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Efficiency of defects generation due to irradiation in silica
Solid State Communications, Vol. 91, No. 8. pp. 66-665, 1994 Elsevier Science Ltd Printed in Great Britain 0038-1098/94 57.00 + .OO
Pergamon
8038-1098(94)E0182-B
EFFICIENCY
OF DEFECTS
GENERATION
DUE TO IRRADIATION
IN SILICA
A.I. Gusarov Research Center “Physic0-Technical (Received
Bureau”, 195427 St. Petersburg, Russia
24 December
1993 by L. V. Keldysh)
The efficiency of generation by irradiation of E/-centers in pure silica glass has been estimated analytically. The ionization of the oxygen nonbonding orbital was considered as a main mechanism of defect creation, allowing us to interpret the known experimental dose dependence of the concentration of the E’centers produced by Xradiation.
THE CHANGE in the properties of glasses due to irradiation is concerned in part with the creation of structural defects, which are related to additional absorption, mechanical stress, induced anisotropy, etc. The performance of an optical device can also be affected by irradiation because of significant changes in glass parameters. Therefore, it is important to estimate the efficiency of defect generation n - the number of elementary defects that can be created by one fast primary particle with the energy Ep. If we know q and absorbed dose of radiation D, we can predict changes in the properties of the glass. Structural defect creation due to irradiation can result from different causes, including elastic scattering (knock-on processes), nuclear reactions and ionization. In this paper, we consider particles of ionizing radiation with energy less than lOMeV, for which the cross-section for nuclear reactions is sufficiently small. For example, the mean free path for nuclear interaction of a proton with energy 10 MeV in silica is about 25 cm [l] and rapidly increases with decreasing particle energy. At the same time, the penetration depth is less than 0.6mm. Of course, a single nuclear interaction can cause macroscopic defect domain creation, but the very small probability of this process means that we need not consider this type of scattering from consideration. The Frenkel pair of defects “vacancy-atom in interstitial position” can be created by a knock-on process. However, the efficiency of energy transformation in this process is small. If elastic scattering would be important, there would be a
threshold for defect generation, but this threshold has not been observed experimentally [2]. Moreover, in accordance with the recent results, the generation of shortlived and stable defects in silica can take place if the energy of ionizing particle is of the order the gap Eg [3, 41. so that we may also neglect elastic scattering. Interaction of photons with the glass matrix is due to photoabsorption. The photon is absorbed completely and the excited atom can then relax radiatively or by the Auger mechanism. As a result, the energy of the photon is converted into the energy of the fast electron. If the spatial distribution of the defects generated is not of our primary concern, the mechanism of energy conversion is nearly the same for a photon, a proton or an electron. It follows that it is possible to consider the ionization as the main mechanism of defect generation, and we use the nonrelativistic approximation of the Bethe theory [6] to describe ionization losses. It is possible to use more accurate relations, but these give rise to serious complications. At the same time, the comparison of the results of the stopping power calculations shows that the influence of relativistic and polarizing effect is small in the energy region considered. For silica the difference between two calculations is less than 8% for protons and less than 2% for electrons. Due to ionization the energy of the primary particle is converted into the kinetic energy of secondary electrons and into the energy of internal excitations (holes in a core level or in the valence band). The energy loss of the fast electron with
661
EFFICIENCY
662 penetration
Vol. 91, No. 8
OF DEFECTS GENERATION channel j) is
length R is equal to the total energy
AE, = C AEi+j = gj(Ep) C t,=~AEj=~&/dX~ln’, i i
J
0
where m, v and e are the mass, the speed and the charge of the fast electron, respectively, and& and 4 are the oscillator strength and ionization potential for levelj; n is the atomic concentration. The bottom of the empty conduction band (c-band) is taken as the zero of energy. To estimate the integral, we use a known equality; if a function f(x) is “slow” in comparison with g(x), then b
1f(x)&)
(2)
dx =f(xo) i g(x) dx, L1
(I
where the point x0 is defined as a solution of the equation b
(x - xo)g(x) dx = 0.
(3)
(I
By applying equation equation (1) to
(2) it is possible to convert
,=jdx?!!!? mu2
’
(4)
0
where vl is defined by equation (3). The energy losses in the channel j are then defined as (El = 2mvf):
AEj = gj(Ep)Ep,
If energy losses due to heating radiation are neglected, then
c
lnrj.
AEi+.j =
dEwi(E)Egj(Ep). f
(9)
We may, therefore, conclude that, in the process of multiple ionizing scattering, the energy saved in the channel j is conserved. The amount of energy stored is defined by equation (5). The equality (9) fails if we take into account that the energy of the secondary electron can be insufficient to ionize the atomic level with maximal energy of ionization, because in that case we have to restrict the upper limit of summation in equation (9). The secondary electron can ionize the atom only if its energy is greater than Zm, (Fig. 1). The internal excitation can also cause the ionization of the atom if the energy of internal excitation 4 > ZmoxN 2Zmin.If li < LX the energy relaxes due to nonionizing (intraband or nonelectronic) processes (Fig. 1). As a result of multiple scattering all the energy of the primary particle is converted into the energy of the internal excitations of the levels with 4 < I,, and kinetic energy of electrons with the energy E < I,,. Therefore, we have to take into account in all summation above only levels which satisfy the condition Ij < Imax, because other levels are not excited in a final state. We suggest below that 1minis the energy level of the metastable defect. We shall show that it is true for (11
(6)
The excited secondary electrons are also able to participate in the ionizing scattering. As a result, the energy AEj is redistributed among all ionizing channels. If wi(E) is the energy distribution of secondary electrons excited from level i, the energy transferred by secondary ionization from channel i to channel j is then
and to emitted
AEi = Ep.
gj(Ep)=fi ln W4MZlnW~)l~ In I = CA
(8)
AEi. i
i
(1)
I
(2)
(3)
c-band __--___-_--___________ min 0
-1
-21
min
min
______--_iT-_-_-----;I
(7)
Because the logarithm is a slowly varying function, it is possible to neglect the energy dependence in E,(E) and move gj(Ep) out of the integral. The remaining part of the integrand gives AEi. In this case the energy that is collected in the channel j as a result of the secondary ionization (including the
hole
Fig. 1. Schematic picture of electron multiplication due to equation (1) ionization and equation (2) Auger mechanisms. Electron with energy E < Zmin (c-band) and holes with -21,, < E < Imin (3) are in a “passive” region and are not able to create secondary electrons.
Vol. 91, No. 8
EFFICIENCY
OF DEFECTS
silica, where ZminN Eg and the valence band (v-band) width is greater than 2E,. The level I,, is then inside the v-band and the energy of the internal excitations can also relax by intraband scattering. This is a fast channel and Z,, is probably shifted towards to the bottom of the v-band. If in an insulator (e.g., LiF) the density of states at Z,,,O.X is zero, then Z,,, is defined by the v-band bottom. To calculate n we have to know the amount of energy (E) that is needed to create one metastable defect. This energy is defined by the energy distribution function of the secondary electrons w,(E). The precise expression for w,(E) can be obtained as a result of the Boltzmann equation for the electron flux. This equation must incorporate all the scattering mechanisms, but the exact analytical solution of this problem is presently impossible. To obtain an estimate, we assume that the energy of the electrons which excites secondary electrons are high in all cases and the energy distribution of the secondaries is w(E) 0: Zm,/(E + Zmin)2. All the electrons with energies E > Zmin will lose energy and fall down into the “passive” region E < Zmi, (Fig. 1). It follows that w,(E) equal to 0 for E > Zm, and w(E) for E < Zm,. In order to satisfy the normalization we must multiply w(E) by the factor 2. Then (E) = Zmin+ s Ew,(E) dE 2 uZ,,,~, a ~2 in 2. A more accurate calculation would change a, but it is obvious that 1 < a < 2. Then the efficiency for defect creation is
GENERATION
663
in low OH silica glasses, but in high OH glasses NBOHC are mainly created. It has been suggested [3, 41 that the E/-center can be created as a result of the process with participation of the self-trapped exciton (STE). The bond ESi-0-Si= is broken due to ionization, the oxygen moves towards interstitial position or creates a peroxyl bond =Si-0-O-S&, and STE is created simultaneously. The decay time of STE is about 10 ZLS at room temperature. Its relaxation is accompanied by blue luminescence (hv N 2.8eV) and leads to the defect stabilization and E’ formation. It is known that E’ is associated with the oxygen vacancy (OV) rSi-Si=, and another possible mechanism for the E/-center creation is the ionization of precursor - OV. To achieve a high concentration of the precursor, the glass must be prepared with oxygen deficiency. There is another way to create the E/-defect [7]. In agreement with [7]. Z? creation in glasses with the low concentration of OV may result from a two-step process. As a first step, OV is formed due to ionization of a normal bond ESi-O-Sir, and secondary ionization of OV creates the E’-defect. In this case it is possible to describe the process of E’ generation by the system of two rate equations: dn,/dt = -nvpe J + nnp,, J,
(11)
dn,/dt = nvpe J.
(12)
Here, n,, n,, n, are the concentrations of the normal bonds, OV and E’; pv, pe are the probabilities for n= g creating OV and E’, J is the intensity of the Here summation includes the levels (with total irradiation dose D = Jr, where t is time of irradiaoscillator strength f,) ionization of that leads to tion. It is easy to see that, if the dose D is low E’-center formation, Z is the total oscillator (n, < n,), n, N 1/2n,p,p,D2, but this result contrastrengths for the states in the v-band “passive” dicts to the experimental data [6]. Therefore, we must region (Fig. 1). In order to calculate fi and Z we assume that E/-center generation is the result of the have to use a detailed model of the v-band of the one-step process. insulator. In glasses, where the concentration of OV is We can also introduce the average energy for negligible, the E/-center creation is due to the first defect creation by primary particle E = cZmimZ/‘fi. mechanism stated above. The parameters that are which takes into account the existence of the different incorporated into (10) can be calculated for a known scattering channels. model of the v-band of silica [8]. It is possible to The nature of mechanisms of the intrinsic defects separate in the silica v-band subbands of bonding generation in silica due to irradiation remains poorly and nonbonding states. It is the ionization of the understood. The spectrum of the defects is very last ones leads to STE and to E-center formation. broad. There are three defects that have been In accordance with [8] fi N 3.87, Z 21 12.52, Zmim N observed at room temperatures by electron spin 10eV. For example, one particle with energy 1 MeV resonance: the E/-center, the nonbridging oxygen creates about 2.2 x lo4 defects. hole center (NBOHC), the peroxyl radical. The kind In the other case, when the precursor concenof defect that is the most likely to be generated tration is high, the contribution of OV ionization depends on glass composition. For example, a may play an important role. Which of the bonds reaction leading to E’ defect formation dominates =Si-0-Si= or &i-Si= that will be ionized is = +&(E,J azi”
2 -&a l?l,”
EFFICIENCY
664
OF DEFECTS GENERATION
defined by the value of the ionizing mean free path I,;’ = nnde4/IdE,
(13)
where nd and Id are the bonds concentration and the energy of ionization of the proper defect. It is easy to see that the smaller the value of Id, the more probable the ionization of the corresponding bond. But because the concentration of OV bonds is considerably smaller than the concentration of normal bonds, the ionization by fast electrons usually leads to the E/-center formation due to STE decay. However, it should be noted that electrons with the E < Eg are not able to ionize a normal bond, but can ionize an OV. In this case the efficiency of E/-center creation is 7’ = ~(1 + (a - l)E&),
(14)
where 1, is the energy of OV ionization. To test the approach used above, we have analyzed the experimental results of [6], where the p-center creation due to X-ray irradiation was investigated. We found that the process of defect generation could be understood on the basis of equation (10). The experimental dose dependence [6] is reproduced in Fig. 2. If D < 3 Mrad, the concentration of E’ grows linearly with dose, increasing both in high OH (Suprasil W 1) and low OH (Suprasil 1) glasses. A further increase of the dose changes the linear dependence for Suprasil Wl to nonlinear until the dose is less than 50Mrad. If the dose is more than 50Mrad the dependence is also linear. The nonlinear growth in Suprasil Wl is due to activation of pre-existing defects, while high dose linear regions in both Suprasil 1 and Suprasil W 1 are due to creation of new E’centers [6]. In agreement with equation (lo), we approximate the dose dependence for Suprasil Wl by two linear
Vol. 91. No. 8
regions (Fig. 2), which cross when the dose is about DI N 20 Mrad. This approximation means that, if D < D1, the creation of E’ is mainly due to precursor ionization, and when D > DI the E’-defects are
created by STE decay alone. It follows from the difference in the slopes of the two lines on Fig. 2 and equation (14), that E.J& N 7.3, i.e., the energy of OV ionization is small, as we assumed. The dose D, corresponds to the total precursor ionization. Because i? is known, it is possible to estimate the concentration of OV prior to irradiation: no N 1.4 x 102’ cme3. It also agrees with the suggestin that primary electrons mainly ionize normal bonds. It is possible to explain the difference in the slope of the two lines in the region D > 50 MeV if we suppose that the probability for E’-center recharging, which makes it nonmagnetic, is different if the precursor for E’-centers was an OV or a normal bond. It can take place, because the surrounding of E/-center in this two cases is different. If this is the case the dose dependence for Suprasil Wl should have a second bend (Fig. 2) in the region D N 300 Mrad, because all OV will be twice ionized. To summarize, the efficiency of the E’centers generation in pure silica by irradiation has been estimated analytically, assuming that ionization is the mechanism for defect creation. The known experimental dose dependence of the concentration of E’centers produced by X-ray irradiation could be explained, and a new feature of this dependence has been predicted. Defect relaxation and etching have not been taken into account, and it is clear that these processes are very important when shortlived defects are considered. We are planning such an investigation. Acknowledgements - I shouid like to thank the Theory Group of the Institute fur Festkorperforschung of the Forschungszentrum Jtilich, where this manuscript was prepared, for hospitality and helpful discussion. Financial support by the Deutsche Forschungsgemeinschaft is also gratefully acknowledged.
E' spins, a.u. (I)
REFERENCES 1. I
I
,
100
300 200 X-Ray Dose, blrad
Fig. 2. E/-spin concentration vs X-ray dose for Suprasil Wl (1) and Suprasil 1 (2). Solid circles, experimental results [6]; lines, theoretical approxima_. I.,.\ non ( 10).
2. 3. 4. 5.
J.I. Janni,
Atomic Data and Nuclear Tables 27, 147 (1982). W. Primak, Phys. Rev. B6,4846 (1972).
Data
K. Tanimura, C. Itoh & N. Itoh, J. Phys. C21, 1869 (1988). T.E. Tsai, D.L. Griscom & E.J. Friebele, Phys. Rev. Lett. 61, 444 (1988). H. Bethe, Ann. der Physik, 5 Folge, Bd. 5, 325 (1930).
Vol. 91, No. 8 6.
EFFICIENCY
OF DEFECTS
D.B. Kerwin & F.L. Galeener, Phys. Rev. Lett. 68, 3208 (1992); D.B. Kerwin, F.L. Galeener, A.J. Miller & J.C. Mikkelsen, Jr., Solid State Commun. 82, 271 (1992).
7. 8.
GENERATION
665
K. Tanimura, T. Tanaka & N. Itoh, Phys. Rev. L&t. 51, 423 (1983). J.C. Ashley & V.E. Anderson, J. Electron. Spectroscop. Relar. Phenom. 24, 127 (1981).
Pergamon
8038-1098(94)E0182-B
EFFICIENCY
OF DEFECTS
GENERATION
DUE TO IRRADIATION
IN SILICA
A.I. Gusarov Research Center “Physic0-Technical (Received
Bureau”, 195427 St. Petersburg, Russia
24 December
1993 by L. V. Keldysh)
The efficiency of generation by irradiation of E/-centers in pure silica glass has been estimated analytically. The ionization of the oxygen nonbonding orbital was considered as a main mechanism of defect creation, allowing us to interpret the known experimental dose dependence of the concentration of the E’centers produced by Xradiation.
THE CHANGE in the properties of glasses due to irradiation is concerned in part with the creation of structural defects, which are related to additional absorption, mechanical stress, induced anisotropy, etc. The performance of an optical device can also be affected by irradiation because of significant changes in glass parameters. Therefore, it is important to estimate the efficiency of defect generation n - the number of elementary defects that can be created by one fast primary particle with the energy Ep. If we know q and absorbed dose of radiation D, we can predict changes in the properties of the glass. Structural defect creation due to irradiation can result from different causes, including elastic scattering (knock-on processes), nuclear reactions and ionization. In this paper, we consider particles of ionizing radiation with energy less than lOMeV, for which the cross-section for nuclear reactions is sufficiently small. For example, the mean free path for nuclear interaction of a proton with energy 10 MeV in silica is about 25 cm [l] and rapidly increases with decreasing particle energy. At the same time, the penetration depth is less than 0.6mm. Of course, a single nuclear interaction can cause macroscopic defect domain creation, but the very small probability of this process means that we need not consider this type of scattering from consideration. The Frenkel pair of defects “vacancy-atom in interstitial position” can be created by a knock-on process. However, the efficiency of energy transformation in this process is small. If elastic scattering would be important, there would be a
threshold for defect generation, but this threshold has not been observed experimentally [2]. Moreover, in accordance with the recent results, the generation of shortlived and stable defects in silica can take place if the energy of ionizing particle is of the order the gap Eg [3, 41. so that we may also neglect elastic scattering. Interaction of photons with the glass matrix is due to photoabsorption. The photon is absorbed completely and the excited atom can then relax radiatively or by the Auger mechanism. As a result, the energy of the photon is converted into the energy of the fast electron. If the spatial distribution of the defects generated is not of our primary concern, the mechanism of energy conversion is nearly the same for a photon, a proton or an electron. It follows that it is possible to consider the ionization as the main mechanism of defect generation, and we use the nonrelativistic approximation of the Bethe theory [6] to describe ionization losses. It is possible to use more accurate relations, but these give rise to serious complications. At the same time, the comparison of the results of the stopping power calculations shows that the influence of relativistic and polarizing effect is small in the energy region considered. For silica the difference between two calculations is less than 8% for protons and less than 2% for electrons. Due to ionization the energy of the primary particle is converted into the kinetic energy of secondary electrons and into the energy of internal excitations (holes in a core level or in the valence band). The energy loss of the fast electron with
661
EFFICIENCY
662 penetration
Vol. 91, No. 8
OF DEFECTS GENERATION channel j) is
length R is equal to the total energy
AE, = C AEi+j = gj(Ep) C t,=~AEj=~&/dX~ln’, i i
J
0
where m, v and e are the mass, the speed and the charge of the fast electron, respectively, and& and 4 are the oscillator strength and ionization potential for levelj; n is the atomic concentration. The bottom of the empty conduction band (c-band) is taken as the zero of energy. To estimate the integral, we use a known equality; if a function f(x) is “slow” in comparison with g(x), then b
1f(x)&)
(2)
dx =f(xo) i g(x) dx, L1
(I
where the point x0 is defined as a solution of the equation b
(x - xo)g(x) dx = 0.
(3)
(I
By applying equation equation (1) to
(2) it is possible to convert
,=jdx?!!!? mu2
’
(4)
0
where vl is defined by equation (3). The energy losses in the channel j are then defined as (El = 2mvf):
AEj = gj(Ep)Ep,
If energy losses due to heating radiation are neglected, then
c
lnrj.
AEi+.j =
dEwi(E)Egj(Ep). f
(9)
We may, therefore, conclude that, in the process of multiple ionizing scattering, the energy saved in the channel j is conserved. The amount of energy stored is defined by equation (5). The equality (9) fails if we take into account that the energy of the secondary electron can be insufficient to ionize the atomic level with maximal energy of ionization, because in that case we have to restrict the upper limit of summation in equation (9). The secondary electron can ionize the atom only if its energy is greater than Zm, (Fig. 1). The internal excitation can also cause the ionization of the atom if the energy of internal excitation 4 > ZmoxN 2Zmin.If li < LX the energy relaxes due to nonionizing (intraband or nonelectronic) processes (Fig. 1). As a result of multiple scattering all the energy of the primary particle is converted into the energy of the internal excitations of the levels with 4 < I,, and kinetic energy of electrons with the energy E < I,,. Therefore, we have to take into account in all summation above only levels which satisfy the condition Ij < Imax, because other levels are not excited in a final state. We suggest below that 1minis the energy level of the metastable defect. We shall show that it is true for (11
(6)
The excited secondary electrons are also able to participate in the ionizing scattering. As a result, the energy AEj is redistributed among all ionizing channels. If wi(E) is the energy distribution of secondary electrons excited from level i, the energy transferred by secondary ionization from channel i to channel j is then
and to emitted
AEi = Ep.
gj(Ep)=fi ln W4MZlnW~)l~ In I = CA
(8)
AEi. i
i
(1)
I
(2)
(3)
c-band __--___-_--___________ min 0
-1
-21
min
min
______--_iT-_-_-----;I
(7)
Because the logarithm is a slowly varying function, it is possible to neglect the energy dependence in E,(E) and move gj(Ep) out of the integral. The remaining part of the integrand gives AEi. In this case the energy that is collected in the channel j as a result of the secondary ionization (including the
hole
Fig. 1. Schematic picture of electron multiplication due to equation (1) ionization and equation (2) Auger mechanisms. Electron with energy E < Zmin (c-band) and holes with -21,, < E < Imin (3) are in a “passive” region and are not able to create secondary electrons.
Vol. 91, No. 8
EFFICIENCY
OF DEFECTS
silica, where ZminN Eg and the valence band (v-band) width is greater than 2E,. The level I,, is then inside the v-band and the energy of the internal excitations can also relax by intraband scattering. This is a fast channel and Z,, is probably shifted towards to the bottom of the v-band. If in an insulator (e.g., LiF) the density of states at Z,,,O.X is zero, then Z,,, is defined by the v-band bottom. To calculate n we have to know the amount of energy (E) that is needed to create one metastable defect. This energy is defined by the energy distribution function of the secondary electrons w,(E). The precise expression for w,(E) can be obtained as a result of the Boltzmann equation for the electron flux. This equation must incorporate all the scattering mechanisms, but the exact analytical solution of this problem is presently impossible. To obtain an estimate, we assume that the energy of the electrons which excites secondary electrons are high in all cases and the energy distribution of the secondaries is w(E) 0: Zm,/(E + Zmin)2. All the electrons with energies E > Zmin will lose energy and fall down into the “passive” region E < Zmi, (Fig. 1). It follows that w,(E) equal to 0 for E > Zm, and w(E) for E < Zm,. In order to satisfy the normalization we must multiply w(E) by the factor 2. Then (E) = Zmin+ s Ew,(E) dE 2 uZ,,,~, a ~2 in 2. A more accurate calculation would change a, but it is obvious that 1 < a < 2. Then the efficiency for defect creation is
GENERATION
663
in low OH silica glasses, but in high OH glasses NBOHC are mainly created. It has been suggested [3, 41 that the E/-center can be created as a result of the process with participation of the self-trapped exciton (STE). The bond ESi-0-Si= is broken due to ionization, the oxygen moves towards interstitial position or creates a peroxyl bond =Si-0-O-S&, and STE is created simultaneously. The decay time of STE is about 10 ZLS at room temperature. Its relaxation is accompanied by blue luminescence (hv N 2.8eV) and leads to the defect stabilization and E’ formation. It is known that E’ is associated with the oxygen vacancy (OV) rSi-Si=, and another possible mechanism for the E/-center creation is the ionization of precursor - OV. To achieve a high concentration of the precursor, the glass must be prepared with oxygen deficiency. There is another way to create the E/-defect [7]. In agreement with [7]. Z? creation in glasses with the low concentration of OV may result from a two-step process. As a first step, OV is formed due to ionization of a normal bond ESi-O-Sir, and secondary ionization of OV creates the E’-defect. In this case it is possible to describe the process of E’ generation by the system of two rate equations: dn,/dt = -nvpe J + nnp,, J,
(11)
dn,/dt = nvpe J.
(12)
Here, n,, n,, n, are the concentrations of the normal bonds, OV and E’; pv, pe are the probabilities for n= g creating OV and E’, J is the intensity of the Here summation includes the levels (with total irradiation dose D = Jr, where t is time of irradiaoscillator strength f,) ionization of that leads to tion. It is easy to see that, if the dose D is low E’-center formation, Z is the total oscillator (n, < n,), n, N 1/2n,p,p,D2, but this result contrastrengths for the states in the v-band “passive” dicts to the experimental data [6]. Therefore, we must region (Fig. 1). In order to calculate fi and Z we assume that E/-center generation is the result of the have to use a detailed model of the v-band of the one-step process. insulator. In glasses, where the concentration of OV is We can also introduce the average energy for negligible, the E/-center creation is due to the first defect creation by primary particle E = cZmimZ/‘fi. mechanism stated above. The parameters that are which takes into account the existence of the different incorporated into (10) can be calculated for a known scattering channels. model of the v-band of silica [8]. It is possible to The nature of mechanisms of the intrinsic defects separate in the silica v-band subbands of bonding generation in silica due to irradiation remains poorly and nonbonding states. It is the ionization of the understood. The spectrum of the defects is very last ones leads to STE and to E-center formation. broad. There are three defects that have been In accordance with [8] fi N 3.87, Z 21 12.52, Zmim N observed at room temperatures by electron spin 10eV. For example, one particle with energy 1 MeV resonance: the E/-center, the nonbridging oxygen creates about 2.2 x lo4 defects. hole center (NBOHC), the peroxyl radical. The kind In the other case, when the precursor concenof defect that is the most likely to be generated tration is high, the contribution of OV ionization depends on glass composition. For example, a may play an important role. Which of the bonds reaction leading to E’ defect formation dominates =Si-0-Si= or &i-Si= that will be ionized is = +&(E,J azi”
2 -&a l?l,”
EFFICIENCY
664
OF DEFECTS GENERATION
defined by the value of the ionizing mean free path I,;’ = nnde4/IdE,
(13)
where nd and Id are the bonds concentration and the energy of ionization of the proper defect. It is easy to see that the smaller the value of Id, the more probable the ionization of the corresponding bond. But because the concentration of OV bonds is considerably smaller than the concentration of normal bonds, the ionization by fast electrons usually leads to the E/-center formation due to STE decay. However, it should be noted that electrons with the E < Eg are not able to ionize a normal bond, but can ionize an OV. In this case the efficiency of E/-center creation is 7’ = ~(1 + (a - l)E&),
(14)
where 1, is the energy of OV ionization. To test the approach used above, we have analyzed the experimental results of [6], where the p-center creation due to X-ray irradiation was investigated. We found that the process of defect generation could be understood on the basis of equation (10). The experimental dose dependence [6] is reproduced in Fig. 2. If D < 3 Mrad, the concentration of E’ grows linearly with dose, increasing both in high OH (Suprasil W 1) and low OH (Suprasil 1) glasses. A further increase of the dose changes the linear dependence for Suprasil Wl to nonlinear until the dose is less than 50Mrad. If the dose is more than 50Mrad the dependence is also linear. The nonlinear growth in Suprasil Wl is due to activation of pre-existing defects, while high dose linear regions in both Suprasil 1 and Suprasil W 1 are due to creation of new E’centers [6]. In agreement with equation (lo), we approximate the dose dependence for Suprasil Wl by two linear
Vol. 91. No. 8
regions (Fig. 2), which cross when the dose is about DI N 20 Mrad. This approximation means that, if D < D1, the creation of E’ is mainly due to precursor ionization, and when D > DI the E’-defects are
created by STE decay alone. It follows from the difference in the slopes of the two lines on Fig. 2 and equation (14), that E.J& N 7.3, i.e., the energy of OV ionization is small, as we assumed. The dose D, corresponds to the total precursor ionization. Because i? is known, it is possible to estimate the concentration of OV prior to irradiation: no N 1.4 x 102’ cme3. It also agrees with the suggestin that primary electrons mainly ionize normal bonds. It is possible to explain the difference in the slope of the two lines in the region D > 50 MeV if we suppose that the probability for E’-center recharging, which makes it nonmagnetic, is different if the precursor for E’-centers was an OV or a normal bond. It can take place, because the surrounding of E/-center in this two cases is different. If this is the case the dose dependence for Suprasil Wl should have a second bend (Fig. 2) in the region D N 300 Mrad, because all OV will be twice ionized. To summarize, the efficiency of the E’centers generation in pure silica by irradiation has been estimated analytically, assuming that ionization is the mechanism for defect creation. The known experimental dose dependence of the concentration of E’centers produced by X-ray irradiation could be explained, and a new feature of this dependence has been predicted. Defect relaxation and etching have not been taken into account, and it is clear that these processes are very important when shortlived defects are considered. We are planning such an investigation. Acknowledgements - I shouid like to thank the Theory Group of the Institute fur Festkorperforschung of the Forschungszentrum Jtilich, where this manuscript was prepared, for hospitality and helpful discussion. Financial support by the Deutsche Forschungsgemeinschaft is also gratefully acknowledged.
E' spins, a.u. (I)
REFERENCES 1. I
I
,
100
300 200 X-Ray Dose, blrad
Fig. 2. E/-spin concentration vs X-ray dose for Suprasil Wl (1) and Suprasil 1 (2). Solid circles, experimental results [6]; lines, theoretical approxima_. I.,.\ non ( 10).
2. 3. 4. 5.
J.I. Janni,
Atomic Data and Nuclear Tables 27, 147 (1982). W. Primak, Phys. Rev. B6,4846 (1972).
Data
K. Tanimura, C. Itoh & N. Itoh, J. Phys. C21, 1869 (1988). T.E. Tsai, D.L. Griscom & E.J. Friebele, Phys. Rev. Lett. 61, 444 (1988). H. Bethe, Ann. der Physik, 5 Folge, Bd. 5, 325 (1930).
Vol. 91, No. 8 6.
EFFICIENCY
OF DEFECTS
D.B. Kerwin & F.L. Galeener, Phys. Rev. Lett. 68, 3208 (1992); D.B. Kerwin, F.L. Galeener, A.J. Miller & J.C. Mikkelsen, Jr., Solid State Commun. 82, 271 (1992).
7. 8.
GENERATION
665
K. Tanimura, T. Tanaka & N. Itoh, Phys. Rev. L&t. 51, 423 (1983). J.C. Ashley & V.E. Anderson, J. Electron. Spectroscop. Relar. Phenom. 24, 127 (1981).