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Crystallization kinetics of thermally evaporated As45.2Te46.6In8.2 thin films
Applied Surface Science 137 Ž1999. 150–156
Crystallization kinetics of thermally evaporated As 45.2Te 46.6 In 8.2 thin films A.H. Moharram ) , M.M. Hafiz, A.A. Abu-Sehly Physics Department, Assiut UniÕersity, Assiut, Egypt Received 11 May 1998; accepted 26 August 1998
Abstract Glassy As 45.2Te 46.6 In 8.2 thin films were thermally evaporated onto chemically cleaned glass substrates. Crystallization kinetics were determined under isothermal conditions. Heating the film up to the isothermal temperature with different rates was found to yield films with different electrical characterization. Conductivity of the investigated film was used as a parameter indicating the crystallized fraction x Ž t .. The obtained values of the activation energy for crystallization, the frequency factor and the Avrami index are Ž100 " 0.5. kJrmol, Ž7.31 " 0.04. 10 8 sy1 and 1.45, respectively. The non-integer value of the Avrami index indicates that two crystallization mechanisms are responsible for the crystal growth. q 1999 Elsevier Science B.V. All rights reserved. Keywords: As 45.2Te 46.6 In 8.2 thin films; Crystallization kinetics; Conductivity
1. Introduction Thermally activated transformations in the solid state can be investigated by isothermal or non-isothermal experiments w1x. For non-isothermal analysis at constant heating rate the crystallization kinetics can be determined using different methods w2,3x. The approximations used in the derivation of the so-called Kissinger w4x and Ozawa w5x methods introduce significant inaccuracies in determination of the overall activation energy for crystallization. Applying a new method w6x gives values an order of magnitude more accurate than the Kissinger and Ozawa methods. In our recent work w7x, a simple and approximation-free method was applied to calculate the crystallization )
Corresponding author. Fax: q20-88312-564; E-mail: [email protected]
kinetics of a glassy specimen from only one DSC scan. In the isothermal method, the sample is brought quickly to a temperature slightly below the onset temperature of crystallization, Tc , and the heat evolved during the crystallization process at a constant temperature is recorded as a function of time. The isothermal crystallization data are usually interpreted in terms of the Johnson–Mehl–Avrami ŽJMA. theoretical model w2x in which the fraction of precursor that has been transformed into the product phase as a function of time Ž t . is given by
x Ž t . s 1 y exp y Ž Kt .
n
Ž 1.
where n the Avrami exponent, which reflects the characteristics of nucleation and the growth process, is found to be constant over a substantial range of temperatures and K the rate constant, which reflects the rates of both nucleation and growth, is usually
0169-4332r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 4 6 7 - X
A.H. Moharram et al.r Applied Surface Science 137 (1999) 150–156
assumed to have an Arrhenian temperature dependence w8x, K s K 0 exp Ž yErRT .
Ž 2.
where the pre-exponential term K 0 Žsy1 . is the frequency factor and E ŽkJrmol. is the activation energy describing the overall crystallization process. The crystallization process is generally well understood when the three kinetic parameters E, n and K 0 are determined. It is important to emphasize that the aforementioned JMA model was formulated only to describe the isothermal transformations. The crystallization kinetics of glassy films can not be determined from the DSC experiments. Therefore, any physical quantity which changes measurably upon crystallization can be taken as a characteristic parameter to evaluate x as a function of time. DC conductivity was found w9–11x to be a suitable parameter in chalcogenide glasses. Since the conductivity of these glasses increases by several orders of magnitude on crystallization, ln s represents the sensitive parameter characterizing crystallization rather than s itself as confirmed by Kotkata et al. w12x. It is worthy to state that a simple ohmmeter may be sufficient for the present technique. Another advantage is that the electrical characterization in addition to the crystallization kinetics have been obtained. The calculation of crystallization kinetics from the conductivity data was applied previously w12,13x for films evaporated from binary alloys. However, in the present work, the investigated films are thermally evaporated from a ternary alloy. A single activation energy for conduction over an extended temperature range is required to get accurate values for crystallization kinetics of the investigated film. Chalcogenide As 45.2Te 46.6 In 8.2 film was found to be a suitable material for the present experiment.
2. Experimental Bulk material was prepared by the well established melt–quench technique. Thin films were thermally evaporated onto ultrasonically cleaned glass substrates, using an Edward E 306 coating system operated at 5 = 10y6 Torr. The evaporation source was fragments of the bulk As 46 Te 46 In 8 materials.
151
The substrate temperature was kept at room temperature during the evaporation process. The evaporation rate as well as the thickness of the investigated films were controlled using a quartz crystal monitor Ed˚ ward FTM5. A constant evaporation rate Ž; 5 A sy1 . was used to deposit 120 nm thick films. Electrical resistivity measurements were done using specimens with evaporated gold gap Ž2 = 10 mm. electrodes. Keithley 610 C electrometer was used as ohmmeter. To avoid oxidation of the sample, the measurements were taken under vacuum ; 10y3 Torr by mounting the sample in a specially designed metallic sample holder inside a Tohr cryogenic cryostat. The temperature was measured using a calibrated copper constantan thermocouple. The annealing temperature was obtained using a fixed heating rate Ž; 10 Krmin. and then maintained constant till the conductivity reaches a limiting value. The morphology and structure of the deposited films were analyzed using Jeol 2000 transmission electron microscope ŽTEM. operated at 100 kV. Freshly evaporated as well as thermally annealed films were floated off substrates precoated with NaCl and carbon films. They were floated by immersion in distilled water, then transferred to copper microscope grids. Thermal treatment for TEM experiments was performed under vacuum ; 10y3 Torr.
3. Results A typical DSC curve of the bulk As 46 Te 46 In 8 glass in powdered form, using a Shimadzu TA-50 differential scanning calorimetry at a heating rate of 10 Krmin, is shown in Fig. 1. Three characteristic phenomena are clear in the studied temperature range. The first one ŽTg s 434.4 K, endo. corresponds to the glass transition temperature, the second one ŽTc s 486.5 K, exo. to the onset temperature of crystallization and the last one to the peak temperature of crystallization ŽTp s 524.4 K.. The slight shoulder appeared in the left-hand side of the exothermic peak means that more than one crystalline phase are growing during the DSC run. Thin films were thermally evaporated from fragments of the bulk As 46 Te 46 In 8 material. The glassy state was expected for the as-prepared films since the quenching rate during deposition process is much
152
A.H. Moharram et al.r Applied Surface Science 137 (1999) 150–156
Fig. 1. A typical DSC curve of the bulk As 46 Te 46 In 8 specimen at a heating rate 10 Krmin.
higher than that of the bulk alloy made from the melt. The composition of the evaporated films was investigated using a computerized energy dispersive X-ray ŽLink Analytical Edx. spectroscopy. The atomic percentages of the As, Te and In in the as-prepared films were found to be 45.2, 46.6, and 8.2, respectively. A small deviation between the composition of the starting bulk As 46 Te 46 In 8 material and the evaporated films was kept constant using ˚ sy1 .. a low evaporation rate Ž; 5 A To study the temperature dependence of the electrical conductivity of the as-prepared As 45.2Te 46.6 In 8.2 specimen, films of 120 nm thick were deposited onto glass substrates held at room temperature. Measurements were carried out during heating the specimen. Fig. 2 shows the temperature dependence of the electrical conductivity of the as-prepared film. A constant rate of 3.0 Krmin was used to heat up the specimen. Two regions ŽI and II. of ln s vs. 1rT plot are shown in the figure. In the first region, which extends from room temperature up to the onset temperature of crystallization, the conductivity varies with temperature according to the Arrhrenian relation s s s 0 expŽyD ErkT ., where s 0 is the pre-exponential factor and D E the activation energy for conduction. After reaching a certain temperature, called the onset temperature of crystallization, the conductivity deviates to higher values than expected as indicated by the second region ŽII.. The small difference between the Tc values obtained from the DSC experiment ŽTc s 486.5 K. and that from the
conductivity data ŽTc s 484 K. of Fig. 2 can be mainly attributed to the heating rate dependence of the Tc value. A result which indicates that the elemental compositions of the bulk material and its evaporated thin films are nearly the same. Heating the specimen at different rates was found to change the slope and intercept of ln s vs. 1rT plot, which means that the values of D E and s 0 are dependent on the heating rate. Fig. 3 shows the monotonic increase of D E and s 0 with increasing the heating rate. Because of this result, only one heating rate, e.g., ; 10 Krmin was used to heat the investigated films to the required isothermal temperatures. Fig. 4 shows the time dependent of the electrical conductivity measured for an amorphous film during isothermal heating at T s 488 K. It is clear that the conductivity increases with time. The transformation from amorphous to crystalline state occurs in three stages represented by AB, BC and CD as shown in the figure. Part AB is linear with time and represents a gradual increase of s as a result of normal heating of the sample. Part BC represents a gradual but less pronounced increase in s which may due to nucleation of the crystalline phase. The CD part shows a
Fig. 2. Temperature dependence of the electrical conductivity of the As 45.2Te 46.6 In 8.2 film heated at constant rates 3.0 Krmin Žthickness of the film s120 nm..
A.H. Moharram et al.r Applied Surface Science 137 (1999) 150–156
Fig. 3. Dependence of the conductivity pre-exponential factor and the activation energy for conduction on the heating rate of the As 45.2Te 46.6 In 8.2 films.
sharp rise in s resulting from rapid growth of the crystalline state. A process which is accompanied by the liberation of heat energy associated with the transition from non-equilibrium to equilibrium thermodynamic state. CD attains a limiting value after certain time Žpoint D.. The point C represents the amorphous state and D corresponds to the complete crystalline state. At any intermediate point ŽI., the conductivity corresponds to a mixture of amorphous and crystalline state. According to Kotkata et al. w12x, the experimental values of ln s was used to determine the value of x Ž t . at any intermediate time by the relation
x Ž t . s w ln s y ln sa x r w ln sc y ln sa x
153
of few sharp rings in the SAED of Fig. 5b. Isothermal growth of crystallization leads to creation of other sharp rings in Fig. 5c. The non-indexed spots shown in the outer rings could be caused from the different crystalline phases. The diffraction pattern of Fig. 5c corresponds to the point D where the crystallized fraction covers most of the amorphous matrix and the electrical conductivity reaches its maximum value. In a parallel work w14x, the crystalline phases resulting from thermal annealing of the As 45.2Te 46.6 In 8.2 films were identified as As 2Te 3 and AsIn phases. Fig. 6 shows the crystallized fraction vs. time x Ž t . plots at four different isothermal temperatures. Increasing the annealing temperature increases the steepness of the resulting curve which means that the crystallization process proceeds faster at higher temperatures than that at lower ones. Taking logarithms and rearranging Eq. Ž1. gives ln yln Ž 1 y x . s n ln K q n ln t.
Ž 4.
Following the above equation, a plot of lnwylnŽ1 y x .x vs. ln t at constant temperature or constant K value should yield a straight line. The degree of constancy of K will specify the possibility limits of using ln s as a parameter for the crystallization rate.
Ž 3.
where sc and sa are the conductivities of the crystalline and amorphous phases having volume fractions x and Ž1 y x ., respectively, and s is the conductivity of a mixture during amorphous to crystalline transformation. To follow up the structure transformations, three identical films were examined by TEM. The films were thermally treated in the same way as the points C, I and D of Fig. 4. The diffuse rings appeared in the SAED of Fig. 5a, confirms the amorphous state of the films which heat treated up to the point C. Increasing the time of annealing to an intermediate point ŽI. enhances the amorphous-crystalline transformations inside the investigated film. The crystallized fraction Ž x . is responsible for the appearance
Fig. 4. Time dependence of the electrical conductivity of the As 45.2Te 46.6 In 8.2 film heated to the isothermal temperature 488 K.
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A.H. Moharram et al.r Applied Surface Science 137 (1999) 150–156
investigated films. The value of n s 1.45 lies near midway between the two integers 1.0 and 2.0 means that the two crystallization mechanisms are working simultaneously with nearly equal share. From Fig. 7, the intercept of the straight line measured at a certain temperature with the lnwylnŽ1 y x .x axis gives the value of nln K corresponding to that temperature. The activation energy for crystal-
Fig. 5. SAED patterns of three As 45.2Te 46.6 In 8.2 films heated to the points C, I and D of Fig. 4, respectively.
Fig. 7 shows the straight lnwylnŽ1 y x .x vs. ln t plots at four different isothermal temperatures. It is obvious that the slope of the straight line, and consequently the n-value, is nearly temperature independent. The average value of n, calculated from Fig. 7, for the glassy As 45.2Te 46.6 In 8.2 films was found to be 1.45. This non-integer value indicates that two mechanisms, one- and two-dimensional growth w15,16x, are responsible for the crystallization process in the
Fig. 6. Crystallized fractions calculated from the conductivity data vs. time x Ž t . at four different isothermal temperatures.
A.H. Moharram et al.r Applied Surface Science 137 (1999) 150–156
Fig. 7. lnwylnŽ1y x .x vs. ln t plots for the As 45.2Te 46.6 In 8.2 films at four different isothermal temperatures.
lization of the investigated film can be obtained by plotting the Arrhenian temperature dependence of the reaction rate Ž K .. Fig. 8 shows the ln K vs. 1000rT representation and the obtained values of the frequency factor and the activation energy for crystallization are Ž7.31 " 0.04.10 8 sy1 and 100 " 0.5 kJrmol, respectively. Another approach proposed by Marseglia w17x was applied to, check the validity of the obtained results, determine the activation energy for crystallization. Accordingly, the time required for x s 1r2 can be
155
Fig. 9. ln t1r 2 vs. 1000r T plot for the As 45.2Te 46.6 In 8.2 films.
given by substituting for K s K 0 expŽyErRT . into Eq. Ž4. and rearranging it as follows ln t 1r2 s const.q ErRT
Ž 5.
a plot of ln t 1r2 as a function of 1rT will give the value of the activation energy for crystallization. With the isothermal hold method, the plot of ln t 1r2 vs. 1rT is shown in Fig. 9. Multiplying R by the least squares line yields the activation energy for crystallization of E s 100.34 kJrmol. A result which is in good agreement with that obtained from Fig. 8.
4. Conclusions
Fig. 8. ln K vs. 1000r T plot for the As 45.2Te 46.6 In 8.2 films.
Ø The electrical conductivity has been used as a good parameter for the crystallization process in the glassy As 45.2Te 46.6 In 8.2 films. Ø The activation energy for conduction of the investigated film was found to increase monotonically with increasing the heating rate. Ø The isothermal data indicates that one- and two-dimensional growth mechanisms are working simultaneously in the crystallization process. Ø The obtained activation energy for crystallization Ž E . under isothermal conditions of the glassy As 45.2Te 46.6 In 8.2 films is 100 " 0.5 kJrmol.
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A.H. Moharram et al.r Applied Surface Science 137 (1999) 150–156
References w1x N. Rysava, T. Spasov, L. Tichy, J. Therm. Anal. 32 Ž1987. 1015. w2x H. Yinnon, D.R. Uhlmann, J. Non-Cryst. Sol. 54 Ž1983. 253. w3x E.J. Mittemeijer, J. Mater. Sci. 27 Ž1992. 3977. w4x H.E. Kisinger, Anal. Chem. 29 Ž1957. 1702. w5x T. Ozawa, Thermochim. Acta 203 Ž1992. 159. w6x M.J. Starink, Thermochim. Acta 288 Ž1996. 97. w7x A.H. Moharram, M.S. Rasheedy, Physica Status Solidi Ža. 169 Ž1998. 33. w8x D.W. Handerson, J. Non-Cryst. Sol. 30 Ž1979. 301. w9x M.F. Kotkata, M.K. El-Mously, F.M. Ayad, Acta Phys. Hung. 46 Ž1979. 19.
w10x M.F. Kotkata, M.K. El-Mously, Acta Phys. Hung. 54 Ž1983. 303. w11x M.F. Kotkata, A.A. El-ela, M.K. El-Mously, Acta Phys. Hung. 52 Ž1982. 3. w12x M.F. Kotkata, A.F. El-Dib, F.A. Gani, Mater. Sci. Eng. 72 Ž1985. 163. w13x P. Agarwal, S. Goel, S.K. Tripathi, A. Kumar, Physica B 172 Ž1991. 511. w14x A.A. Abu-Sehly, submitted for publication to J. Phys. D ŽApplied Physics.. w15x S. Mahadevan, A. Giridhar, A.K. Singh, J. Non-Cryst. Sol. 88 Ž1986. 11. w16x N. Afify, J. Non-Cryst. Sol. 128 Ž1991. 279. w17x E.A. Marseglia, J. Non-Cryst. Sol. 41 Ž1980. 31.
Crystallization kinetics of thermally evaporated As 45.2Te 46.6 In 8.2 thin films A.H. Moharram ) , M.M. Hafiz, A.A. Abu-Sehly Physics Department, Assiut UniÕersity, Assiut, Egypt Received 11 May 1998; accepted 26 August 1998
Abstract Glassy As 45.2Te 46.6 In 8.2 thin films were thermally evaporated onto chemically cleaned glass substrates. Crystallization kinetics were determined under isothermal conditions. Heating the film up to the isothermal temperature with different rates was found to yield films with different electrical characterization. Conductivity of the investigated film was used as a parameter indicating the crystallized fraction x Ž t .. The obtained values of the activation energy for crystallization, the frequency factor and the Avrami index are Ž100 " 0.5. kJrmol, Ž7.31 " 0.04. 10 8 sy1 and 1.45, respectively. The non-integer value of the Avrami index indicates that two crystallization mechanisms are responsible for the crystal growth. q 1999 Elsevier Science B.V. All rights reserved. Keywords: As 45.2Te 46.6 In 8.2 thin films; Crystallization kinetics; Conductivity
1. Introduction Thermally activated transformations in the solid state can be investigated by isothermal or non-isothermal experiments w1x. For non-isothermal analysis at constant heating rate the crystallization kinetics can be determined using different methods w2,3x. The approximations used in the derivation of the so-called Kissinger w4x and Ozawa w5x methods introduce significant inaccuracies in determination of the overall activation energy for crystallization. Applying a new method w6x gives values an order of magnitude more accurate than the Kissinger and Ozawa methods. In our recent work w7x, a simple and approximation-free method was applied to calculate the crystallization )
Corresponding author. Fax: q20-88312-564; E-mail: [email protected]
kinetics of a glassy specimen from only one DSC scan. In the isothermal method, the sample is brought quickly to a temperature slightly below the onset temperature of crystallization, Tc , and the heat evolved during the crystallization process at a constant temperature is recorded as a function of time. The isothermal crystallization data are usually interpreted in terms of the Johnson–Mehl–Avrami ŽJMA. theoretical model w2x in which the fraction of precursor that has been transformed into the product phase as a function of time Ž t . is given by
x Ž t . s 1 y exp y Ž Kt .
n
Ž 1.
where n the Avrami exponent, which reflects the characteristics of nucleation and the growth process, is found to be constant over a substantial range of temperatures and K the rate constant, which reflects the rates of both nucleation and growth, is usually
0169-4332r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 4 6 7 - X
A.H. Moharram et al.r Applied Surface Science 137 (1999) 150–156
assumed to have an Arrhenian temperature dependence w8x, K s K 0 exp Ž yErRT .
Ž 2.
where the pre-exponential term K 0 Žsy1 . is the frequency factor and E ŽkJrmol. is the activation energy describing the overall crystallization process. The crystallization process is generally well understood when the three kinetic parameters E, n and K 0 are determined. It is important to emphasize that the aforementioned JMA model was formulated only to describe the isothermal transformations. The crystallization kinetics of glassy films can not be determined from the DSC experiments. Therefore, any physical quantity which changes measurably upon crystallization can be taken as a characteristic parameter to evaluate x as a function of time. DC conductivity was found w9–11x to be a suitable parameter in chalcogenide glasses. Since the conductivity of these glasses increases by several orders of magnitude on crystallization, ln s represents the sensitive parameter characterizing crystallization rather than s itself as confirmed by Kotkata et al. w12x. It is worthy to state that a simple ohmmeter may be sufficient for the present technique. Another advantage is that the electrical characterization in addition to the crystallization kinetics have been obtained. The calculation of crystallization kinetics from the conductivity data was applied previously w12,13x for films evaporated from binary alloys. However, in the present work, the investigated films are thermally evaporated from a ternary alloy. A single activation energy for conduction over an extended temperature range is required to get accurate values for crystallization kinetics of the investigated film. Chalcogenide As 45.2Te 46.6 In 8.2 film was found to be a suitable material for the present experiment.
2. Experimental Bulk material was prepared by the well established melt–quench technique. Thin films were thermally evaporated onto ultrasonically cleaned glass substrates, using an Edward E 306 coating system operated at 5 = 10y6 Torr. The evaporation source was fragments of the bulk As 46 Te 46 In 8 materials.
151
The substrate temperature was kept at room temperature during the evaporation process. The evaporation rate as well as the thickness of the investigated films were controlled using a quartz crystal monitor Ed˚ ward FTM5. A constant evaporation rate Ž; 5 A sy1 . was used to deposit 120 nm thick films. Electrical resistivity measurements were done using specimens with evaporated gold gap Ž2 = 10 mm. electrodes. Keithley 610 C electrometer was used as ohmmeter. To avoid oxidation of the sample, the measurements were taken under vacuum ; 10y3 Torr by mounting the sample in a specially designed metallic sample holder inside a Tohr cryogenic cryostat. The temperature was measured using a calibrated copper constantan thermocouple. The annealing temperature was obtained using a fixed heating rate Ž; 10 Krmin. and then maintained constant till the conductivity reaches a limiting value. The morphology and structure of the deposited films were analyzed using Jeol 2000 transmission electron microscope ŽTEM. operated at 100 kV. Freshly evaporated as well as thermally annealed films were floated off substrates precoated with NaCl and carbon films. They were floated by immersion in distilled water, then transferred to copper microscope grids. Thermal treatment for TEM experiments was performed under vacuum ; 10y3 Torr.
3. Results A typical DSC curve of the bulk As 46 Te 46 In 8 glass in powdered form, using a Shimadzu TA-50 differential scanning calorimetry at a heating rate of 10 Krmin, is shown in Fig. 1. Three characteristic phenomena are clear in the studied temperature range. The first one ŽTg s 434.4 K, endo. corresponds to the glass transition temperature, the second one ŽTc s 486.5 K, exo. to the onset temperature of crystallization and the last one to the peak temperature of crystallization ŽTp s 524.4 K.. The slight shoulder appeared in the left-hand side of the exothermic peak means that more than one crystalline phase are growing during the DSC run. Thin films were thermally evaporated from fragments of the bulk As 46 Te 46 In 8 material. The glassy state was expected for the as-prepared films since the quenching rate during deposition process is much
152
A.H. Moharram et al.r Applied Surface Science 137 (1999) 150–156
Fig. 1. A typical DSC curve of the bulk As 46 Te 46 In 8 specimen at a heating rate 10 Krmin.
higher than that of the bulk alloy made from the melt. The composition of the evaporated films was investigated using a computerized energy dispersive X-ray ŽLink Analytical Edx. spectroscopy. The atomic percentages of the As, Te and In in the as-prepared films were found to be 45.2, 46.6, and 8.2, respectively. A small deviation between the composition of the starting bulk As 46 Te 46 In 8 material and the evaporated films was kept constant using ˚ sy1 .. a low evaporation rate Ž; 5 A To study the temperature dependence of the electrical conductivity of the as-prepared As 45.2Te 46.6 In 8.2 specimen, films of 120 nm thick were deposited onto glass substrates held at room temperature. Measurements were carried out during heating the specimen. Fig. 2 shows the temperature dependence of the electrical conductivity of the as-prepared film. A constant rate of 3.0 Krmin was used to heat up the specimen. Two regions ŽI and II. of ln s vs. 1rT plot are shown in the figure. In the first region, which extends from room temperature up to the onset temperature of crystallization, the conductivity varies with temperature according to the Arrhrenian relation s s s 0 expŽyD ErkT ., where s 0 is the pre-exponential factor and D E the activation energy for conduction. After reaching a certain temperature, called the onset temperature of crystallization, the conductivity deviates to higher values than expected as indicated by the second region ŽII.. The small difference between the Tc values obtained from the DSC experiment ŽTc s 486.5 K. and that from the
conductivity data ŽTc s 484 K. of Fig. 2 can be mainly attributed to the heating rate dependence of the Tc value. A result which indicates that the elemental compositions of the bulk material and its evaporated thin films are nearly the same. Heating the specimen at different rates was found to change the slope and intercept of ln s vs. 1rT plot, which means that the values of D E and s 0 are dependent on the heating rate. Fig. 3 shows the monotonic increase of D E and s 0 with increasing the heating rate. Because of this result, only one heating rate, e.g., ; 10 Krmin was used to heat the investigated films to the required isothermal temperatures. Fig. 4 shows the time dependent of the electrical conductivity measured for an amorphous film during isothermal heating at T s 488 K. It is clear that the conductivity increases with time. The transformation from amorphous to crystalline state occurs in three stages represented by AB, BC and CD as shown in the figure. Part AB is linear with time and represents a gradual increase of s as a result of normal heating of the sample. Part BC represents a gradual but less pronounced increase in s which may due to nucleation of the crystalline phase. The CD part shows a
Fig. 2. Temperature dependence of the electrical conductivity of the As 45.2Te 46.6 In 8.2 film heated at constant rates 3.0 Krmin Žthickness of the film s120 nm..
A.H. Moharram et al.r Applied Surface Science 137 (1999) 150–156
Fig. 3. Dependence of the conductivity pre-exponential factor and the activation energy for conduction on the heating rate of the As 45.2Te 46.6 In 8.2 films.
sharp rise in s resulting from rapid growth of the crystalline state. A process which is accompanied by the liberation of heat energy associated with the transition from non-equilibrium to equilibrium thermodynamic state. CD attains a limiting value after certain time Žpoint D.. The point C represents the amorphous state and D corresponds to the complete crystalline state. At any intermediate point ŽI., the conductivity corresponds to a mixture of amorphous and crystalline state. According to Kotkata et al. w12x, the experimental values of ln s was used to determine the value of x Ž t . at any intermediate time by the relation
x Ž t . s w ln s y ln sa x r w ln sc y ln sa x
153
of few sharp rings in the SAED of Fig. 5b. Isothermal growth of crystallization leads to creation of other sharp rings in Fig. 5c. The non-indexed spots shown in the outer rings could be caused from the different crystalline phases. The diffraction pattern of Fig. 5c corresponds to the point D where the crystallized fraction covers most of the amorphous matrix and the electrical conductivity reaches its maximum value. In a parallel work w14x, the crystalline phases resulting from thermal annealing of the As 45.2Te 46.6 In 8.2 films were identified as As 2Te 3 and AsIn phases. Fig. 6 shows the crystallized fraction vs. time x Ž t . plots at four different isothermal temperatures. Increasing the annealing temperature increases the steepness of the resulting curve which means that the crystallization process proceeds faster at higher temperatures than that at lower ones. Taking logarithms and rearranging Eq. Ž1. gives ln yln Ž 1 y x . s n ln K q n ln t.
Ž 4.
Following the above equation, a plot of lnwylnŽ1 y x .x vs. ln t at constant temperature or constant K value should yield a straight line. The degree of constancy of K will specify the possibility limits of using ln s as a parameter for the crystallization rate.
Ž 3.
where sc and sa are the conductivities of the crystalline and amorphous phases having volume fractions x and Ž1 y x ., respectively, and s is the conductivity of a mixture during amorphous to crystalline transformation. To follow up the structure transformations, three identical films were examined by TEM. The films were thermally treated in the same way as the points C, I and D of Fig. 4. The diffuse rings appeared in the SAED of Fig. 5a, confirms the amorphous state of the films which heat treated up to the point C. Increasing the time of annealing to an intermediate point ŽI. enhances the amorphous-crystalline transformations inside the investigated film. The crystallized fraction Ž x . is responsible for the appearance
Fig. 4. Time dependence of the electrical conductivity of the As 45.2Te 46.6 In 8.2 film heated to the isothermal temperature 488 K.
154
A.H. Moharram et al.r Applied Surface Science 137 (1999) 150–156
investigated films. The value of n s 1.45 lies near midway between the two integers 1.0 and 2.0 means that the two crystallization mechanisms are working simultaneously with nearly equal share. From Fig. 7, the intercept of the straight line measured at a certain temperature with the lnwylnŽ1 y x .x axis gives the value of nln K corresponding to that temperature. The activation energy for crystal-
Fig. 5. SAED patterns of three As 45.2Te 46.6 In 8.2 films heated to the points C, I and D of Fig. 4, respectively.
Fig. 7 shows the straight lnwylnŽ1 y x .x vs. ln t plots at four different isothermal temperatures. It is obvious that the slope of the straight line, and consequently the n-value, is nearly temperature independent. The average value of n, calculated from Fig. 7, for the glassy As 45.2Te 46.6 In 8.2 films was found to be 1.45. This non-integer value indicates that two mechanisms, one- and two-dimensional growth w15,16x, are responsible for the crystallization process in the
Fig. 6. Crystallized fractions calculated from the conductivity data vs. time x Ž t . at four different isothermal temperatures.
A.H. Moharram et al.r Applied Surface Science 137 (1999) 150–156
Fig. 7. lnwylnŽ1y x .x vs. ln t plots for the As 45.2Te 46.6 In 8.2 films at four different isothermal temperatures.
lization of the investigated film can be obtained by plotting the Arrhenian temperature dependence of the reaction rate Ž K .. Fig. 8 shows the ln K vs. 1000rT representation and the obtained values of the frequency factor and the activation energy for crystallization are Ž7.31 " 0.04.10 8 sy1 and 100 " 0.5 kJrmol, respectively. Another approach proposed by Marseglia w17x was applied to, check the validity of the obtained results, determine the activation energy for crystallization. Accordingly, the time required for x s 1r2 can be
155
Fig. 9. ln t1r 2 vs. 1000r T plot for the As 45.2Te 46.6 In 8.2 films.
given by substituting for K s K 0 expŽyErRT . into Eq. Ž4. and rearranging it as follows ln t 1r2 s const.q ErRT
Ž 5.
a plot of ln t 1r2 as a function of 1rT will give the value of the activation energy for crystallization. With the isothermal hold method, the plot of ln t 1r2 vs. 1rT is shown in Fig. 9. Multiplying R by the least squares line yields the activation energy for crystallization of E s 100.34 kJrmol. A result which is in good agreement with that obtained from Fig. 8.
4. Conclusions
Fig. 8. ln K vs. 1000r T plot for the As 45.2Te 46.6 In 8.2 films.
Ø The electrical conductivity has been used as a good parameter for the crystallization process in the glassy As 45.2Te 46.6 In 8.2 films. Ø The activation energy for conduction of the investigated film was found to increase monotonically with increasing the heating rate. Ø The isothermal data indicates that one- and two-dimensional growth mechanisms are working simultaneously in the crystallization process. Ø The obtained activation energy for crystallization Ž E . under isothermal conditions of the glassy As 45.2Te 46.6 In 8.2 films is 100 " 0.5 kJrmol.
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