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Laser-enhanced crystallization of Ge and Si
Journal of Crystal Growth 65 (1983) 231-234 North-Holland, Amsterdam
231
LASER-ENHANCED CRYSTALLIZATION OF Ge AND Si M. WAUTELET, R. A N D R E W and L.D. L A U D E IR1S Mons, Facult@ des Sciences, Universit@de I'Etat, B-7000 Mons, Belgium
It is shown experimentally that laser irradiation of amorphous Ge and Si films results in a much larger nucleation rate and growth velocity than under thermal annealing conditions. In particular, the observed nucleation rate enhancement attains more than four orders of magnitude at temperatures around 400°C. Crystal dimensions are also much larger than under thermal annealing conditions. These data are interpreted as due to a combination of thermal effects (temperature, strains) and non-thermal mechanisms (laser-induced metastable states formation, recombination enhanced diffusion). All these mechanisms modify the parameters involved in the diffusion of the vectors of the amorphous to crystal transformation, namely the so-called dangling bonds.
1. Introduction Among the techniques used for processing materials, so-called laser annealing is a very interesting one. Up to now, recrystallization of ion-implanted Si and Ge has been very much studied under various conditions [1], and where a melting and resolidification model is most usually assumed. In this work, we choose to consider laserinduced amorphous to crystal transitions in which no intermediate melting is involved [2,3]. Results are presented which clearly show that the nucleation rate, R(T), can be far larger than the corresponding rate measured during thermal annealing. In order to explain this results, we discuss the role of dangling bonds (DBs) in the amorphous to crystal transition. Then, we propose that the enhancement of R(T) and of crystal growth under laser irradiation arises from the optical excitation of DBs, which modifies their energy of migration.
2. Experimental results 1000 ,~ thick Ge films are condensed onto NaC1 single crystals maintained at room temperature by thermal evaporation of 9N poure Ge, performed in 10 -5 Torr vacuum. 2400 A thick Si films are condensed onto the same kind of substrate by electron gun evaporation of 9N pure Si, performed
in 10 -8 Torr vacuum. Films are then floated off onto transmission electron microscope (TEM) copper grids, with 80 x 80/~m mesh size. Grid-supported samples are irradiated in air via a diaphragm of 0.5 mm diameter, by means of two different lasers: either a pulsed dye laser (2.08 eV photon energy, 1.8 x 10 - 6 S pulse duration), or a Kr + laser operating on all red lines (647-676 nm), and delivering, via a system of choppers, pulses from 2 x 10 - 4 to 1 S in duration. This laser, operating in TEM00 mode, has a rather uniform gaussian beam profile with F W H M radius of about 1.5 mm and thus 8% variation in beam intensity between the centre and edge of the defining aperture. For the dye laser, the spatial profile and net intensity of the output can change from pulse to pulse and there is also more tendency to speckle or " h o t spots '~ than with the Kr + laser. However, several years of experience with this laser in the determination of threshold intensities for a wide range of laser induced effects in materials, plus comparative work with a beam homogenizer, tells us that variations in intensity across a 0.5 mm diameter aperture will be typically 10-15%, with an additional 5-20% pulse to pulse jitter in total energy. The effect of this latter variation in the determination of threshold energy can of course be offset by averaging over a large number of experiments. When the films prepared as described are ex-
0022-0248/83/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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M. Wautelet et al. / Laser- enhanced crystallization of Ge and Si
posed to the pulsed dye laser irradiation, there is no observable effect below a critical threshold energy Ec, which is corrected for reflection, transmission and thus represents the energy actually deposited in the film. At Ec we see, at the rate of 2-5 per 80/~m grid square per pulse, crystallized zones some 5-10/~m in diameter, each one being characterized by a number of large wedge-shaped crystals leading from a single point near the centre of the zone to the surrounding amorphous material where they terminate rather abruptly. Increasing the energy above Eo leads to a slight increase in the frequency, but not the size, of these zones and, at 5-10% above E¢, to the development of concentrically textured rings of finer polycrystalline material surrounding each of the star-shaped zones and which eventually spread out to cover the whole of the grid hole area at energies 15-20% above E¢. The form of these rings resembles absolutely that seen in so-called explosive crystallization of these [20] and other [21] materials, where the crystallization front is driven along by a combination of strain and liberation of the heat of crystallization. At much higher energies, typically 100% above E¢ for Ge and 170% above E~ for Si, we see clear signs of local melting of the film, such as hole formation. In this paper we are primarily concerned with the first kind of crystallization described, and more particularly with the nucleation of the centre of this zone from the amorphous phase. It seems clear that each star-shaped zone results from rapid outward growth following at least one nucleation event near the centre, and so at E~ we can take a minimum of 2-5 nucleation events per grid square. Since there is obviously some heating effect of the laser, we would like to know the temperature rise induced and the duration of the thermal pulse. These two parameters are determined experimentally by measuring E¢ as a function of laser pulse duration [4]. Here we find two regimes: a constant energy region at pulse duration t << ~" and a constant power region for t > r, with a smooth transition between the two. Here, ~- is the thermal relaxation time of the film on its grid support and is found as 4 × 10 -5 s for Ge and 2 × 10 -5 s for Si, in good agreement with estimates of heat flow in
the films. The temperature rise T¢ due to a pulse of duration t << ~- is now given by E c divided by the thermal capacity of the film. We find T¢ = 400°C for Ge and T~ = 500°C for si. Note that these temperatures, estimated precise to 50°C, are supported by the observed threshold for melting, particularly when account is taken of the hot-spots already discussed and expected to amount to peak local temperatures about 15% above the average value deduced here. Note also that we never see any crystallized zones at more than 15% below Ec, so that the effect of hot-spots can be considered as of secondary importance. We can now easily calculate R(T)>1 1014 cm -3 s-1 for both Ge and Si at these temperatures, to be compared with the thermal values of R(400°C) --- 105-106 cm -3 s -1 for Si [5] and R(400°C)-= 107 cm -3 s -1 for Ge [6]. Under thermal annealing conditions, it is also known that R increases with temperature, but only up to a maximum of R(800°C)---1011 cm -3 s -1 for Si [7] and then decreases at higher temperatures. Altogether, our data indicate that nucleation involves some thermal effect (as also shown by other authors [8]), but that non-thermal mechanisms might also have to be included. In order to interpret these results, we look now at the fundamentals of the crystallization process.
3. Nucleation The amorphous-crystalline transition, when it takes place in the solid phase, implies the relocation of some of the covalent bonds, and this latter most easily occurs via a migrating DB. The basic step is to break a bond nearby and to tie up the original DB with one half Qf the broken bond, whose remaining half now becomes the DB, but in a new position. It is not difficult to see that the material can be restructured in this way, but it is rather less easy to see why we should get a crystal as a result, at least in terms of bond relocation. Part of the problem is the lack of a good description of the structure surrounding a DB, and indeed the lack of a tolerably finite description of the whole amorphous structure itself. Let us introduce the concepts of topologically
M. Wautelet et al. / Laser-enhanced crystallization of Ge and Si
good crystal (TGC) and topologically disordered solid (TDS). The T G C is defined as any assembly of atoms which are bonded together in a manner topologically equivalent to normal crystal [9], i.e. the assembly could, with no internal bond relocation, be incorporated into a suitably sized hole in a perfect crystal, even though the atom core positions may not correspond at all to those in a crystal owing to b o n d stretching, bending and twisting. Note that the addition of one wrongly connected atom to a region of T G C renders the whole lot a TDS and that therefore the classification of a region depends very much on where we make the cuts. Any region of TDS will include smaller sub-regions of TGC. Also, we postulate that the limits of bond deformation restrict the size of TDS that can be built without introducing DBs. The amorphous structure is described as consisting of interwoven regions of T G C and TDS plus DBs. The following consequences are easy to be deduced: (i) all DBs are connected to TDS in some direction; (ii) it is impossible to embed a single DB and its associated TDS into T G C without introducing another (or any odd number of) DB on the joining surface. It can also be shown that most DBs are associated with a vacancy or, more precisely, with half a vacancy. Since the Gibbs energy of the good crystal is less than that of the amorphous phase, it follows that the T G C tends to grow, via the migration of DBs, which leave T G C behind them. Note that a critical size of crystallized zone is required to inviolate disruption by other wandering DBs. Thermodynamically, this nucleation process is treated as arising from a competition between bulk and surface energies: at small nuclear dimension, the crystalline structure is unstable, while above a critical dimension, the crystal tends to grow [10]. From the previous reasoning, it is obvious that nucleation is due to the migration of DBs. So, any process which affects the properties of the DBs (hybridization, charge transfer, etc.) is expected to modify the nucleation rate, via the migration properties. This means that R is proportional to the jump probability of DBs, i.e.
R = RoN exp( - Em/kT ),
(1)
233
where N is the total number of DBs. R 0 is constant for a given temperature and includes any term related with the critical nucleus stability [6]. E m is the DBs energy of migration, i.e. E m = H m TSm, where H m and S m are the corresponding enthalpy and entropy, respectively. H m is known to be related to the energy necessary to break bonds during the migration event [11], while S m is a function of the interatomic force constants between the defect atom and its nearest neighbours [12]. It turns out that a softening of the force constants (by elongation of the bonds) leads to an increase of S m. Optical excitation of amorphous Si and Ge films leads to the creation of very long-lived metastable states [13,14]. These are interpreted as due to the presence of optically excited DB states in the form either of pairs of charged DBs ( D B + - D B -) (the so-called self-trapped excitons [15]), or dehybridized sp2-pz DBs [16]. In the framework of the self-trapped exciton model, the configurational properties of DB ÷ and D B - are different from those of DB °. Indeed, the lengths of the back bonds are larger for the D B - than for the DB ° and DB ÷, respectively. This implies that Sm(DB-)> Sm(DB°)> Sm(DB+). H m is modified in the other direction, since the covalent bond energy is known to decrease with decreasing atomic bond overlapping, i.e. increasing length. Altogether, one finds that Em(DB- ) = Em(DB °) - 3 and Em(DB +) = Em(DB °) + A, where 3 and A are positive energies. In this case, eq. (1) is replaced by:
Rl=R[(N-n)+2exp(~-~)+2exp(-~)],
(2) where n is the number of excited DBs. Provided (3/kT) is equal or larger than unity, it is obvious that R 1 is larger than R. Also, one sees that a DB + migrates less easily than a D B - or DB °. From a comparison with crystal growth rate measurements under laser [17] or electron [18] irradiation (in which the migration of DBs play a similar role), one may conclude that the nucleation rate may increase by a maximum of two orders of magnitude. Another mechanism is also possible, related to
234
M. Wautelet et al. / Laser- enhanced crystallization of Ge and Si
the recombination process at the DB site. Just after optical excitation, the D B site and its surr o u n d i n g decays rapidly via emission of phonons. The same is true during the de-excitatlon of the metastable state to the fundamental one. If the emitted p h o n o n s remain localized near the DB site for a sufficiently long time (due, f o r instance, to the lack of periodicity), the local vibrational energy of the system would be increased. Moreover, some transfer of m o v e m e n t is possible to some vibrational modes parallel to the migration direction, since any shift of the a t o m perpendicularly to the D B orbital affects the geometry of all bonds a r o u n d the cavity and, therefore, modifies slightly the orbital overlaps and, then, the energy of the bonds. These conditions are k n o w n to reduce E m b y a substantial amount, E R [19]. This is called recombination-enhanced diffusion. A numerical evaluation of E R is unfortunately not meaningful, due to the n u m b e r of u n k n o w n parameters in the a m o r p h o u s phase (force constants, b o n d angles and length in the cavity, p h o n o n spectrum etc.). Let us also mention the influence of strains, similarly to what occurs in shock crystallization [20]. Simple estimates give a decrease of E m b y at most 0.1 eV due to the effect of thermal expansion [3], i.e. well below the nucleation energy of G e and Si.
4. Conclusions Altogether laser-enhanced nucleation of Si and G e is proposed to be due mainly to enhanced migration efficiency of the keys to the a m o r p h o u s to crystal transition, namely the dangling bonds. A combination of temperature and strain effects with non-thermal mechanisms is necessary to explain the observed enhancement of the nucleation rate under laser irradiation.
References [1] J.M. Poate and W.L. Brown, Phys. Today 35 (6) (1982) 24. [2] R. Andrew, L. Baufay, L.D. Laude, M. Lovato and M. Wautelet, J. Physique 41 (1980) C4-71. [3] M. Failly-Lovato, Doctor Thesis, University of Mons (1982); M. Failly-Lovato, M.C. Joliet, L.D. Laude and M. Wautelet, to be published. [4] R. Andrew, L. Baufay, A. Pigeolet and L.D. Laude, J. Appl. Phys. 53 (1982) 4862. [5] K. Zellama, P. Germain, S. Squelard, J.C. Bourgoin and P.A. Thomas, J. Appl. Phys. 50 (1979) 6986. [6] P. Germain, K. Zellama, S. Squelard, J.C. Bourgoin and A. Gheorghiu, J. Appl. Phys. 50 (1979) 6995. [7] U. KOster, Phys. Status Solidi (a) 48 (1978) 313. [8] R.K. Sharma, S.K. Bansal, R. Nath and G.P. Srivastava, Thin Solid Films 97 (1982) 1. [9] J.M. Ziman, in: Models of Disorder (Cambridge University Press, Cambridge, UK, 1979) p. 36. [10] K.A. Jackson, in: Crystal Growth: A Tutorial Approach, Eds. W. Bardsley, D.T.T. Hurle and J.B. Mullin (NorthHolland, Amsterdam, 1979) p. 139. [11] M. Wautelet, in: Cohesive Properties of Semiconductors under Laser Irradiation, Ed. L.D. Laude (Nijhoff, Den Haag, 1983) p. 483. [12] M. Lannoo and J.C. Bourgoin, Solid State Commun. 32 (1979) 913. [13] D.L. Staebler and C.R. Wronski, Appl. Phys. Letters 31 (1977) 292. [14] M. Failly-Lovato, R. Andrew, L.D. Laude and M. Wautelet, Appl. Phys. A29 (1982) 163. [15] D. Adler, J. Physique 42 (1981) C4-3, [16] M. Wautelet, L.D. Laude and R. Andrew, Phys. Letters A77 (1980) 274. [17] A. Lietoila, R.B. Gold and J.F. Gibbons, Appl. Phys. Letters 32 (1981) 810. [18] P. Germain, S. Squelard and J.C. Bourgoin, J. Non-Crystalline Solids 23 (1977) 159. [19] J.D. Weeks, J.C. Tully and L.C. Kimerling, Phys. Rev. B12 (1975) 3286. [20] T. Takamori, R. Messier and R. Roy, J. Mater. Sci. 8 (1973) 1809. ' [21] C.E. Wickersham, G. Bajor and J.E. Greene, Solid State Commun. 27 (1978) 17.
231
LASER-ENHANCED CRYSTALLIZATION OF Ge AND Si M. WAUTELET, R. A N D R E W and L.D. L A U D E IR1S Mons, Facult@ des Sciences, Universit@de I'Etat, B-7000 Mons, Belgium
It is shown experimentally that laser irradiation of amorphous Ge and Si films results in a much larger nucleation rate and growth velocity than under thermal annealing conditions. In particular, the observed nucleation rate enhancement attains more than four orders of magnitude at temperatures around 400°C. Crystal dimensions are also much larger than under thermal annealing conditions. These data are interpreted as due to a combination of thermal effects (temperature, strains) and non-thermal mechanisms (laser-induced metastable states formation, recombination enhanced diffusion). All these mechanisms modify the parameters involved in the diffusion of the vectors of the amorphous to crystal transformation, namely the so-called dangling bonds.
1. Introduction Among the techniques used for processing materials, so-called laser annealing is a very interesting one. Up to now, recrystallization of ion-implanted Si and Ge has been very much studied under various conditions [1], and where a melting and resolidification model is most usually assumed. In this work, we choose to consider laserinduced amorphous to crystal transitions in which no intermediate melting is involved [2,3]. Results are presented which clearly show that the nucleation rate, R(T), can be far larger than the corresponding rate measured during thermal annealing. In order to explain this results, we discuss the role of dangling bonds (DBs) in the amorphous to crystal transition. Then, we propose that the enhancement of R(T) and of crystal growth under laser irradiation arises from the optical excitation of DBs, which modifies their energy of migration.
2. Experimental results 1000 ,~ thick Ge films are condensed onto NaC1 single crystals maintained at room temperature by thermal evaporation of 9N poure Ge, performed in 10 -5 Torr vacuum. 2400 A thick Si films are condensed onto the same kind of substrate by electron gun evaporation of 9N pure Si, performed
in 10 -8 Torr vacuum. Films are then floated off onto transmission electron microscope (TEM) copper grids, with 80 x 80/~m mesh size. Grid-supported samples are irradiated in air via a diaphragm of 0.5 mm diameter, by means of two different lasers: either a pulsed dye laser (2.08 eV photon energy, 1.8 x 10 - 6 S pulse duration), or a Kr + laser operating on all red lines (647-676 nm), and delivering, via a system of choppers, pulses from 2 x 10 - 4 to 1 S in duration. This laser, operating in TEM00 mode, has a rather uniform gaussian beam profile with F W H M radius of about 1.5 mm and thus 8% variation in beam intensity between the centre and edge of the defining aperture. For the dye laser, the spatial profile and net intensity of the output can change from pulse to pulse and there is also more tendency to speckle or " h o t spots '~ than with the Kr + laser. However, several years of experience with this laser in the determination of threshold intensities for a wide range of laser induced effects in materials, plus comparative work with a beam homogenizer, tells us that variations in intensity across a 0.5 mm diameter aperture will be typically 10-15%, with an additional 5-20% pulse to pulse jitter in total energy. The effect of this latter variation in the determination of threshold energy can of course be offset by averaging over a large number of experiments. When the films prepared as described are ex-
0022-0248/83/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
232
M. Wautelet et al. / Laser- enhanced crystallization of Ge and Si
posed to the pulsed dye laser irradiation, there is no observable effect below a critical threshold energy Ec, which is corrected for reflection, transmission and thus represents the energy actually deposited in the film. At Ec we see, at the rate of 2-5 per 80/~m grid square per pulse, crystallized zones some 5-10/~m in diameter, each one being characterized by a number of large wedge-shaped crystals leading from a single point near the centre of the zone to the surrounding amorphous material where they terminate rather abruptly. Increasing the energy above Eo leads to a slight increase in the frequency, but not the size, of these zones and, at 5-10% above E¢, to the development of concentrically textured rings of finer polycrystalline material surrounding each of the star-shaped zones and which eventually spread out to cover the whole of the grid hole area at energies 15-20% above E¢. The form of these rings resembles absolutely that seen in so-called explosive crystallization of these [20] and other [21] materials, where the crystallization front is driven along by a combination of strain and liberation of the heat of crystallization. At much higher energies, typically 100% above E¢ for Ge and 170% above E~ for Si, we see clear signs of local melting of the film, such as hole formation. In this paper we are primarily concerned with the first kind of crystallization described, and more particularly with the nucleation of the centre of this zone from the amorphous phase. It seems clear that each star-shaped zone results from rapid outward growth following at least one nucleation event near the centre, and so at E~ we can take a minimum of 2-5 nucleation events per grid square. Since there is obviously some heating effect of the laser, we would like to know the temperature rise induced and the duration of the thermal pulse. These two parameters are determined experimentally by measuring E¢ as a function of laser pulse duration [4]. Here we find two regimes: a constant energy region at pulse duration t << ~" and a constant power region for t > r, with a smooth transition between the two. Here, ~- is the thermal relaxation time of the film on its grid support and is found as 4 × 10 -5 s for Ge and 2 × 10 -5 s for Si, in good agreement with estimates of heat flow in
the films. The temperature rise T¢ due to a pulse of duration t << ~- is now given by E c divided by the thermal capacity of the film. We find T¢ = 400°C for Ge and T~ = 500°C for si. Note that these temperatures, estimated precise to 50°C, are supported by the observed threshold for melting, particularly when account is taken of the hot-spots already discussed and expected to amount to peak local temperatures about 15% above the average value deduced here. Note also that we never see any crystallized zones at more than 15% below Ec, so that the effect of hot-spots can be considered as of secondary importance. We can now easily calculate R(T)>1 1014 cm -3 s-1 for both Ge and Si at these temperatures, to be compared with the thermal values of R(400°C) --- 105-106 cm -3 s -1 for Si [5] and R(400°C)-= 107 cm -3 s -1 for Ge [6]. Under thermal annealing conditions, it is also known that R increases with temperature, but only up to a maximum of R(800°C)---1011 cm -3 s -1 for Si [7] and then decreases at higher temperatures. Altogether, our data indicate that nucleation involves some thermal effect (as also shown by other authors [8]), but that non-thermal mechanisms might also have to be included. In order to interpret these results, we look now at the fundamentals of the crystallization process.
3. Nucleation The amorphous-crystalline transition, when it takes place in the solid phase, implies the relocation of some of the covalent bonds, and this latter most easily occurs via a migrating DB. The basic step is to break a bond nearby and to tie up the original DB with one half Qf the broken bond, whose remaining half now becomes the DB, but in a new position. It is not difficult to see that the material can be restructured in this way, but it is rather less easy to see why we should get a crystal as a result, at least in terms of bond relocation. Part of the problem is the lack of a good description of the structure surrounding a DB, and indeed the lack of a tolerably finite description of the whole amorphous structure itself. Let us introduce the concepts of topologically
M. Wautelet et al. / Laser-enhanced crystallization of Ge and Si
good crystal (TGC) and topologically disordered solid (TDS). The T G C is defined as any assembly of atoms which are bonded together in a manner topologically equivalent to normal crystal [9], i.e. the assembly could, with no internal bond relocation, be incorporated into a suitably sized hole in a perfect crystal, even though the atom core positions may not correspond at all to those in a crystal owing to b o n d stretching, bending and twisting. Note that the addition of one wrongly connected atom to a region of T G C renders the whole lot a TDS and that therefore the classification of a region depends very much on where we make the cuts. Any region of TDS will include smaller sub-regions of TGC. Also, we postulate that the limits of bond deformation restrict the size of TDS that can be built without introducing DBs. The amorphous structure is described as consisting of interwoven regions of T G C and TDS plus DBs. The following consequences are easy to be deduced: (i) all DBs are connected to TDS in some direction; (ii) it is impossible to embed a single DB and its associated TDS into T G C without introducing another (or any odd number of) DB on the joining surface. It can also be shown that most DBs are associated with a vacancy or, more precisely, with half a vacancy. Since the Gibbs energy of the good crystal is less than that of the amorphous phase, it follows that the T G C tends to grow, via the migration of DBs, which leave T G C behind them. Note that a critical size of crystallized zone is required to inviolate disruption by other wandering DBs. Thermodynamically, this nucleation process is treated as arising from a competition between bulk and surface energies: at small nuclear dimension, the crystalline structure is unstable, while above a critical dimension, the crystal tends to grow [10]. From the previous reasoning, it is obvious that nucleation is due to the migration of DBs. So, any process which affects the properties of the DBs (hybridization, charge transfer, etc.) is expected to modify the nucleation rate, via the migration properties. This means that R is proportional to the jump probability of DBs, i.e.
R = RoN exp( - Em/kT ),
(1)
233
where N is the total number of DBs. R 0 is constant for a given temperature and includes any term related with the critical nucleus stability [6]. E m is the DBs energy of migration, i.e. E m = H m TSm, where H m and S m are the corresponding enthalpy and entropy, respectively. H m is known to be related to the energy necessary to break bonds during the migration event [11], while S m is a function of the interatomic force constants between the defect atom and its nearest neighbours [12]. It turns out that a softening of the force constants (by elongation of the bonds) leads to an increase of S m. Optical excitation of amorphous Si and Ge films leads to the creation of very long-lived metastable states [13,14]. These are interpreted as due to the presence of optically excited DB states in the form either of pairs of charged DBs ( D B + - D B -) (the so-called self-trapped excitons [15]), or dehybridized sp2-pz DBs [16]. In the framework of the self-trapped exciton model, the configurational properties of DB ÷ and D B - are different from those of DB °. Indeed, the lengths of the back bonds are larger for the D B - than for the DB ° and DB ÷, respectively. This implies that Sm(DB-)> Sm(DB°)> Sm(DB+). H m is modified in the other direction, since the covalent bond energy is known to decrease with decreasing atomic bond overlapping, i.e. increasing length. Altogether, one finds that Em(DB- ) = Em(DB °) - 3 and Em(DB +) = Em(DB °) + A, where 3 and A are positive energies. In this case, eq. (1) is replaced by:
Rl=R[(N-n)+2exp(~-~)+2exp(-~)],
(2) where n is the number of excited DBs. Provided (3/kT) is equal or larger than unity, it is obvious that R 1 is larger than R. Also, one sees that a DB + migrates less easily than a D B - or DB °. From a comparison with crystal growth rate measurements under laser [17] or electron [18] irradiation (in which the migration of DBs play a similar role), one may conclude that the nucleation rate may increase by a maximum of two orders of magnitude. Another mechanism is also possible, related to
234
M. Wautelet et al. / Laser- enhanced crystallization of Ge and Si
the recombination process at the DB site. Just after optical excitation, the D B site and its surr o u n d i n g decays rapidly via emission of phonons. The same is true during the de-excitatlon of the metastable state to the fundamental one. If the emitted p h o n o n s remain localized near the DB site for a sufficiently long time (due, f o r instance, to the lack of periodicity), the local vibrational energy of the system would be increased. Moreover, some transfer of m o v e m e n t is possible to some vibrational modes parallel to the migration direction, since any shift of the a t o m perpendicularly to the D B orbital affects the geometry of all bonds a r o u n d the cavity and, therefore, modifies slightly the orbital overlaps and, then, the energy of the bonds. These conditions are k n o w n to reduce E m b y a substantial amount, E R [19]. This is called recombination-enhanced diffusion. A numerical evaluation of E R is unfortunately not meaningful, due to the n u m b e r of u n k n o w n parameters in the a m o r p h o u s phase (force constants, b o n d angles and length in the cavity, p h o n o n spectrum etc.). Let us also mention the influence of strains, similarly to what occurs in shock crystallization [20]. Simple estimates give a decrease of E m b y at most 0.1 eV due to the effect of thermal expansion [3], i.e. well below the nucleation energy of G e and Si.
4. Conclusions Altogether laser-enhanced nucleation of Si and G e is proposed to be due mainly to enhanced migration efficiency of the keys to the a m o r p h o u s to crystal transition, namely the dangling bonds. A combination of temperature and strain effects with non-thermal mechanisms is necessary to explain the observed enhancement of the nucleation rate under laser irradiation.
References [1] J.M. Poate and W.L. Brown, Phys. Today 35 (6) (1982) 24. [2] R. Andrew, L. Baufay, L.D. Laude, M. Lovato and M. Wautelet, J. Physique 41 (1980) C4-71. [3] M. Failly-Lovato, Doctor Thesis, University of Mons (1982); M. Failly-Lovato, M.C. Joliet, L.D. Laude and M. Wautelet, to be published. [4] R. Andrew, L. Baufay, A. Pigeolet and L.D. Laude, J. Appl. Phys. 53 (1982) 4862. [5] K. Zellama, P. Germain, S. Squelard, J.C. Bourgoin and P.A. Thomas, J. Appl. Phys. 50 (1979) 6986. [6] P. Germain, K. Zellama, S. Squelard, J.C. Bourgoin and A. Gheorghiu, J. Appl. Phys. 50 (1979) 6995. [7] U. KOster, Phys. Status Solidi (a) 48 (1978) 313. [8] R.K. Sharma, S.K. Bansal, R. Nath and G.P. Srivastava, Thin Solid Films 97 (1982) 1. [9] J.M. Ziman, in: Models of Disorder (Cambridge University Press, Cambridge, UK, 1979) p. 36. [10] K.A. Jackson, in: Crystal Growth: A Tutorial Approach, Eds. W. Bardsley, D.T.T. Hurle and J.B. Mullin (NorthHolland, Amsterdam, 1979) p. 139. [11] M. Wautelet, in: Cohesive Properties of Semiconductors under Laser Irradiation, Ed. L.D. Laude (Nijhoff, Den Haag, 1983) p. 483. [12] M. Lannoo and J.C. Bourgoin, Solid State Commun. 32 (1979) 913. [13] D.L. Staebler and C.R. Wronski, Appl. Phys. Letters 31 (1977) 292. [14] M. Failly-Lovato, R. Andrew, L.D. Laude and M. Wautelet, Appl. Phys. A29 (1982) 163. [15] D. Adler, J. Physique 42 (1981) C4-3, [16] M. Wautelet, L.D. Laude and R. Andrew, Phys. Letters A77 (1980) 274. [17] A. Lietoila, R.B. Gold and J.F. Gibbons, Appl. Phys. Letters 32 (1981) 810. [18] P. Germain, S. Squelard and J.C. Bourgoin, J. Non-Crystalline Solids 23 (1977) 159. [19] J.D. Weeks, J.C. Tully and L.C. Kimerling, Phys. Rev. B12 (1975) 3286. [20] T. Takamori, R. Messier and R. Roy, J. Mater. Sci. 8 (1973) 1809. ' [21] C.E. Wickersham, G. Bajor and J.E. Greene, Solid State Commun. 27 (1978) 17.