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On the photoconductivity of vitreous GeO2
JOURNAL OF NON-CRYSTALLINESOLIDS 7 (1972) 192-202 © North-Holland Publishing Co., Amsterdam
O N T H E P H O T O C O N D U C T I V I T Y OF V I T R E O U S GeO2 H. F. BOHM Corporate Research Laboratories, Owens-Illinois Technical Center, Toledo, Ohio 43651, U.S.A.
Received 11 January 1971; revised manuscript received 16 August 1971 Photoconductivity experiments on vitreous GeO2 were carried out and the results are described in terms of current models. The photocurrent was measured as a function of wavelength, frequency of the applied field and sample temperature. The derivative of the photocurrent with respect to wavelength was measured by a modulation technique and the results are compared with optical absorption data. The current-voltage relation appears to be non-Ohmic and there is evidence for a space charge controlled conductivity process. 1. Introduction
Studies of the electrical properties of amorphous materials have become important in the recent years because of potential technological applications and our lack of basic knowledge about these materials. A central problem is the question about the nature of the electronic state structure of amorphous solids. Well-established theories, like the band theory, exist for crystalline solids, but for amorphous materials knowledge is still fragmentary. Considering a one-dimensional model G u b a n o v 1) concluded that the lack of long-range order does not preclude the existence of energy bands, but that the band model which applies to crystals has to be modified. Anderson 2) has demonstrated that for an electron moving in a rigid lattice such that the Hamiltonian has random matrix elements, the states at the band edges are localized; and if the disorder is high enough all states in the band become localized. Synthesizing these results, Mott ~) proposed a model for the electronic state structure of amorphous materials in which bands of extended states are separated by an energy gap, and tails of localized states extend into the gap from the band edges. The penetration into the otherwise forbidden gap depends upon the degree to which the material deviates from crystalline structure. Such a model, in which tails from the valence and conduction states overlap in the middle of the gap, was applied by Cohen et al.4), to interpret some experimental results in the chalcogenides. The present understanding of amorphous solids is therefore based on a modified band model in which extended band-like states tail off into localized states. I f the degree 192
PHOTOCONDUCTIV1TY OF VITREOUS G e O 2
193
of disorder is great enough these tails may overlap in the middle of the gap. In addition, the idea that the transition from extended to localized states is sudden leads to the concept of a mobility edge, at which the electronic mobility drops sharply. The present article presents experimental evidence which supports the basic model outlined above. For our experiments we chose a simple covalent glass with tetrahedral network structure: GeO 2, With GeO2 one does not encounter serious problems of sample preparation and the optical absorption edge is in a wavelength range where conventional quartz optics can be used. Like SiO2, GeO 2 consists of a network of closely packed tetrahedra where the cation is surrounded by four oxygens and the structure exhibits a high degree of short-range order. It is therefore nearly an "ideal" glass in the sense that it is a solid with almost perfect short-range order and no long-range order. Because of the high degree of short-range order we can speculate that the tails of localized states do not extend across the entire gap, which is about 5 eV wide, and that there will consequently be no overlap of localized states in the middle of the gap. One way to obtain information about the electronic state structure is to study the mechanisms of electronic charge transport in an external electric field. As previous experiments have shown, the dark conductivity is ionic in origin 5) and does not yield any information about the electronic state structure. Photoconductivity experiments can, on the other hand, provide such information because the charge carriers are electrons or holes. The photoconductivity experiments can be interpreted in terms of the model shown in fig. 1. This model is based on the present understanding of STATE DENSITY
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.
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Model of the electronoc state structure of vitreous Ge02.
the electronic state structure in amorphous solids as outlined above and on some physical data from vitreous GeO2. In addition to the extended states and the tails of localized states, localized defect levels are shown in the gap
194
H.F. B()HM
between the extended states, inasmuch as optical absorption data prove such defect levels can exist in a glass: For GeO2, an optical absorption band at 245 nm is observed and, according to Garino-Canina6), is believed to be due to oxygen vacancies. The density of defects depends on the thermal history of the glass. In general we will define a defect level in a glass as a state which is caused by a local perturbation of short-range order. The model of fig. 1 is hypothetical to a certain extent, and some details are still a matter of debate: What is the shape of the state density of the band-like states as a function of energy? Do tails of localized levels really exist, and what is their nature? How steep is the decrease in mobility at the mobility edge? In the case of GeO2 it is known that the lack of long-range order is due to fluctuations of the bond angles between the tetrahedra 7), and it is reasonable to conjecture that the tails of localized states are due to these fluctuations. In amorphous germanium, however, Spicer 8) found no such tails, but rather sharp band edges. Although the structure of amorphous germanium is still a matter of debate, a current model assumes it to consist of ordered microdomains separated by micro-voids a). Such highly ordered domains are not likely to be present in glasses with the network structure that characterizes GeO2, and their presence in amorphous germanium could account for the absence of tails of localized levels in this material.
2. Experimental results The photoconductivity experiments were carried out on flat, disc-like samples with a platinum electrode on one side and an evaporated gold grid on the other side. The'side with the grid was irradiated by a high pressure Xenon lamp. The diameter of the sample was 15 mm and the thickness 0.1 mm. 2.1. PHOTOCURRENTAND OPTICAL ABSORPTION In fig. 2 the photocurrent and the optical absorption are shown as a function of wavelength. Apparently there is a simultaneous increase in optical absorption and photocurrent. This indicates that the photoelectrons which originate from valence or defect states are raised across the optical gap of 5 eV to produce a photocurrent. Thus, the optical and the photo-conductivity gap are identical. The sample of fig. 2 was melted at 1350 °C in an oxygen atmosphere, and the optical absorption band at 245 nm appears as only a shoulder; other samples which were melted at higher temperatures and/or in reducing atmospheres show a much stronger absorption band at that wavelength. Samples heat treated just above the melting point of the crystalline material (1115°C) do not show any such absorption. All samples exhibit a long tail in both the optical absorption and photoconductivity. The
PHOTOCONDUCTIVITYOF VITREOUSGeO2
195
Mott model suggests that this tail is due to transitions between localized valence states and conduction states. This argument, however, is not conclusive, because it is conceivable that strong phonon interactions could also give rise to such tails in the absorption curve. 2.2.
FREQUENCY DEPENDENCE OF THE PHOTOCURRENT
From fig. 2 we conclude that in the photoconductivity process electrons are raised across the gap of ,~ 5 eV into conduction states. The question as to the nature of these states remains. Are they extended only over microscopic dimensions or are they band-like states as in crystalline solids? In order to answer this question the photoconductivity as a function of frequency of the applied field was measured in the range 0 ~
to
"~'~1 - -...,d~._.. I i 200 Fig. 2.
2.3.
250
300 X nrn
350
400
Photoconductivity (a) and optical absorption (b) of vitreous GeO2.
MODULATION EXPERIMENT
In order to obtain more information about the state density of the localized states, the fine structure in the curve of fig. 2 was investigated by a modulation technique. In this experiment a monochromator is used to modulate the wavelength of the incident light so that the derivative of the photocurrent with respect to wavelength is obtained. Fig. 3 shows a block-diagram of the apparatus. Since the light intensity varied with wavelength a phototube with constant quantum efficiency as a function of wavelength was used
196
H.F.BOHM
to monitor the light intensity; the photocurrent was normalized to the light intensity by feeding the signals into logarithmic converters and taking the difference in the output signals. The light beam was modulated by a fiat fused silica window in front of the exit slit of the monochromator; this window was vibrated by the reference signal of the lock-in amplifier. The result of the modulated experiment is plotted in fig. 4 for two samples.
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Fig. 3. Block-diagram of the modulation experiment: (a) Xenon lamp; (b) monochrr; mator; (c) vibrating quartz window; (d) photomultiplier; (e) sample; (f) preamplifieo (g) amplifier and phase shifter; (h) log converter; (i) lock-in amplifier; (k) recorder; (1) loudspeaker.
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Fig. 4. Derivative curves of two samples with different thermal histories.
~50
PHOTOCONDUCTIVITY OF VITREOUS G e O 2
197
Fig. 4a shows the result for a glass which was heat treated at 1130°C in a nitrogen atmosphere just above the melting point of the crystalline material. There is little structure and the steepest negative slope is found at 262 nm. The slope becomes zero at 230 nm and indicates a maximum in the photocurrent. The optical absorption for this sample does not exhibit any structure. The absorption peak around 245 nm, which is associated with oxygen vacancies, is absent, and there is no correlation with the photoconductivity maximum at 230 nm. Fig. 4b shows results for a glass which was melted at 1550°C in nitrogen. The derivative curve exhibits a more complex structure than that in the curve of fig. 4a; the structure in fig. 4b corresponds to two shoulders in the (integral) i versus 2 curve: one at 230 nm and one at about 260 nm. The latter one is always observed in samples which were heat treated at temperatures higher than 1250°C and which also show a strong absorption peak due to oxygen vacancies. In this sample the optical absorption exhibited a shoulder at 255 nm with an absorption of 2.7. Both the optical absorption and the photoconductivity indicate that defect states were formed in the gap as a result of the heat treatment. These states are about 0.75 eV above the valence band, if we assume that the band to band transitions start at about 230 nm. These experiments demonstrate that melting at high temperatures produces localized defect states in the band gap and the presence of these states can be monitored in a sensitive way by the modulation technique. 2.4. TEMPERATUREDEPENDENCEOF THE PHOTOCURRENT In order to study the photocurrent as a function of the sample temperature the light had to be chopped at 400 Hz. This was necessary because the dark current was much higher than the photocurrent above 100 °C. With chopped light the photocurrent was an ac signal which was fed into an ac amplifier to block the dark current. The photocurrent as a function of temperature is shown in fig. 5 in a log/versus 1/Tplot. Apparently it is thermally activated with a slope varying between 0.05 eV at low temperatures and 0.75 eV at higher temperatures. Instead of being smooth, the curve exhibits some structure at higher temperatures. Immediately after being excited into conduction states the charge carriers are trapped in localized levels for which the mobility in an external electric field is due to tunneling processes and is therefore low. The mobility in the conduction states is therefore controlled by trapping and the temperature dependence of the photocurrent arises from a thermally activated mobility. Between - 140 °C and + 140 °C the curve shows a smooth increase with a slope between 0.05 eV and 0.2 eV. We may assume that in this temperature range electrons are thermally activated from the tail of localized levels adjacent to the conduction band (see fig. 1). This behavior
198
H.F. BOHM
constitutes experimental evidence which seems to indicate that these tails really exist. The deepest level in the tail would be about 0.2 eV below the extended states. Between 140 °C and 180 °C the photocurrent is constant and above that temperature it increases with a slope of 0.75 eV. This is in agreement with the energy difference between the valence band and defect states found in the modulation experiment. Above 240 °C the photocurrent decays abruptly by more than one order of magnitude. This decay can be correlated T
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Fig. 5. Photocurrent as a function of temperature. with a decay of the dc dark conductivity at about the same temperature 5). For the dark conductivity it was found that this decay can be explained by an electrolysis effect in which mobile ions (probably Na +) polarize the electrodes. This polarization cancels the internal electric field and inhibits the photoconductivity. In fact, the rapid decay of the photocurrent above 240 °C can be observed on an oscilloscope whenever the electric field is reversed. 2.5. ESR AND THERMOLUMINESCENCE Trapping of electrons in localized levels is also observed by thermoluminescence and ESR experiments. In thermoluminescence experiments on GeO 2 trapped electrons are thermally released between - 1 8 0 ° C and 140 °C1°). Trapped electrons also give rise to an ESR signal which is shown in fig. 6. The sample of fig. 6a was heated up to 300 °C and the measurement was performed at 20 °C prior to any irradiation. Fig. 6b shows the signal
199
PHOTOCONDUCTIVITY OF VITREOUS GcO2
after the sample was exposed to uv light. A strong line appeared which decreases when the sample temperature is increased. At about 140°C the new signal has disappeared completely; only a signal similar to that in fig. 6a is observed. The thermoluminescence and the ESR absorption both disappear at about the same temperature, at which the photocurrent in the i versus 1/Tplot of fig. 5 reaches a maximum and levels out. Therefore we can assume
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ESR signal before (a) and after (b) uv irradiation.
that the ESR and thermoluminescence are due to electrons trapped in the localized levels of the tail below the extended conduction states. The signal of fig. 6a also decreases with increasing sample temperature, and it disappears when the sample is heated above 400 °C; the measurement itself was carried out at 20 °C. We may speculate that this signal is associated with the defect states which give rise to the strong increase in photocurrent above 180 °C. These experiments show that traps are present in a glass and that they affect the electronic charge transport. 2.6. SPACE CHARGE EFFECTS The sample in our experiments was fiat and disc-like, and the surface with a grid electrode was exposed to light. The electron-hole pairs were therefore produced in a thin layer close to the surface with the grid electrode. If the polarity of the applied voltage is such that, say, the holes are neutralized at
200
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the grid electrode, then the electrons will have to migrate through the sample. Some of them may be trapped on their way to the opposite electrode and this would result in a build up of a space charge. It is conceivable that the space charge may become strong enough to reduce the electric field in the sample considerably. The influence of the space charge is observed in the following experiment: If the applied voltage is suddenly decreased, for instance from 60 V to 40 V, the photocurrent does not drop to the 40 V level instantaneously, but it drops to a much lower value and approaches the 40 V level slowly (fig. 7). This behavior can be explained as a space charge effect:
-~
c
sb
o
TIME
sec
Fig. 7. Time behavior of the current when the voltage is switchedfrom 60 V to 40 V at t = 0: (a) photocurrent at --50°C; (b) photocurrent at +100°C; (c) dark current.
When the voltage is lowered the space charge causes a reverse polarity; charge carriers of the opposite sign will migrate into the sample until the space charge is reduced to the value which is appropriate to the lower external voltage. This strong reverse current causes the initial drop in the photocurrent. The same effect is observed for both increases and decreases in voltage and for both polarities. If the same experiment is carried out without light an initial current drop is also observed because of the discharge of the sample capacitance, but as fig. 7 indicates the time constant for this process is much shorter, which proves that the space charge effect in the photoconductivity is not an artifact. As fig. 7 shows the time constant for the space charge decay is temperature dependent, which is expected for a process in which traps are involved. If the experiment described above is carried out with chopped light, an ac signal can be monitored on the oscilloscope. If, for instance, the voltage is changed from 200 V to some lower value the ampli-
P H O T O C O N D U C T I V 1 T Y OF V I T R E O U S C ~ O 2
201
tude of the ac signal shows a time behavior similar to the curve of fig. 7: an initial strong drop and a slow increase thereafter. If the voltage change is high enough the ac signal becomes inverted as the result of a current which flows against the external applied field. This shows that the internal electric field due to the space charge becomes stronger than the external applied field. The reverse current continues to flow until the space charge is reduced sufficiently. 2.7. NON-OHMICBEHAVIOR Since trapping and space charge apparently affect the photoconductivity, non-Ohmic behavior is expected. In fact, the current-voltage relation is expected to be of the Poole-Frenkel n) type rather than of the Ohmic type. In the Poole-Frenkel mechanism the influence of the electric field on the release of trapped charge carriers is given by the law log i,-,x/E(E= electric field). Hill 1~) has shown the dependence on x/E is not valid if the density of defects is sufficiently great to give overlap of the Coulombic potentials surrounding the defects. In this case a dependence upon E (Poole's law) instead of x/E is a better approximation. In a glass a certain overlap of the Coulombic potentials of the localized defect states is expected and as shown in fig. 8, a linear depencdence of logip~ on the external field is found to be a good approximation. However, the formulas given by Hill 12) do not describe the data quantitatively. The reason may be that a variable space charge, which results in
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Fig. 8. Photocurrent as a function of the applied electric field: (a) at ÷I00°C; (b) at 20°C; (c) at --50°C.
202
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a variable internal field, and a distribution of traps over different energies complicate the situation.
3. Conclusions The photoconductivity experiments on vitreous GeO 2 show that (1) the charge carriers move in band-like states because no frequency dependence is found; (2) the charge carriers originate from valence states and must be raised across the optical gap of ~ 5 eV; (3) localized defect levels, which act as traps, exist in the gap; (4) there is evidence for tails of localized states adjacent to the extended states; the localized states reach about 0.2 eV into the gap; (5) trapping in localized states limits the mobility of the carrier; (6) space charge effects are observed due to trapping of the charge carriers.
Acknowledgements I would like to acknowledge the assistance of Dr. G. R. Mather and Mr. J. A. Lorenc in carrying out the ESR experiment. The help of Mr. E. F. Hinebaugh in preparing the samples and carrying out the measurements is greatly appreciated.
References I) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)
A. I. Gubanov, Zh. Eksperim. i Teor. Fiz. 26 (1954) 139. P. W. Anderson, Phys. Rev. 109 (1958) 1492. N. F. Mott, Advan. Phys. 16 (1967) 49. M. H. Cohen, H. Fritsche and S. R. Ovshinsky, Phys. Rev. Letters 22 (1969) 1065. H. Brhm, submitted for publication in J. Appl. Phys. V. Garino-Canina, Compt. Rend. (Paris) 247 (1958) 1319. B. E. Warren, Third Intern. Conf. on the Physics of Non-Crystalline Solids, Sheffield, 1970. T. M. Donovan and W. E. Spicer, Phys. Rev. Letters 21 0968) 1572. W. E. Spicer, private communication. H. Brhm, Phys. Chem. Glasses 11 (1970) 177. J. Frenkel, Phys. Rev. 54 (1938) 647. R. M. Hill, Phil. Mag. 23 (1971) 59.
O N T H E P H O T O C O N D U C T I V I T Y OF V I T R E O U S GeO2 H. F. BOHM Corporate Research Laboratories, Owens-Illinois Technical Center, Toledo, Ohio 43651, U.S.A.
Received 11 January 1971; revised manuscript received 16 August 1971 Photoconductivity experiments on vitreous GeO2 were carried out and the results are described in terms of current models. The photocurrent was measured as a function of wavelength, frequency of the applied field and sample temperature. The derivative of the photocurrent with respect to wavelength was measured by a modulation technique and the results are compared with optical absorption data. The current-voltage relation appears to be non-Ohmic and there is evidence for a space charge controlled conductivity process. 1. Introduction
Studies of the electrical properties of amorphous materials have become important in the recent years because of potential technological applications and our lack of basic knowledge about these materials. A central problem is the question about the nature of the electronic state structure of amorphous solids. Well-established theories, like the band theory, exist for crystalline solids, but for amorphous materials knowledge is still fragmentary. Considering a one-dimensional model G u b a n o v 1) concluded that the lack of long-range order does not preclude the existence of energy bands, but that the band model which applies to crystals has to be modified. Anderson 2) has demonstrated that for an electron moving in a rigid lattice such that the Hamiltonian has random matrix elements, the states at the band edges are localized; and if the disorder is high enough all states in the band become localized. Synthesizing these results, Mott ~) proposed a model for the electronic state structure of amorphous materials in which bands of extended states are separated by an energy gap, and tails of localized states extend into the gap from the band edges. The penetration into the otherwise forbidden gap depends upon the degree to which the material deviates from crystalline structure. Such a model, in which tails from the valence and conduction states overlap in the middle of the gap, was applied by Cohen et al.4), to interpret some experimental results in the chalcogenides. The present understanding of amorphous solids is therefore based on a modified band model in which extended band-like states tail off into localized states. I f the degree 192
PHOTOCONDUCTIV1TY OF VITREOUS G e O 2
193
of disorder is great enough these tails may overlap in the middle of the gap. In addition, the idea that the transition from extended to localized states is sudden leads to the concept of a mobility edge, at which the electronic mobility drops sharply. The present article presents experimental evidence which supports the basic model outlined above. For our experiments we chose a simple covalent glass with tetrahedral network structure: GeO 2, With GeO2 one does not encounter serious problems of sample preparation and the optical absorption edge is in a wavelength range where conventional quartz optics can be used. Like SiO2, GeO 2 consists of a network of closely packed tetrahedra where the cation is surrounded by four oxygens and the structure exhibits a high degree of short-range order. It is therefore nearly an "ideal" glass in the sense that it is a solid with almost perfect short-range order and no long-range order. Because of the high degree of short-range order we can speculate that the tails of localized states do not extend across the entire gap, which is about 5 eV wide, and that there will consequently be no overlap of localized states in the middle of the gap. One way to obtain information about the electronic state structure is to study the mechanisms of electronic charge transport in an external electric field. As previous experiments have shown, the dark conductivity is ionic in origin 5) and does not yield any information about the electronic state structure. Photoconductivity experiments can, on the other hand, provide such information because the charge carriers are electrons or holes. The photoconductivity experiments can be interpreted in terms of the model shown in fig. 1. This model is based on the present understanding of STATE DENSITY
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.
.
.
.
.
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Model of the electronoc state structure of vitreous Ge02.
the electronic state structure in amorphous solids as outlined above and on some physical data from vitreous GeO2. In addition to the extended states and the tails of localized states, localized defect levels are shown in the gap
194
H.F. B()HM
between the extended states, inasmuch as optical absorption data prove such defect levels can exist in a glass: For GeO2, an optical absorption band at 245 nm is observed and, according to Garino-Canina6), is believed to be due to oxygen vacancies. The density of defects depends on the thermal history of the glass. In general we will define a defect level in a glass as a state which is caused by a local perturbation of short-range order. The model of fig. 1 is hypothetical to a certain extent, and some details are still a matter of debate: What is the shape of the state density of the band-like states as a function of energy? Do tails of localized levels really exist, and what is their nature? How steep is the decrease in mobility at the mobility edge? In the case of GeO2 it is known that the lack of long-range order is due to fluctuations of the bond angles between the tetrahedra 7), and it is reasonable to conjecture that the tails of localized states are due to these fluctuations. In amorphous germanium, however, Spicer 8) found no such tails, but rather sharp band edges. Although the structure of amorphous germanium is still a matter of debate, a current model assumes it to consist of ordered microdomains separated by micro-voids a). Such highly ordered domains are not likely to be present in glasses with the network structure that characterizes GeO2, and their presence in amorphous germanium could account for the absence of tails of localized levels in this material.
2. Experimental results The photoconductivity experiments were carried out on flat, disc-like samples with a platinum electrode on one side and an evaporated gold grid on the other side. The'side with the grid was irradiated by a high pressure Xenon lamp. The diameter of the sample was 15 mm and the thickness 0.1 mm. 2.1. PHOTOCURRENTAND OPTICAL ABSORPTION In fig. 2 the photocurrent and the optical absorption are shown as a function of wavelength. Apparently there is a simultaneous increase in optical absorption and photocurrent. This indicates that the photoelectrons which originate from valence or defect states are raised across the optical gap of 5 eV to produce a photocurrent. Thus, the optical and the photo-conductivity gap are identical. The sample of fig. 2 was melted at 1350 °C in an oxygen atmosphere, and the optical absorption band at 245 nm appears as only a shoulder; other samples which were melted at higher temperatures and/or in reducing atmospheres show a much stronger absorption band at that wavelength. Samples heat treated just above the melting point of the crystalline material (1115°C) do not show any such absorption. All samples exhibit a long tail in both the optical absorption and photoconductivity. The
PHOTOCONDUCTIVITYOF VITREOUSGeO2
195
Mott model suggests that this tail is due to transitions between localized valence states and conduction states. This argument, however, is not conclusive, because it is conceivable that strong phonon interactions could also give rise to such tails in the absorption curve. 2.2.
FREQUENCY DEPENDENCE OF THE PHOTOCURRENT
From fig. 2 we conclude that in the photoconductivity process electrons are raised across the gap of ,~ 5 eV into conduction states. The question as to the nature of these states remains. Are they extended only over microscopic dimensions or are they band-like states as in crystalline solids? In order to answer this question the photoconductivity as a function of frequency of the applied field was measured in the range 0 ~
to
"~'~1 - -...,d~._.. I i 200 Fig. 2.
2.3.
250
300 X nrn
350
400
Photoconductivity (a) and optical absorption (b) of vitreous GeO2.
MODULATION EXPERIMENT
In order to obtain more information about the state density of the localized states, the fine structure in the curve of fig. 2 was investigated by a modulation technique. In this experiment a monochromator is used to modulate the wavelength of the incident light so that the derivative of the photocurrent with respect to wavelength is obtained. Fig. 3 shows a block-diagram of the apparatus. Since the light intensity varied with wavelength a phototube with constant quantum efficiency as a function of wavelength was used
196
H.F.BOHM
to monitor the light intensity; the photocurrent was normalized to the light intensity by feeding the signals into logarithmic converters and taking the difference in the output signals. The light beam was modulated by a fiat fused silica window in front of the exit slit of the monochromator; this window was vibrated by the reference signal of the lock-in amplifier. The result of the modulated experiment is plotted in fig. 4 for two samples.
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Fig. 3. Block-diagram of the modulation experiment: (a) Xenon lamp; (b) monochrr; mator; (c) vibrating quartz window; (d) photomultiplier; (e) sample; (f) preamplifieo (g) amplifier and phase shifter; (h) log converter; (i) lock-in amplifier; (k) recorder; (1) loudspeaker.
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200
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Fig. 4. Derivative curves of two samples with different thermal histories.
~50
PHOTOCONDUCTIVITY OF VITREOUS G e O 2
197
Fig. 4a shows the result for a glass which was heat treated at 1130°C in a nitrogen atmosphere just above the melting point of the crystalline material. There is little structure and the steepest negative slope is found at 262 nm. The slope becomes zero at 230 nm and indicates a maximum in the photocurrent. The optical absorption for this sample does not exhibit any structure. The absorption peak around 245 nm, which is associated with oxygen vacancies, is absent, and there is no correlation with the photoconductivity maximum at 230 nm. Fig. 4b shows results for a glass which was melted at 1550°C in nitrogen. The derivative curve exhibits a more complex structure than that in the curve of fig. 4a; the structure in fig. 4b corresponds to two shoulders in the (integral) i versus 2 curve: one at 230 nm and one at about 260 nm. The latter one is always observed in samples which were heat treated at temperatures higher than 1250°C and which also show a strong absorption peak due to oxygen vacancies. In this sample the optical absorption exhibited a shoulder at 255 nm with an absorption of 2.7. Both the optical absorption and the photoconductivity indicate that defect states were formed in the gap as a result of the heat treatment. These states are about 0.75 eV above the valence band, if we assume that the band to band transitions start at about 230 nm. These experiments demonstrate that melting at high temperatures produces localized defect states in the band gap and the presence of these states can be monitored in a sensitive way by the modulation technique. 2.4. TEMPERATUREDEPENDENCEOF THE PHOTOCURRENT In order to study the photocurrent as a function of the sample temperature the light had to be chopped at 400 Hz. This was necessary because the dark current was much higher than the photocurrent above 100 °C. With chopped light the photocurrent was an ac signal which was fed into an ac amplifier to block the dark current. The photocurrent as a function of temperature is shown in fig. 5 in a log/versus 1/Tplot. Apparently it is thermally activated with a slope varying between 0.05 eV at low temperatures and 0.75 eV at higher temperatures. Instead of being smooth, the curve exhibits some structure at higher temperatures. Immediately after being excited into conduction states the charge carriers are trapped in localized levels for which the mobility in an external electric field is due to tunneling processes and is therefore low. The mobility in the conduction states is therefore controlled by trapping and the temperature dependence of the photocurrent arises from a thermally activated mobility. Between - 140 °C and + 140 °C the curve shows a smooth increase with a slope between 0.05 eV and 0.2 eV. We may assume that in this temperature range electrons are thermally activated from the tail of localized levels adjacent to the conduction band (see fig. 1). This behavior
198
H.F. BOHM
constitutes experimental evidence which seems to indicate that these tails really exist. The deepest level in the tail would be about 0.2 eV below the extended states. Between 140 °C and 180 °C the photocurrent is constant and above that temperature it increases with a slope of 0.75 eV. This is in agreement with the energy difference between the valence band and defect states found in the modulation experiment. Above 240 °C the photocurrent decays abruptly by more than one order of magnitude. This decay can be correlated T
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Fig. 5. Photocurrent as a function of temperature. with a decay of the dc dark conductivity at about the same temperature 5). For the dark conductivity it was found that this decay can be explained by an electrolysis effect in which mobile ions (probably Na +) polarize the electrodes. This polarization cancels the internal electric field and inhibits the photoconductivity. In fact, the rapid decay of the photocurrent above 240 °C can be observed on an oscilloscope whenever the electric field is reversed. 2.5. ESR AND THERMOLUMINESCENCE Trapping of electrons in localized levels is also observed by thermoluminescence and ESR experiments. In thermoluminescence experiments on GeO 2 trapped electrons are thermally released between - 1 8 0 ° C and 140 °C1°). Trapped electrons also give rise to an ESR signal which is shown in fig. 6. The sample of fig. 6a was heated up to 300 °C and the measurement was performed at 20 °C prior to any irradiation. Fig. 6b shows the signal
199
PHOTOCONDUCTIVITY OF VITREOUS GcO2
after the sample was exposed to uv light. A strong line appeared which decreases when the sample temperature is increased. At about 140°C the new signal has disappeared completely; only a signal similar to that in fig. 6a is observed. The thermoluminescence and the ESR absorption both disappear at about the same temperature, at which the photocurrent in the i versus 1/Tplot of fig. 5 reaches a maximum and levels out. Therefore we can assume
V 3180
3;;20 MAGNETIC FIELD Gouts
Fig. 6.
i 5260
ESR signal before (a) and after (b) uv irradiation.
that the ESR and thermoluminescence are due to electrons trapped in the localized levels of the tail below the extended conduction states. The signal of fig. 6a also decreases with increasing sample temperature, and it disappears when the sample is heated above 400 °C; the measurement itself was carried out at 20 °C. We may speculate that this signal is associated with the defect states which give rise to the strong increase in photocurrent above 180 °C. These experiments show that traps are present in a glass and that they affect the electronic charge transport. 2.6. SPACE CHARGE EFFECTS The sample in our experiments was fiat and disc-like, and the surface with a grid electrode was exposed to light. The electron-hole pairs were therefore produced in a thin layer close to the surface with the grid electrode. If the polarity of the applied voltage is such that, say, the holes are neutralized at
200
H.F. BOHM
the grid electrode, then the electrons will have to migrate through the sample. Some of them may be trapped on their way to the opposite electrode and this would result in a build up of a space charge. It is conceivable that the space charge may become strong enough to reduce the electric field in the sample considerably. The influence of the space charge is observed in the following experiment: If the applied voltage is suddenly decreased, for instance from 60 V to 40 V, the photocurrent does not drop to the 40 V level instantaneously, but it drops to a much lower value and approaches the 40 V level slowly (fig. 7). This behavior can be explained as a space charge effect:
-~
c
sb
o
TIME
sec
Fig. 7. Time behavior of the current when the voltage is switchedfrom 60 V to 40 V at t = 0: (a) photocurrent at --50°C; (b) photocurrent at +100°C; (c) dark current.
When the voltage is lowered the space charge causes a reverse polarity; charge carriers of the opposite sign will migrate into the sample until the space charge is reduced to the value which is appropriate to the lower external voltage. This strong reverse current causes the initial drop in the photocurrent. The same effect is observed for both increases and decreases in voltage and for both polarities. If the same experiment is carried out without light an initial current drop is also observed because of the discharge of the sample capacitance, but as fig. 7 indicates the time constant for this process is much shorter, which proves that the space charge effect in the photoconductivity is not an artifact. As fig. 7 shows the time constant for the space charge decay is temperature dependent, which is expected for a process in which traps are involved. If the experiment described above is carried out with chopped light, an ac signal can be monitored on the oscilloscope. If, for instance, the voltage is changed from 200 V to some lower value the ampli-
P H O T O C O N D U C T I V 1 T Y OF V I T R E O U S C ~ O 2
201
tude of the ac signal shows a time behavior similar to the curve of fig. 7: an initial strong drop and a slow increase thereafter. If the voltage change is high enough the ac signal becomes inverted as the result of a current which flows against the external applied field. This shows that the internal electric field due to the space charge becomes stronger than the external applied field. The reverse current continues to flow until the space charge is reduced sufficiently. 2.7. NON-OHMICBEHAVIOR Since trapping and space charge apparently affect the photoconductivity, non-Ohmic behavior is expected. In fact, the current-voltage relation is expected to be of the Poole-Frenkel n) type rather than of the Ohmic type. In the Poole-Frenkel mechanism the influence of the electric field on the release of trapped charge carriers is given by the law log i,-,x/E(E= electric field). Hill 1~) has shown the dependence on x/E is not valid if the density of defects is sufficiently great to give overlap of the Coulombic potentials surrounding the defects. In this case a dependence upon E (Poole's law) instead of x/E is a better approximation. In a glass a certain overlap of the Coulombic potentials of the localized defect states is expected and as shown in fig. 8, a linear depencdence of logip~ on the external field is found to be a good approximation. However, the formulas given by Hill 12) do not describe the data quantitatively. The reason may be that a variable space charge, which results in
~3 ,..=.
o
2
I 0
I
!
2
4
ELECTRIC FIELD
xlO4 Vlcm
Fig. 8. Photocurrent as a function of the applied electric field: (a) at ÷I00°C; (b) at 20°C; (c) at --50°C.
202
n.v. aOi~M
a variable internal field, and a distribution of traps over different energies complicate the situation.
3. Conclusions The photoconductivity experiments on vitreous GeO 2 show that (1) the charge carriers move in band-like states because no frequency dependence is found; (2) the charge carriers originate from valence states and must be raised across the optical gap of ~ 5 eV; (3) localized defect levels, which act as traps, exist in the gap; (4) there is evidence for tails of localized states adjacent to the extended states; the localized states reach about 0.2 eV into the gap; (5) trapping in localized states limits the mobility of the carrier; (6) space charge effects are observed due to trapping of the charge carriers.
Acknowledgements I would like to acknowledge the assistance of Dr. G. R. Mather and Mr. J. A. Lorenc in carrying out the ESR experiment. The help of Mr. E. F. Hinebaugh in preparing the samples and carrying out the measurements is greatly appreciated.
References I) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12)
A. I. Gubanov, Zh. Eksperim. i Teor. Fiz. 26 (1954) 139. P. W. Anderson, Phys. Rev. 109 (1958) 1492. N. F. Mott, Advan. Phys. 16 (1967) 49. M. H. Cohen, H. Fritsche and S. R. Ovshinsky, Phys. Rev. Letters 22 (1969) 1065. H. Brhm, submitted for publication in J. Appl. Phys. V. Garino-Canina, Compt. Rend. (Paris) 247 (1958) 1319. B. E. Warren, Third Intern. Conf. on the Physics of Non-Crystalline Solids, Sheffield, 1970. T. M. Donovan and W. E. Spicer, Phys. Rev. Letters 21 0968) 1572. W. E. Spicer, private communication. H. Brhm, Phys. Chem. Glasses 11 (1970) 177. J. Frenkel, Phys. Rev. 54 (1938) 647. R. M. Hill, Phil. Mag. 23 (1971) 59.