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Thermal evolution of trapped gas from extended subsurface layers during a linear tempering schedule
Vacuum/volume Printed in Great
34/number Britain
0042-207X/84$3.00 Pergamon
6/pages 669 to 672/1994
+ .OO Press Ltd
Thermal evolution of trapped gas from extended subsurface layers during a linear tempering schedule 2 A Iskanderova, T D Radjabov Sciences, Tashkent, USSR received
1 August
and F K Tukfatullin,
Arifov Institute of Electronics, Uzbek Academy of
1983
Numerical computer calculations for the thermal evolution of gas trapped by defects in extended subsurface layers of solids or coatings under a linear tempering schedule have been carried out. The dependence of the shape and location of thermal evolution transients upon the extension (width) of the initially trapped gas distribution has been found in comparison with the case of an initial planar concentration of trapped gas some lattice units below the surface. A comparative study has been performed concerning the effect of the thermal release mechanism (for ‘tandem’ and pure diffusive mechanism) upon the thermal evolution transients having a given initial extended distribution and specific ratios of the migration energy to detrapping energy.
Introduction
The technique of gaseous thermal evolution has been widely used during the last two decades for studying the trapping and release of gases implanted into solids in a wide energy and mass range of bombarding ionsle6. The use of this technique, (for instance, as a method for definition of concentration profiles) has especially increased in recent years in connection with the problem of the first wall of thermonuclear reactors, ion beam modification of materials and radiation damage studies. As the results of experimental and theoretical investigations have shown, the shape and position of maxima in the thermal desorption spectra allow conclusions to be reached concerning gas atom migration and release mechanisms, to obtain desorption and/or diffusion activation energy values and information on gas-defect interactions. Desorption from directly beneath the surface’, thermal diffusion release of implanted gas’** (including the presence of traps’*“) for the various tempering schedules (exponential, reciprocal, linear) have been studied in some theoretical works. A very interesting ‘tandem’-mechanism, the process of gas atom detrapping and subsequent diffusion to the surface by tempering, has also been theoretically investigated’ ‘-’ 3. Analytical solution for such a process is possible only for the case of fast tempering and subsequent target exposure at high temperature”. For the linear tempering schedule it is necessary to use numerical computer calculations’ 3. It should be noted that, in most theoretical papers (e.g. Donnelly et a1i3, where the ‘tandem’-mechanism has been studied) the distribution of implanted gas has been mainly imitated by the gas location at a plane some lattice units below the surface’*‘-iO~’3.Gaussian or similar functionslc16 were used mainly to account for the influence of the implanted gas distribution on the thermal desorption spectra. However, physical conditions
exist under which ion implantation results in the creation of sufficiently extended gas distributions in sub-surface layers or coatings. For example, it may occur as a result of long-time ion implantation into a’hot’ target with significant diffusive ‘broadening’ of the concentration profile, under polyenergetic ion implantation occurring in high voltage gas discharges or at the first wall of thermonuclear devices, or, under film growth during simultaneous ion bombardment. If intensive trapping of the implanted gas atoms by defects may occur under these conditions, then the distribution of the trapped gas (i.e. gas-defect complexes) may also have considerable extension and uniformity. (Such a possibility, for instance, has been theoretically predicted for the case of film deposition under simultaneous ion bombardment1’~i8.) In the present paper theoretical considerations of gas thermal release according to the ‘tandem’-mechanism for extended initial distributions of gas-defect complexes in sub-surface layers and coatings, for the most frequently employed linear tempering schedule T= To + at, have been performed. Such calculations are important both for the correct interpretation of the thermal desorption experimental data and for the determination of the intensity and temperature ranges for the retention and release of gas trapped in sufficiently ‘thick’ sub-surface layers or coatings.
Theoretical considerations
An initial extended distribution of complexes in the first approximation is described by the following function: n,=O, n(X)=
XP,
no
1 (P2--PI)’
PI
(1) 669
.? A lskenderova,
T D Radjabov
and F K Tukfatullin:
Thermal
evolution
where no is the total number of the implanted gas atoms, trapped by defects; pr and p2 are the minimum and maximum depths for the location of complexes under the surface, in lattice units i.. It is assumed13, that the release of gas atoms into the diffusive continuum is first order in the gas concentration: dn -_= dT
kc
-
Q/RP(r)
(2)
-ane
where n is the concentration of the trapped gas at the temperature T(t); k, is the rate constant; Q is the activation energy for detrapping; a is the linear ramp rate; R is the gas constant. The diffusion of the ‘free’ atoms is described by the equation:
$ =o(t)%+A,,
n
of trapped
gas
rate range from l-2 up to 50 K s- ’ with appropriate normahzation of the total quantity of the trapped gaseous atoms. Results and discussion As the results obtained show (Figure 1), an initial width of the trapped gas distribution extending over tens of atomic layers practically has almost no influence on the transient shape and temperature of maximum release rate 7, for the ‘tandem’mechanism for release at various Q and E values (the complete coincidence of our results in curves 2,3,4 with those of Donnelly et a/r3 for a plane distribution of complexes under the surface is strong evidence for the correctness of our computing program).
e-QikT(fJ
where C(X, t) is the concentration of freely diffusible atoms; D(r) = D,e- E’RT(” is the gas diffusion coefficient with preexponential D,, =f k. A2 (where i. is the lattice constant) and activation energy for diffusion E. The boundary conditions: c=o, c=o,
x=0 x=co
(4)
correspond to the permeable surface of a semi-infinite target. The evolution rate of gas from the surface was numerically calculated using the solution of equations (2) and (3) with the boundary conditions (4) according to an approach, suggested by Donnelly et aI’ 3 for the case of thermal release of gas, trapped by defects in a plane at the definite depth I lattice units below the surface. A method, suggested by Donnelly et a113,is based on using the solution of equation (3) without the last term and is obtained by substitution T e- EIRT’ dT’ Z=1 r a UT, and subsequent concentration
substitution in this solution of the initial C, of the freely diffusible gas for the relation
Figure 1. Evolution transient resulting from detrapping and diffusion for ‘plane’ (-, p= 10) and ‘narrow’ (- - -, p= 5, p= 15) depth distributions of the trapped gas: Q=1.5eV, E=1.2eV (1, 1’); Q=2.0eV, E (cVI= 1.2 (2, 2’); 1.6 (3, 3’); 1.8 (4, 4’). (. equation (6).
T-dT
I p,=q= ’
p=p,
T=O
X=0
IO
’
(P2*’
{CCX,2, (T, To)l-CL-X,
3 P, -10 P,=20 2F;=IO Pz= too 4 y-10 P,=200
Z (T-dT,
To)]).
A program for numerical calculations using an ES-2622-a computer was compiled on the basis of expression (5). A computing increment of 1 K was used for the summation over temperature, and the increment of one atomic layer was used for the summation over the distribution depth. The accuracy of the total quantity of released gas was N 10e6 from the total trapped gas value. Calculations according to this program were performed for a wide range of inputs Q and E for an initial distribution extension from tens up to hundreds of atomic layers for the ramp 670
E=IGeV a-20 K S-’
m
P(T,=CCC
function, see
Figure 2 shows the evolution transients resulting from fixed Q and E values (Q=2 eV, E= 1.6 eV), but for various widths of initial distributions of complexes, including those extending over hundreds of atomic layers. Calculations show that the increase of the initial distribution to hundreds of atomic layers results in a significant decrease of the thermal release intensity (curves 2, 3 and 4) by a factor of two or more, the transient broadening and
In order to obtain the evolution rate of gas at the surface p(T) as a function of time, numerical integration of the solution (by finite differences) over X and T have been carried out. A similar method of calculation in our case, i.e. for an extended initial distribution of complexes (type (l)), results in the final expression: p2
.)-detrapping
Temperature
( K)
Figure 2. Variation of evolution transient with the ‘width’ of initially
trapped gas distribution.
Z A Iskanderova, T D Radjabov and F K Tukfatullin: Thermal evolution of trapped
the release rate maximum moving to a higher temperature range. For instance, with an initial distribution width from pi = 10 to p2 = 200 atomic layers (curve 4), T,,, increases almost by ~100 K in comparison to the case of a ‘narrow’ distribution, pi = 10, p2= 20. Figure 3 illustrates the influence of the initial distribution I
10314 -
I3 -;
s
gas
release transients, in particular, the T,,, value is sufficiently well revealed under such a replacement scheme which can be used in the computer treatment of experimental results. In addition to the calculations performed for the influence of distribution width on the transients under the ‘tandem’mechanism, a comparable investigation of the influence of thermal release mechanism upon the shape and location of the transients for the same initial distribution width is of interest. Figure 5 represents the results for the pure diffusive release
,2-
,, -
x lo-;
e IO-
A I
a=20KS’
K=l@S“
loo 800 900 lcm 1100 I200 Temperature ( K)
Figure 3. Variation of evolution transient with the activation energy of diffusion E for “plane” (p= 10) and ‘extended’ (- - -, p, = 10, p2= 100) initially trapped gas d&ribution. Q=2.0 eV, E= 1.6 eV (1, 1’); 1.8 eV (2, 2’); 2.0 eV (3, 3’).
Tempemture
(K)
Figure 5. Transient resulting from ‘tandem’-mechanism with Q = 2.0 eV
extension on the transients for a fixed Q value, but for various .& values. Two families of curves for thermal evolution are calculated according to the ‘plane’ distribution with p= 10 and an extended distribution of p, = 10 to p2 = 100. The transient broadening and shift AT,,, to the higher temperatures, while making a transition from a ‘plane’distribution to an extended one, is greater, the larger is the E value. Thus, for instance, for the curves 1 and 1’ (E= 1.6 eV), AT,,, is of order tens of degrees (-30 K), for the curves 3 and 3’ (E= 2.0 eV) the shift AT,,, is more than a hundred degrees (- 130 K). It should be noted that calculation of thermal release according to our program for extended distributions requires considerably more computer time, an order of magnitude greater than for the case of ‘plane’ distributions. In this connection a series of computer experiments with the extended distribution replaced by an equal gas quantity located in the plane at the middle of the initial distribution were carried out, as well as the variation of pi and p2 location relative to this plane. Figure 4 illustrates the main characteristics for the thermal
Q=2eV E=l6eV a=20 K~S+K~Id%-’
) and ‘diffusive’ mechanism (---) for ‘extended’ initial gas (---distribution (p, = 5, p2= 100). E Cev,=1.0 (1, 1’); 1.6 (2, 2’); 2.0 (3, 3’).
mechanism (based on Begrambekov et ~1’~) for E = 2.0 eV and for a ‘tandem’-mechanism for Q = 2.0 eV, and corresponding E values at pi = 5, pz = 100 atomic layers. The differences in thermal release curves at E/Q _ 1 for both mechanisms at the extended distribution are negligible (curves 2 and 2’, 3 and 3’), i.e. these curves are mainly determined by the diffusive activation energy E and p2-p1 values. For E considerably lower than Q (curve 1, Q=2.0 eV, E= 1.0 eV), the thermal desorption curve practically coincides with the ‘source’ function :
(6) which is independent of E and pl, pz values, i.e. it does not contain information about these parameters. A ‘sharp’ and ‘narrow’ peak characterizes the first order process which is dependent only on the activation energy of detrapping, Q, at the given ramp rate, a. It is located (curve 1) in the temperature range between corresponding curves for diffusive release with E = 1.0 eV (curve 1’) and E = 2.0 eV (curve 3’).
Conclusions
Temperabe
1K I
Figure 4. Evolution transient resulting from various initially trapped gas distributions with a ‘centre’ of ‘masses at the depth p= 100.
A detailed analysis of the influence of the extended initial distribution of gas, trapped by defects, on the thermal release spectra has been carried out. The results show that distribution of complexes over a width of tens of atomic layers does not influence the shape and location of thermal release curves in comparison to the case of gas location in a plane at a corresponding depth under 671
Z A lskanderova,
T D Radjabov
and F K Tukfatullin:
Thermal evolution of trapped gas
the surface. This fact creates a basis for application of the results’3 to the treatment and discussion of the experiments on thermal release after relatively low energy ion implantation, where the profile ‘width’ is small. The distribution extension over the order of hundreds of atomic layers, in comparison with ‘plane’ location. results essentially in spectral broadening and a shift of the maximum of the thermal release rate to the higher temperature range, and these changes are correlated with the higher widths of initial distribution of complexes and diffusion activation energy value. Such important characteristics for thermal evolution transients as the ‘peak’location, i.e. T,,,value, may be defined with a good accuracy by model calculations, based on replacement of the extended distributions by the same quantity of complexes, located at a plane at the middle of the initial distribution. This result may be used for computer treatment of experimental data,
essentially minimizing the computer calculation time. A comparable investigation of the influence of thermal release mechanism on the main characteristics of thermal desorption spectra at the given initial trapped gas distribution width is carried out. It is shown that at E/Q - 1 thermal evolution curves for a ‘tandem’ mechanism are nearly the same, conditioned by the pure diffusive mechanism with the same E value, at the corresponding given initial distribution extension p2-pI, i.e. these transients are mainly defined by the diffusion activation energy E and pz-p, value. For E values considerably lower than Q (for example, E/QrO.S), the transients correspond to the first order process with the detrapping activation energy Q, but are independent of p2-p1 and E values. The regularities and peculiarities revealed should be used both for correct treatment of
672
thermal desorption experimental data, and for definition or prediction of the temperature range for preferential retention and release of implanted gases.
References
’ G Carter and J S Colligon. Ion bombnrdmenr of solids, Hememann, London (1968). ’ U A Arifov and T D Radjabov, Sorption processes under charged particles interaction with solid surfaces, Tashkent (1974). 3 G Farrell and S E Donnelly, J Nucl Mat, 76/77, 322 (1978). 4 S E Donnelly, Vacuum, 28, 163 (1978). ’ A A van Gorkum and S V Kornelsen, Rad E/t 42, 93 (1979). 6 S V Kornelsen and A A van Gorkum, Rad ,t& 42, 113 (1979). ’ G Farrell. W A Grant. K Erents and G Carter. Vacuum. 16. 295 (19661. ’ G Farrell and G Carter, Vacuum, 17, 15 (1966). 9 G Carter, Vacuum, 26, 21 (1976). ” S E Donnelly and D G Armour, Vacuum, 27, 21 (1976). ” G Carter, B J Evans and G Farrell, Vacuum, 25, 197 (1975). ‘* Z A Iskanderova and E 0 Arutjunova, Proc Symp Interacrionoj Atomic Particles wirh Solid Surface, dedicated to the memory of academic U A Arifov, Tashkent. p 202 (1979). I3 S E Donnelly and D C Ingram, Vacuum, 28, 69 (1977). ” L B Begrambekov, V A Kurnaev, A A Pisarev, V M Sotnikov and V G Telkovski, Aromic Energy, 31, 625 (1971). I5 A A Pisarev and V A Pisarev, Atomic Energy, 37, 340 (1974). I6 G Carter and S E Donnelly, Vacuum, 29, 303 (1978). ” T D Radjabov, Z A Iskaqderova, E 0 Arutjunova and K Samigulin, Zh Techn Fiz, 52, 2238 (1982). ‘* Z A Iskanderova, L F Lifanova and 1‘ D Radjabov, Vacuum. 32,269 (1982).
34/number Britain
0042-207X/84$3.00 Pergamon
6/pages 669 to 672/1994
+ .OO Press Ltd
Thermal evolution of trapped gas from extended subsurface layers during a linear tempering schedule 2 A Iskanderova, T D Radjabov Sciences, Tashkent, USSR received
1 August
and F K Tukfatullin,
Arifov Institute of Electronics, Uzbek Academy of
1983
Numerical computer calculations for the thermal evolution of gas trapped by defects in extended subsurface layers of solids or coatings under a linear tempering schedule have been carried out. The dependence of the shape and location of thermal evolution transients upon the extension (width) of the initially trapped gas distribution has been found in comparison with the case of an initial planar concentration of trapped gas some lattice units below the surface. A comparative study has been performed concerning the effect of the thermal release mechanism (for ‘tandem’ and pure diffusive mechanism) upon the thermal evolution transients having a given initial extended distribution and specific ratios of the migration energy to detrapping energy.
Introduction
The technique of gaseous thermal evolution has been widely used during the last two decades for studying the trapping and release of gases implanted into solids in a wide energy and mass range of bombarding ionsle6. The use of this technique, (for instance, as a method for definition of concentration profiles) has especially increased in recent years in connection with the problem of the first wall of thermonuclear reactors, ion beam modification of materials and radiation damage studies. As the results of experimental and theoretical investigations have shown, the shape and position of maxima in the thermal desorption spectra allow conclusions to be reached concerning gas atom migration and release mechanisms, to obtain desorption and/or diffusion activation energy values and information on gas-defect interactions. Desorption from directly beneath the surface’, thermal diffusion release of implanted gas’** (including the presence of traps’*“) for the various tempering schedules (exponential, reciprocal, linear) have been studied in some theoretical works. A very interesting ‘tandem’-mechanism, the process of gas atom detrapping and subsequent diffusion to the surface by tempering, has also been theoretically investigated’ ‘-’ 3. Analytical solution for such a process is possible only for the case of fast tempering and subsequent target exposure at high temperature”. For the linear tempering schedule it is necessary to use numerical computer calculations’ 3. It should be noted that, in most theoretical papers (e.g. Donnelly et a1i3, where the ‘tandem’-mechanism has been studied) the distribution of implanted gas has been mainly imitated by the gas location at a plane some lattice units below the surface’*‘-iO~’3.Gaussian or similar functionslc16 were used mainly to account for the influence of the implanted gas distribution on the thermal desorption spectra. However, physical conditions
exist under which ion implantation results in the creation of sufficiently extended gas distributions in sub-surface layers or coatings. For example, it may occur as a result of long-time ion implantation into a’hot’ target with significant diffusive ‘broadening’ of the concentration profile, under polyenergetic ion implantation occurring in high voltage gas discharges or at the first wall of thermonuclear devices, or, under film growth during simultaneous ion bombardment. If intensive trapping of the implanted gas atoms by defects may occur under these conditions, then the distribution of the trapped gas (i.e. gas-defect complexes) may also have considerable extension and uniformity. (Such a possibility, for instance, has been theoretically predicted for the case of film deposition under simultaneous ion bombardment1’~i8.) In the present paper theoretical considerations of gas thermal release according to the ‘tandem’-mechanism for extended initial distributions of gas-defect complexes in sub-surface layers and coatings, for the most frequently employed linear tempering schedule T= To + at, have been performed. Such calculations are important both for the correct interpretation of the thermal desorption experimental data and for the determination of the intensity and temperature ranges for the retention and release of gas trapped in sufficiently ‘thick’ sub-surface layers or coatings.
Theoretical considerations
An initial extended distribution of complexes in the first approximation is described by the following function: n,=O, n(X)=
X
no
1 (P2--PI)’
PI
(1) 669
.? A lskenderova,
T D Radjabov
and F K Tukfatullin:
Thermal
evolution
where no is the total number of the implanted gas atoms, trapped by defects; pr and p2 are the minimum and maximum depths for the location of complexes under the surface, in lattice units i.. It is assumed13, that the release of gas atoms into the diffusive continuum is first order in the gas concentration: dn -_= dT
kc
-
Q/RP(r)
(2)
-ane
where n is the concentration of the trapped gas at the temperature T(t); k, is the rate constant; Q is the activation energy for detrapping; a is the linear ramp rate; R is the gas constant. The diffusion of the ‘free’ atoms is described by the equation:
$ =o(t)%+A,,
n
of trapped
gas
rate range from l-2 up to 50 K s- ’ with appropriate normahzation of the total quantity of the trapped gaseous atoms. Results and discussion As the results obtained show (Figure 1), an initial width of the trapped gas distribution extending over tens of atomic layers practically has almost no influence on the transient shape and temperature of maximum release rate 7, for the ‘tandem’mechanism for release at various Q and E values (the complete coincidence of our results in curves 2,3,4 with those of Donnelly et a/r3 for a plane distribution of complexes under the surface is strong evidence for the correctness of our computing program).
e-QikT(fJ
where C(X, t) is the concentration of freely diffusible atoms; D(r) = D,e- E’RT(” is the gas diffusion coefficient with preexponential D,, =f k. A2 (where i. is the lattice constant) and activation energy for diffusion E. The boundary conditions: c=o, c=o,
x=0 x=co
(4)
correspond to the permeable surface of a semi-infinite target. The evolution rate of gas from the surface was numerically calculated using the solution of equations (2) and (3) with the boundary conditions (4) according to an approach, suggested by Donnelly et aI’ 3 for the case of thermal release of gas, trapped by defects in a plane at the definite depth I lattice units below the surface. A method, suggested by Donnelly et a113,is based on using the solution of equation (3) without the last term and is obtained by substitution T e- EIRT’ dT’ Z=1 r a UT, and subsequent concentration
substitution in this solution of the initial C, of the freely diffusible gas for the relation
Figure 1. Evolution transient resulting from detrapping and diffusion for ‘plane’ (-, p= 10) and ‘narrow’ (- - -, p= 5, p= 15) depth distributions of the trapped gas: Q=1.5eV, E=1.2eV (1, 1’); Q=2.0eV, E (cVI= 1.2 (2, 2’); 1.6 (3, 3’); 1.8 (4, 4’). (. equation (6).
T-dT
I p,=q= ’
p=p,
T=O
X=0
IO
’
(P2*’
{CCX,2, (T, To)l-CL-X,
3 P, -10 P,=20 2F;=IO Pz= too 4 y-10 P,=200
Z (T-dT,
To)]).
A program for numerical calculations using an ES-2622-a computer was compiled on the basis of expression (5). A computing increment of 1 K was used for the summation over temperature, and the increment of one atomic layer was used for the summation over the distribution depth. The accuracy of the total quantity of released gas was N 10e6 from the total trapped gas value. Calculations according to this program were performed for a wide range of inputs Q and E for an initial distribution extension from tens up to hundreds of atomic layers for the ramp 670
E=IGeV a-20 K S-’
m
P(T,=CCC
function, see
Figure 2 shows the evolution transients resulting from fixed Q and E values (Q=2 eV, E= 1.6 eV), but for various widths of initial distributions of complexes, including those extending over hundreds of atomic layers. Calculations show that the increase of the initial distribution to hundreds of atomic layers results in a significant decrease of the thermal release intensity (curves 2, 3 and 4) by a factor of two or more, the transient broadening and
In order to obtain the evolution rate of gas at the surface p(T) as a function of time, numerical integration of the solution (by finite differences) over X and T have been carried out. A similar method of calculation in our case, i.e. for an extended initial distribution of complexes (type (l)), results in the final expression: p2
.)-detrapping
Temperature
( K)
Figure 2. Variation of evolution transient with the ‘width’ of initially
trapped gas distribution.
Z A Iskanderova, T D Radjabov and F K Tukfatullin: Thermal evolution of trapped
the release rate maximum moving to a higher temperature range. For instance, with an initial distribution width from pi = 10 to p2 = 200 atomic layers (curve 4), T,,, increases almost by ~100 K in comparison to the case of a ‘narrow’ distribution, pi = 10, p2= 20. Figure 3 illustrates the influence of the initial distribution I
10314 -
I3 -;
s
gas
release transients, in particular, the T,,, value is sufficiently well revealed under such a replacement scheme which can be used in the computer treatment of experimental results. In addition to the calculations performed for the influence of distribution width on the transients under the ‘tandem’mechanism, a comparable investigation of the influence of thermal release mechanism upon the shape and location of the transients for the same initial distribution width is of interest. Figure 5 represents the results for the pure diffusive release
,2-
,, -
x lo-;
e IO-
A I
a=20KS’
K=l@S“
loo 800 900 lcm 1100 I200 Temperature ( K)
Figure 3. Variation of evolution transient with the activation energy of diffusion E for “plane” (p= 10) and ‘extended’ (- - -, p, = 10, p2= 100) initially trapped gas d&ribution. Q=2.0 eV, E= 1.6 eV (1, 1’); 1.8 eV (2, 2’); 2.0 eV (3, 3’).
Tempemture
(K)
Figure 5. Transient resulting from ‘tandem’-mechanism with Q = 2.0 eV
extension on the transients for a fixed Q value, but for various .& values. Two families of curves for thermal evolution are calculated according to the ‘plane’ distribution with p= 10 and an extended distribution of p, = 10 to p2 = 100. The transient broadening and shift AT,,, to the higher temperatures, while making a transition from a ‘plane’distribution to an extended one, is greater, the larger is the E value. Thus, for instance, for the curves 1 and 1’ (E= 1.6 eV), AT,,, is of order tens of degrees (-30 K), for the curves 3 and 3’ (E= 2.0 eV) the shift AT,,, is more than a hundred degrees (- 130 K). It should be noted that calculation of thermal release according to our program for extended distributions requires considerably more computer time, an order of magnitude greater than for the case of ‘plane’ distributions. In this connection a series of computer experiments with the extended distribution replaced by an equal gas quantity located in the plane at the middle of the initial distribution were carried out, as well as the variation of pi and p2 location relative to this plane. Figure 4 illustrates the main characteristics for the thermal
Q=2eV E=l6eV a=20 K~S+K~Id%-’
) and ‘diffusive’ mechanism (---) for ‘extended’ initial gas (---distribution (p, = 5, p2= 100). E Cev,=1.0 (1, 1’); 1.6 (2, 2’); 2.0 (3, 3’).
mechanism (based on Begrambekov et ~1’~) for E = 2.0 eV and for a ‘tandem’-mechanism for Q = 2.0 eV, and corresponding E values at pi = 5, pz = 100 atomic layers. The differences in thermal release curves at E/Q _ 1 for both mechanisms at the extended distribution are negligible (curves 2 and 2’, 3 and 3’), i.e. these curves are mainly determined by the diffusive activation energy E and p2-p1 values. For E considerably lower than Q (curve 1, Q=2.0 eV, E= 1.0 eV), the thermal desorption curve practically coincides with the ‘source’ function :
(6) which is independent of E and pl, pz values, i.e. it does not contain information about these parameters. A ‘sharp’ and ‘narrow’ peak characterizes the first order process which is dependent only on the activation energy of detrapping, Q, at the given ramp rate, a. It is located (curve 1) in the temperature range between corresponding curves for diffusive release with E = 1.0 eV (curve 1’) and E = 2.0 eV (curve 3’).
Conclusions
Temperabe
1K I
Figure 4. Evolution transient resulting from various initially trapped gas distributions with a ‘centre’ of ‘masses at the depth p= 100.
A detailed analysis of the influence of the extended initial distribution of gas, trapped by defects, on the thermal release spectra has been carried out. The results show that distribution of complexes over a width of tens of atomic layers does not influence the shape and location of thermal release curves in comparison to the case of gas location in a plane at a corresponding depth under 671
Z A lskanderova,
T D Radjabov
and F K Tukfatullin:
Thermal evolution of trapped gas
the surface. This fact creates a basis for application of the results’3 to the treatment and discussion of the experiments on thermal release after relatively low energy ion implantation, where the profile ‘width’ is small. The distribution extension over the order of hundreds of atomic layers, in comparison with ‘plane’ location. results essentially in spectral broadening and a shift of the maximum of the thermal release rate to the higher temperature range, and these changes are correlated with the higher widths of initial distribution of complexes and diffusion activation energy value. Such important characteristics for thermal evolution transients as the ‘peak’location, i.e. T,,,value, may be defined with a good accuracy by model calculations, based on replacement of the extended distributions by the same quantity of complexes, located at a plane at the middle of the initial distribution. This result may be used for computer treatment of experimental data,
essentially minimizing the computer calculation time. A comparable investigation of the influence of thermal release mechanism on the main characteristics of thermal desorption spectra at the given initial trapped gas distribution width is carried out. It is shown that at E/Q - 1 thermal evolution curves for a ‘tandem’ mechanism are nearly the same, conditioned by the pure diffusive mechanism with the same E value, at the corresponding given initial distribution extension p2-pI, i.e. these transients are mainly defined by the diffusion activation energy E and pz-p, value. For E values considerably lower than Q (for example, E/QrO.S), the transients correspond to the first order process with the detrapping activation energy Q, but are independent of p2-p1 and E values. The regularities and peculiarities revealed should be used both for correct treatment of
672
thermal desorption experimental data, and for definition or prediction of the temperature range for preferential retention and release of implanted gases.
References
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