Densification and microstructure evolution during sintering of silicon under controlled water vapor pressure

Available online at www.sciencedirect.com

Journal of the European Ceramic Society 33 (2013) 2993–3000

Densification and microstructure evolution during sintering of silicon under controlled water vapor pressure J.M. Lebrun ∗ , A. Sassi, C. Pascal, J.M. Missiaen Laboratoire de Science et Ingénierie des Matériaux et Procédés, SIMaP, Grenoble INP-CNRS-UJF, Domaine Universitaire, BP 75, F-38402, Saint-Martin d’Hères, France Received 12 March 2013; received in revised form 12 June 2013; accepted 28 June 2013 Available online 25 July 2013

Abstract Sintering of fine silicon powder was studied under controlled water vapor pressures using the Temperature–Pressure–Sintering Diagram approach. The water vapor pressure surrounding the sample was deduced from thermogravimetric analysis and related to the water content of the incoming gas flux with a simple mass transfer model. The thickness of the silica layer covering silicon particles was then monitored by the water vapor pressure and the microstructure evolution and densification during sintering could be controlled. Stabilizing the silica layer indeed inhibits grain coarsening and allows better densification of the compacts under humidified atmosphere as compared to dry atmosphere. © 2013 Elsevier Ltd. All rights reserved. Keywords: Silicon; Sintering; Atmosphere control; Microstructure evolution; Kinetics

1. Introduction Silicon is largely available on earth, but photovoltaic applications require crystallization of silicon ingots of high purity obtained through high energy consuming processes. Ingot cutting is responsible for a large material loss and leads to expensive production costs. Sintering of near net shape silicon wafers is thus an important issue. Previous works showed that densification of silicon is not favored during sintering because of significant grain coarsening. Depending on the authors, the coarsening mechanism could be surface transport [1,2] or vapor transport [3–5]. Actually, both mechanisms can dominate sintering kinetics, depending on the stability of the silica layer at the silicon particle surface [6–8]. Recently, Temperature–Pressure–Sintering diagram approach (TPS diagrams) [9] has been proposed to monitor the silica layer reduction kinetics in order to control the

∗

Corresponding author at: SIMaP, GPM2, ENSE3 – Site Ampère, 101 rue de la Physique, Domaine Universitaire, BP 46 – 38402 St. Martin d’Hères Cedex, France. Tel.: +33 4 76 82 66 76; fax: +33 4 76 82 63 82. E-mail addresses: [email protected], [email protected] (J.M. Lebrun). 0955-2219/$ – see front matter © 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jeurceramsoc.2013.06.024

sintering kinetics of silicon, i.e., microstructure evolution and densification. In this paper, oxidation kinetics of silicon powder compacts, i.e., the thickness of the silica layer at the particle surfaces, is monitored by controlling the water vapor pressure surrounding the sample as a function of the temperature cycle using thermogravimetric analysis. A promising gain of 15% is observed on the final density for samples sintered under humidified atmosphere compared to dry atmosphere. Eventually, the importance of the furnace geometry design on sample mass loss is discussed.

2. Experimental procedure 2.1. Powder and powder compact characteristics The powder consists of fine spherical particles of 220 nm estimated from BET specific surface area measurements (11.7 m2 g−1 , Micromeritics ASAP 2020). The morphology of the powder is observed using FEG-SEM (CARL ZEISS ULTRA55). The oxygen content (0.61 wt.%) is estimated from an instrumental gas analysis (IGA ELTRA ON900). The thickness of the native oxide layer calculated from the oxygen content

2994

J.M. Lebrun et al. / Journal of the European Ceramic Society 33 (2013) 2993–3000

and the specific surface area is 0.43 ± 0.10 nm. The global amount of metallic impurities is less than 1 ppm. Cylindrical compacts (54% relative density) are obtained by uniaxial pressing at 50 MPa followed by cold isostatic pressing at 450 MPa. Samples are about 400 mg mass, 7 mm diameter and approximately 8 mm height. 2.2. Thermogravimetric measurements and humidity controller system Thermogravimetric analyses (TGA) are performed in a SETARAM Setsys apparatus. Compacts are hung up to a tungsten suspension in order to limit interactions with silicon. He-4 mol.% H2 carrier gas (2 l h−1 ) is used to avoid the oxidation of the tungsten part. The furnace temperature, T, is monitored with a tungstenrhenium thermocouple and is homogenous over a range of 30 mm. In this part of the tube, the atmosphere can be assimilated as quasi-stagnant, i.e., the transport of mass species can be considered as essentially diffusive [7]. The water vapor pressure is monitored with a humidity controller system made of two gas lines. One line is the carrier dry gas while the other is obtained by circulating the carrier dry gas in a water container. Both gases are mixed and a humidity probe controller (Vaisala HUMIDICAP® HMT333 – West N8800) allows to regulate thermal mass flow (Brooks SLA5850S) to give a water vapor pressure, PHProbe , comprised between 100 2O and 2000 Pa. The microstructure of the sintered compact is observed on polish surfaces using FEG-SEM and sample densities are measured using the Archimedes method. 3. Theory

Fig. 1. Temperature–(water vapor) Pressure–Sintering rate (TPS) diagram. Lines of constant sintering time are calculated for particles with a diameter 2a = 220 nm. Top of the diagram: silicon monoxide pressure, PSiO , or probe , at which the silica layer ought to be stabilized water vapor pressure, PHProbe 2O with respect to the temperature. Section (A): Neck growth kinetics with reduced R1 ). Section (B): Neck growth kinetics with stabilized silica silica (PSiO < PSiO R1 ). Position of samples a, b and c, and samples a*, b* and c* sintered (PSiO < PSiO at 1225, 1260 and 1315 ◦ C.

3.1. Temperature–Pressure–Sintering diagram Silicon sintering kinetics is strongly affected by the presence of a silica layer at the silicon particle surface. This behavior is described in Fig. 1 using a Temperature–Pressure–Sintering diagram approach [9]. Using thermogravimetric experiments the reduction kinetics of the silica layer under standard He-4 mol.% H2 (2 l h−1 ) atmosphere has been studied for powders of various particle size [6]. The silica layer does not preclude the SiO(g) release at temperatures above 1000 ◦ C, so that the reaction (R1 ) controls the stability of the silica layer. Si(s) + SiO2(s) = 2SiO(g)

(R1)

The conditions for the stability of the silica layer can then be given in terms of silicon monoxide partial pressure, PSiO , as a function of the temperature, as represented at the top of the TPS diagram in Fig. 1. The effect of the silica layer on silicon sintering kinetics can be estimated using appropriate approximations [9]. This can be summarized using a sintering diagram approach [11], where x is the neck size radius between two connecting spherical particles of radius a.

(A) If the effective partial pressure of silicon monoxide at the sample surface is less than the equilibrium partial presR1 [10], the silica layer sure of SiO from reaction (R1 ), PSiO is reduced. Neck growth kinetics is given in the section (A) of the diagram where surface diffusion (s(nd) nondensifying mechanism) controls the neck growth rate at all temperatures and neck to particle size ratio. This leads to grain coarsening without densification as experimentally observed in a previous paper [7]. (B) If the effective partial pressure of silicon monoxide at the R1 , the silica layer is stabilized. sample surface is equal to PSiO Neck growth kinetics is given in the section (B) of the diagram. Surface diffusion is then strongly slowed down by the presence of the silica layer at the silicon particle surface. Lattice diffusion from the grain boundary (l(d), densifying mechanism) and from the surface (l(nd) non-densifying mechanism) dominate sintering kinetics at high temperature in the early stage of sintering, while vapor transport (v(nd) non-densifying) dominates at low temperature and in the late stage of sintering. Since lattice diffusion from the grain boundary (l(d)) can play a significant role, higher

J.M. Lebrun et al. / Journal of the European Ceramic Society 33 (2013) 2993–3000

2995

densification with less grain coarsening is expected in this case.1 3.2. Control of the silica layer stability: design of the water vapor pressure controller Reaction (R1 ) is a combination of two others, (R2 ) and (R3 ) that describes the oxidation of silicon under hydrogenated and humidified atmospheres: - If the supply of water from the atmosphere is lower than the silicon monoxide produced through reaction (R1 ), then the sample is under active oxidation (R2 ): Si(s) + H2 O(g) = SiO(g) + H2(g)

(R2 )

The amount of water molecules hitting the silicon surface is then not large enough to maintain the equilibrium partial R1 [10], and the silica layer pressure of silicon monoxide, PSiO is reduced as equilibrium (R1 ) is shifted to the right. This is usually the case at high temperature and/or low surrounding water vapor pressure. - If the supply of water to the sample is higher than the silicon monoxide produced through reaction (R1 ), then the sample is under passive oxidation (R3 ): Si(s) + 2H2 O(g) = SiO2(s) + 2H2(g)

the semi-empiric approach of Chapman–Enskog [13,14]. The temperature, T, is assumed constant at the sample surroundings.

R3

The silicon monoxide pressure at the silicon-silica interface overpass the equilibrium partial pressure of silicon monoxide, R1 . The silica layer grows as equilibrium (R ) is shifted to PSiO 1 the left. This is usually the case at low temperature and/or high surrounding water vapor pressure. Accordingly, in order to stabilize the silica layer, i.e., to prevent both growth and dissociation, the molar flux density of water, jH2 O , should equal the silicon monoxide flux density produced through reaction (R1 ), jSiO (Eq. (1)). jSiO + jH2 O = 0

(1)

The temperature at which this condition is satisfied is called the transition temperature, T*, and is a function of the water vapor pressure. The furnace tube geometry is sketched in Fig. 2. The atmosphere surrounding the sample is approximated as a quasistagnant gas mixture [7]. Assuming steady-state conditions for the diffusion, the molar flux density of a molecule j, jj , can be derived in linear coordinates in Eq. (2), where Pj is the partial pressure of the molecule, z is the vertical position in the furnace tube, R is the gas constant and Djmol is the molecular diffusion coefficient estimated as a function of the temperature from

1

Fig. 2. Schematic representation of mass transport kinetics involved in the furnace tube during sintering under equilibrium conditions, jSiO + jH2 O = 0.

However, one may notice that sintering kinetics in the presence of a stabilized silica layer is slightly different from those introduced in a previous paper [9]. Here, the effect of a silica layer of nanometric thickness on lattice diffusion and vapor transport kinetics is taken into account.

jj = −

Djmol Pjz − Pjz=0 RT

z

(2)

The molar flux density of silicon monoxide is expressed in Eq. (3) at the transition temperature T*, assuming the following boundary conditions: z=0 R1 as the silica layer ought to be stabilized at the = PSiO - PSiO particle surfaces. zf = 0. At a given position, z , the temperature is lower - PSiO f than the temperature at the sample position. Accordingly, the silicon monoxide pressure is larger than the equilibrium value, R1 , and silicon monoxide molecules condensate in the form PSiO silicon and silica as observed in Fig. 3 [7].

jSiO =

mol P R1 DSiO SiO RT zf

(3)

The molar flux density of water is expressed in Eq. (4) assuming PHz=0 << PHzf2 O since the water is entirely consumed through 2O reaction (R2 ) at the sample surface. z

j H2 O = −

mol P f DH H2 O 2O

RT

zf

(4)

The molar flux density of water in one direction corresponds to half the amount of water supplied by the water vapor pressure controller in Eq. (5), where Q is the volume gas flux, Stube is the is the water vapor pressure at section of the furnace tube, PHProbe 2O

2996

J.M. Lebrun et al. / Journal of the European Ceramic Society 33 (2013) 2993–3000

Fig. 3. View of the silicon monoxide condensate film on the thermocouple, underneath the zf position.

the probe position (in the incoming gas flux), and T◦ is the room temperature. jH2O =

1 Probe Q jH2 O = − tube ◦ PHProbe 2O 2 2S RT

(5)

The critical water vapor pressure to be controlled, PHProbe∗ , 2O such as to stabilize the silica layer at the transition temperature, T*, can be estimated from Eqs. (1), (3) and (5) in Eq. (6). PHProbe∗ =2 2O

mol S tube ◦ DSiO T R1 ∗ P (T ) Qzf T ∗ SiO

(6)

PHProbe∗ actually corresponds to a critical water vapor pressure 2O at the sample surroundings, PHzf2∗O , calculated from Eqs. (1), (3) and (4) in Eq. (7), as done in a previous work [9] or in the pioneer work of Wagner [12]. PHzf2∗O =

mol (T ∗ ) DSiO mol (T ∗ ) DH 2O

R1 (T ∗ ) PSiO

(7)

Depending on the water vapor pressure, PHProbe∗ , the tempera2O ture at which the silica layer ought to be stabilized, T*, is plotted in Fig. 4 using a diffusion length zf = 40 mm, as estimated from a previous study of silica reduction kinetics under dry atmosphere in the same TGA apparatus [7]. According to this plot, the silica layer can be stabilized from 1100 to 1350 ◦ C using probe water vapor pressures ranging from 100 to 2000 Pa. At the top of the TPS diagram (Fig. 1), the conditions for the silica layer stability were initially given in terms of silicon monoxide pressure, PSiO , as the function of the temperature. These conditions can now also be drawn in terms of water pressure at the probe position, PHProbe . In Fig. 1, a diffusion length 2O as estimated of zf = 25 mm is used for the calculation of PHProbe∗ 2O from the results presented in the following section. - If the effective partial pressure of water is lower than PHProbe∗ , 2O the silica layer is reduced. Neck growth kinetics is given in section (A) of the diagram. Grain coarsening without densification is then expected. - If the effective partial pressure of water is equal to PHProbe∗ , 2O the silica layer is stabilized. Neck growth kinetics is given in

Fig. 4. Model and experimental transition temperatures, T*, for several water vapor pressures in the incoming gas flux, PHProbe . The temperature at which 2O the mass flux are equals, T*m , is also given as well as the equivalent silicon z=0 R1 , and the critical water monoxide pressure at the sample surface, PSiO = PSiO vapor pressure in the sample surroundings, PHzf2∗O , at which the silica layer ought to be stabilized.

section (B) of the diagram and densification is favored at high temperatures. 4. Results 4.1. Control of the water vapor pressure In order to study the effect of the atmosphere humidity on sintering of a silicon compact, it is necessary to identify the passive ∗ to active transition temperatures, TP→A , and the active to passive ∗ transition temperatures, TA→P , depending on the water vapor ∗ ∗ and TA→P respecpressure controlled in the gas flux. TP→A tively corresponds to the temperatures at which silica starts to be reduced during heating and to the temperatures at which silica starts to grow during cooling. This identification is done by analyzing the mass variation rate using TGA. Mass loss rates for samples sintered under dry and humidified atmospheres (PHProbe = 200, 400, 800 and 1600 Pa) are given in Fig. 5. The 2O temperature cycle is described below (Fig. 5(a)): - Heating to 1350 ◦ C at 40 ◦ C min−1 . A rapid heating rate was chosen such as to limit the formation of a silica layer at the sample surface which might delay the passive to active tran∗ sition temperature, TP→A . - Holding time of 90 min at 1350 ◦ C, in order to remove the silica covering the silicon particles at the sample surface. - Cooling to 1100 ◦ C at 2.5 ◦ C min−1 . A slow cooling rate was chosen to better identify the temperature at which silica starts to grow again at the sample surface, i.e., the active to passive ∗ transition temperature, TA→P . Four steps are identified for all water vapor pressures (Fig. 5(b)):

J.M. Lebrun et al. / Journal of the European Ceramic Society 33 (2013) 2993–3000

2997

Fig. 5. TGA curves of powder compacts under 2 l h−1 He–4 mol.% H2 atmosphere, dry or humidified (PHProbe = 200, 400, 800 and 1600 Pa). (a) Thermal cycle. (b) 2O Rate of mass variation during the whole experiment. (c) Rate of mass variation during heating (passive to active transition). (d) Rate of mass variation during cooling (active to passive transition).

(i) During heating, samples first experience a slight mass gain related to the passive oxidation of silicon along reaction (R3 ). Higher water vapor pressures give rise to higher mass gain since the amount of silica to be grown is higher. (ii) Then, samples start to experience the passive to active transition. The rate of mass variation becomes negative ∗m that depends on the water vapor at a temperature TP→A pressure. The observed mass loss corresponds to the reduction of the silica layer according to reaction (R1 ). As the ∗m is also increased water vapor pressure is increased, TP→A (Fig. 5(c)). (iii) During holding at 1350 ◦ C, the rate of mass loss decreases and becomes constant. The constant mass loss is related to the active oxidation of silicon according to reaction (R2 ), once the silica covering the particles has been removed. (iv) During cooling, the rate of mass variation suddenly increases. This corresponds to the active to passive ∗ transition, TA→P , since the silica, which becomes thermodynamically stable, starts to grow again at the sample surface according to reaction (R3 ). The rate of mass vari∗m . As the water ation becomes nil at a temperature TA→P ∗ ∗m increase vapor pressure is increased, TA→P as well as TA→P (Fig. 5(d)).

The temperature at which the rate of mass variation is nil, T*m , both during heating (P→A) and cooling (A→P), corresponds to a mass flux equality between H2 O(g) arrival and SiO(g) departure (Eq. (8)). MSiO jSiO + MO jH2 O = 0

(8)

At T*m , the molar flux of silicon monoxide is lower than the molar flux of water, since the molar mass of SiO (MSiO ) is higher than the molar mass of O (MO ). Silica is then still growing on silicon particles at the sample surface and Eq. (3) can still be applied. Using Eqs. (3), (5) and (8), PHProbe∗ can be estimated 2O from T*m in Eq. (9). PHProbe∗ =2 2O

mol (T ∗m )S tube T ◦ R1 ∗m MSiO DSiO P (T ) MO Qzf T ∗m SiO

(9)

Eq. (10) is derived using Eqs. (6) and (9) since the molecular diffusion coefficient of SiO(g) is almost constant within the temperature range (T*m ; T*). R1 PSiO (T ∗ ) =

mol ∗m (T ) T ∗ R MSiO DSiO MSiO R1 ∗m P 5 (T ∗m ) ≈ P (T ) mol MO DSiO (T ∗ ) T ∗m SiO MO SiO

(10)

Using Eq. (10), temperatures at which the rate of mass variation is nil, T*m , can be converted in the transition temperature at

2998

J.M. Lebrun et al. / Journal of the European Ceramic Society 33 (2013) 2993–3000

Fig. 6. Top frame: microstructures and Archimedes’ densities of samples a*, b* and c*, sintered under controlled humidified atmospheres for 3 h at respectively 1125 ◦ C, 1260 ◦ C and 1315 ◦ C. Bottom frame: microstructures and Archimedes’ densities of samples a, b and c sintered at the same temperatures but under dry reducing atmospheres. The heating rate is 40 ◦ C min−1 and the carrier gas is 2 l h−1 He–4 mol.% H2 flow.

which the molar fluxes of silicon monoxide and water are equal, T*, and vice versa. This is done for the passive to active (during heating, Fig. 5(c)) as well as the active to passive (during cooling, Fig. 5(d)) transitions. These temperatures are reported in  Fig. 4 and so called “T* estimated from T*m . During cooling, the transition temperatures, T*, can be directly estimated from the moment where the rates of mass variation suddenly increase ∗ (Fig. 5(d)). These temperatures are then simply called TA→P and are also reported in Fig. 4. 4.2. Effect of the water pressure on silicon densification and microstructure The effect of the water vapor pressure and subsequent silica layer stabilization on the densification and microstructure evolution is now investigated. According to Fig. 1, for a given sintering temperature, TS , the water vapor pressure in the incoming gas, PHProbe , is chosen: 2O

(A) As low as possible, under dry reducing atmosphere, for the same sintering temperatures (TS = 1225, 1260 and 1315 ◦ C–3 h dwelling time) with a high heating rate (40 ◦ C min−1 ), such as to favor silica reduction and coarsening through surface diffusion. These conditions correspond to samples a, b and c respectively. (T S = T ∗ ), such as to keep the silica layer (B) Equal to PHProbe∗ 2O stable. A rapid heating of 40 ◦ C min−1 is chosen in order to reach the equilibrium state rapidly. Such rapid heating rate should also favor lattice diffusion and densification against surface diffusion and vapor transport. Sintering temperatures, TS , for the samples a*, b* and c* are 1225, 1260 and 1315 ◦ C (3 h dwelling time). According to Fig. 4, for the silica layer to be stabilized, these temperatures respectively , of 400, 800 correspond to water vapor pressures, PHProbe∗ 2O and 1600 Pa. Samples microstructures and densities are given in Fig. 6:

J.M. Lebrun et al. / Journal of the European Ceramic Society 33 (2013) 2993–3000

- Samples a*, b* and c* show a fine porous microstructure from 200 nm (close to the initial particle size) for the sample sintered at 1225 ◦ C to approximately 500 nm for the sample sintered at 1315 ◦ C. Sample densities are respectively 65, 73 and 80%TDSi (theoretical density of silicon). Sample mass losses are respectively 14.1, 19.5 and 22.5% of the initial sample mass. - Samples a, b and c microstructures are about ten times coarser than the microstructures of samples a*, b* and c*. Large grains (∼1 ␮m), highly twinned, are surrounded by very coarse pores (5–10 ␮m). Sample densities are respectively 61, 64 and 65%TDSi . Sample mass losses are respectively 6.4, 8.5 and 10.1% of the initial sample mass. 5. Discussion On Fig. 4, the measured transition temperatures, T*, are lower than those predicted from Eq. (6), using zf = 40 mm. A lower value of zf (25 mm), leads to a very good fit of the experimental data, as if the silicon monoxide would condensate closer to the sample. This shift of the zf value compared to experiments carried out under dry atmosphere is not clearly understood. We can first allege the model simplicity to explain this discrepancy. We can also propose that the condensate of silicon monoxide, partly made of silicon, consumes some water molecules before they can reach the sample. The water vapor pressure at the sample surroundings, PHzf2 O , would then be lower than expected and the water vapor pressure to be imposed in the incoming flux would have to be larger than the value given in Eq. (6). ∗ Measured passive to active transition temperatures, TP→A , ∗ are slightly larger than the active to passive ones, TA→P . During cooling (Fig. 5, step iv), the active to passive transition actually requires the germination of silica on a bare silicon compact surface through reaction (R3 ). Supersaturation of SiO(g) and H2 O(g) may be necessary to activate the nucleation and silica growth, thus shifting the active to passive transition to lower temperatures. Accordingly the measured passive to active transition temperatures would give a better estimation of T*. During active oxidation (Fig. 5, step iii), (R2 ) is assumed to be controlled by the diffusion of water vapor to the powder compact and the rate of mass loss should increase when increasing PHProbe as observed 2O for experimentations carried out under water vapor pressures lower than 800 Pa. However, experiments realized under higher water vapor pressures deviates from this prediction: ∗ - Measured active to passive transition temperatures, TA→P , are lower than the predicted ones (Fig. 4). - Mass loss rates measured during step (iii) do not increase (Fig. 5(d)).

Nucleation of silica along reaction (R3 ) may occur in the furnace tube during step (iii) and would decrease the water vapor pressure at the sample surroundings and explain these observations. Nucleation is favored at high temperatures and deviation from the model would then be more important, as observed in Fig. 4.

2999

Model and experiments are then consistent, at least when looking at the sample behavior during the passive to active tran∗m . The water probe vapor pressure to be controlled, sition, TP→A Probe∗ PH2 O , in order to stabilize the silica layer at a temperature, T*, can then be estimated from Eq. (6) using zf = 25 mm. Fig. 6 shows that the grain size and densification can be controlled over a wide range by an appropriate choice of the water vapor pressure and sintering temperature. Stabilizing the silica layer at high temperatures inhibited surface diffusion and grain coarsening to enable neck growth through lattice diffusion. Accordingly, samples a*, b* and c* relative densities are higher than samples a, b and c densities. As the temperature is increased, the relative density increases which is consistent with Fig. 1 where the lattice diffusion domain expands at higher temperature when the silica layer is stabilized. However, full densification is never observed because of the competition with vapor transport which is responsible for non-densifying neck growth and coarsening of the microstructure. Controlling the water vapor pressure allows a direct control of the silicon monoxide pressure at the sample surroundings. This solution is interesting as the silica layer can be real time controlled. For example, in order to improve the densification, the sample might first be placed in the silica stability domain. Then, as regards the electronic properties of the material, the water vapor pressure may be decreased (or the temperature increased for the same water vapor pressure), in order to remove silica and increase the grain size through surface diffusion. However, increasing the water vapor pressure leads to a concomitant oxidation of the sample and to important material losses compared to sintering under dry atmosphere. Indeed, for every water molecule reaching the sample, a silicon atom is lost in the form of silicon monoxide. Actually, the experimental mass loss in Eq. (11), is directly related to the flux of water coming to the sample that is estimated from Eqs. (5) and (6) and to the duration, t*, of the sintering treatment during which the silica layer is stabilized, i.e., during which the water vapor pressure is . maintained to the equilibrium value, PHProbe∗ 2O ∗ mSi = −2S tube × MSi × t ∗ × |jH | 2O

= −2

mol (T ∗ ) MSi S tube t ∗ DSiO R1 PSiO (T ∗ ) RT ∗ zf

(11)

As the sintering temperature, TS = T*, is increased, the water vapor pressure, PHProbe∗ , must be increased to stabilize the sil2O ica layer. In Fig. 7, expected and measured mass losses are plotted as a function of the sintering temperature for a typical sintering time, t*, of 3 h and a sample mass of 400 mg. For temperatures higher than 1350 ◦ C, and for the diffusion length zf = 25 mm, the mass loss exceeds 50%. Actually, the control of the diffusion length, zf , which is directly related to the furnace thermal profile, seems more appropriate than the control of the water vapor pressure. Typically, if the homogeneous temperature range is increased, supersaturation and accordingly condensation of silicon monoxide occurs further from the sample and zf increases. zf being increased, the flux of water and

3000

J.M. Lebrun et al. / Journal of the European Ceramic Society 33 (2013) 2993–3000

From an appropriate choice of the sintering temperature and water vapor pressures, the sample density and grain size could be controlled over a range of 65 to 80% TDSi and 300 nm to 10 ␮m respectively. Vapor transport, which is assumed to dominate in the late stage of sintering, is responsible for coarsening of the microstructure and explains the incomplete densification of the samples. Better densifications are eventually expected by sintering the sample at higher temperatures with a stabilized silica layer. This may be done by controlling the furnace thermal profile and surrounding water vapor pressure in order to limit the sample mass loss that occurs at very high temperature. Fig. 7. Expected and measured mass losses for samples sintered under equilibrium conditions jSiO + jH2 O = 0. The sample mass is 400 mg and sintering time, t*, is 3 h.

silicon monoxide decreases and the material loss should be less important. 6. Conclusions Sintering of silicon under controlled humidified atmospheres has been investigated. A water vapor pressure controller was designed in order to fit our experimental requirements. In order to stabilize the silica layer, the incoming flux of water must equal the flux of silicon monoxide produced by the sample. Two parameters define the water vapor pressure to be controlled: - The sintering temperature. As the sintering temperature increases, the flux of silicon monoxide produced by the sample increases as the equilibrium partial pressure of silicon R1 , increases. The flux of water to be applied monoxide, PSiO in order to balance the silicon monoxide departure must then be increased. - The furnace geometry. Mass transport kinetics strongly depend on the furnace tube section (area of the flux) as well as on the diffusion length of the species, zf , which corresponds to the position where silicon monoxide condensates. As zf is increased, the flux of water to be applied in order to balance the silicon monoxide departure must be decreased. Controlling the temperature profile of the furnace should allow controlling the zf position. More precisely, as the homogeneous temperature range is enlarged the position of silicon monoxide condensation should be increased. This would give rise to a concomitant decrease in the mass loss experienced by the sample. Sintering under controlled water vapor pressure eventually permitted the stabilization of the silica layer at high temperatures. Grain coarsening through surface diffusion was then inhibited, and densification through lattice diffusion could occur.

Acknowledgments This work was supported by the Rhône-Alpes region through the cluster of research “Energies”. The authors wish to thank Frederic Charlot (CMTC, Grenoble INP) for microstructure observations and helpful advices as regards polishing procedures. References [1] Robertson WM. Thermal etching and grain-boundary grooving silicon ceramics. J Am Ceram Soc 1981;64:9–13. [2] Coblenz WS. The physics and chemistry of the sintering of silicon. J Mater Sci 1990;25:2754–64. [3] Greskovich C, Rosolowski JH. Sintering of covalent solids. J Am Ceram Soc 1976;59:336–43. [4] Shaw NJ, Heuer AH. On particle coarsening during sintering of silicon. Acta Metall 1983;31:55–9. [5] Möller HJ, Welsch G. Sintering of ultrafine silicon powder. J Am Ceram Soc 1985;68:320–5. [6] Lebrun JM, Missiaen JM, Pascal C. Elucidation of mechanisms involved during silica reduction on silicon powders. Scr Mater 2011;64: 1102–5. [7] Lebrun JM, Pascal C, Missiaen JM. The role of silica layer on sintering kinetics of silicon powder compact. J Am Ceram Soc 2012;95: 1514–23. [8] Lebrun JM, Missiaen JM, Pascal C. Elucidation of densification behavior of fine silicon powder particles covered with a native silica layer. Scr Mater 2013;69:175–8. [9] Lebrun JM, Pascal C, Missiaen JM. Temperature–Pressure–Sintering (TPS) diagrams approach for sintering of silicon. Mater Lett 2012;83:65–8. [10] Malcolm W, Chase Jr. Nist-janaf thermochemical tables. In: J Phys Chem Ref Data. 4th ed American Chemical Society; American Institute of Physics; 1998. [11] Ashby MF. A first report on sintering diagrams. Acta Metall 1974;22:275–89. [12] Wagner C. Passivity during the oxidation of silicon at elevated temperatures. J Appl Phys 1958;29:1295–7. [13] Bird RB, Stewart WE, Lightfoot EN. Transport phenomena. 2nd ed NewYork: John Wiley & Sons; 2001. [14] Svehla RA. Estimated viscosities and thermal conductivities of gases at high temperatures. Technical Report TR R-132. NASA; 1962.