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Irradiation induced crystalline to amorphous transition
Ø~
25—27. Solid State Communications, Vol.34,inpp. Pergamon Press Ltd. 1980. Printed Great Britain.
IRRADIATION INDUCED CRYSTALLINE TO ANORPHOUS TRM~SITION .7. Bourgoin Laboratoire d’Etude des Surfaces et Interfaces (Associ~au CNRS) Physique des Solides, ISEN, 3, rue François Ba~és, 59046 Lille Cedex, France (Received 5
September 1979 by M. Balkanski)
Irradiation of a crystalline solid with energetic heavy particles results in cascades of defects which,with increasing dose, overlap and form a continuous disordered layer. In semiconductors the physical properties of such disordered layers are found to be similar to those of amorphous layers produced by evaporation. It is shown in the case of silicon, that the transition from a disordered crystalline (X) layer to an amorphous (a) layer occurs when the Gibbs energy of the X phase and of the defects it contains becomes larger than the Gibbs energy of the a phase.
When an energetic particle penetrates in a solid it makes collisions withthe electrons and the nuclei of this solid. Nuclear collisions result in atomic displacements. In case of ener— getic ions the energy transmitted to the primary knock—on atom is very large compared to the threshold energy Td for atomic displacement and a cascade of displacements is produced. The to— tal number of defects in this cascade is, in the simple model of Kinchin and Pease’, related to the energy T~lost in nuclear collisions through:
and
~R
2V’~~
(3)
The c.d.l. is formed when the number of cascades per unit area (i.e. the dose +.~), is such that
•~
2 6R)
1
(4)
that is —2
•~
2
—~—~ ~ —
wR (1) d The factor K describes the efficiency of the displacements to produce defects and accounts for the eventual annealing which can take place;
E
°
—j--— exp o
—
~~-)
(5)
N=K~_
As shown in Fig. I the experimental variation of •c versus temperature, for three different ions of 200 keV in silicon5 is fitted by expression 5 using values of R 0, ~/~~/R0 and E given in ta— ble I • It can be observed that the temperature (‘~400K) at which becomes larger than is the temperature at which the negative vacancy V has been observed 6 to become mobile ; the value of E obtained is slightly smaller than the for VeV): D . Taking fo~ migration energy of V6 (0.18 we an measured evaluation of r(given0 in 1). D0 obtain the value — table 1.6x lOs~ Th~fact that the parameters D 0, t and E do not depend on the energy and nature of the ion used for the irradiation implies that a universal ture into atomic processes curveof canthe be energy used : deposited the variation with tempera— corresponding to the critical dose. This energy T , lost into atomic collisions is proportional to t~edefect concentration according to relation 1. For the asymptot T~~°’ this energy is7: T = 6x iø23 eV cm c
its value in silicon is 2 : K = 0.8. When the dose of irradiation becomes larger than a critical dose $ , the volumes of the cascades overlap and accontinuous disordered layer (c.d.l.) is produced. This critical dose, i.e. the dose for which the saturation of the disorder is reached, is independent 3of(electron the tech— paramagnetic (EPR), Raman scattering, nique used to resonance monitor this disorder optical absorption, ion backscattering, etc.). Aphenomenological model for the formation of 4which been shown by in Morehead case of silicon such c.d.l. has has been proposed and Crowder to account quantitatively for the variation of • with the different parameters which define t~econditions of irradiation (nature, mass and energy of the incident particles) and the irra— diated solid (atomic mas~and temperature). In this model the cascade is assimilated to a cy— lindrical volume of radius R 0—~R, the initial radius R of the cascade being eventually de— creased ~y a quantity ~SRdue to a possible dif— fusion of some defects out of the volume of the cascade. This diffusion occurs during a charac— teristic time r (the probability that two or more incident particles damage the same volume within t is zero) with a diffusion coefficient:
Is this c.d.l. amorphous ? To answer this question a comparison between the physical pro— perties of amorphous silicon layers, produced by evaporation, and of c,d,l. produced by irradia— tion has been made. These properties (optical absorption edge, Raman scattering, conductivity, EPR) have been found 8 to be similar in both t~es of layers. They cannot be identical since, in evaporated layers, all these properties vary with the conditions of preparation and of annealing. Moreover, the above properties are not very appro—
E D
D0 exp
(—
—~.
)
(2) 25
26
IRRADIATION INDUCED CRYSTALLINE TO AMORPHOUS TRANSITION
Vol. 34, No. I
priate for a comparison between different kinds of disordered or amorphous layers because they are not sensitive to the detailed, short range, atomic configuration but rather to the amount of disorder. Transport atomic properties, sensitive to short range order, have recently been found 9 (in case of germanium) to be similar in both10has types of layers. Transmission electron microscopy shown that single damage regions can be amorphous. It is therefore reasonable to think that c.d.l. are similar to evaporated layers, i.e. are amor—
~17
An irradiation cannot create directly an amorphous layer. Indeed, the atomic structure of a disordered crystalline phase, which contains inter— stitials and vacancy defects (various kinds of Vacancy clusters), is different from an ideal amor— phous covalent phase in which all the bonds are satisfied (with the exception of ~ iol9 cm3 uniformly distributed Thisinduces is phous, illustrated by the dangling fact that bonds~~). irradiation
E1°
0
G~iO15 16
changes in various properties in amorphous mate— rjals’2’5. The transformation of a disordered crystalline phase into an amorphous phase occurs when the concentration of defects in the crystalline phase is such that the Gibbs free energy of the crystalline phase Cx plus the Gibbs energy Gd of the defects it contains becomes larger than iü14
the Gibbs energy Ga of the amorphous phase C +G >G (6) x d a If this transition occurs for the critical dose
_______________________________________
0
5
XJ
15
1000/T(°K’)
Fig. I.
Fit of the experimental data of ref.5, describing the variation of the critical dose with temperature for B, P and
~c (i.e.
when the energy deposited is Tc), then: c ~
Nc=
N
~
0
(7)
Sb ions, with expression 5.
TABLE I
Variation of the critical dose •
versus temperature for three different c ions in silicon according to ref. 5, The fit of these variations with expression 5 provides the values of the parameters E, R, V~/R and r (see text).
Ions (200 keV) B
P
T (K)
c2) (cm
(eV) E
VD r/R _______
R (A)
100
Ix io15
0.12
9.7
2
200
2x IO~
300
8x io16
°
°
(s) 2.6x IO~
9 U
100
2x IO~
200
2x IO~
0,12
5.2 5.4
300
6x ~
5.4
350
2x IO~~
5
5.5
U
4.6
9 fl
3x IO~
13
Sb
100
3x 10
—11 0,12
300
1 x io14
37
425
5x 1O~’
3•9
3.7x JO U
IRRADIATION INDUCED CRYSTALLINE TO AMORPHOUS TRANSITION 27 4,7 eV, Ssd 12k) contain a where is the Gibbs energy per’N.defect, g and diffusion (H g the g~ibbs energies per atom, 5d= 3the atom~c contribution due to migration of the vacancy. The d~nsityandNc the number of defects created by theory 18 provides about I eV for the 5only migration 0.18 to one incident particle, i.e, : enthalpy H.~ : but KT 0.33 eV. Then hd —the Hsdexperiment — ~ 4.4 eV. N~4’c = (8) The entropy term Sd can be neglected at d low temperature in front of hd. Introducing the numerical values given above in expression The Gibbs energy per defect is therefore related (9) the equality is verified for Td — 15 eV to T~through : which is precisely the value measured for the
Vol. 34, No. I
T K 2Ta ~
= N(
—
)
A quantitative verification of this equality im— plies the knowledge of the entropy 5d and enthal— py h~ per defect and of the difference between the gibbs energies in the crystalline and in the amorphous phases, In silicon the quantity ~ has been deduced from the variation with teinpe— rature of the growth rate and nucleation rate of the crystallisation 16 : at 300 K, g~~gx0.14 eV. An evaluation of hd and 5d is more difficult. A first approximation consists (1) to consider tha~ because self—interstitials are mobile at very low temperature in silicon, the only defects left in the cascades in case of irradiation at low tempe— rature are only vacancy clusters (vacancy, diva— cancy, etc.) ; (ii) to approximate the Gibbs energy of a vacancy cluster by the sum of the Gibbs energies of the vacancies it contains. Then hd and can be obtained from self—diffusion 17 data. The enthalpy Hsd and entropy S 5d of self—
threshold energy for atomic displacement in Silicon critical doseof•cdefects corresponds therefore19~ to The a concentration for which the relation(7)holds, i,e. a disordered crystalline layer transforms into an amorphous layer for this dose ; the layers produced by irradiation are amorphous when the dose of irradiation exceeds •c’ In practice two diffe— rent types of irradiation must be considered depending on the mass and the energy of the incident ion : for heavy ions the concentra— tion of defects in the volume of the cascade can be large enough to induce the transforma— tion and isolated amorphous regions are di— rectly formed. For light ions the critical concentration of defects is reached only after several ions have irradiated the same region. Experimental indications that heavy ions crea— ted directly isolated amorphous regions and that light ions result in the abrupt transfor— nation of an irradiated layer can be found in the litterature 20
REFERENCES
I. KINCHIN G.W, and PEASE R.S., Repts. Prog. Phys. 18, 1 (1955) 2. SIGMUND P., Appl. Phys. Letters, 14, 114 (1969) 3. BOURGOIN J.C,, MORHANGE J.F. and BESERMAN R., Rad. Effects, 22, 205 (1974) t~. NORE}1EAD F.F. -and CROWDER B.L.. ,~,.ad Effects, 6, 27 (1970) 5. MOREHEAD F.F., CROWDER B,L. and TITLE R.S., J. Appl. Phys., 43, 1112 (1972) 6. WATKINS G.D. in “Radiation Effects in Semiconductors”, ed. F.L. Vook (Plenum Press, New York, 1968), p. 67. 7. VOOK F.L., in “Radiation Damage and Defects in Semiconductors” (The Institute of Physics, London, 1973) Conf.series 16, p. 60. 8. CROWDER B.L., in “Ion Implantation in Semiconductors”, ed, S. Namba (Japan, Soc. for the Promotion of Science, 1972), p. 63. 9. ZELLMIA K., GER}IAIN P., SQUELARD S. and BOIJRGOIN J.C., Solid State Comm,, 26, 901 (1978). 10. SWANSON M.L,, PARSONS J.R. and HOELKE C.W., Rad. Effects, 9, 249 (1971). II. THOMAS P.A. and KAPLAN D,, in “Structure and Excitations of Amorphous Solids”, ed. C. Lucovsky and F.L. Gabener (American Inst. of Phys., New—York, 1976), AlP Conf. Proc. n°31, p. 85. 12. DESHMUKH R.S., GUHA S. and NARASIMHAN K.L,, J~Phys. C : Solid State Phys., I0,L 625 (1977). 13. BAYER W., STUKE J. and WAGNER H., Phys. Stat, Sol. (a) 30, 231 (1975). 14. BENMAIEK H., THOMAS J.P. and MACKOWSKI J.M. in “Ion Implantation in Semiconductors”, ed. F. Chernow, A. Borders and D.K. Brice (Plenum Press, New—York, 1976), p. 637. 15. ADLER D., BOWEN H.K., FERRAO L.P.C. MARCH.ANT D.D. SINCII R.N. and SAUVAGE J.A., J. Non Cryst. Solids, 8—10, 844 (1972) 16. ZELLANA, K., GERMAIN P., SQUELARD S., BOURGOIN J.C. and THOMAS P.A., .7. Appl. Phys, to be published. 17. For a recent discussion on self—discussion in Si, see : BOURGOIN J.C. and LANNOO N., Rad. Effects, to be published. 18. SWALIN R.A., J. Phys. Chem. Solids, 18, 290 (1961). 19. See for instance C9RBETT J.W. and BOWGOIN J.C. in “Point Defects in Solids”, ed. J.H. Crowford, Jr and L.M. Slifkin (Plenum Press, New York, 1975), vol. 2, chap. I. 20. BARANOVA E.C.,GIJSEV V.M.,MARTYNENKO Yu.V., STARININ C.V. and HAIBULIN I.B, Rad. Effects, 18, 21 (1973)
25—27. Solid State Communications, Vol.34,inpp. Pergamon Press Ltd. 1980. Printed Great Britain.
IRRADIATION INDUCED CRYSTALLINE TO ANORPHOUS TRM~SITION .7. Bourgoin Laboratoire d’Etude des Surfaces et Interfaces (Associ~au CNRS) Physique des Solides, ISEN, 3, rue François Ba~és, 59046 Lille Cedex, France (Received 5
September 1979 by M. Balkanski)
Irradiation of a crystalline solid with energetic heavy particles results in cascades of defects which,with increasing dose, overlap and form a continuous disordered layer. In semiconductors the physical properties of such disordered layers are found to be similar to those of amorphous layers produced by evaporation. It is shown in the case of silicon, that the transition from a disordered crystalline (X) layer to an amorphous (a) layer occurs when the Gibbs energy of the X phase and of the defects it contains becomes larger than the Gibbs energy of the a phase.
When an energetic particle penetrates in a solid it makes collisions withthe electrons and the nuclei of this solid. Nuclear collisions result in atomic displacements. In case of ener— getic ions the energy transmitted to the primary knock—on atom is very large compared to the threshold energy Td for atomic displacement and a cascade of displacements is produced. The to— tal number of defects in this cascade is, in the simple model of Kinchin and Pease’, related to the energy T~lost in nuclear collisions through:
and
~R
2V’~~
(3)
The c.d.l. is formed when the number of cascades per unit area (i.e. the dose +.~), is such that
•~
2 6R)
1
(4)
that is —2
•~
2
—~—~ ~ —
wR (1) d The factor K describes the efficiency of the displacements to produce defects and accounts for the eventual annealing which can take place;
E
°
—j--— exp o
—
~~-)
(5)
N=K~_
As shown in Fig. I the experimental variation of •c versus temperature, for three different ions of 200 keV in silicon5 is fitted by expression 5 using values of R 0, ~/~~/R0 and E given in ta— ble I • It can be observed that the temperature (‘~400K) at which becomes larger than is the temperature at which the negative vacancy V has been observed 6 to become mobile ; the value of E obtained is slightly smaller than the for VeV): D . Taking fo~ migration energy of V6 (0.18 we an measured evaluation of r(given0 in 1). D0 obtain the value — table 1.6x lOs~ Th~fact that the parameters D 0, t and E do not depend on the energy and nature of the ion used for the irradiation implies that a universal ture into atomic processes curveof canthe be energy used : deposited the variation with tempera— corresponding to the critical dose. This energy T , lost into atomic collisions is proportional to t~edefect concentration according to relation 1. For the asymptot T~~°’ this energy is7: T = 6x iø23 eV cm c
its value in silicon is 2 : K = 0.8. When the dose of irradiation becomes larger than a critical dose $ , the volumes of the cascades overlap and accontinuous disordered layer (c.d.l.) is produced. This critical dose, i.e. the dose for which the saturation of the disorder is reached, is independent 3of(electron the tech— paramagnetic (EPR), Raman scattering, nique used to resonance monitor this disorder optical absorption, ion backscattering, etc.). Aphenomenological model for the formation of 4which been shown by in Morehead case of silicon such c.d.l. has has been proposed and Crowder to account quantitatively for the variation of • with the different parameters which define t~econditions of irradiation (nature, mass and energy of the incident particles) and the irra— diated solid (atomic mas~and temperature). In this model the cascade is assimilated to a cy— lindrical volume of radius R 0—~R, the initial radius R of the cascade being eventually de— creased ~y a quantity ~SRdue to a possible dif— fusion of some defects out of the volume of the cascade. This diffusion occurs during a charac— teristic time r (the probability that two or more incident particles damage the same volume within t is zero) with a diffusion coefficient:
Is this c.d.l. amorphous ? To answer this question a comparison between the physical pro— perties of amorphous silicon layers, produced by evaporation, and of c,d,l. produced by irradia— tion has been made. These properties (optical absorption edge, Raman scattering, conductivity, EPR) have been found 8 to be similar in both t~es of layers. They cannot be identical since, in evaporated layers, all these properties vary with the conditions of preparation and of annealing. Moreover, the above properties are not very appro—
E D
D0 exp
(—
—~.
)
(2) 25
26
IRRADIATION INDUCED CRYSTALLINE TO AMORPHOUS TRANSITION
Vol. 34, No. I
priate for a comparison between different kinds of disordered or amorphous layers because they are not sensitive to the detailed, short range, atomic configuration but rather to the amount of disorder. Transport atomic properties, sensitive to short range order, have recently been found 9 (in case of germanium) to be similar in both10has types of layers. Transmission electron microscopy shown that single damage regions can be amorphous. It is therefore reasonable to think that c.d.l. are similar to evaporated layers, i.e. are amor—
~17
An irradiation cannot create directly an amorphous layer. Indeed, the atomic structure of a disordered crystalline phase, which contains inter— stitials and vacancy defects (various kinds of Vacancy clusters), is different from an ideal amor— phous covalent phase in which all the bonds are satisfied (with the exception of ~ iol9 cm3 uniformly distributed Thisinduces is phous, illustrated by the dangling fact that bonds~~). irradiation
E1°
0
G~iO15 16
changes in various properties in amorphous mate— rjals’2’5. The transformation of a disordered crystalline phase into an amorphous phase occurs when the concentration of defects in the crystalline phase is such that the Gibbs free energy of the crystalline phase Cx plus the Gibbs energy Gd of the defects it contains becomes larger than iü14
the Gibbs energy Ga of the amorphous phase C +G >G (6) x d a If this transition occurs for the critical dose
_______________________________________
0
5
XJ
15
1000/T(°K’)
Fig. I.
Fit of the experimental data of ref.5, describing the variation of the critical dose with temperature for B, P and
~c (i.e.
when the energy deposited is Tc), then: c ~
Nc=
N
~
0
(7)
Sb ions, with expression 5.
TABLE I
Variation of the critical dose •
versus temperature for three different c ions in silicon according to ref. 5, The fit of these variations with expression 5 provides the values of the parameters E, R, V~/R and r (see text).
Ions (200 keV) B
P
T (K)
c2) (cm
(eV) E
VD r/R _______
R (A)
100
Ix io15
0.12
9.7
2
200
2x IO~
300
8x io16
°
°
(s) 2.6x IO~
9 U
100
2x IO~
200
2x IO~
0,12
5.2 5.4
300
6x ~
5.4
350
2x IO~~
5
5.5
U
4.6
9 fl
3x IO~
13
Sb
100
3x 10
—11 0,12
300
1 x io14
37
425
5x 1O~’
3•9
3.7x JO U
IRRADIATION INDUCED CRYSTALLINE TO AMORPHOUS TRANSITION 27 4,7 eV, Ssd 12k) contain a where is the Gibbs energy per’N.defect, g and diffusion (H g the g~ibbs energies per atom, 5d= 3the atom~c contribution due to migration of the vacancy. The d~nsityandNc the number of defects created by theory 18 provides about I eV for the 5only migration 0.18 to one incident particle, i.e, : enthalpy H.~ : but KT 0.33 eV. Then hd —the Hsdexperiment — ~ 4.4 eV. N~4’c = (8) The entropy term Sd can be neglected at d low temperature in front of hd. Introducing the numerical values given above in expression The Gibbs energy per defect is therefore related (9) the equality is verified for Td — 15 eV to T~through : which is precisely the value measured for the
Vol. 34, No. I
T K 2Ta ~
= N(
—
)
A quantitative verification of this equality im— plies the knowledge of the entropy 5d and enthal— py h~ per defect and of the difference between the gibbs energies in the crystalline and in the amorphous phases, In silicon the quantity ~ has been deduced from the variation with teinpe— rature of the growth rate and nucleation rate of the crystallisation 16 : at 300 K, g~~gx0.14 eV. An evaluation of hd and 5d is more difficult. A first approximation consists (1) to consider tha~ because self—interstitials are mobile at very low temperature in silicon, the only defects left in the cascades in case of irradiation at low tempe— rature are only vacancy clusters (vacancy, diva— cancy, etc.) ; (ii) to approximate the Gibbs energy of a vacancy cluster by the sum of the Gibbs energies of the vacancies it contains. Then hd and can be obtained from self—diffusion 17 data. The enthalpy Hsd and entropy S 5d of self—
threshold energy for atomic displacement in Silicon critical doseof•cdefects corresponds therefore19~ to The a concentration for which the relation(7)holds, i,e. a disordered crystalline layer transforms into an amorphous layer for this dose ; the layers produced by irradiation are amorphous when the dose of irradiation exceeds •c’ In practice two diffe— rent types of irradiation must be considered depending on the mass and the energy of the incident ion : for heavy ions the concentra— tion of defects in the volume of the cascade can be large enough to induce the transforma— tion and isolated amorphous regions are di— rectly formed. For light ions the critical concentration of defects is reached only after several ions have irradiated the same region. Experimental indications that heavy ions crea— ted directly isolated amorphous regions and that light ions result in the abrupt transfor— nation of an irradiated layer can be found in the litterature 20
REFERENCES
I. KINCHIN G.W, and PEASE R.S., Repts. Prog. Phys. 18, 1 (1955) 2. SIGMUND P., Appl. Phys. Letters, 14, 114 (1969) 3. BOURGOIN J.C,, MORHANGE J.F. and BESERMAN R., Rad. Effects, 22, 205 (1974) t~. NORE}1EAD F.F. -and CROWDER B.L.. ,~,.ad Effects, 6, 27 (1970) 5. MOREHEAD F.F., CROWDER B,L. and TITLE R.S., J. Appl. Phys., 43, 1112 (1972) 6. WATKINS G.D. in “Radiation Effects in Semiconductors”, ed. F.L. Vook (Plenum Press, New York, 1968), p. 67. 7. VOOK F.L., in “Radiation Damage and Defects in Semiconductors” (The Institute of Physics, London, 1973) Conf.series 16, p. 60. 8. CROWDER B.L., in “Ion Implantation in Semiconductors”, ed, S. Namba (Japan, Soc. for the Promotion of Science, 1972), p. 63. 9. ZELLMIA K., GER}IAIN P., SQUELARD S. and BOIJRGOIN J.C., Solid State Comm,, 26, 901 (1978). 10. SWANSON M.L,, PARSONS J.R. and HOELKE C.W., Rad. Effects, 9, 249 (1971). II. THOMAS P.A. and KAPLAN D,, in “Structure and Excitations of Amorphous Solids”, ed. C. Lucovsky and F.L. Gabener (American Inst. of Phys., New—York, 1976), AlP Conf. Proc. n°31, p. 85. 12. DESHMUKH R.S., GUHA S. and NARASIMHAN K.L,, J~Phys. C : Solid State Phys., I0,L 625 (1977). 13. BAYER W., STUKE J. and WAGNER H., Phys. Stat, Sol. (a) 30, 231 (1975). 14. BENMAIEK H., THOMAS J.P. and MACKOWSKI J.M. in “Ion Implantation in Semiconductors”, ed. F. Chernow, A. Borders and D.K. Brice (Plenum Press, New—York, 1976), p. 637. 15. ADLER D., BOWEN H.K., FERRAO L.P.C. MARCH.ANT D.D. SINCII R.N. and SAUVAGE J.A., J. Non Cryst. Solids, 8—10, 844 (1972) 16. ZELLANA, K., GERMAIN P., SQUELARD S., BOURGOIN J.C. and THOMAS P.A., .7. Appl. Phys, to be published. 17. For a recent discussion on self—discussion in Si, see : BOURGOIN J.C. and LANNOO N., Rad. Effects, to be published. 18. SWALIN R.A., J. Phys. Chem. Solids, 18, 290 (1961). 19. See for instance C9RBETT J.W. and BOWGOIN J.C. in “Point Defects in Solids”, ed. J.H. Crowford, Jr and L.M. Slifkin (Plenum Press, New York, 1975), vol. 2, chap. I. 20. BARANOVA E.C.,GIJSEV V.M.,MARTYNENKO Yu.V., STARININ C.V. and HAIBULIN I.B, Rad. Effects, 18, 21 (1973)