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Delayed radiation-induced conductivity in nickel polymethacrylate: II
Polymer Degradation and Stability 41 (1993) 17-24
Delayed radiation-induced conductivity in nickel polymethacrylate: II Farid A. Khwaja, M. M. Pasha & M. Asghar Materials Research Laboratory, Department of Physics, Quaid-e-Azam University, lslamabad, Pakistan (Received 6 May 1992; accepted 23 May 1992)
Generation and transport of charge carriers in nickel polymethacrylate (NiPMA) in the post-irradiation phase have been investigated by means of DC conductivity as a function of temperature, exposure rate and electric field strength. The delayed radiation-induced conductivity due to the temperatureand field-assisted dissociation of electron-holes excitation of the chain segment is appropriately described within the framework of the onedimensional Onsager theory of geminate-pair dissociation. At high temperatures the conductivity is dominated by the local, liquid-like motion of the heteroeharges moving in an amorphous or locally disordered environment. After a certain radiation dose the transition from increasing to decreasing conductivity with increase of exposure rate is due to the radiation-hardening of the material. It is concluded that prolonged irradiation of the material produces new trap-centres which cause a decrease in conductivity.
1 INTRODUCTION
terephthalate) under high electric fields. ~ A slowly increasing induced current, due to electron injection from the cathode, has been observed in SiO2 metal oxide semiconductor (MOS) in the high-field region. 5 It has also been observed that after termination of the irradiation, components of the induced current, IDRIC, decay approximately hyperbolically to zero. However, the experimental data on this last aspect of RICs are too scanty to give any understanding of the conduction processes in these materials. In a number of recent investigations, we have successfully synthesized polymethacrylate and polyacrylate doped with nickel, iron, chromium, palladium, etc., and have investigated the conduction mechanisms therein. 6-~° Different types of conduction mechanisms have been revealed depending upon the nature of the metal-containing polymer, the temperature and the electric field strength. In particular, in the previous paper, 1° it has been shown that the conductivity in nickel polymethacrylate increases exponentially with increase of applied electric field at higher temperatures. It is conjectured that at higher temperatures the H ÷ ion along with the metal ions are the main source of ionic
Radiation-induced currents (RICs) have been recorded as a function of applied field in a large number of insulating polymeric materials, mainly organic polymers. ~-4 These investigations are extremely important because power controls and coaxial cables in the primary container of a nuclear power plant are usually exposed to a radiation environment. These studies are of fundamental importance, too, because they yield some insight into the various conduction processes which occur in these materials. To the present time, a number of polymeric materials have been exposed to X-rays, electrons and ),-radiation and a variety of conduction mechanisms have been revealed. The RIC has been observed to be voltage-dependent; for low radiation exposure rates it decreases initially with increase in voltage and eventually becomes constant in certain polymeric materials. On the contrary, an initial increase of RIC has been observed in ),-ray irradiated poly(ethylene Polymer Degradation and Stability 0141-3910/93/$06.00 © 1993 Elsevier Science Publishers Ltd. 17
18
F. A. Khwaja, M. M. Pasha, M. Asghar
conduction in the material. This has prompted us to explore further the ionic character of the conductivity in this material in an ionizing environment. In this paper we report the measurement of delayed induced conductivity in post-irradiated nickel polymethacrylate as a function of temperature and field strength.
where Do is the diameter of the effective area which is given as Do = (0~ + 02)/2 where D~ is diameter of the inner edge of the annular silver painted strip and DE is that of the central painted area; the values were 0-69 cm and 0.71 cm, respectively. The samples were exposed to doses ranging from 3.0×109 to 2 . 4 × 10 ~°particles/cm 2.
EXPERIMENTAL TECHNIQUE 3 RESULTS AND DISCUSSION Sample preparation, design of the sample holder, the technique of conductivity measurement and the circuit employed were described previously.~° The samples used were 0.09cm in thickness, 0.74 cm in diameter, and weighed 365 mg. They were prepared under a pressure of 140 MPs. The sample was irradiated with a 5-5 MeV 241Am a~-source for 4 h. The irradiation of the samples was carried out in a jar as shown in Fig. 1. The dose is defined as the number of re-particles received by the sample per unit area and is given by: Dose - Strength of source × time 4~r x R 2 where R is the distance between the source and the sample which was maintained constant at 0-35 cm. The strength of the source was 9#Ci; 1 Ci is 3.7 x 101° particles/s. After each dose the conductivity of the irradiated NiPMA was calculated using the relationship:
where L is the thickness of the sample and Ao• = ~rD2/4
Fig. 1. Arrangement for the irradiation of the sample with oc-particles.
3.1 Field dependence of RIC The delayed radiation-induced current versus voltage nickel polymethacrylate relationship in the post-irradiated phase of NiPMA is shown in Fig. 2 for various radiation doses at a fixed temperature. The delayed induced radiation current is seen to increase exponentially with increase in the voltage for all the radiation doses. The increase is slower for low radiation doses but increases for higher doses. It is clear that the induced current in the voltage region under investigation follows an I oc Vn_power law, where n is the power coefficient. The values of the coefficient n may be obtained from the slope of the straight line fitted to the experimental data. For NiPMA the coefficient has been found to be 1.4-2.0, indicating that a space-charge limited phenomenon is operative. The mobility of the delayed radiation induced current is fielddependent, as has been found for many organic solids) ° On suddenly cooling a previously heated sample from 60°C to 20°C, and measuring the I - V characteristics, similar behaviour is obtained. On the other hand, on measuring the conducting current as a function of increasing and decreasing voltage at various temperatures, coincidence is not obtained at temperatures of 300 K or higher. One of these plots, measured at 300 K, is shown in Fig. 3. The current increases with reversal of the voltage. This suggests that a phenomenon of space-charge limited conduction mechanism with relaxation predominates in this material. The increase of I with V might also be rationalized on the basis of Onsager's theory of geminate-pair recombination, which was successfully applied to molecularly doped polymers. H The essential assumption of Onsager's theory ~2 is that the rate of geminate recombination is
Conductivity in nickel polymethacrylate
19
J
12
x = 1.2x1010
12
10
10
~b
t..~\
~6
6~ t,-
E
(J
/,
4
I
loo
I
1so
I
200
I
2so
I
300
I
L
35o
40o 4'oo
3~o
3bo
2;0
2;0
~.~o
16o
VOLTAGE (Volts)
l~g. 2. Delayed radiation-induced current versus voltage for various doses at room temperature.
12 DOSE = 2.4 xl010 Parlicles/Cm 2 ot room temperature
10
6 E
(o
4
-oo -,'oo -3o'o-2oo -,oo!_
/
100
200
300
400
500
VOLTAGE (Volts)
-8
Fig. 3. Hysteresis curve for irradiated NiPMA at room temperature.
:) U
20
F. A. Khwaja, M. M. Pasha, M. Asghar
reduced on increasing the field. Thus the generation of charge carriers is also increased, making more charge carriers become available. It would perhaps be safe to conclude that upon irradiating NiPMA with m-particles, excitation of the electrons and the holes sitting on neighbouring chains takes place. The initial excitations can expand to form more loosely bound electronhole pairs by the electron (hole) jumping to an adjacent polymer segment with lower energy than the lowest unoccupied orbital. High electric fields are likely to assist pair expansion and can thus result in a quantum yield of charge carriers. Another noteworthy result is that the rate of exponential growth of the delayed induced current with field strength increases initially with increase in the radiation dose, reaches a
maximum value at a dose of about 1.5x 101° particles/cm 2 and then starts decreasing with further increase of the dose. The increase and decrease of the delayed induced current might be tentatively ascribed to traps filling and deep trapping, respectively. It is, perhaps, likely that the prolonged one-shot exposure of the material produces new traps or increases the cross-section for trapping, with the result that the value of the delayed RIC is reduced to the value that would have been obtained if the irradiation had been performed from the beginning.
3.2 Temperature dependence Figure 4 shows the temperature dependence of the delayed RIC versus voltage for the irradiated 98"C
0.8 ~
DOSE : 2.4x1010
Porticles/Crn 2
0.7
0.6
90' C 0.5
~0.4 E c
80"C
0.3
0.2 60 "C
0.1
~ _ _ ~ ~ . ~ - .
L
0
"1"-
~
.
22"C
4
50
100
150
200 250 300 VOLTAGE ( Volts}
350
400
Fig. 4. Delayed radiation-induced current versus voltage at various temperatures.
21
Conductivity in nickel polymethacrylate NiPMA. It is noteworthy that at temperatures above 60°C and voltages above 200V, the delayed RIC increases by an order of magnitude compared with its value at room temperature for the same field strength. A charge carrier in an irradiationally deformed lattice of the material should give rise to temperature-activated transport. This becomes evident when one compares the delayed RIC in irradiated and unirradiated samples at the same temperature and field strength (Fig. 5). Again, one finds that the charge carrier yield is almost three orders of magnitude greater in the irradiated sample as compared with the unirradiated sample at the same temperature and field strength. Figure 6 shows that the slope in the log o vs 1/T plots obeys the Arrhenius equation with a constant activation energy in the temperature range 294 K - T - 337 K, although there is some curvature at higher temperatures. The values of the activation energy for different field strengths are given in Table 1 for the two temperature
0.3
BO'C
0,2
0.1
0.0
IlL
s'o
^
~
~
22'C
GO'C
v
1oo
1'so
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2~o
3'0o
3'so
4bo
VOLTAGE (Volts)
Fill. 5. Comparison of the currents in irradiated (F:l) and unirradiated ( 0 ) samples at 80°C and the radiation-induced current ((9) at room temperature.
Table 1. Field dependence of activation energies of NiPMA
at low and high temperatures Voltage (V)
100 200 300 400
Activation Activation energy energy 295 K_< T_<337 K 337 K _ T_<371K (eV) (eV) 0.330 0.340 0.352 0-367
0-454 0.471 0.494 0-566
regions. It is interesting to note that the values of activation energy in both temperature regions shift to higher values with increase in voltage, although the field dependence of the activation energy appears to be lower in the lowtemperature as compared with the hightemperature region. The temperature-activated conductivity has average values of activation energy of 0.35 eV and 0-49 eV in the low- and high-temperature regions respectively. The linear increase in the activation energy with the electric field shows electric field dependent generation of charge carriers, as has been discussed in Onsager's model. The difference in the activation energies in the two temperature regions indicates differences between the conduction mechanisms in the two regions. The results demonstrate that a hole conduction mechanism is expected to be dominant at low temperature and an electronic conduction mechanism is operative at higher temperatures. These electrons which are excited by ionization and dissociated by the radiation at the beginning, are caught (trapped) in shallow traps, perhaps 0-5 eV deep, from which they are released at an increasing rate as the temperature is raised. However, the electric field dependence in both regions is the same. The positive deviation from Arrhenius behaviour of the observed field and temperature dependence of the conductivity above a certain critical temperature, To, in this material can only be explained on the basis of a hopping model involving local, liquid-like motion of the solvent with the electrons and holes/ions then moving in an amorphous, locally disordered, and inhomogeneously broadened disordered distribution of the states as in fused salts, molecularly doped polymers or pendant-group polymers. It depends on the idea that charge carriers execute random walks within a random potential. 13 According to this, Gaussian shape of the charge
6.3
6.5 6.7
"7E
6.9
I
o
7.1
J=
E ~ o ...J
7.3
7.5
l
Tc
7.7
8.1 2.6
2-7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
I000/T (K) -I Fig. 6. Plot of the log of the conductivity versus reciprocal temperature for irradiated NiPMA. The arrow indicates the
transition temperature. J
O-65
0.55
0.45
400V
x
";'E 0.35 (J i
025
i
0.15
0.05
I
0.3
I
0.6
I
i
I
0.9 1.2 1.5 DOSE (1010Particles/crn 2)
'
1.8
I
•
"2-1
Fig. 7. Delayed radiation-induced conductivity versus dose rate at room temperature for various field strengths.
Conductivity in nickel polymethacrylate
transport is assumed in order to explain the random generation of the charge carriers during the initial excitations. These relax towards deeper states to settle finally at a mean occupational energy that decreases with decreasing temperature. This explains the curved In cr vs 1 / T plots and enhanced conductivity above a certain critical temperature T~. Thus Tc here is the onset temperature of the micro-Brownian motion of the disordered chain which enhances the migration of charge carriers above the critical temperature. 3.3 Exposure-rate d e p e n d e n c e
The dependence of the delayed R I C on the dose rate is also of interest in determining the mechanism of electric charge transport. In Fig. 7 is shown the delayed radiation-induced conductivity O'DRIC, estimated from IDRIC, as a function of dose rate X for different field strengths. It is interesting to note that ODRIC goes through a shallow maximum, and subsequently decreases slowly at low field strength. At higher field strengths, however, the m a x i m u m increases, the position of the m a x i m u m remaining at the same dose rate. The delayed induced conductivity is found to vary with exponential rate according to a power law: 14 O'DRIC O( X )'
The value of the coefficient y has been determined previously for a large n u m b e r of polymers and found to be in the range 0.5<_),___1. The values of the coefficient y in NiPMA, shown in Table 2, vary monotonically with the electric field strength. The field dependence of the coefficient ), has been reported by Maeda et al. ~ for y-ray induced conduction in poly(ethylene terephthalate). Table 2. Variation of the coefficient ¥ with field
Voltage (V)
100 200 300 400
23
The prolonged irradiation of the material with c~-particles may result in 'radiation hardening' and thus a many-fold increase of the resistivity. This explains the negative sign of the coefficient y in Table 2 for the decreasing portion of the ODmc curves in Fig. 7. The value of the coefficient y also relates to the depth and distribution of the traps and hence explains the conduction mechanism in a material. Our results indicate that the coefficient y has an average value of 0-6 for the increasing portion of the O'DRIC curve. These results again lead to the conclusion that a considerable portion, d e p e n d e n t u p o n the temperature and the applied voltage, of the electrons which are released by the ionizing radiation do not combine with the holes/ions and are caught in shallow traps, from which they are released at an increasing rate as the field is increased. Not all of them move to the anode thus increasing the conductance, but some may recombine with the holes/ions or are trapped in deeper traps. More traps are created by prolonged irradiation of the material, accounting for the decreased conductance at higher dose rates.
4 CONCLUSION (1) In NiPMA, charge-carrier generation involves temperature, dose rate and field-assisted dissociation of the electron-hole lattice excitation. (2) The formation of geminate pairs and the transport of the liberated charges is in accord with the Onsager concept of one-dimensional systems. (3) The high conductivity at higher temperatures and electric fields is due to the liquid-like motion of the heterocharges (holes/ions) in the disordered m e d i u m with weak e l e c t r o n - p h o n o n coupling.
REFERENCES
y
For increasing portion of the o vs X curves
For decreasing portion of the tr vs X curves
0.60 0-61 0-63 0.67
-1-10 - 1.01 -0.99 -0-97
1. Maeda, H., Kurashige, M. & Nakakita, T., J. Appl. Phys., 50 (1979) 758. 2. Faria, R. M. & Gross, G., J. Appl. Phys., 62 (1987) 1429. 3. Mochizuki, S., Tamura, N. & Yahagi, K., J. Appl. Phys., 54 (1983) 4433. 4. Mizutani, T. B., Suigiura, N., Suzuoki, Y. & Ieda, M., Jap. J. Appl. Phys., 20 (1981) 59. 5. Farmer, J. W. & Lee, R. S., J. Appl. Phys., 46 (1975) 2710.
24
F. A. Khwaja, M. M. Pasha, M. Asghar
6. Farid Khwaja, A., Iqbal, M., Razmi, M. S. K. & Chohan, M. H., Mod. Phys. Lett., !!3 (1989) 1025. 7. Chohan, M. H., Khwaja, F. A. & Bukhari, A. H. S., Mod. Phys. Lett., !14 (1990) 871. 8. Chohan, M. H. & Khwaja, F. A., Polym. Sci. Symp., 3 (1990) 81. 9. Khwaja, F. A. & Chohan, M. H., Polym. Sci. Symp., 3 (1990) 37. 10. Khwaja, F. A., Din, M. & Zulfiqar, M., Polym. Deg.
and Stab., 36 (1992) (in press). 11. Borsenberger, P. M., Contois, L. E. & Hoesterey, D. C.,J. Chem. Phys., 68 (1978)637. 12. Onsager, L., Phys. Rev., 54 (1938) 554. 13. Bassler, H. In: Hopping and Related Phenomena, ed. H. Fritsch & M. Pdak. World Scientific, Singapore (1991). 14. Fowler, J. F., Proc. Roy. Soc. Lond., ~ (1956) 464.
Delayed radiation-induced conductivity in nickel polymethacrylate: II Farid A. Khwaja, M. M. Pasha & M. Asghar Materials Research Laboratory, Department of Physics, Quaid-e-Azam University, lslamabad, Pakistan (Received 6 May 1992; accepted 23 May 1992)
Generation and transport of charge carriers in nickel polymethacrylate (NiPMA) in the post-irradiation phase have been investigated by means of DC conductivity as a function of temperature, exposure rate and electric field strength. The delayed radiation-induced conductivity due to the temperatureand field-assisted dissociation of electron-holes excitation of the chain segment is appropriately described within the framework of the onedimensional Onsager theory of geminate-pair dissociation. At high temperatures the conductivity is dominated by the local, liquid-like motion of the heteroeharges moving in an amorphous or locally disordered environment. After a certain radiation dose the transition from increasing to decreasing conductivity with increase of exposure rate is due to the radiation-hardening of the material. It is concluded that prolonged irradiation of the material produces new trap-centres which cause a decrease in conductivity.
1 INTRODUCTION
terephthalate) under high electric fields. ~ A slowly increasing induced current, due to electron injection from the cathode, has been observed in SiO2 metal oxide semiconductor (MOS) in the high-field region. 5 It has also been observed that after termination of the irradiation, components of the induced current, IDRIC, decay approximately hyperbolically to zero. However, the experimental data on this last aspect of RICs are too scanty to give any understanding of the conduction processes in these materials. In a number of recent investigations, we have successfully synthesized polymethacrylate and polyacrylate doped with nickel, iron, chromium, palladium, etc., and have investigated the conduction mechanisms therein. 6-~° Different types of conduction mechanisms have been revealed depending upon the nature of the metal-containing polymer, the temperature and the electric field strength. In particular, in the previous paper, 1° it has been shown that the conductivity in nickel polymethacrylate increases exponentially with increase of applied electric field at higher temperatures. It is conjectured that at higher temperatures the H ÷ ion along with the metal ions are the main source of ionic
Radiation-induced currents (RICs) have been recorded as a function of applied field in a large number of insulating polymeric materials, mainly organic polymers. ~-4 These investigations are extremely important because power controls and coaxial cables in the primary container of a nuclear power plant are usually exposed to a radiation environment. These studies are of fundamental importance, too, because they yield some insight into the various conduction processes which occur in these materials. To the present time, a number of polymeric materials have been exposed to X-rays, electrons and ),-radiation and a variety of conduction mechanisms have been revealed. The RIC has been observed to be voltage-dependent; for low radiation exposure rates it decreases initially with increase in voltage and eventually becomes constant in certain polymeric materials. On the contrary, an initial increase of RIC has been observed in ),-ray irradiated poly(ethylene Polymer Degradation and Stability 0141-3910/93/$06.00 © 1993 Elsevier Science Publishers Ltd. 17
18
F. A. Khwaja, M. M. Pasha, M. Asghar
conduction in the material. This has prompted us to explore further the ionic character of the conductivity in this material in an ionizing environment. In this paper we report the measurement of delayed induced conductivity in post-irradiated nickel polymethacrylate as a function of temperature and field strength.
where Do is the diameter of the effective area which is given as Do = (0~ + 02)/2 where D~ is diameter of the inner edge of the annular silver painted strip and DE is that of the central painted area; the values were 0-69 cm and 0.71 cm, respectively. The samples were exposed to doses ranging from 3.0×109 to 2 . 4 × 10 ~°particles/cm 2.
EXPERIMENTAL TECHNIQUE 3 RESULTS AND DISCUSSION Sample preparation, design of the sample holder, the technique of conductivity measurement and the circuit employed were described previously.~° The samples used were 0.09cm in thickness, 0.74 cm in diameter, and weighed 365 mg. They were prepared under a pressure of 140 MPs. The sample was irradiated with a 5-5 MeV 241Am a~-source for 4 h. The irradiation of the samples was carried out in a jar as shown in Fig. 1. The dose is defined as the number of re-particles received by the sample per unit area and is given by: Dose - Strength of source × time 4~r x R 2 where R is the distance between the source and the sample which was maintained constant at 0-35 cm. The strength of the source was 9#Ci; 1 Ci is 3.7 x 101° particles/s. After each dose the conductivity of the irradiated NiPMA was calculated using the relationship:
where L is the thickness of the sample and Ao• = ~rD2/4
Fig. 1. Arrangement for the irradiation of the sample with oc-particles.
3.1 Field dependence of RIC The delayed radiation-induced current versus voltage nickel polymethacrylate relationship in the post-irradiated phase of NiPMA is shown in Fig. 2 for various radiation doses at a fixed temperature. The delayed induced radiation current is seen to increase exponentially with increase in the voltage for all the radiation doses. The increase is slower for low radiation doses but increases for higher doses. It is clear that the induced current in the voltage region under investigation follows an I oc Vn_power law, where n is the power coefficient. The values of the coefficient n may be obtained from the slope of the straight line fitted to the experimental data. For NiPMA the coefficient has been found to be 1.4-2.0, indicating that a space-charge limited phenomenon is operative. The mobility of the delayed radiation induced current is fielddependent, as has been found for many organic solids) ° On suddenly cooling a previously heated sample from 60°C to 20°C, and measuring the I - V characteristics, similar behaviour is obtained. On the other hand, on measuring the conducting current as a function of increasing and decreasing voltage at various temperatures, coincidence is not obtained at temperatures of 300 K or higher. One of these plots, measured at 300 K, is shown in Fig. 3. The current increases with reversal of the voltage. This suggests that a phenomenon of space-charge limited conduction mechanism with relaxation predominates in this material. The increase of I with V might also be rationalized on the basis of Onsager's theory of geminate-pair recombination, which was successfully applied to molecularly doped polymers. H The essential assumption of Onsager's theory ~2 is that the rate of geminate recombination is
Conductivity in nickel polymethacrylate
19
J
12
x = 1.2x1010
12
10
10
~b
t..~\
~6
6~ t,-
E
(J
/,
4
I
loo
I
1so
I
200
I
2so
I
300
I
L
35o
40o 4'oo
3~o
3bo
2;0
2;0
~.~o
16o
VOLTAGE (Volts)
l~g. 2. Delayed radiation-induced current versus voltage for various doses at room temperature.
12 DOSE = 2.4 xl010 Parlicles/Cm 2 ot room temperature
10
6 E
(o
4
-oo -,'oo -3o'o-2oo -,oo!_
/
100
200
300
400
500
VOLTAGE (Volts)
-8
Fig. 3. Hysteresis curve for irradiated NiPMA at room temperature.
:) U
20
F. A. Khwaja, M. M. Pasha, M. Asghar
reduced on increasing the field. Thus the generation of charge carriers is also increased, making more charge carriers become available. It would perhaps be safe to conclude that upon irradiating NiPMA with m-particles, excitation of the electrons and the holes sitting on neighbouring chains takes place. The initial excitations can expand to form more loosely bound electronhole pairs by the electron (hole) jumping to an adjacent polymer segment with lower energy than the lowest unoccupied orbital. High electric fields are likely to assist pair expansion and can thus result in a quantum yield of charge carriers. Another noteworthy result is that the rate of exponential growth of the delayed induced current with field strength increases initially with increase in the radiation dose, reaches a
maximum value at a dose of about 1.5x 101° particles/cm 2 and then starts decreasing with further increase of the dose. The increase and decrease of the delayed induced current might be tentatively ascribed to traps filling and deep trapping, respectively. It is, perhaps, likely that the prolonged one-shot exposure of the material produces new traps or increases the cross-section for trapping, with the result that the value of the delayed RIC is reduced to the value that would have been obtained if the irradiation had been performed from the beginning.
3.2 Temperature dependence Figure 4 shows the temperature dependence of the delayed RIC versus voltage for the irradiated 98"C
0.8 ~
DOSE : 2.4x1010
Porticles/Crn 2
0.7
0.6
90' C 0.5
~0.4 E c
80"C
0.3
0.2 60 "C
0.1
~ _ _ ~ ~ . ~ - .
L
0
"1"-
~
.
22"C
4
50
100
150
200 250 300 VOLTAGE ( Volts}
350
400
Fig. 4. Delayed radiation-induced current versus voltage at various temperatures.
21
Conductivity in nickel polymethacrylate NiPMA. It is noteworthy that at temperatures above 60°C and voltages above 200V, the delayed RIC increases by an order of magnitude compared with its value at room temperature for the same field strength. A charge carrier in an irradiationally deformed lattice of the material should give rise to temperature-activated transport. This becomes evident when one compares the delayed RIC in irradiated and unirradiated samples at the same temperature and field strength (Fig. 5). Again, one finds that the charge carrier yield is almost three orders of magnitude greater in the irradiated sample as compared with the unirradiated sample at the same temperature and field strength. Figure 6 shows that the slope in the log o vs 1/T plots obeys the Arrhenius equation with a constant activation energy in the temperature range 294 K - T - 337 K, although there is some curvature at higher temperatures. The values of the activation energy for different field strengths are given in Table 1 for the two temperature
0.3
BO'C
0,2
0.1
0.0
IlL
s'o
^
~
~
22'C
GO'C
v
1oo
1'so
2bo
2~o
3'0o
3'so
4bo
VOLTAGE (Volts)
Fill. 5. Comparison of the currents in irradiated (F:l) and unirradiated ( 0 ) samples at 80°C and the radiation-induced current ((9) at room temperature.
Table 1. Field dependence of activation energies of NiPMA
at low and high temperatures Voltage (V)
100 200 300 400
Activation Activation energy energy 295 K_< T_<337 K 337 K _ T_<371K (eV) (eV) 0.330 0.340 0.352 0-367
0-454 0.471 0.494 0-566
regions. It is interesting to note that the values of activation energy in both temperature regions shift to higher values with increase in voltage, although the field dependence of the activation energy appears to be lower in the lowtemperature as compared with the hightemperature region. The temperature-activated conductivity has average values of activation energy of 0.35 eV and 0-49 eV in the low- and high-temperature regions respectively. The linear increase in the activation energy with the electric field shows electric field dependent generation of charge carriers, as has been discussed in Onsager's model. The difference in the activation energies in the two temperature regions indicates differences between the conduction mechanisms in the two regions. The results demonstrate that a hole conduction mechanism is expected to be dominant at low temperature and an electronic conduction mechanism is operative at higher temperatures. These electrons which are excited by ionization and dissociated by the radiation at the beginning, are caught (trapped) in shallow traps, perhaps 0-5 eV deep, from which they are released at an increasing rate as the temperature is raised. However, the electric field dependence in both regions is the same. The positive deviation from Arrhenius behaviour of the observed field and temperature dependence of the conductivity above a certain critical temperature, To, in this material can only be explained on the basis of a hopping model involving local, liquid-like motion of the solvent with the electrons and holes/ions then moving in an amorphous, locally disordered, and inhomogeneously broadened disordered distribution of the states as in fused salts, molecularly doped polymers or pendant-group polymers. It depends on the idea that charge carriers execute random walks within a random potential. 13 According to this, Gaussian shape of the charge
6.3
6.5 6.7
"7E
6.9
I
o
7.1
J=
E ~ o ...J
7.3
7.5
l
Tc
7.7
8.1 2.6
2-7
2.8
2.9
3.0
3.1
3.2
3.3
3.4
I000/T (K) -I Fig. 6. Plot of the log of the conductivity versus reciprocal temperature for irradiated NiPMA. The arrow indicates the
transition temperature. J
O-65
0.55
0.45
400V
x
";'E 0.35 (J i
025
i
0.15
0.05
I
0.3
I
0.6
I
i
I
0.9 1.2 1.5 DOSE (1010Particles/crn 2)
'
1.8
I
•
"2-1
Fig. 7. Delayed radiation-induced conductivity versus dose rate at room temperature for various field strengths.
Conductivity in nickel polymethacrylate
transport is assumed in order to explain the random generation of the charge carriers during the initial excitations. These relax towards deeper states to settle finally at a mean occupational energy that decreases with decreasing temperature. This explains the curved In cr vs 1 / T plots and enhanced conductivity above a certain critical temperature T~. Thus Tc here is the onset temperature of the micro-Brownian motion of the disordered chain which enhances the migration of charge carriers above the critical temperature. 3.3 Exposure-rate d e p e n d e n c e
The dependence of the delayed R I C on the dose rate is also of interest in determining the mechanism of electric charge transport. In Fig. 7 is shown the delayed radiation-induced conductivity O'DRIC, estimated from IDRIC, as a function of dose rate X for different field strengths. It is interesting to note that ODRIC goes through a shallow maximum, and subsequently decreases slowly at low field strength. At higher field strengths, however, the m a x i m u m increases, the position of the m a x i m u m remaining at the same dose rate. The delayed induced conductivity is found to vary with exponential rate according to a power law: 14 O'DRIC O( X )'
The value of the coefficient y has been determined previously for a large n u m b e r of polymers and found to be in the range 0.5<_),___1. The values of the coefficient y in NiPMA, shown in Table 2, vary monotonically with the electric field strength. The field dependence of the coefficient ), has been reported by Maeda et al. ~ for y-ray induced conduction in poly(ethylene terephthalate). Table 2. Variation of the coefficient ¥ with field
Voltage (V)
100 200 300 400
23
The prolonged irradiation of the material with c~-particles may result in 'radiation hardening' and thus a many-fold increase of the resistivity. This explains the negative sign of the coefficient y in Table 2 for the decreasing portion of the ODmc curves in Fig. 7. The value of the coefficient y also relates to the depth and distribution of the traps and hence explains the conduction mechanism in a material. Our results indicate that the coefficient y has an average value of 0-6 for the increasing portion of the O'DRIC curve. These results again lead to the conclusion that a considerable portion, d e p e n d e n t u p o n the temperature and the applied voltage, of the electrons which are released by the ionizing radiation do not combine with the holes/ions and are caught in shallow traps, from which they are released at an increasing rate as the field is increased. Not all of them move to the anode thus increasing the conductance, but some may recombine with the holes/ions or are trapped in deeper traps. More traps are created by prolonged irradiation of the material, accounting for the decreased conductance at higher dose rates.
4 CONCLUSION (1) In NiPMA, charge-carrier generation involves temperature, dose rate and field-assisted dissociation of the electron-hole lattice excitation. (2) The formation of geminate pairs and the transport of the liberated charges is in accord with the Onsager concept of one-dimensional systems. (3) The high conductivity at higher temperatures and electric fields is due to the liquid-like motion of the heterocharges (holes/ions) in the disordered m e d i u m with weak e l e c t r o n - p h o n o n coupling.
REFERENCES
y
For increasing portion of the o vs X curves
For decreasing portion of the tr vs X curves
0.60 0-61 0-63 0.67
-1-10 - 1.01 -0.99 -0-97
1. Maeda, H., Kurashige, M. & Nakakita, T., J. Appl. Phys., 50 (1979) 758. 2. Faria, R. M. & Gross, G., J. Appl. Phys., 62 (1987) 1429. 3. Mochizuki, S., Tamura, N. & Yahagi, K., J. Appl. Phys., 54 (1983) 4433. 4. Mizutani, T. B., Suigiura, N., Suzuoki, Y. & Ieda, M., Jap. J. Appl. Phys., 20 (1981) 59. 5. Farmer, J. W. & Lee, R. S., J. Appl. Phys., 46 (1975) 2710.
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F. A. Khwaja, M. M. Pasha, M. Asghar
6. Farid Khwaja, A., Iqbal, M., Razmi, M. S. K. & Chohan, M. H., Mod. Phys. Lett., !!3 (1989) 1025. 7. Chohan, M. H., Khwaja, F. A. & Bukhari, A. H. S., Mod. Phys. Lett., !14 (1990) 871. 8. Chohan, M. H. & Khwaja, F. A., Polym. Sci. Symp., 3 (1990) 81. 9. Khwaja, F. A. & Chohan, M. H., Polym. Sci. Symp., 3 (1990) 37. 10. Khwaja, F. A., Din, M. & Zulfiqar, M., Polym. Deg.
and Stab., 36 (1992) (in press). 11. Borsenberger, P. M., Contois, L. E. & Hoesterey, D. C.,J. Chem. Phys., 68 (1978)637. 12. Onsager, L., Phys. Rev., 54 (1938) 554. 13. Bassler, H. In: Hopping and Related Phenomena, ed. H. Fritsch & M. Pdak. World Scientific, Singapore (1991). 14. Fowler, J. F., Proc. Roy. Soc. Lond., ~ (1956) 464.