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Growth of semiconductors from the solid phase
Volume 101A, number 3
PHYSICS LETTERS
19 March 1984
GROWTH OF SEMICONDUCTORS FROM THE SOLID PHASE J.C. BOURGOIN 1 and R. ASOMOZA Departamento de lngenierfa Eldctrica, Centro de Investigaci6n y Estudios Avanzados del I.P.N., Ap. Postal 14-740, 07000, M~xico, DF, Mexico Received 7 December 1983
A detailed discussion of the variation of the growth rate versus temperature in evaporated (EL) and implanted (IL) layers allows us to deduce a model for the growth which accounts quantitatively for the associated activation energies for both Si and Ge, different in EL and IL. It also explains the effects of the nature of the implanted ions and demonstrates that IL are not amorphous but disordered.
Crystal growth from the amorphous phase (AP) has been studied in Ge [1-4] and Si [5-12] on epitaxial or semiepitaxial configurations using two types of materials: layers deposited by evaporation (EL) on various substrates [2-6,13] and layers produced by ion implantation (IL) [ 1,7-12]. The variation of the growth rate Og with temperature [ I - 8 ] , crystalline orientation [7], nature of the implanted ion [9-11] and various parameters (such as ionization [ 13], laser irradiation [ 12]) have been determined. These studies reveal a striking difference of behaviour between EL and IL, namely that the activation energies associated with Og are found to be 3 eV [2-4] in EL for Ge, 4.6-4.9 eV [5,6] in EL for Si, 2 eV [1] in IL for Ge and 2.3-2.7 eV [7,8] in IL for Si. The aim of this letter is to provide a model for the growth, able to explain this difference of behaviour. It is justified by several arguments: first, it accounts for the value of the activation energies associated with Og in EL and IL for both Si and Ge. Second, it provides the correct variation of Vg with the crystalline orientation. Finally, it explains qualitatively the dependence Of Og with the nature of the implanted ions. Consider first the case of EL. The activation energies associated with the growth process in these 1 Permanent address: Groupe de Physique des Solides de FENS, Universit6 Paris 7, Tour 23, 2 Place Jussieu, 75221 Paris, France. 0.375-9601/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
layers are,for both Ge and Si, equal to the activation energies QSD associated with self-diffusion in crystalline materials: 3 eV and 4.7-5.1 eV in Ge andSi respectively [ 14]. This strongly suggests that the factor which limits this growth process is self-diffusion. In this case, the growth model should be the following: atomic rearrangement occurs at the interface between the crystalline phase (CP) and the AP when vacancies, produced thermally in the vicinity of the interface, get trapped at the interface, thus allowing atoms to jump from the AP into the CP. The growth rate is then: Og = ~ p e x p ( - E ~ / k T ) exp(-EVm/kT) = 5 v exp(.-QsD/kT),
(1)
where v(3 X lO 13 s - l ) i s the vibrational frequency, 6(2.5,8,) the interatomic distance, E~ and E v the formation and migration energies of the vacancy. This model fits the experimental curves og(T) using one single parameter, the entropy term AS, which is omittedin the preexponential factor of expression (1); the fitting values are AS = 0.3k and - 2 k for Ge and Si, respectively [ 4 - 6 ] . In order to justify the above model, it is necessary to show that vacancies or dangling bond diffusion to the interface does not occur from the AP. This will be done elsewhere; here we shall just argue that this can be accepted intuitively on the following grounds: the vacancies and dangling 151
Volume I01A, number 3
PHYSICS LETTERS
bonds which can be created thermally in the amorphous phase are, at the growth temperature, in maall concentration compared to the dangling bonds (~1020 cm-3), which accompany the formation of the material in order to release local strains. As a result, the created defects will get trapped on the native dangling bond sites (in order to further release local stresses) and will not reach the interface. With this model, the orientation dependence of the growth with the crystalline orientation (hkl) is the following: vg is proportional to the jump distance 8 i.e., to the distance between (hkl) planes, and inversely proportional to the density of atoms in these planes. Calculation of these two quantities leads to the variation ofog shown in fig. 1., which reproduces qualitatively the experimental one [7]. The amplitude of variation between (100) and <111) directions predicted by the model, smaller than the experimental one, can be understood as follows: as is known from experimental observations [ 15], for crystalline orientations close to (111), the regrown layer exhibits a large amount of defects; the corresponding defects inhibit atomic rearrangement. We now come to the case of IL and discuss the difference between growth behaviour in IL and EL. The growth rate in IL is associated with an activation energy "-'2 times smaller than in EL. This implies that the growth rate is not limited by the same phenomena as in EL and, consequently, that the implanted phase
_o
I
,100
~.5,,
>
-~_ 0 . 5
X';-----/'o
> I
I
~
I
I
20 40 60 80 ORIENTATION (degrees) Fig. 1. Comparison between m e expetimentaa var~tuon of the growth rate versus crystalline orientation (full lines), from ref. [7], and the variation obtained with the proposed growth model.
152
19 March 1984
(IP) in contact with the crystalline phase (CP) is of different nature than the evaporated phase (EP). The difference cannot be accounted for by the eventual presence of H since outdiffusion occurs prior to the crystallization [16]. The picture of the EP, when "perfect", which has been deduced from experimental observations [ 17], is that of an AP, i.e. a phase in which local order is preserved, each atom being connected to four neighbors by slightly distorted bonds. The defects present are dangling bonds introduced during the formation of the material when local strains become too large. The picture of an IP is quite different. Indeed, an implanted material is highly disordered: short range order is not preserved. The reason is that ions create cascades of displacements which result in the forma. tion of vacancy clusters (the vacancies being mobile well below room temperature agglomerate). It is commonly said that, when the disordered regions produced by each ion overlap, the layer is amorphous. This, however, is not true: the layer is uniformly disordered. Of course, it can undergo a change of phase, i.e., it can transform from a disordered phase (DP) to an AP if the free energy of the CP plus defects it contains becomes larger than the free energy of the AP [18]. But even if such a change occurs, further irradiation will anyway disorder the new phase, which again will contain vacancy dusters. Thus, the IL always contains a certain amount of disorder in the form of vacancy clusters. (Direct evidence that the IL cannot be a perfect AP is given below in the discussion of the dependence of og with the doping impurities.) In this case, the growth occurs faster than in EL because the energy necessary to generate vacancies is not QSD but ~0.5 QSD- Indeed it has been shown [ 19] that the energy necessary to generate a vacancy cluster is only half of the vacancy formation energy. This is verified experimentally since the activation energy of Og in IL is half the activation energy of Og in EL. Thus, in IL, growth occurs because of the vacancy generation inside the DP. Verification that growth in IL is induced by the disorder cannot be made by monitoring the variation of Vg with the dose of implantation because all the growth studies are performed using doses for which the amount of disorder is saturated. However, the variation Of Og with the nature of the ions, because it can be explained in terms of the proposed growth
Volume 101A, number 3
PHYSICS LETTERS
model, is a good indication of its validity. We now discuss this point. Two types of ions have been used: group III and V "doping" impurities, and impurities which do not give rise to shallow levels in the CP. Consider first the case of implantation with O, N, C and rare gases ions [7] ;Og is found to decrease linearly with O concentration; similar results, less documented however, are obtained for the other ions. Such a decrease can be readily understood in a model of growth induced by vacancy diffusion, the argument being the following: the vacancies released by the clusters get trapped on O, then released when the V + O centers dissociate (the existence and behaviour of A-centers is well known from radiation damage studies), thus reducing the rate at which the vacancies reach the interface. A similar phenomenon should happen with C and N (association of vacancies with N are not known, but complexes involving vacancies and C are also known from radiation damage studies). In the case of rare gas ions, the growth rate is much slower because the vacancies get trapped in the bubbles that these ions are known to form [201. As to P, As or B ions [ 10,11 ], they all produce an increase of Og for very large concentrations (>1020 cm - 3 ) which must be related to a doping effect of these impurities since n-type ones compensate the effect of p.type ones and viceversa [ 10]. This means that (i) at least part of these impurities occupy substitutional sites, i.e., some annealing has occurred below the growth temperature (this implies the existence o f a DP and not of an AP), (ii) when the impurity concentration is large enough, it overcomes the compensation effect of the disorder and the Fermi level moves from the middle of the gap. Again, the variation Of Og can be easily explained since vacancy mobility is charge state dependent. This point will be discussed elsewhere, together with the effects of ionization and ion irradiation, in a more quantitative way using a comparison between doping effects on Og and on self-diffusion (which is also enhanced by n and p doping [14]). In conclusion, we have proposed a model of growth, based on vacancy diffusion to the interface amorphous --crystal which justifies the value of the associated activation energies determined experimentally in evaporated layers, for both Ge and Si. The model accounts also for the crystalline orientation depen-
19 March 1984
dence Of Og. We have also shown that the difference of behaviour between evaporated and implanted layers is due to the fact that implanted layers are not amorphous but disordered. In that case, the growth is induced by the vacancies originating from this disorder. This explains simply the effects of the nature of the implanted ions and doping on the growth rate and the value of the associated activation energy.
References [1] L. Csepregi, R.P. Kullen, J.W. Mayer and T.W. Sigmon, Solid State Commun. 21 (1977) 1019. [2] M.A. Blum and C. Feldman, J. Non-Cryst. Solids 22 (1976) 1019. [3] K.P. Chick and P.K. Lim, Thin Solid Films 35 (1976)45. [4] P. Germain, K. Zellama, S. Squelaxd, J.C. Bourgoin and A. Gheorghiu, J. Appl. Phys. 50 (1979)6986. [5] G.C. Jain, B.K. Das and S.P. Battacherge¢, Appl. Phys. Lett. 33 (1978)445. [6] K. Zellama, P. Germain, S. Squelard, J.C. Bourgoin and P.A. Thomas, J. Appl. Phys. 50 (1979)6995. [7] L. Csepregi, E.F. Kennedy, J.W. Mayer and T.W. Sigmon, J. Appl. Phys. 49 (1978) 3906. [8] L. Csepregi, J.W. Mayer and T.W. Sigmon, Phys. Lett. 54A (1975) 157. [9] E.F. Kennedy, L. Csepregi, J.W. Mayer and T.W. Sigmon, J. Appl. Phys. 48 (1977) 4241, [ 10] I. Suni, G. Goltz, M.G. Grimaldi, M.A. Nieolet and S.S. Lau, Appl. Phys. Lett. 40 (1982) 269. [11] L. Csepregi, E.K. Kennedy, T.J. Callagher, LW. Mayer and T.W. Sigmon, J. Appl. Phys. 48 (1977) 4234. [12] A. Lietoila, R.B. Gold and J.F. Gibbons, AppI. Phys. Lett. 39 (1981) 810. [13] P. Germain, S. Squelard and J.C. Bourgoin, J. NonCryst. Solids 23 (1977) 159; in: Radiation effects in semiconductors (Inst. Phys., London, 1977)Conf. Ser. 31, p. 326. [14] R.B. Fair, in: Impurity doping processes in silicon, ed. F.Y.Y. Wang (North-Holland, Amsterdam, 1981) ch. 7. [15] A. Golanski et al., Phys. Stat. Sol. 38 (1976) 139; P.D. Pronko et al, Proc. Conf. on Ion implantation on semiconductors, eds. F. Chemow, J.A. Borders and D.K. Brice (Plenum, New York, 1977) p. 503. [16] K. Zellama, P. Germain, S. Squelard, J. Monge and E. Ligeon, J. Non-Cryst. Solids 35, 36 (1980) 225. [17] K. Biegelsen, in: Proc. Material research SOc. Meeting (Boston, 1982), to be published. [ 18] J.C. Bourgoin and M. Lannoo, Point defects in semiconductors II. Experimental aspects (Springer, Berlin, 1981) ch. 8.
[19] J.C. Bourgoin, unpublished. [20] S. Mader and K.M. Tu, J. Vac.' Sci. Technol. 12 (1975) 501.
153
PHYSICS LETTERS
19 March 1984
GROWTH OF SEMICONDUCTORS FROM THE SOLID PHASE J.C. BOURGOIN 1 and R. ASOMOZA Departamento de lngenierfa Eldctrica, Centro de Investigaci6n y Estudios Avanzados del I.P.N., Ap. Postal 14-740, 07000, M~xico, DF, Mexico Received 7 December 1983
A detailed discussion of the variation of the growth rate versus temperature in evaporated (EL) and implanted (IL) layers allows us to deduce a model for the growth which accounts quantitatively for the associated activation energies for both Si and Ge, different in EL and IL. It also explains the effects of the nature of the implanted ions and demonstrates that IL are not amorphous but disordered.
Crystal growth from the amorphous phase (AP) has been studied in Ge [1-4] and Si [5-12] on epitaxial or semiepitaxial configurations using two types of materials: layers deposited by evaporation (EL) on various substrates [2-6,13] and layers produced by ion implantation (IL) [ 1,7-12]. The variation of the growth rate Og with temperature [ I - 8 ] , crystalline orientation [7], nature of the implanted ion [9-11] and various parameters (such as ionization [ 13], laser irradiation [ 12]) have been determined. These studies reveal a striking difference of behaviour between EL and IL, namely that the activation energies associated with Og are found to be 3 eV [2-4] in EL for Ge, 4.6-4.9 eV [5,6] in EL for Si, 2 eV [1] in IL for Ge and 2.3-2.7 eV [7,8] in IL for Si. The aim of this letter is to provide a model for the growth, able to explain this difference of behaviour. It is justified by several arguments: first, it accounts for the value of the activation energies associated with Og in EL and IL for both Si and Ge. Second, it provides the correct variation of Vg with the crystalline orientation. Finally, it explains qualitatively the dependence Of Og with the nature of the implanted ions. Consider first the case of EL. The activation energies associated with the growth process in these 1 Permanent address: Groupe de Physique des Solides de FENS, Universit6 Paris 7, Tour 23, 2 Place Jussieu, 75221 Paris, France. 0.375-9601/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
layers are,for both Ge and Si, equal to the activation energies QSD associated with self-diffusion in crystalline materials: 3 eV and 4.7-5.1 eV in Ge andSi respectively [ 14]. This strongly suggests that the factor which limits this growth process is self-diffusion. In this case, the growth model should be the following: atomic rearrangement occurs at the interface between the crystalline phase (CP) and the AP when vacancies, produced thermally in the vicinity of the interface, get trapped at the interface, thus allowing atoms to jump from the AP into the CP. The growth rate is then: Og = ~ p e x p ( - E ~ / k T ) exp(-EVm/kT) = 5 v exp(.-QsD/kT),
(1)
where v(3 X lO 13 s - l ) i s the vibrational frequency, 6(2.5,8,) the interatomic distance, E~ and E v the formation and migration energies of the vacancy. This model fits the experimental curves og(T) using one single parameter, the entropy term AS, which is omittedin the preexponential factor of expression (1); the fitting values are AS = 0.3k and - 2 k for Ge and Si, respectively [ 4 - 6 ] . In order to justify the above model, it is necessary to show that vacancies or dangling bond diffusion to the interface does not occur from the AP. This will be done elsewhere; here we shall just argue that this can be accepted intuitively on the following grounds: the vacancies and dangling 151
Volume I01A, number 3
PHYSICS LETTERS
bonds which can be created thermally in the amorphous phase are, at the growth temperature, in maall concentration compared to the dangling bonds (~1020 cm-3), which accompany the formation of the material in order to release local strains. As a result, the created defects will get trapped on the native dangling bond sites (in order to further release local stresses) and will not reach the interface. With this model, the orientation dependence of the growth with the crystalline orientation (hkl) is the following: vg is proportional to the jump distance 8 i.e., to the distance between (hkl) planes, and inversely proportional to the density of atoms in these planes. Calculation of these two quantities leads to the variation ofog shown in fig. 1., which reproduces qualitatively the experimental one [7]. The amplitude of variation between (100) and <111) directions predicted by the model, smaller than the experimental one, can be understood as follows: as is known from experimental observations [ 15], for crystalline orientations close to (111), the regrown layer exhibits a large amount of defects; the corresponding defects inhibit atomic rearrangement. We now come to the case of IL and discuss the difference between growth behaviour in IL and EL. The growth rate in IL is associated with an activation energy "-'2 times smaller than in EL. This implies that the growth rate is not limited by the same phenomena as in EL and, consequently, that the implanted phase
_o
I
,100
~.5,,
>
-~_ 0 . 5
X';-----/'o
> I
I
~
I
I
20 40 60 80 ORIENTATION (degrees) Fig. 1. Comparison between m e expetimentaa var~tuon of the growth rate versus crystalline orientation (full lines), from ref. [7], and the variation obtained with the proposed growth model.
152
19 March 1984
(IP) in contact with the crystalline phase (CP) is of different nature than the evaporated phase (EP). The difference cannot be accounted for by the eventual presence of H since outdiffusion occurs prior to the crystallization [16]. The picture of the EP, when "perfect", which has been deduced from experimental observations [ 17], is that of an AP, i.e. a phase in which local order is preserved, each atom being connected to four neighbors by slightly distorted bonds. The defects present are dangling bonds introduced during the formation of the material when local strains become too large. The picture of an IP is quite different. Indeed, an implanted material is highly disordered: short range order is not preserved. The reason is that ions create cascades of displacements which result in the forma. tion of vacancy clusters (the vacancies being mobile well below room temperature agglomerate). It is commonly said that, when the disordered regions produced by each ion overlap, the layer is amorphous. This, however, is not true: the layer is uniformly disordered. Of course, it can undergo a change of phase, i.e., it can transform from a disordered phase (DP) to an AP if the free energy of the CP plus defects it contains becomes larger than the free energy of the AP [18]. But even if such a change occurs, further irradiation will anyway disorder the new phase, which again will contain vacancy dusters. Thus, the IL always contains a certain amount of disorder in the form of vacancy clusters. (Direct evidence that the IL cannot be a perfect AP is given below in the discussion of the dependence of og with the doping impurities.) In this case, the growth occurs faster than in EL because the energy necessary to generate vacancies is not QSD but ~0.5 QSD- Indeed it has been shown [ 19] that the energy necessary to generate a vacancy cluster is only half of the vacancy formation energy. This is verified experimentally since the activation energy of Og in IL is half the activation energy of Og in EL. Thus, in IL, growth occurs because of the vacancy generation inside the DP. Verification that growth in IL is induced by the disorder cannot be made by monitoring the variation of Vg with the dose of implantation because all the growth studies are performed using doses for which the amount of disorder is saturated. However, the variation Of Og with the nature of the ions, because it can be explained in terms of the proposed growth
Volume 101A, number 3
PHYSICS LETTERS
model, is a good indication of its validity. We now discuss this point. Two types of ions have been used: group III and V "doping" impurities, and impurities which do not give rise to shallow levels in the CP. Consider first the case of implantation with O, N, C and rare gases ions [7] ;Og is found to decrease linearly with O concentration; similar results, less documented however, are obtained for the other ions. Such a decrease can be readily understood in a model of growth induced by vacancy diffusion, the argument being the following: the vacancies released by the clusters get trapped on O, then released when the V + O centers dissociate (the existence and behaviour of A-centers is well known from radiation damage studies), thus reducing the rate at which the vacancies reach the interface. A similar phenomenon should happen with C and N (association of vacancies with N are not known, but complexes involving vacancies and C are also known from radiation damage studies). In the case of rare gas ions, the growth rate is much slower because the vacancies get trapped in the bubbles that these ions are known to form [201. As to P, As or B ions [ 10,11 ], they all produce an increase of Og for very large concentrations (>1020 cm - 3 ) which must be related to a doping effect of these impurities since n-type ones compensate the effect of p.type ones and viceversa [ 10]. This means that (i) at least part of these impurities occupy substitutional sites, i.e., some annealing has occurred below the growth temperature (this implies the existence o f a DP and not of an AP), (ii) when the impurity concentration is large enough, it overcomes the compensation effect of the disorder and the Fermi level moves from the middle of the gap. Again, the variation Of Og can be easily explained since vacancy mobility is charge state dependent. This point will be discussed elsewhere, together with the effects of ionization and ion irradiation, in a more quantitative way using a comparison between doping effects on Og and on self-diffusion (which is also enhanced by n and p doping [14]). In conclusion, we have proposed a model of growth, based on vacancy diffusion to the interface amorphous --crystal which justifies the value of the associated activation energies determined experimentally in evaporated layers, for both Ge and Si. The model accounts also for the crystalline orientation depen-
19 March 1984
dence Of Og. We have also shown that the difference of behaviour between evaporated and implanted layers is due to the fact that implanted layers are not amorphous but disordered. In that case, the growth is induced by the vacancies originating from this disorder. This explains simply the effects of the nature of the implanted ions and doping on the growth rate and the value of the associated activation energy.
References [1] L. Csepregi, R.P. Kullen, J.W. Mayer and T.W. Sigmon, Solid State Commun. 21 (1977) 1019. [2] M.A. Blum and C. Feldman, J. Non-Cryst. Solids 22 (1976) 1019. [3] K.P. Chick and P.K. Lim, Thin Solid Films 35 (1976)45. [4] P. Germain, K. Zellama, S. Squelaxd, J.C. Bourgoin and A. Gheorghiu, J. Appl. Phys. 50 (1979)6986. [5] G.C. Jain, B.K. Das and S.P. Battacherge¢, Appl. Phys. Lett. 33 (1978)445. [6] K. Zellama, P. Germain, S. Squelard, J.C. Bourgoin and P.A. Thomas, J. Appl. Phys. 50 (1979)6995. [7] L. Csepregi, E.F. Kennedy, J.W. Mayer and T.W. Sigmon, J. Appl. Phys. 49 (1978) 3906. [8] L. Csepregi, J.W. Mayer and T.W. Sigmon, Phys. Lett. 54A (1975) 157. [9] E.F. Kennedy, L. Csepregi, J.W. Mayer and T.W. Sigmon, J. Appl. Phys. 48 (1977) 4241, [ 10] I. Suni, G. Goltz, M.G. Grimaldi, M.A. Nieolet and S.S. Lau, Appl. Phys. Lett. 40 (1982) 269. [11] L. Csepregi, E.K. Kennedy, T.J. Callagher, LW. Mayer and T.W. Sigmon, J. Appl. Phys. 48 (1977) 4234. [12] A. Lietoila, R.B. Gold and J.F. Gibbons, AppI. Phys. Lett. 39 (1981) 810. [13] P. Germain, S. Squelard and J.C. Bourgoin, J. NonCryst. Solids 23 (1977) 159; in: Radiation effects in semiconductors (Inst. Phys., London, 1977)Conf. Ser. 31, p. 326. [14] R.B. Fair, in: Impurity doping processes in silicon, ed. F.Y.Y. Wang (North-Holland, Amsterdam, 1981) ch. 7. [15] A. Golanski et al., Phys. Stat. Sol. 38 (1976) 139; P.D. Pronko et al, Proc. Conf. on Ion implantation on semiconductors, eds. F. Chemow, J.A. Borders and D.K. Brice (Plenum, New York, 1977) p. 503. [16] K. Zellama, P. Germain, S. Squelard, J. Monge and E. Ligeon, J. Non-Cryst. Solids 35, 36 (1980) 225. [17] K. Biegelsen, in: Proc. Material research SOc. Meeting (Boston, 1982), to be published. [ 18] J.C. Bourgoin and M. Lannoo, Point defects in semiconductors II. Experimental aspects (Springer, Berlin, 1981) ch. 8.
[19] J.C. Bourgoin, unpublished. [20] S. Mader and K.M. Tu, J. Vac.' Sci. Technol. 12 (1975) 501.
153