Thermochemical Processes Episode 4 docx

Chapter 3Vapour phase transport processes Vapour transport processes A rapidly developing technique in the materials science of thin film and singlecrystal growth involves the transport

80 Thermochemical Processes: Principles and Models

time is eliminated as a variable by using the Laplace transform Lx, t thusL[Qx, t] D

1 0

Q D Q0erfcx

2

p

˛twhich is given above for the solution to the laser heating problem

An alternative method of solution to these analytical procedures, which is

particularly useful in computer-assisted calculations, is the finite-difference technique The Fourier equation describes the accumulation of heat in a thin

slice of the heated solid, between the values x0and x0Cdx, resulting from theflow of heat through the solid The accumulation of heat in the layer is thedifference between the flux of energy into the layer at x D x0, Jx0 and the fluxout of the layer at x D x0Cdx, Jx0 Cdx Therefore the accumulation of heat inthe layer may be written as

but at any given point in the heat profile in the solid

which is the Fourier equation For the numerical solution of this equation thevariables are first changed to dimensionless variables

q D Q/Q0; ˇ D x/l; 6 D ˛t/l2

where l is the total thickness of the substrate

The heat conduction equation in terms of these variables has the components

differentials at the mth slice in the Fourier equation can be expressed in terms

in the heat conduction equation,

commer-Returning to laser heating of the film which is deposited on a substrate, it

is possible to control the temperature of the film and the substrate through thepower of the light source or by scanning the laser beam across the surface

of the substrate at a speed which will allow enough time for the deposit to

be formed (laser writing) In the practical situation it is simpler to move thesubstrate relative to the laser beam in order to achieve this The speed must beselected so as to optimize the rate of formation of the film while maintainingthe desired relation of the physical properties of the film and the substratesuch as cohesion and epitaxial growth

82 Thermochemical Processes: Principles and Models

Radiation and convection cooling of the substrate

This calculation is subject to two further considerations The first of these isthat a substrate such as quartz, which is transparent in the visible region, willnot absorb all of the incident light transmitted through the gas phase The

Fourier calculation shown above considers only the absorbed fraction of the

energy at the surface Secondly, if the absorption of radiation at the surface ofthe substrate is complete, leading to the formation of a hot spot, this surfacewill lose heat to its cooler surroundings by radiation loss The magnitude ofthis loss can be assessed using the Stefan–Boltzmann law,

QxDFeT4s T4m

Here, Qr is the energy loss per second by a surface at temperature Ts to itssurroundings at temperature Tm, the emissivity of the substrate being e, theview factor F being the fraction of the emitted radiation which is absorbed bythe cool surroundings, and  being the Stefan–Boltzmann radiation constant(5.67 ð 108J m2s1K4) In the present case, the emissivity will have avalue of about 0.2–0.3 for the metallic substrates, but nearly unity for thenon-metals The view factor can be assumed to have a value of unity in thenormal situation where the hot substrate is enclosed in a cooled container.There will also be heat loss from the substrate due to convection currentscaused by the temperature differential in the surrounding gas phase, but thiswill usually be less than the radiation loss, because of the low value of theheat transfer coefficient, h, of gases The heat loss by this mechanism, Qc, can

be calculated, approximately, by using the Richardson–Coulson equation

QcDhTsTm D5.6TsTm1/4J m2s1K1

which indicates a heat loss by this mechanism which is about one quarter ofthe radiation loss for a substrate at 1000 K and a wall temperature of 300 K.The major effect of the convection currents will be to mix the gas phase sothat the surface of the substrate does not become surrounded by the reactionproducts

Laser production of thin films

There are therefore two ways in which lasers may be used to bring aboutphoton-assisted film formation If the laser emits radiation in the near-ultra-violet or above, photochemical decomposition occurs in the gas phase andsome unabsorbed radiation arrives at the substrate, but this latter should be a

minor effect in the thin film formation This procedure is referred to as ysis Alternatively, if the laser emits radiation in the infra-red, and the photons

photol-are only feebly absorbed to raise the rotational energy levels of the gaseous

species, the major absorption occurs at the substrate, which therefore generates

a ‘hot-spot’, as described above, at the point where the beam impinges Thisspot heats the gas phase in its immediate environment to bring about thermal

dissociation This is therefore a pyrolytic process Lasers which provide a

continuous source of infra-red are of much greater power than the pulsedsources which operate at higher frequencies, so the pyrolytic process is moreamenable to industrial processing where a specific photochemical reaction isnot required

Because of the possibility of focusing laser beams, thin films can beproduced at precisely defined locations Using a microscope train of lenses

to focus a laser beam makes possible the production of microregions suitablefor application in computer chip production The photolytic process producesislands of product nuclei, which act as preferential nucleation sites for furtherdeposition, and thus to some unevenness in the product film This is becausethe substrate is relatively cool, and therefore the surface mobility of thedeposited atoms is low In pyrolytic decomposition, the region over whichdeposition occurs depends on the thermal conductivity of the substrate, beingwider the lower the thermal conductivity For example, the surface area of

a deposit of silicon on silicon is narrower than the deposition of silicon onsilica, or on a surface-oxidized silicon sample, using the same beam geometry.The energy densities of laser beams which are conventionally used in theproduction of thin films is about 103104J cm2s1, and a typical substrate

in the semiconductor industry is a material having a low thermal conductivity,and therefore the radiation which is absorbed by the substrate is retained near

to the surface Table 2.8 shows the relevant physical properties of some typicalsubstrate materials, which can be used in the solution of Fourier’s equationgiven above as a first approximation to the real situation

Table 2.8 Thermal conductivities and heat capacities of

some metals and oxides

Material Thermal conductivity Heat capacity

84 Thermochemical Processes: Principles and Models

Molecular decomposition in plasma systems

Apart from thermal and photon decomposition, the production of atoms andradicals in gaseous systems always occurs in plasma This is because of thepresence of both high energy electrons as well as photons in the plasmavolume The energy spectrum of the electrons is determined by the ioniza-tion potential of the plasma gas, the mean free path of the electrons betweencollisions, which depends on the pressure, and the applied electric poten-tial gradient Measurements of the energy spectrum in a glow discharge haveyielded electron energy values of the order of 2–10 eV (200–1000 kJ mole1),and the photon spectrum can extend to 40 eV The plasma therefore containselectrons and photons which can produce the free radicals which initiate chainreactions, and the novel feature is the capability to produce significant quanti-ties of ionized gaseous species The ions which are co-produced in the plasmahave a much lower temperature, around 7–800 K, and hence the possibilitythat the target will be excessively heated during decomposition using plasma

is very unlikely However, there is not the capability of easy control of theenergy of the dissociating species as may be exercised in photodecomposition.All of the atomic species which may be produced by photon decompositionare present in plasma as well as the ionized states The number of possiblereactions is therefore also increased As an example, the plasma decomposition

of silane, SiH4, leads to the formation of the species, SiH3, SiH2, H, SiHC2,SiH3Cand H2C Recombination reactions may occur between the ionized statesand electrons to produce dissociated molecules either directly, or through theintermediate formation of excited state molecules

AB C e!A C B : AB C e !ABŁCe !A C B C e

where ABŁrepresents a molecule in an excited state in which an energy level

is reached involving some electron re-arrangement, such as spin decoupling

in the stable bonding configuration of the molecule The lifetime of theseexcited states is usually very short, of the order of 107 seconds, and thusthey do not play a significant part in reactions which normally occur throughthe reaction of molecules or atoms in the ground, most stable, state They mayprovide the activation energy for a reaction by collision with normal moleculesbefore returning to the ground state, similar to the behaviour of the activatedmolecules in first-order reactions

A useful application of plasma is in the nitriding of metals or the formation

of nitrides Thermal methods for this require very high temperatures usingnitrogen gas as the source, due to the high stability of the nitrogen molecule,and usually the reaction is carried out with ammonia, which produces nitrogenand hydrogen by dissociation There is therefore a risk of formation of a nitro-hydride in some metals, such as titanium and zirconium, which form stablehydrides as well as the nitrides In a nitrogen plasma, a considerable degree of

dissociation of the nitrogen molecules occurs, together with positively chargedspecies such as NC and N2C The rate of nitriding of metals such as titaniummay be increased by imposing a negative potential on the metal to be nitridedwith respect to the plasma.

Carbides may also be prepared, either by direct carburizing, as in the case

of steel, in which a surface carbide film dissolves into the substrate steel, or byrefractory metal carbide formation as in the cases when one of the refractorymetal halides is mixed with methane in the plasma gas

Bibliography

D.A Eastham Atomic Physics of Lasers, Taylor & Francis, London (1986) QC 688 E37.

J Mazumdar and A Kar Laser Chemical Vapor Deposition, Plenum NY (1995) TS 695 M39 J.G Eden Photochemical Vapor Deposition, J Wiley (1992) TS 693 E33.

B Koplitz, Z Xu and C Wittig, Appl Phys Lett., 52, 860 (1988).

K Kamisako, T Imai, and Y Tarui, Jpn J Appl Phys., 27, 1092 (1988).

L Hellner, K.T.V Grattan and M.H.R Hutchinson, J Chem Phys., 81, 4389 (1984).

V.G Jenson and G.V Jeffreys Mathematical Methods in Chemical Engineering, Academic Press,

London (1963).

M Venugopalan and R Avni, Chapter 3 in Klabunde loc cit (1985).

Chapter 3

Vapour phase transport processes

Vapour transport processes

A rapidly developing technique in the materials science of thin film and singlecrystal growth involves the transport of atoms across a temperature gradient

by means of gas–solid reactions The objectives may be many, and includethe separation of elements from an unwanted impurity and the removal ofatoms from a polycrystalline sample to form a single crystal among others.The atomic species are transported by molecules which are formed by reaction

of the solid with a specially chosen reactant gas, and may occur up or downthe temperature gradient, depending on the nature of the transport reaction

In most circumstances, it can be assumed that the gas–solid reaction ceeds more rapidly than the gaseous transport, and therefore that local equi-librium exists between the solid and gaseous components at the source andsink This implies that the extent and direction of the transport reaction at eachend of the temperature gradient may be assessed solely from thermodynamicdata, and that the rate of transport across the interface between the gas andthe solid phases, at both reactant and product sites, is not rate-determining.Transport of the gaseous species between the source of atoms and the sinkwhere deposition takes place is the rate-determining process

pro-Thermodynamics and the optimization of vapour phase transport

The choice of the transporting reagent for a given material is made so thatthe reaction is as complete as possible in one direction, in the uptake, and thereverse reaction in the opposite direction at the deposition site This requiresthat not only the choice of the reagent, but also the pressure and temper-ature ranges under which the reaction is most effectively, or quantitatively,performed, must be calculated (Alcock and Jeffes, 1967; 1968) There willalways be limitations placed on this choice by the demands of the chemicalinertness and temperature stability of the containing materials in which thereaction is carried out

These considerations apart, the selection of the optimum conditions forthe performance of a transporting reaction requires the choice of the bestaverage value of the equilibrium constant The effect of the range in the

Table 3.1 Values of pXY2 at

equilibrium with Xs at varying

values of Kp D 1 atmos for the

equilibrium constant of a transporting reaction on the partial pressure variation

of a transporting gas is exemplified by Table 3.1 for the reaction:

X(s) C Y2(g) D XY2(g)

This shows the partial pressure of transporting molecules which are formed

at various values of the equilibrium constant, for the reaction carried out at oneatmosphere pressure It can be seen that the greatest change in the equilibriumpartial pressure occurs around the value of the equilibrium constant of unity,and hence where the standard Gibbs energy change has the value zero It istrue that the greatest value of the partial pressure of the transporting molecule

is to be found at the highest value of the equilibrium constant, but the greatestchange is about the value of unity

The optimal choice depends on the total pressure of the system, and on thestoichiometry of the reaction As an example, the transportation of zirconium

as the tetra-iodide is made at low pressure, while the purification of nickel

by tetracarbonyl formation is made at high pressure These reactions may bewritten as

Zr C 4I(g) D ZrI4(g) G°D 784 900 C 321.73T J mol1

D0 at 2440 Kand

Ni C 4CO(g) D Ni(CO)4 G°D 138 860 C 368.7T J mol1

D0 at 377 K

88 Thermochemical Processes: Principles and Models

Both reactions involve the formation of a vapour-transporting species fromfour gaseous reactant molecules, but whereas the tetra-iodide of zirconium

is a stable molecule, the nickel tetracarbonyl has a relatively small stability.The equilibrium constants for these reactions are derived from the followingconsiderations:

For the general reaction

X(s) C 4Y(g) D XY4(g)

when x moles of product are formed, leaving 41  x moles of reactant gas,and yielding a total number of moles 4  3x, the equilibrium constant isgiven by

the efficiency function

F D pdp/dK

for the product gas

Efficient transport of material across a temperature gradient depends notonly on the change in the equilibrium constant of the transporting reaction,but also on the mean partial pressure of the transporting species The product

pdp/dK can be used to assess the effectiveness of a given reaction, and themaximum of this function is to be found at different values of K, depending onthe total pressure and the stoichiometry According to Le Chatelier’s principle

it is to be expected that a change in total pressure will have an effect onthe maximum of this function, and in the examples of zirconium and nickelrefining given above, there is a marked difference in the optimum conditionsfor carrying out these reactions This is due to the large difference in the heats

of formation of these transporting species and the effect of these heats on thevalue of the equilibrium constants Figure 3.1 shows that the optimum for areaction involving no change in the number of gaseous molecules, which weshall call a 1:1 reaction, is independent of the total pressure The change due

to pressure in a 4:1 reaction, such as the refining reactions discussed above, isvery marked however, leading to different values in the optimum value of theequilibrium constant, thus a low pressure system is best for zirconium transportwhere the equilibrium favours the iodide, while a high-pressure system is usedfor nickel purification, since the equilibrium constant produces a small partialpressure of the carbonyl at one atmosphere pressure

The direction of vapour transport across a thermal gradient

In some transport reactions the transporting species is carried up a temperaturegradient and in others the transport is in the opposite direction For examplethe transport of aluminium by reaction with AlCl3 to form the monochloride,AlCl, occurs down the temperature gradient This reaction is written as2Al C AlCl3(g) D 3AlCl(g) G°D391 600  261.3T J mol1

and the lower chloride is the transporting gas The difference between this tion, a 1:3 reaction, and the zirconium transport reaction 4:1, which occurs up

reac-a temperreac-ature grreac-adient, lies in the entropy chreac-ange This is mreac-ainly determined

by the change in the number of gaseous molecules which occurs in each tion The 1:3 reaction shown above will be accompanied by an increase in the

∑P = 0.1 atm

∑P = 0.01 atm

tetra-iodide, which is much more stable, is favoured by low pressures

90 Thermochemical Processes: Principles and Models

entropy content, while the zirconium refining 4:1 reaction shows a decreasefrom left to right in the equation of transport.

The standard entropies of monatomic gases are largely determined by thetranslational partition function, and since this involves the logarithm of themolecular weight of the gas, it is not surprising that the entropy, which isrelated to the translational partition function by the Sackur–Tetrode equation,

S D3/2R ln M C 5/2R ln T  2.300

should also be an approximately linear function of the logarithm of the ular weight, having a value of 200 J K1 at 298 K for light molecules, rising

molec-to about 600 J K1 at a molecular weight of 200 for polyatomic molecules

It also follows that the iodides will have the largest entropy change whencompared with the other halides due to this mass effect in transporting reac-tions, especially when combined with light metals

The choice of halogen in transport reactions

The value of the change in partial pressure of the transporting gas, atone atmosphere where pressure, with temperature indicates the balancebetween the standard heat of the reaction and temperature times the standardentropy change In the case of chloride transport this balance sometimesoccurs only at an unacceptably high temperature due to the large heats offormation of most chlorides The optimum temperature for vapour transport issignificantly reduced by the use of bromine, by approximately 100 kJ mol1,and even more by the use of iodine, by roughly double that amount,

as the transporting halogen This is because the heats of formation ofcorresponding gaseous halides reflect the decrease in the electron affinities ofthe halogens in the sequence Cl > Br > I, and the fact that the metal–halogenbond length increases in the opposite sequence, M–Cl < M–Br < M–I Theelectron affinities determine the magnitude of the ionic contribution to themetal–halogen bond, and the bond length determines the covalent as well asthe ionic contributions Furthermore, iodine is the most practical species whenthe reaction is carried out on a small scale in a sealed system, or under vacuumconditions, because it may be introduced into the container in solid form, andthe container can be sealed at room temperature before the experiment orapplication is begun

The vapour phase refining and separation of metals

The classical examples of the transporting of metals by halogens are the vanArkel refining of metals, and the prolongation of the working life of tung-sten lamps Both of these use iodine to provide the transporting moleculeand function by transporting the metal across a temperature gradient In van

92 Thermochemical Processes: Principles and Models

Arkel refining a sample of the impure metal, for example zirconium, is heated

to a temperature around 550 K in contact with low pressure iodine gas in asealed system which has a heated tungsten filament in the centre The filamenttemperature is normally about 1700 K At the source the iodides of zirconiumand some of the impurities are formed and these diffuse across the interveningspace, where the total pressure is maintained at 103 atmos, and are decom-posed on the filament The iodine then returns to form fresh iodide at thesource, and the transport continues

The anticipated content of impurities in the refined metal may be calculated

a priori by assuming thermodynamic equilibrium at both metal/gas interfaces,

and using the relevant stabilities of the gaseous iodides Adequate namic data could provide the activities of the impurities with that of zirconiumclose to unity, but the calculation of the impurity transport obviously requires

thermody-a knowledge of thermody-activity coefficients in the originthermody-al impure mthermody-aterithermody-al, which thermody-arenot sufficiently well known

The three impurities, iron, silicon and aluminium are present in the metalproduced by the Kroll reduction of zirconium tetrachloride by magnesium tothe extent of about 1100 ppm After the iodide refining process the levels ofthese impurities are 350, 130 and 700 ppm respectively The relative stabilities

of the iodides of these metals compared to that of zirconium can be calculatedfrom the exchange reactions

Zr C SiI4(g) D Si C ZrI4(g) : G°550D 241 600  8.26T D 246 500

log K D logaSipZrI4(g)

aZrpSiI4(g)D21.53Zr C 2Al2I6(g) D 4Al C 3ZrI4(g) : G°D 89 040  150.4T D 171 019

log K D log a

4AlpZrI4(g)

a3Zrp2Al2I6(g)D16.20and there are no reliable data for the iron gaseous iodides Since silicon andaluminium are both present in the impure zirconium as the stable compounds

Zr3Si and Zr3Al respectively, their activity coefficients should be less than one,and it is clear that the thermodynamic data suggest that zirconium should betransported preferentially initially The final experimental amounts of siliconand aluminum transported are significantly higher than these data would indi-cate They must therefore be transported as a result of iodination when thesurface has been depleted of zirconium The low temperature at which thereaction with iodine is carried out supports the conclusion that thermody-namic data will only be of limited value in the estimation of the transport ofimpurities in this process

This is an instructive example of the fact that thermodynamic data canonly be used to calculate the extent to which a reaction can be carried out

before equilibrium is reached, but the kinetics of the reaction depend on themechanism of the reaction in the context of the reacting substances.

The separation of niobium from tantalum through the gaseous chlorides

is carried out at higher temperature, about 900 K, and it is therefore to beexpected, as is the case, that the thermodynamic data will provide a usefulguide These metals form a number of chlorides, mainly the tri- tetra- andpentachlorides These latter are much more volatile than the tetrahalides, andthe exchange reaction at 900 K

NbCl5(g) C TaCl4 DTaCl5(g) C NbCl4 :

G°D 181 300 C 180.4T J mol1

D0 at 1005 K

and hence this reaction, which is not affected by a change in the total pressure,

is found to be an efficient means of separating the two metal chlorides

The thermodynamics of the vapour phase transport of compounds

In this more complicated case, both components must be transported in theproportions indicated by the chemical composition In the simplest cases, one

of the components is an elementary species during transport, which is ally so in the transport of oxides and arsenides by elementary halogens, forexample The identity of the gas or gases which may be transporting themetal are frequently difficult to decide because of the complexity resultingfrom the possibility of forming a number of species For example, the trans-port of niobium oxides by chlorine could involve the species NbCl5, NbCl4

gener-and NbCl3 as well as some oxychlorides such as NbOCl3

The Gibbs energy of formation of the more important molcules are,NbO2C3/2Cl2DNbOCl3(g) C 1/2O2

G°D34 140  59.1T J mol1NbO2C5/2Cl2DNbCl5(g) C O2

94 Thermochemical Processes: Principles and Models

of formation of the monochloride may be determined from the data for thereaction

GaCl3(g) C 2Ga D 3GaCl(g) G°D196 900  249.4T J mol1

D0 at 790 KBelow this temperature, mainly GaCl3 transports gallium, but above thistemperature, the monochloride will begin to predominate

A graphical method involving the Gibbs energies of formation per atom can be used to assess the feasibility of potential transport reactions

gram-If the Gibbs energy of formation of the various gaseous species which can

be formed in a ternary system are known, the relative partial pressures ofall of these gases can be calculated for known activities of the elements inthe solid phase to be transported The feasibility of a vapour phase transportreaction of a binary solid such as SiC in the ternary Si–C–Cl requires that thetransport reactions carry the proper amounts of each component in the solid, forexample the transport of silicon and carbon in SiC in 1:1 proportion This can

be assessed from the chemical potential diagrams for the gases in the binarysystems Si–Cl, Si–C and C–Cl, by joining the common axes in the sequence(Cl–Si)-(Si–C)-(C–Cl) The Cl–Si system must have a common chemicalpotential of chlorine with the C–Cl system in any equilibrium situation Inthis the partial pressures of each of the gaseous species in the transportingreaction must be calculated for all of those silicon and carbon activities whichare together in equilibrium with SiC It is clear from the graph (Figure 3.2)that the process cannot be used because of the much lower stability of CCl4

than SiCl4 For the quaternary system Si–C–H–Cl the Gibbs energy data arejoined in the following sequence, Cl–Si–C–H–Cl, and a common chlorineactivity must apply to the Si–Cl and H–Cl systems

This technique is a useful graphical approach to the problem togetherwith the solution of the multicomponent Gibbs minimization equations usingcomputerized procedures and the ancillary data for the Gibbs energies for all

of the potential species For example, it is clear that whereas chlorine cannot

be used as a transporting agent for silicon carbide, hydrogen chloride gas is agood choice The Gibbs energy of this reaction

Zr C 4I(g) D ZrI4< /small>(g) G°D 7 84 900 C 321.73T J mol1

D0 at 244 0 Kand

Ni C 4CO(g) D Ni(CO)4< /sub> G°D...

Zr C SiI4< /small>(g) D Si C ZrI4< /small>(g) : G°550D  241 600  8.26T D  246 500

log K D logaSipZrI4< /sup>(g)...

aZrpSiI4< /sub>(g)D21.53Zr C 2Al2I6(g) D 4Al C 3ZrI4< /small>(g) : G°D 89 040  150.4T D 171 019