilibrium temperature of system raises in addition.If obviously k
0, represent it is a pure material system at=1 o'clock.
No matter k
0< 1 or k
0> 1, in the time solidifying, the solute concentration in crystal and melt, will move down along solidus and liquidus respectively, when initial concentration is c
lmelt while starting to solidify, the solid of initial solidification, its concentration is c
s.Form a certain amount of c
safter, the concentration of melt must produce corresponding variation, so the concentration of melt is with c
lfor starting point declines along liquidus, the concentration of solid is with c
sfor starting point declines along solidus.
K for most of solutes
0< 1.To this common situation be discussed below.
Under equilibrium conditions, interface movement speed is negligible, and in melt, solute concentration is everywhere identical.But, in actual process of growth, always departing from equilibrium state, interface movement is not very slow, the mixing of solute neither be very sufficient, work as k
0when < 1, the speed that solute is got rid of at initial interface is greater than solute and enters the speed of melt main body, so will there is superfluous solute in the melt of near interface, but along with the increase of near interface solute concentration, the speed that solute enters melt main body also increases gradually, so that and the mutual balance of speed of solute, the at this moment solute concentration c near interface melt are got rid of in interface
l(l)just reached stationary value, and higher than the concentration c of melt main body
l(B), as shown in FIG. 8 and 9.Therefore for crystal growing process, also need to propose following other two kinds of segregation coefficients.
Interface segregation coefficient k*=
(8)
Effective segregation coefficient k
e=
(9)
As long as the volume of melt is much larger than the volume in frictional belt, c so
l(B)just can use the mean concns c of melt
lrepresent, the latter is one and is convenient to the concentration value of measuring.
K
*and k
ebe all and the closely-related segregation coefficient of process of growth, k
erepresentation provided by people such as Burton.
k
e＝
…（10）
The rate travel that in formula, f is interface is δ
cthe thickness of solute boundary layer, and D is the spread coefficient of solute in melt.
In document [G. A. Bogomolova, D. N. Vylegzhanin, A. A. Kaminskii, Sov. Phys. JETP, 1976,42:440], give δ
cexpression
δ
c=1.6D
1/3ν
1/6ω
-1/2 …（11）
The viscous rate that in formula, ν is melt, ω is Crystal Rotation speed, above formula is often applied to pulling growth system.
For convenience's sake, also can regard equilibrium process as by approximate the interface fractional condensation process of nonequilibrium state, so (10) formula is just reduced in this case
ke＝
…（12）
Because within the scope of common admixture, k
0can regard as constant, and usually can find k
0numerical value.
Situation about two kinds of limit:
(level off to equilibrium state) or δ in the time of f → 0
c→ 0(melt has sufficient stirring that the solute concentration in melt is uniformly distributed), at this moment exp(-f δ
c/ D)=1, so k
e=k
*=k
0;
When f →
time (condensate depression is very big) or δ
c→ 0(Melt Stirring is very poor, not to flow transmission), at this moment exp(-f δ
c/ D)=0, so k
e=1.
Actual process of growth, always between above-mentioned two kinds of special cases, so the effective segregation coefficient k of actual process of growth
ebetween k
0and between 1, i.e. k
0< k
e< 1(k
0when < 1), or k
0> k
e> 1(k
0when > 1).
From (12) formula, can see k
ewhen < 1, along with the increase of f, k
ealso increase.In addition just generally speaking, flowing of melt is more fierce, δ
cless (under the condition of vigorous stirring, δ
c~ 10
-3cm, under the stirring a little less than level, δ
c~ 10
-1cm).Therefore, along with weakening of Melt Stirring (or convection current), δ
cincrease, thereby also made k
eincrease, and f reduces or liquid flows while enhancing, k
ewhile reducing.
After (12) formula is rewritten, take the logarithm and just can obtain in equal sign both sides
Ln(1/k
e－1)＝Ln(1/k
0－1)－fδ
c/D …（13）
(δ under the condition of identical stirring
cregard constant as), the crystal effective segregation coefficient k while measuring different growth rate f
evalue, and Ln (1/k
e-1) f is mapped, the straight slope drawing is-δ
c/ D.There is the intercept Ln (1/k of this straight line
0-1) can obtain k
0.
If know viscous rate ν (ω is known number), the δ that available (11) formula and experiment are obtained
c/ D value, just can obtain respectively δ
cand D.
Process of growth always exists the fluctuation of temperature, therefore, and f and k that experiment is measured
evalue is all a mean value, calculates δ by mean value
c/ D has error naturally.
(3) solute transport in melt and solute distribution
Solute transport in melt completes by diffusion and convection current.The solute concentration gradient that the passing of growth interface produces is determining the diffusion transport process of solute; Buoyancy in melt and additional whipping force, determining solute to stream transmission procedure.These two kinds of transmitting procedures have determined the solute distribution in melt, and solute distribution near interface melt has also just determined the solute distribution situation in crystal.
Adopt the concept of solute boundary layer, can describe easily mass transfer process and solute distribution situation in melt.According to the theory of solute boundary layer, nestling up the melt frictional belt (δ of solid-liquid interface
c) in, the main mechanism of solute transport makes diffusion; Among melt main body outside frictional belt, the sufficient stirring that convection current is carried out, therefore the distribution of solute is that so mass transfer problem is just reduced to uniformly: the effect of flow transmission is only limited to the thickness that changes frictional belt, and the solute outside frictional belt is uniformly distributed.So just can only consider the diffusion equation of solute, and by effective segregation coefficient k
ewith boundary layer thickness δ
crelation the impact of convection current on solute distribution is described.
According to above-mentioned boundary layer theory, we discuss solute transport and solute distribution problem in melt.The solute concentration of setting solid-liquid interface place (z=0) melt is c
l(l), in melt main body, (c), molten matter concentration is c to z>=δ
l(B).Obviously, work as k
ewhen < 1, c
l(l)> c
l(B)so, at 0 < z < δ
cscope in (in frictional belt) exist certain concentration gradient
.
In the time that planar interface moves along interface normal direction (Z) with constant rate of speed f, the diffusion equation of (initial point of rectangular coordinate system is fixed on interface, and with interface movement) solute is:
D▽
2c?=D（
）＝
…（14）
In formula, D is the spread coefficient of solute in melt, is ▽ Laplace's operation symbol.
Suppose solute concentration c and x, y irrelevant (vertical Z side c to plane in, c is uniformly distributed), and suppose c and time-independent, so can be drawn by above formula
D
＝0 …（15）
Being subject to growth interface repulsion solute must keep constant by spreading, and can try to achieve thus the final condition of above formula.In the time of z=0
－D（
）＝（c
l（l）－c
s）f …（16）
C in formula
sfor the solute concentration of crystal.
In addition, as z=δ
ctime, can obtain according to the concept of solute boundary layer
c（δ
c）＝c
l（B） …（17）
At 0 < z < δ
cscope in, have (15) formula and final condition thereof, can obtain
So
c（z）＝c
s?＋
exp
＝k
ec
l（B）＋c
l（B）（1－k
e）exp
…（19）
At z > δ
cscope in
c（z）?c
l（B） …（20）
So the solute distribution in melt will be represented by (19) and (20) formula.As long as the volume in melting zone is much larger than the volume of solute boundary layer, the c in above-mentioned two formulas
l(B)just can use the average solute concentration c of melt
lreplace.
Can facilitate body to draw below famous Burton equation by (18) formula: when z=0(interface), (18) formula can become
＝exp
…（21）
In addition
k
e＝
，?k*＝
；
So can obtain
k
e＝
…（22）
Be positioned at the rotating-disk model on the infinitely-great melt of radius according to infinitely-great rotating-disk, and calculate solute boundary layer thickness δ
cfor:
δ
c?1.6D
1/3ν
1/6ω
-1/2 …（23）
Can calculate Crystal Rotation speed ω to δ according to (23) and (22) formula
cand k
eimpact.Then calculate the impact of rotational speed omega on the solute distribution in melt by (19) formula.
Four, hot transmission, convection current and temperature distribution:
(1) by the heat transmission of solid-liquid interface:
Point out above, the latent heat discharging when crystal growth must be led away near interface, and crystal could keep steady-state growth.If latent heat is led away by melt, this just means apart from the temperature of interface melt far away lower.Under such condition, even the growth of pure material, it is unstable that interface also can become, and occurs dendritic growth.This situation must be avoided in the time of growing single-crystal.Conventionally far away apart from interface, the temperature of melt is higher, so heat just imports crystal by melt by interface.
Suppose that near crystal planar interface and the thermograde of melt are respectively
with
(normal direction that Z is planar interface); A crystal and melt thermal conductivity is respectively K
sand K
l.If the latent heat discharging when the material solidification of unit volume is L, crystal growth rate is in the z-direction f, and the latent heat that discharges is that fAL(A is interfacial area the unit time), the heat that the unit time imports interface by melt is K
l a, and the heat of being led away from interface by crystal is K
s 
a.
When steady-state growth, interface makes isothermal surface, and energy is conservation, in
K
s ＝fL＋K
l 
…（24）
The hot-fluid continuity equation at Here it is interface.Although this equation is very simple, but a fundamental equation of melt growth, many theoretical analysises all be unable to do without it, and the problem of many reality can also be described qualitatively with this equation.For example, above formula also can be write as and be
AfL＝Q
s－Q
l …（25）
Q in formula
s=K
s 
a, is the heat (dissipating among growing environment through crystal) of interface loss, Q
l=K
l 
a is the heat that interface is obtained by well heater.Known in the time that f is constant by (25) formula, increase the heat radiation of crystal, or reduce the heat supply to interface, the diameter of crystal all will increase thereupon; Vice versa.If when A and f remain unchanged, increase the heat radiation of crystal, Q
lmust do corresponding increase,
increase.
Say in principle, as long as keep (Q
s-Q
l) constant, crystal just can the more growth of speed of equal diameter.For example, in the growth of crucible Mobile Method, A is normally constant; In crystal pulling method, f is normally constant.Therefore, as long as Q
s-Q
l=constant, it is constant that A and f all can keep.But in actual process of growth, Q
sconstantly to change, in crystal pulling method, if by A and Q
lregard as constant, so just can be by monitoring that A(monitors crystal diameter) monitor Q
lvariation, and regulate Q by accurate servosystem
l, make Q
s-Q
l=constant.But be just difficult to monitor Q for crucible Mobile Method
svariation, therefore the growth rate of crystal often gradually strengthen (Q
sincrease).
2) temperature distribution in crystal
Temperature distribution in melt and crystal, particularly interface shape is between the two a major issue in melt growth, it directly affects the internal soundness of crystal, temperature distribution in growing system depends on the heat transfer process in system, and it relates to conduction, convection current and three kinds of transmission mechanisms of radiation and the interaction between them.If considered in melt growth, various possible influence factors (comprising transient effect), this problem, by being very complicated, there is no perfect quantitative theory so far so, so can only go out to send the Solve problems of processing hot transmission equation from the condition of simplifying.
At document [D. S. Sumida & T. Y. Fan, Opt. Lett. 1995,20(23): 2384] once discussed the heat transfer problem in crystal in detail, he has proposed simplifying model, and carried out mathematics manipulation, the parsing of book Laplace equation please.
In a stable solid, due to mass transport very slowly thereby can ignore, the heat transmission in solid just only has conduction and two kinds of modes of radiation.In document [U. Brauch, A. Giesen, et al., Opt. Lett. 1995,20(7): 713], point out that a uptake factor is the transmission medium that α, specific refractory power are n, because radiative transfer produces thermal conductivity is
K
R＝
…（26）
In formula, σ
0be Stefan constant, T is absolute temperature.
Total thermal conductivity K=
, K
nfor general thermal conductivity.The thermal conductivity of discussion supposition solid has below been above-mentioned correction (K
s=K
n).
The solid moving along z axle with speed f, motion itself also produces the transmission of heat, considers in solid certain any heat graduated sate, and the general differential equation of temperature is as follows:
ρc
＋fρc
－K▽
2T＝0 …（27）
In formula, t is the time, and ρ and c are density and the specific heat of solid, and this formula also can be write as
Thermal diffusivity κ in formula=
.
Such solid has following 4 class borders:
(1) solid-liquid interface
K
s▽T
s＝K
l▽T
l＋fL …（29）
Subscript s and l represent respectively solid and liquid, and f is growth rate, the latent heat that L is unit volume.In melt growth process, conventionally to crystal transmission latent heat.
(2) only has the interface of radiant heat loss.This consume is
Q
R＝σσ
0（T
4－T
0 4） …（30）
In formula, σ is emittance, T
0envrionment temperature (supposing all identical everywhere).Also can make θ=T-T
0so utilize curtain series expansion to obtain
Q
R＝4σσ
0T
0 3【1＋
＋
＋
】θ＝ε
Rθ …（31）
ε in formula
r=4 σ σ
0t
0 3[1+
+
+
] be under the unit temperature difference, the specific heat rejection of per unit area.
(3) there is no solid, the vapour interface of mass transport.The thermal losses that gaseous exchange causes is
Q
c＝ε
cθ，
ε in formula
c=0.548
, g is universal gravity constant, the length that l is solid, T
0for the temperature of gas, and σ
0, c
0, K
0with η be respectively the density, specific heat, thermal conductivity of gas, dynamically year system [under normal pressure, ε
0be estimated as 1-10(mW/cm
2℃)].If exist thermal radiation consume simultaneously, loss is altogether
Q＝
cθ＝（ε
R＋ε
c）θ …（32）
When in formula, ε is temperature than high 1 ℃ of environment, the thermosteresis of crystal unit surface within the unit time.
(4) solid, liquid/solid interface (as the interface between crystal and seed chuck).If bi-material is respectively with s
1and s
2represent, hot-fluid is
Qs＝K
sl▽T
sl＝K
s2▽T
s2 …（33）
Under steady state conditions, the hot-fluid on above-mentioned various interfaces in total heat Q and the solid of loss balances each other, so Q=K
s 
(r is vertical and surperficial).
Consider now simplified system as shown in figure 10.The radius of crystal is a, and in crystal, the coordinate of any point is (r, ψ, z).Under the condition of stable state, ρ c
can ignore.If 8 ε K in addition
s> a
2(f ρ c)
2c, f ρ c
can ignore, so ▽
2t=0
Adopt cylindrical-coordinate system to obtain
＋
＋
＋
＝0 …（34）
Suppose that thermal field has rotational symmetry, θ and ψ are irrelevant, so
The final condition of above formula is in the time of z=0, θ=θ m; In the time of r=a, K
+ ε θ=0; In the time of z=l, K
+ ε θ=0, just can be obtained the general solution of this formula by (35) formula and final condition thereof.(h=under the condition of very little h
< < 1cm
-1), show that the numerical solution of (35) formulas is
θ（r、z）~
exp
…（36）
And obtain
~?－
?exp
…（38）
θ in formula
m=T
m-T
0, T
mfor fusing point, h is heat exchange coefficient.
In the time that h is very little, can be found out a by (37) and (39) formula
1/2 and a
all level off to 0, irrelevant with crystal radius a.
Conventionally h≤1cm,
-1, and only cms magnitude of crystal radius a, so (1-
ha) > 0 this point variously also can be seen by above-mentioned.
The in the situation that of h > 0 (crystal is to function of environment heat emission), in the time that z is constant, θ and
all reduce along with the increase of r; And
increase with the increase of r.In the time that r is constant, θ,
with
press index reduces along with the increase of z.For example, the in the situation that of h < 0 (crystal absorbs heat from sidewall of crucible), can analyze equally.
Although above-mentioned analysis has drawn valuable analytic solution, the verisimilitude of the result of gained must be subject to the restriction of simplifying model itself.For example, above-mentioned analysis is not considered to stir, the impact of the temperature factor of temperature distribution in melt and sidewall of crucible on heat transfer process in crystal.More perfect analysis must be considered the impact of above-mentioned factor, in this case, just very difficult to solving of Laplace equation.
(3) temperature distribution and interface shape.According to the essential characteristic of Czochralski grown system, the model of simplifying has been proposed, and take Ge as object (his characteristic parameter is known).In the situation that not considering melt flow, draw the relation curve between solid-liquid interface shape and some growth parameter(s).Here introduce qualitatively the Main Conclusions that they obtain.
(a) impact of gaseous exchange: light (recessed interface refers to the side of interfacial curvature center at melt) that under venting condition the interface of growing system under vacuum condition is recessed.
(b) impact of crystal length: along with the increase of crystal length l, the degree that planar interface etc. is departed from recessed interface reduces gradually.The degree that departs from planar interface etc. can represent with z/r, z be the summit at recessed (or protruding) interface to the distance of planar interface, r is the radius of crystal.
(c) impact of crystal radius: basic condition is that the recessed degree in interface increases along with the increase of radius, only has in the time that radius exceedes a certain numerical value, just has the trend reducing.
(d) impact of crucible temperature: when crucible temperature raises, the variation tendency of interface shape is: recessed → flat → protruding.
(e) impact of growth rate on interface shape: contrary with the impact of crucible temperature.
Many experimental results that the above-mentioned result being calculated by Ge crystal and crystal pulling method obtain make qualitative meeting.
In above-mentioned, also consider the impact of melt flow, after it has considered the effect of the revolving force (forced convection) that welfare (natural convection) that inhomogeneous temperature distribution produces and Crystal Rotation produce, appoint computing technique and solve hot transmission equation in melt and the Navier-Stokes equation (only considering hot transmission equation in crystal) of restriction liquid stream.Thereby draw temperature profile while rotation from crystal shown in Figure 11 between temperature distribution in crystal and in melt and interface shape and crystal rotating speed (representing with a series of thermoisopleths), the liquid stream moving downward along axis direction in melt, passes the isothermal surface in melt downwards.
Temperature profile while rotation from crystal shown in Figure 11 (representing with a series of thermoisopleths), the liquid stream moving downward along axis direction in melt, passes the isothermal surface in melt downwards.
Temperature profile during from Crystal Rotation shown in Figure 12.The rotation of crystal has weakened natural convection, has occurred that the liquid moving upward flows under interface, and this liquid stream makes isothermal surface be subject to passing upwards.So there is corresponding variation (Crystal Rotation makes the more recessed of recessed interface change) in interface.
If rotating crucible, liquid stream type is similar to natural convection, but with the mobile circulation of line central shaft.In the time increasing crucible rotation, isothermal surface is only subject to slight downward passing.If crystal and crucible rotate (equidirectional and opposite direction) simultaneously, situation is with regard to more complicated, and by and large, along with the increase of Crystal Rotation, it is more recessed that recessed interface becomes.
Above-mentioned these calculation result and many experimental results of actual growth also make qualitative meeting.Although it should be pointed out that the quantitative result providing in above-mentioned mentioned document, what these results conventionally can not be quantitative is applied to actual crystal growth.Because these results are from specific simplifying model, (Ge fusing point is 937 ℃, K with specific material
l~ 3K
setc.).Different materials and growing apparatus will bring very large singularity, therefore can only apply qualitatively these results.
Generally speaking, due to temperature distribution and liquid flowing state closely related, therefore the variation meeting of crystal rotating speed obviously changes interface shape.In the time that natural convection is dominant, Shi Tu interface, interface, along with the speed of Crystal Rotation increases, the impact of natural convection will make way for forced convection, become recessed interface so You Tu interface, interface turns to.Be noted that introduction is above under the condition for stable state.About unstable state (with t about) condition under liquid flowing state and temperature distribution can consult document [D. S. Sumida, H. Bruesselbach, et al., Pro. SPIE, 1997,100:3265], and document [E. C. Honea, R.J. Beach, et al., Opt. Lett. 1999,24(3): 154] set forth unstable state liquid flow equation and asked the step of digital solution.
(4) liquid flowing state in melt: the liquid stream in crucible, is driven by the revolving force of buoyancy and crystal conventionally.Under different buoyancy and revolving force, melt there will be different liquid flowing states.People once adopted the liquid flowing state in the method research melt of physical object simulating.For example, in transparent crucible, pack transparent liquid (water, glycerine etc.) and the plastic disc (replacement crystal) of different viscosity into, and inject dyestuff to show liquid fluid line.So just can at lower temperature, carry out simulated experiment.The impact of the parameter such as geometric condition, heating condition, diameter, rotating speed and the liquid viscosity of disk on liquid stream of container can directly be observed and study easily to this practice analogue method.In simulation test, exist three kinds of types of flow, they depend on diameter and the rotating speed of crystal.
When Crystal Rotation obtains a kind of types of flow that (or crystal diameter is very little) occurs when very slow, as Figure 13 and Figure 14 represented.This flowing is to be arranged by natural convection, and his natural convection when thering is no crystal is very similar.Unique different be that the former has an angular velocity component because the rotation of crystal makes fluid.Along with the diameter of crystal rotating speed or crystal increases, the second type that flows and become, as Figure 15 and Figure 16 represented.The annular zone that is characterized in liquid external remains the natural convection being produced by side heat and arranges, and the forced convection that centre portions is caused by Crystal Rotation is arranged.Frictional belt between Zhe Liangzhongliu district there will be vortex, when actual growing crystal, also may see.In the time further adding the rotating speed of macrocrystal or diameter, flow and become the third type, as Figure 17 and Figure 18 represented.The 3rd and second difference little, all reflected the balance between two kinds of convection current, but for the third types of flow, the frontier district in inside and outside Liang Zhongliu district is positioned at below liquid level, therefore often do not observe when actual growth.In these three kinds of types of flow, liquid bottom is being arranged by natural convection.At GGG(Gd
3ga
5o
12) in crystal growing process, can observe above-mentioned three kinds of types of flow.The first type appears at early growth period (lower seed crystal and expansion shoulder stage); After the second type appears at interface and flattens; The third type occurs at later stages.
The method of can't deny simulation is a kind of effective and easy method of research melt flow.But liquid flowing state and growth method, the geometric condition of growing apparatus and the characteristic of melt etc. in melt to be permitted multifactorial relation be very complicated, the result that therefore obtained can only be reacted some rule under specified conditions qualitatively.
Five, interface stability and constitutional supercooling:
From melt, the process of growing crystal is the process that solid-liquid interface is passed to melt, does the kenel at interface change in this process? what does this variation have associated with growth parameter(s)? the quality of crystal is there again to what impact? only these problems are carried out to macroscopical analysis below.
One of feature of melt growth, is exactly one of them compulsory interface movement speed, thereby produces compulsory heat exchange condition.Although also may there is little crystal face on interface, in general can think that interface gets isothermal surface form.Consider now an isotropic planar interface face, if an interface that macroscopic view is smooth, it is constant that its configuration of surface remains in process of growth, that is to say, on interface, can die away in the random outstanding or depression position forming in process of growth, and this interface is stable.Otherwise if the outstanding or depression position that on macroscopical smooth interface, moment forms continues along with the carrying out of growth to develop, this interface is unsettled.In crystal, there is the common defects such as wrap, strain, solute uneven distribution by making in the passing at unsettled interface.Obviously, the differentiation of interface stability is that disturbance on growth interface decays along with the carrying out of growth.
For convenience's sake, the condensate depression near interface melt is carried out the stability problem of assay surface with the variation of distance.
Condensate depression △ T=T
f-T, T in formula
ffor equilibrium temperature (zero pour), the actual temperature that T is melt.The actual temperature that so-called condensate depression refers near interface melt is lower than equilibrium temperature.Growing crystal from melt, the certain condensate depression of needs provides the motivating force of crystal, if there is no condensate depression, i.e. T
f=T, interface is in solid-liquid equilibria state, and can not continued growth.Therefore, the growth rate that affects crystal of condensate depression itself, and directly do not destroy the stability at interface.
The melt of now only considering near interface, rectangular coordinate system is still fixed on planar interface, and Z axis is perpendicular to interface, and its forward points to melt.If △ is T(z) increase with the increase of z, from interface, more go deep into melt, condensate depression is larger, and in this case, interface will be unsettled.Apart from interface, there is larger condensate depression in place far away, and must there be higher growth rate at this place, therefore, once there is thrust on smooth interface, the growth rate in the forward position of the part of this projection is by the growth rate in projecting indentation region, at this moment, prominence only can continue development, and can not disappear.If △ is T(z) be that this situation is called constitutional supercooling because the existence of solute produces with the trend of z increase.At this moment, constitutional supercooling has identical connotation with interface unstable.
For pure melt (pure element or the compound with composition fusing), this local equilibrium temperature in melt is identical, i.e. T
fhave nothing to do but 1 constant with z.If require △ T to increase with z, can only be that T increases and reduces with z.So
< 0(is as Figure 19), the unsettled condition in interface that Here it is.At this moment the temperature of crystal is higher than the temperature of melt, and the latent heat discharging when crystallization is led away by melt.Interface projection thing more gos deep into melt, and growth velocity is higher, if development is continued at this unstable interface, will cause free dendritic growth (if having sufficiently high condensate depression).
The condition of interface stability is
And
K
l 
＋ρfL＝K
s 
…（41）
So
f≦
…（42）
Therefore, to keep stable maximum growth rate be f at interface
max=
,
with
be respectively near interface melt and crystal in thermograde, K
sfor the thermal conductivity of crystal, ρ, L are density and latent heat.
For pure melt, the constitutional supercooling problem that does not certainly exist solute to cause, also there will not be interface unstable conventionally, because the condition of above-mentioned interface stability is easy to meet, and can have higher safe growth rate.
For impure melt, crystal and melt have different compositions conventionally, therefore, near melt growth interface, will occur the concentration gradient of solute.Due to solute concentration difference everywhere in this part melt, therefore zero pour T
falso not identical (under equilibrium state, being determined by the liquidus of phasor).The solute that is less than 1 for segregation coefficient, from interface, solute concentration reduces along with the increase of z, the solute that is greater than 1 for segregation coefficient, concentration increases along with the increase of z.From Fig. 6 and 7, can find out, in both cases, zero pour T
fall to raise gradually along with the increase of z, at that time, (being the zero pour of melt main body).Supposing that melt main body mixes, has been both constant.Figure 20 table is segregation coefficient to be less than the relation curve between 1 o'clock near interface solute concentration c and distance z.Figure 21 table is near interface zero pour T
frelation curve and two kinds of possible actual temperatures distributions (A and B) with distance z.If the actual temperature in melt distributes as shown in A line, this more gos deep into melt from interface, and condensate depression is less, so interface is stable, does not occur in other words constitutional supercooling.If the actual temperature in melt distributes as shown in B line, from interface, more go deep into melt, condensate depression is larger, so interface is unsettled, there is constitutional supercooling phenomenon, as can see from Figure 21, for B line, the temperature of melt is still higher than interface, and it is higher more to go deep into melt temperature,
> 0.If melt is not containing solute, interface is obviously stable, just because of the existence of solute, has just produced the interface unstable that condensate depression increases with the increase of z.Therefore this unstable is called constitutional supercooling.For the material of doping or the material of non-same composition fusing, more difficult while wishing to get high-quality monocrystalline than pure material, wherein one of important reason is also this.
There is not the needed condition of constitutional supercooling.The critical condition that condensate depression does not increase with the increase of z is, actual temperature distribution curve and zero pour T in melt
fcurve has identical slope.Obviously, Here it is there is not the critical condition of constitutional supercooling.
Still consider now 0 < z < δ
cthis 1 region, supposes in melt and exists convection current, and according to the concept of solute boundary layer, outside frictional belt, the main part of melt provides sufficient mixing by convection current, therefore has uniform solute concentration c
l(B), and to zero pour T that should be constant
f.Within this frictional belt, mass transfer process is to be arranged by diffusion, and molten matter concentration is the function (having ignored transverse dispersion) of z, and uses c
l(z)represent it, the zero pour of its correspondence is T
f(z).If m is liquidus slope, and regard approx m as constant.M=
, work as k
0when > 1, m is honest, and k
0when < 1, m is negative value, so
T
f（z）＝T
0＋mc
l（z） …（43）
Can be known by (19) formula
c
l（z）＝c
s＋（c
l（B）－c
s）exp（
－
） …（44）
Bring this formula into (43) formula, and z is asked to difference quotient, can obtain
At z=0 place, the slope of freezing point curve is
Because k
e=
=
(47)
Bring (47) formula into (46) formula, can obtain
Suppose that the actual temperature gradient in melt is
(actual distribution slope of a curve), does not produce a constitutional supercooling condition and is
So
≧
…（50）
Obviously, if the left end of above formula is less than right-hand member, occur constitutional supercooling, and both differences are larger, the phenomenon of constitutional supercooling will be more serious.
As previously mentioned, for convenience's sake, can get k*～k
0, c
l(B)～c
0.C
0for the average solute concentration of melt, k
0for equilibrium segregation coefficient.What (50) formula can be similar to so is expressed as
It should be pointed out that and work as k
0when < 1, be m negative value, and work as k
0when > 1, m is honest, therefore, the right-hand member of above formula always on the occasion of.
If there is not convection current in melt, both diffusion process was arranged whole melt, (51) formula can Jianization Wei≤
≤
(52)
The critical condition that does not occur constitutional supercooling is
=
, for definite material
/ f=constant × c
0, therefore,
/ f and c
0pass be 1 by the straight line of initial point.One side of this straight line is constitutional supercooling district, and opposite side is non-constitutional supercooling district.
Generally speaking, the excessively cold theoretical analysis of said components, by many experimental results are confirmed, can go to analyze the problem of melt growth with it time, obtains satisfied result.
Under the condition of constitutional supercooling, the crystal of growth is inhomogeneous, incomplete.Particularly, in the time that constitutional supercooling phenomenon is serious, the ununiformity of solute lateral distribution will make crystal produce macroscopical defect.Constitutional supercooling makes to occur in crystal cell structure (also referred to as bag shape structure, polynuclear plane or reticulated structure).As noted before, the random small embossment occurring of flat interface, under larger condensate depression, its forward position is grown sooner than interface rest part.Along with the carrying out of growth, the disturbance of temperature and concentration makes to occur on interface more small embossment, and the solute that region ejects from towards periphery further suppressed the growth (having reduced zero pour) of non-bossing, so formed the channel of solute between each projection.Because prominence can not exceed cold-zone, therefore, the thrust that the initial stage forms and the thrust occurring successively afterwards will have close height gradually, and they form closely packed array.Figure 22 has demonstrated the process of this development.If observe XY plane, this cell structure often has the form of six side's grids.The crystal obtaining under this condition is extremely inhomogeneous, and solute in each six sides' " grid " edge enrichment, even there will be Second Phase Precipitation thing, and sheet, thread macroscopic defects, and has reduced the transparency of crystal.Serious constitutional supercooling can make interface become dendritic growth from cellular growth.Certainly, if growth conditions just departs from or the instantaneous condition that departs from interface stability a little, so the defect in crystal will make that disperse, discontinuous appearance.
The crystal of growing, if rapid and melt disengaging, the configuration of surface of growth interface has just been reacted cell structure.At this moment, surface is no longer the smooth surface of macroscopic view, and has corrugated or pyramidal macroscopic form, and for semi-conductor and insulativity crystal, a point trellis interface is made up of the little crystal face of low index of many certain orientations conventionally; For metal, because they do not form little crystal face, lattice state generally adopts the form of close-packed 6 square arrays.
The growth method of large size oxide crystal of the present invention, as basis by crystal growing principle, in conjunction with melt growth Track character, the motivating force of crystallisation process, mass transfer, fractional condensation and solute distribution, hot transmission, convection current and temperature distribution, the theoretical model of interface stability and constitutional supercooling forms a kind of oxide crystalgrowth technology.The present invention need set up a set of stable warm field condition, the mode growing crystal that adopts seed crystal to sow, crystal and solid-liquid interface of melt self-assembling formation after completing seed crystal and sowing, the movement of recycling growth parameter(s) control solid-liquid interface completes the technique of crystal growth, combine the advantage of various conventional crystal growth, feature with different crystal growth changes growth parameter(s), reduces the generation of lattice defect and reaches the object of optimizing crystal mass, further reaches the target of industrialization.
The foregoing is only embodiments of the invention; not thereby limit the scope of the claims of the present invention; every equivalent structure or conversion of equivalent flow process that utilizes description of the present invention to do; or be directly or indirectly used in other relevant technical field, be all in like manner included in scope of patent protection of the present invention.
Claims (8)
1. the growth method of a large size oxide crystal, it is characterized in that, according to crystal growing principle in conjunction with melt growth Track character, the motivating force of crystallisation process, mass transfer, fractional condensation and solute distribution, heat transmission, convection current and temperature distribution, the theory of interface stability and constitutional supercooling is set up a set of stable temperature, the mode growing crystal that adopts seed crystal to sow, crystal and solid-liquid interface of melt self-assembling formation after completing seed crystal and sowing, utilize the movement of growth parameter(s) control solid-liquid interface to complete crystal growth, the process of growth of its crystal specifically comprises the following steps:
A, the growth of beginning crystal: in temperature field, be warming up to 1500-2500 ℃, seed crystal declines until 3-5mm under the melt liquid level that submerges, if the trend of the diameter zero growth of seed crystal start crystal growth after 5-10min, according to growing crystal characteristic, design different growth velocitys, and the actual observation of utilizing crystal weight to increase, feedback crystal growth equipment operating device output growth parameter(s);
B, pull finish growth: after crystal weight no longer increases, increase pull rate, make crystal depart from crucible completely and stop growing;
C, annealing discharge residual stress in crystal: comprise high temperature section, middle-temperature section and low-temperature zone, high temperature section setting declines with 5-60 ℃/h, and middle-temperature section setting declines with 10-80 ℃/h, and low-temperature zone setting declines with 10-50 ℃/h.
2. the growth method of large size oxide crystal according to claim 1, is characterized in that, the thermoscreen that make for metallic substance described temperature field, and wherein, described metallic substance is tungsten, molybdenum, platinum or stainless steel.
3. the growth method of large size oxide crystal according to claim 1, is characterized in that, the insulation layer that make for insulating material described temperature field, and wherein, described insulating material is zirconium white, aluminum oxide or asbestos.
4. the growth method of large size oxide crystal according to claim 1, is characterized in that, described temperature is the thermal field that thermoscreen and insulation layer collocation form, and wherein, described metallic substance is tungsten, molybdenum, platinum or stainless steel; Described insulating material is zirconium white, aluminum oxide or asbestos.
5. according to the growth method of the large size oxide crystal one of claim 2-4 Suo Shu; it is characterized in that; described temperature field also comprises crystal growth atmosphere; described crystal growth atmosphere is vacuum, shielding gas or air; wherein, described shielding gas is nitrogen, argon gas, helium or hydrogen.
6. the growth method of large size oxide crystal according to claim 1, is characterized in that, pulling rate, rotating speed, weight, power, shield gas flow rate, cooling water flow and water temperature that described growth parameter(s) comprises crystal growth equipment operating device.
7. the growth method of large size oxide crystal according to claim 6, is characterized in that, described pulling rate is at different growth phases, and the scope of pulling rate is between 0-10mm/h; Rotating speed is at different growth phases, and the scope of rotating speed is between 0-100rpm; Weight is at different growth phases, and the scope of weight rate of increase changes span of control corresponding between 0-3kg/h between 0-5Kw/h for rate; Shield gas flow rate scope is between 0-10KL/h; Cooling water flow is variable at equipment different positions, and cooling-water flowing weight range is situated between between 0-5KL/h.
8. the growth method of large size oxide crystal according to claim 1, is characterized in that, described crystal is LT, LN, YAG, GGG, YVO4, LSO, LYSO, YSO or Sapphire crystal.
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| CN104264213A (en) * | 2014-09-30 | 2015-01-07 | 元亮科技有限公司 | EFG (edge-defined film-fed growth) device of large-size doped sapphire crystals and growth process thereof |
| CN104372408A (en) * | 2014-12-15 | 2015-02-25 | 山东大学 | Large size gallium oxide single crystal Czochralski growing method under normal pressure |
| CN106119963A (en) * | 2016-02-03 | 2016-11-16 | 江苏浩瀚蓝宝石科技有限公司 | The impact on thermal field of a kind of kyropoulos sapphire single-crystal furnace heat shielding |
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| CN101580963A (en) * | 2009-06-26 | 2009-11-18 | 哈尔滨工大奥瑞德光电技术有限公司 | SAPMAC method for preparing sapphire single-crystal with size above 300mm |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN101580963A (en) * | 2009-06-26 | 2009-11-18 | 哈尔滨工大奥瑞德光电技术有限公司 | SAPMAC method for preparing sapphire single-crystal with size above 300mm |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104264213A (en) * | 2014-09-30 | 2015-01-07 | 元亮科技有限公司 | EFG (edge-defined film-fed growth) device of large-size doped sapphire crystals and growth process thereof |
| CN104372408A (en) * | 2014-12-15 | 2015-02-25 | 山东大学 | Large size gallium oxide single crystal Czochralski growing method under normal pressure |
| CN106119963A (en) * | 2016-02-03 | 2016-11-16 | 江苏浩瀚蓝宝石科技有限公司 | The impact on thermal field of a kind of kyropoulos sapphire single-crystal furnace heat shielding |
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