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Electron hall mobility and photoconductivity of coloured KBr crystals at moderate temperatures
J. Phys. Chem. Solids, 1975, Vol, 36, pp. 213-214. Pergamon Press. Printed in Great Britain
ELECTRON OF COLOURED
HALL KBr
MOBILITY
AND
CRYSTALS
PHOTOCONDUCTIVITY
AT MODERATE
TEMPERATURES
I. S. AL-SAFFAR and J. H. CALDERWOOD Department of Electrical Engineering, University of Salford, England and
K. C. KAO Department of Electrical Engineering, University of Mantiboa, Canada
(Received 20 June 1974) KBr crystals of high purity supplied from Hilgar and Watts Limited were used for this investigation. By means of additive colouration with excess potassium, F centers were produced in the crystals with the concentration of about 6.1 × 10~5cm -3 which was determined by optical absorption measurements based on Smakula's equation. The Hall sample of size 10 × 5 × 5 mm with silver-dag painted electrodes was held in a holder made of Teflon with a window on one side so that the sample could be illuminated through an external light source, and with a small heater built in it so that the sample temperature could be adjusted by an external temperature control unit. For Hall effect measurements a double a.c. method was adopted in order to minimize the errors possibly caused by the misalignment of the Hall electrodes, the generation of thermopotential and the Ettinghouse effect. We used a 50 Hz, 10kG electromagnet and a 70Hz, 1KV generator, so the measured Hall voltage was at the frequency of 20Hz, the difference between the frequency of electric field and that of the transverse magnetic field. The light source was a 1 KW profector with a Kodak Wratten filter (Type 29) which transmits light from 6100 ,~ to 10,000 ,~. At a constant low electric field the Hall voltage was linearly proportional to magnetic field for the fields up to 10 kG, and at a constant magnetic field the Hall voltage was also linearly proportional to applied electric field for the fields up to 400 V/cm indicating that the Hall effect was due to the conduction in the bulk of the sample, the surface effect being negligible. Figure 1 shows the photo-current density as a function of electric field at various temperatures. From this set of curves it can be seen that the photoconductivity at 80°C is higher than that at both 60°C and 100°C indicating that there must be a peak at the temperature between 60°C and 100°C. To find this peak accurately we used a pen recorder to record simultaneously the continuous variation of both photoconduction current and temperature at a fixed electric field, and the continuous variation of both Hall voltage and temperature at a fixed electric field and a fixed magnetic field. We have repeated this experiment several times using three samples with the same concentration of F centers (within 3 per cent) and found that the results are repeatable and consistent although the absolute values vary slightly from sample to sample. Typical results presented in terms of photoconductivity and Hall mobility as functions of temperature are shown in Fig. 2. The light corresponding to the energy range of 1-2 eV absorbed by the crystal can raise the electrons in the F centers either to higher excited states or to the conduction band, and those in 213
higher excited states are then thermally excited to the conduction band, thus causing the photocurrent or photoconductivity temperature-dependent as shown in Figs. 1 and 2. From the curves of photoconductivity as a function of temperature for temperatures below 82°C, we have calculated the activation energy and it is of the order of 0.14-0.16eV for the average fields between 130V/cm and 1050V/cm. The activation energy is fielddependent; the higher the field, the lower is the activation energy. This phonomenon may be interpreted as a lowering of the energy barrier for thermal ionization of the excited stated [1]. Our results, however, are in good agreement with those of Swank and
9x~C
/•
/ / /////~
%
/~
4¸
BO°C O0°C 0oC 40°C 2o0c
/ I 0
250
I
20°C (dark) I
I
electric~i¢lc(V/ l cm) SO0
750
1000
I
1250
Fig. h Photo-current density as a function of electric field at various temperatures for coloured KBr crystals with initial concentration of F center of 6.1 × 10'~ cm -3.
Technical Notes
214 tOx~(
'--
-
-
photo
conductivity
(mogneticfield
Holl Mob'flity (rnognetic field
--
~
-T
E
/
~
- 40
/ / / ~ ~ ' ~
///Y \ /// ,, / / / / / ,4 ',
7-
-45
OkG)
2kG)
t30 V/cm
35
\X "oV,oo \~800 Vlcm
~C"
" ov1o° 3o..>
e~
2s~
0
4-
20
~
tS
40
I 60 temperature
I 80
I ~00
:to 120
(°C)
Fig. 2. Electron Hall mobility and photoconductivity as functions of temperature for coloured KBr crystals with initial concentration of F center of 6.1 x 10'~ cm -3. Brown[2] who reported the activation energy to be 0.135 eV in the low temperature range but at a field of 7 kV/cm which is much higher than the fields used in our experiments. The average Hall mobility of electrons in the coloured KBr crystals containing 6.I × 10~' F centers cm -3 is about 16 cm2/Vsec at 20°C, increases with increasing temperature and reaches a maximum value of about 35 cm2/V-sec at about 82°C, and then decreases gradually as temperature is further increased. The value at 20°C is in good agreement with 12.5 cm2/V-sec obtained by Macdonald et al.[3] and with 15 cm2/V-sec obtained by Zelm[4] using different methods. At temperatures below 82°C the temperature dependence of the Hall mobility may result from the trap-emptying process[5]. That the results in Fig. 2 do not show clearly an exponential form may indicate that inside the crystal other types of aggregate centers such as M, R and F' centers are also formed during photo-excitation. At temperatures higher than 82°C the decrease of both Hall mobility and photoconductivity with increasing temperature may be attributed to the electron interaction with the optical mode of lattice vibration, which may become predominantly important at high temperatures. It is of interest to note that the photocurrent-field curve in Fig. 1
is quite linear at 20°C and at low fields, but becomes non-linear at high temperatures and at high fields. This phenomenon may be explained by the fact that at high fields more F centers themselves would act as trapping centers. This means that one F center may be destroyed by field ionization and a second F center may be destroyed by capturing the electron freed from the first F center, and this process is more efficient at higher temperatures and at higher fields[6]. It is the second F center, which acts as a trap, to cause the photo-current tending to reach a saturation value at higher fields. REFERENCES I. Spino]o G. and Fowler W. B., Phys. Rev. 138, A661 (1965). 2. Swank R. K. and Brown F. C., Phys. Rev. Lett. 8, 10 (1962); idem. Phys. Rev. 130, 34 (1963). 3. MacDonald J. R. and Robinson J. E., Phys. Rev. 95, 44 (1954). 4. Zelm M., Z. Phys. 212, 280 (1968). 5. Rose A., R.C.A. Rev. 12, 362 (1951). 6. Schulman J. H. and Compton W. D., Color Centers in Solids, p. 101. Pergamon Press, Oxford (1962).
ELECTRON OF COLOURED
HALL KBr
MOBILITY
AND
CRYSTALS
PHOTOCONDUCTIVITY
AT MODERATE
TEMPERATURES
I. S. AL-SAFFAR and J. H. CALDERWOOD Department of Electrical Engineering, University of Salford, England and
K. C. KAO Department of Electrical Engineering, University of Mantiboa, Canada
(Received 20 June 1974) KBr crystals of high purity supplied from Hilgar and Watts Limited were used for this investigation. By means of additive colouration with excess potassium, F centers were produced in the crystals with the concentration of about 6.1 × 10~5cm -3 which was determined by optical absorption measurements based on Smakula's equation. The Hall sample of size 10 × 5 × 5 mm with silver-dag painted electrodes was held in a holder made of Teflon with a window on one side so that the sample could be illuminated through an external light source, and with a small heater built in it so that the sample temperature could be adjusted by an external temperature control unit. For Hall effect measurements a double a.c. method was adopted in order to minimize the errors possibly caused by the misalignment of the Hall electrodes, the generation of thermopotential and the Ettinghouse effect. We used a 50 Hz, 10kG electromagnet and a 70Hz, 1KV generator, so the measured Hall voltage was at the frequency of 20Hz, the difference between the frequency of electric field and that of the transverse magnetic field. The light source was a 1 KW profector with a Kodak Wratten filter (Type 29) which transmits light from 6100 ,~ to 10,000 ,~. At a constant low electric field the Hall voltage was linearly proportional to magnetic field for the fields up to 10 kG, and at a constant magnetic field the Hall voltage was also linearly proportional to applied electric field for the fields up to 400 V/cm indicating that the Hall effect was due to the conduction in the bulk of the sample, the surface effect being negligible. Figure 1 shows the photo-current density as a function of electric field at various temperatures. From this set of curves it can be seen that the photoconductivity at 80°C is higher than that at both 60°C and 100°C indicating that there must be a peak at the temperature between 60°C and 100°C. To find this peak accurately we used a pen recorder to record simultaneously the continuous variation of both photoconduction current and temperature at a fixed electric field, and the continuous variation of both Hall voltage and temperature at a fixed electric field and a fixed magnetic field. We have repeated this experiment several times using three samples with the same concentration of F centers (within 3 per cent) and found that the results are repeatable and consistent although the absolute values vary slightly from sample to sample. Typical results presented in terms of photoconductivity and Hall mobility as functions of temperature are shown in Fig. 2. The light corresponding to the energy range of 1-2 eV absorbed by the crystal can raise the electrons in the F centers either to higher excited states or to the conduction band, and those in 213
higher excited states are then thermally excited to the conduction band, thus causing the photocurrent or photoconductivity temperature-dependent as shown in Figs. 1 and 2. From the curves of photoconductivity as a function of temperature for temperatures below 82°C, we have calculated the activation energy and it is of the order of 0.14-0.16eV for the average fields between 130V/cm and 1050V/cm. The activation energy is fielddependent; the higher the field, the lower is the activation energy. This phonomenon may be interpreted as a lowering of the energy barrier for thermal ionization of the excited stated [1]. Our results, however, are in good agreement with those of Swank and
9x~C
/•
/ / /////~
%
/~
4¸
BO°C O0°C 0oC 40°C 2o0c
/ I 0
250
I
20°C (dark) I
I
electric~i¢lc(V/ l cm) SO0
750
1000
I
1250
Fig. h Photo-current density as a function of electric field at various temperatures for coloured KBr crystals with initial concentration of F center of 6.1 × 10'~ cm -3.
Technical Notes
214 tOx~(
'--
-
-
photo
conductivity
(mogneticfield
Holl Mob'flity (rnognetic field
--
~
-T
E
/
~
- 40
/ / / ~ ~ ' ~
///Y \ /// ,, / / / / / ,4 ',
7-
-45
OkG)
2kG)
t30 V/cm
35
\X "oV,oo \~800 Vlcm
~C"
" ov1o° 3o..>
e~
2s~
0
4-
20
~
tS
40
I 60 temperature
I 80
I ~00
:to 120
(°C)
Fig. 2. Electron Hall mobility and photoconductivity as functions of temperature for coloured KBr crystals with initial concentration of F center of 6.1 x 10'~ cm -3. Brown[2] who reported the activation energy to be 0.135 eV in the low temperature range but at a field of 7 kV/cm which is much higher than the fields used in our experiments. The average Hall mobility of electrons in the coloured KBr crystals containing 6.I × 10~' F centers cm -3 is about 16 cm2/Vsec at 20°C, increases with increasing temperature and reaches a maximum value of about 35 cm2/V-sec at about 82°C, and then decreases gradually as temperature is further increased. The value at 20°C is in good agreement with 12.5 cm2/V-sec obtained by Macdonald et al.[3] and with 15 cm2/V-sec obtained by Zelm[4] using different methods. At temperatures below 82°C the temperature dependence of the Hall mobility may result from the trap-emptying process[5]. That the results in Fig. 2 do not show clearly an exponential form may indicate that inside the crystal other types of aggregate centers such as M, R and F' centers are also formed during photo-excitation. At temperatures higher than 82°C the decrease of both Hall mobility and photoconductivity with increasing temperature may be attributed to the electron interaction with the optical mode of lattice vibration, which may become predominantly important at high temperatures. It is of interest to note that the photocurrent-field curve in Fig. 1
is quite linear at 20°C and at low fields, but becomes non-linear at high temperatures and at high fields. This phenomenon may be explained by the fact that at high fields more F centers themselves would act as trapping centers. This means that one F center may be destroyed by field ionization and a second F center may be destroyed by capturing the electron freed from the first F center, and this process is more efficient at higher temperatures and at higher fields[6]. It is the second F center, which acts as a trap, to cause the photo-current tending to reach a saturation value at higher fields. REFERENCES I. Spino]o G. and Fowler W. B., Phys. Rev. 138, A661 (1965). 2. Swank R. K. and Brown F. C., Phys. Rev. Lett. 8, 10 (1962); idem. Phys. Rev. 130, 34 (1963). 3. MacDonald J. R. and Robinson J. E., Phys. Rev. 95, 44 (1954). 4. Zelm M., Z. Phys. 212, 280 (1968). 5. Rose A., R.C.A. Rev. 12, 362 (1951). 6. Schulman J. H. and Compton W. D., Color Centers in Solids, p. 101. Pergamon Press, Oxford (1962).