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Mechanism of surface conduction in alkali halides
__ _l!B
SOLID STATE
cQ&
IONICS
EUEVIER
Solid State Ionics 79 (1995) 315-318
Mechanism of surface conduction in alkali halides Akira Fukai, Hiroshi Asechi, Kazuhisa Nakagawa Physics Department,
Kagoshima
University, l-21 -35 Kohrimoto,
Kagoshima-Shi
890, Japan
Abstract Both surface and bulk conductivity measurement have been simultaneously performed in NaCl single crystals cantaining Ca*’ of 10 ppm purity in the temperature range of 200-650°C. The experimental results have been analyzed in terms of a double layer near the crystal surface. The formation energy of positive ion vacancy at the surface is found to be 0.57 eV. Keywords:
Alkali halides; Surface double layer; Surface conductivity;
1. Background
Isoelectric
of the present research
It is well known that an intrinsic point defect is of Schottky type in an alkali halide crystal. The formation energy of positive ion vacancy is smaller than that of negative ion vacancy, which causes any sink or source to be electrically charged. For instance, one may observe that a crystal surface is positively charged due to an excess of negative ion vacancies, while the region just below the surface contains an excess of positive ion vacancies, thus constituting the so-called surface double layer (to be called SDL hereafter) extending over the crystal surface. Since crystals usually contain doubly ionized positive ions as impurities, there is a particular temperature at which a surface double layer will vanish; this is termed the isoelectric temperature T,. At lower temperature the crystal surface is negatively charged due to the precipitation of positive ion vacancies caused by the presence of positively charged impurity. There have been several authors who treated the SDL theoretically [l-3]. Kliewer and Koehler [l] have extensively developed the theory of SDL which will underlie the basis of analyses of the present experimental data. In order to confirm the presence 0167-2738/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0167-2738(95)00080-l
temperature;
Formation
energy
of SDL, in the experimental work a considerable amount of research has been done in silver halides [4] from the viewpoint of technical applications. As to the experimental works in alkali halides, B.L. Harris [5] has recently measured the surface potential due to SDL at room temperature. Meanwhile one of the present authors [6], by means of SIMS at ambient temperature, has observed the build-up of impurity ions toward the surface after cleaving NaCl single crystal. The purpose of the present work is to study the effect of positive ion vacancies associated with the SDL on the surface conductivity in the temperature range including an isoelectric temperature.
2. Method of measurement sults
and experimental
re-
The layout of electrodes for the measurement of dc current is shown in Fig. la. The electrodes A and B, placed on the upper surface of crystal, are to pick up the surface current i,, with electrode C located on the lower side of the overall surface. Applying a voltage to the electrodes as shown in the figure,
316
A. Fukai et al. /Solid
State Ionics 79 (1995) 315-318
temperatures while lowering the temperature at a rate of lOO”C/h. At each measurement temperature, readings of currents were performed in 20 s. after applying the voltages. Given that the current usually decreases with time, such procedures assure reproducible results. Experimental results are shown in Fig. lb. Here log cr. T is plotted against 1000/T where (+ stands for conductivity. Surface conductivity is defined here as (a/b)(i,/V), where a is the distance between electrode A and B over the crystal surface, b is the width of electrode, and V the applied voltage. It becomes, thus, necessary to divide surface conductivity by the effective thickness of surface current zAB in order to compare with bulk conductivity. Although there is no way to assess the effective thickness in which i, flows beneath the surface, the surface conductivity thus corrected must converge to almost the same as that of bulk conductivity at high temperatures. It is because the thickness of SDL becomes thinner at such a temperature. In Fig. lb, the surface conductivity is superimposed on the bulk conductivity so that they converge to the same value at high temperatures.
(a) Crystal Crystal
No.5.8(10ppm) Size(cm)
-loI
j
10100
1
700
800 500
700 400
600
3
’ ’ 2 1000/T 500
300
(K 200
)
(“C 1
(b) Fig. 1. (a). The layout of electrodes for measuring both surface and bulk conductivities. Current i, flowing into the crystal interior at electrode A consists of i, and i,. Electrode B picks up running just beneath the surface. Current i, the current i, flowing out of electrode C contributes the bulk conductivity; (b) The experimental results in cleaved-cut NaCl single crystal containing 10 ppm Ca *+ Surface conductivity, indicated by solid circles is compared with bulk conductivity after being shifted by 6d. These two conductivity curves cross at 590 K as indicated by the arrow.
makes it possible to obtain simultaneously both surface and bulk conductivities through i, and i,, respectively. The samples used in the present work were cleaved into suitable sizes from home-grown NaCl ingots. The samples were found to contain Ca2+ with the concentration as low as 10 ppm according to the SIMS analysis. Measurement procedures were as follows: after maintaining 650°C for one to two hours i, and i, were measured at predetermined
3. Analyses of the data
The following are worth mentioning from the close examination of Fig. lb: (i) The amount of upward shift, i.e. an effective thickness of current i,, is about 18 pm in this particular run. This corresponds to 1.5% of the sample thickness. (ii) Two curves seem to cross at a well defined temperature as shown by an arrow in the figure. (iii) At temperatures above the cross-over point, the surface conductivity is slightly larger than the bulk conductivity, while, at lower temperatures, the surface conductivity is considerably smaller. Before going into the detail of the analyses, the structure of SDL, as proposed by Kliewer and Koehler, is worth mentioning. Referring to Fig. 2, one sees that thickness of SDL, K-' , decreases gradually with increasing temperatures. N,.,, , the total number of excess of positive ion vacancies inside SDL varies from negative to positive through the isoelectric temperature. In other words, there are
317
A. Fukai et al./Solid State Ionics 79 (1995) 315-318
fewer charge carriers just beneath the crystal surface, below temperatures T,, which reduce the local conductivity. The total number of excess positive ion vacancies above the surface, N,.,, changes from positive to negative with increasing temperature. Judging from the considerations just mentioned above, the cross-over point of Fig. lb is suspected to correspond to an isoelectric temperature. The temperature of the cross-over point is found to be 590 K, lower by 35 K than theoretically expected temperature for NaCl with 10 ppm divalent impurity content. Since T, is dependent on the formation energy of positive ion vacancy, this means that such a formation at the surface is 0.57 eV in contrast to 0.80 eV which has been found by the experiments on the charged dislocations. It has been mentioned in Section 2 that the effective thickness of the current i, is about 18 Km. In order to understand the physical meaning of “effective thickness”, the path of i,, has been calculated with the help of distribution of line of force inside the crystal, as shown in Fig. 3a. The current i, flows through SDL with estimated thickness K- ’
-.r,,1
\
6’ /
-At
c
A
II
d
Ic i +0
(a) ‘0
.”
+b
(b)
K-’ vs.T
Nc.ex.Nc.s, Nc.ex Nc.s
.._ I
I&+&
I AS a
NaCl(C=lOppm)
K’G) Fig. 3. (al. The sideview of Fig. la. The current i, flowing into the crystal at electrode A is presumed to consist of i,, and i,,,,. The former runs above the surface, while the latter flows in the dotted region, including the surface double layer of effective thickness K-’ . (b) and (cl explain how the total conductance 5, has been calculated. In order to work out total resistance between electrode A and B, R,, the dotted region that iAB,, traverses is divided into many hollow pipes along the force lines.
600
400
I 100
I
I 300
800
I
1 500
1060
I
(K)
I 700
(“c)
Fig. 2. The temperature influence on the physical quantities relating to the structure of surface double layer in NaCl containing 10 ppm divalent impurity. The three curves have been calculated on the basis of the theory of Kliewer and Koehler. Here N,,, N,,,, and K-I are: total number of positive ion vacancy above the surface, total number of excess positive ion vacancy beneath the surface and an effective thickness of surface double layer, respectively. N,,, and N,,,, vanish at the isoelectric temperature T,.
when it passes between electrode A and B, thus carrying the information of SDL before it is picked up by electrode B. It must be noticed at this point that current i,, flows along two separate paths; one that runs over the crystal surface, i,,,, the other below the surface, iA,,,. Then “effective thickness” may be as well understood as an average depth of flow line of i,,,. By the way, i, may effectively contribute to bulk conductivity, as mentioned previously. For the purpose of calculating i,,, in detail, one has to know total conductance Gt between electrodes
318
A. Fukai et al./Solid
State lottics 79 tI995) 315-318
Comparing the calculated conductance with the experimental results shown in Fig. lb, one observes that the surface conductivity is much lower than that theoretically expected at low temperatures. The difference between these two is slight in the region of high temperatures, as expected. This situation may be explained by a smaller formation energy of positive ion vacancy, i.e. experimental value 0.57 eV is 28% smaller than 0.80 eV which has been used in calculating the total conductance. Smaller formation energy may induce greater precipitation of positive ion vacancies over the surface, causing greater deficiency of charge carriers beneath the crystal surface.
Fig. 4. the calculated total conductance 5, as a function of temperature for three different values of 6d, the maximum depth of current i,,,. In obtaining I?,, it is necessary to know the concentration of positive ion vacancies nc as a function of depth and its diffusion coefficient 0,.
A and B. The portion of electrode A from which i,,,, flows is divided into narrow strips, of width Ab, as shown in Fig. 3b. Since the concentration of positive ion vacancy charge carriers, depends on the depth from the surface, it follows that the ionic conductivity is also dependent on the depth. Fig. 3c shows how to estimate the conductance of each strip. Here pi is the specific resistivity at the distance xi along the line of force. The expression shown below the figure gives the total conductance of a strip with width of unity. Fig. 4 shows the calculated conductance for three different ad, maximum depth of line of force (refer to Fig. 3c), which may be varied by reducing the crystal thickness. Total conductance is plotted in arbitrary unit against 1000/T. Physical quantities in working out these curves are as follows: formation energy of positive ion vacancy 0.8 eV -3.1 kT, activation energy of diffusion of positive ion vacancy 0.8 eV. 6d can be taken as an effective thickness of i,,,,. It is seen in this figure that the effect of SDL becomes noticeable for the thickness as thin as 0.15 pm, i.e. about 200 times the thickness of SDL.
4. Conclusions (i) Both surface and bulk conductivities have been simultaneously measured in the temperature range of 200°C up to 650°C for cleaved-cut NaCl single crystals. (ii) The corrected surface conductivity intersects with the bulk conductivity at a well defined temperature which may correspond to an isoelectric temperature of the surface double layer. The temperature thus obtained gives 0.57 eV as formation energy of positive ion vacancy at the surface, 28% smaller than that at the dislocation. (iii) It seems that the deficiency of positive ion vacancies below the surface is greater than that so far reported.
References [l] K. KIiewer and J. Koehler, Phys. Rev. 140 (1965) A1226, A1241. [2] 1. Lifshitz, A. Kosevich and Ya. Geguzin, J. Phys. Chem. Solids 28 (1967) 78. [3] R. Poeppel and J. Blakely, Surface Sci. 15 (1969) 507. [4] M.E. van HuIIe and W. Maenhout-van der Vorst, Phys. Status Solidi (a) 39 (1977) 253. [5] L.B. Harris, Radiat. Eff. Defects Solids, 119-121 (1991) 481. f6] A. Fukai, Y. Sato, T. Shimoide and H. Usuki in: Secondary Ion Mass Spectrometry SIMS IX, eds. A. Benninghoven, R. Shimizu, M. Nihei and H.W. Werner (Wiley, Chichester, 1994) p. 480.
SOLID STATE
cQ&
IONICS
EUEVIER
Solid State Ionics 79 (1995) 315-318
Mechanism of surface conduction in alkali halides Akira Fukai, Hiroshi Asechi, Kazuhisa Nakagawa Physics Department,
Kagoshima
University, l-21 -35 Kohrimoto,
Kagoshima-Shi
890, Japan
Abstract Both surface and bulk conductivity measurement have been simultaneously performed in NaCl single crystals cantaining Ca*’ of 10 ppm purity in the temperature range of 200-650°C. The experimental results have been analyzed in terms of a double layer near the crystal surface. The formation energy of positive ion vacancy at the surface is found to be 0.57 eV. Keywords:
Alkali halides; Surface double layer; Surface conductivity;
1. Background
Isoelectric
of the present research
It is well known that an intrinsic point defect is of Schottky type in an alkali halide crystal. The formation energy of positive ion vacancy is smaller than that of negative ion vacancy, which causes any sink or source to be electrically charged. For instance, one may observe that a crystal surface is positively charged due to an excess of negative ion vacancies, while the region just below the surface contains an excess of positive ion vacancies, thus constituting the so-called surface double layer (to be called SDL hereafter) extending over the crystal surface. Since crystals usually contain doubly ionized positive ions as impurities, there is a particular temperature at which a surface double layer will vanish; this is termed the isoelectric temperature T,. At lower temperature the crystal surface is negatively charged due to the precipitation of positive ion vacancies caused by the presence of positively charged impurity. There have been several authors who treated the SDL theoretically [l-3]. Kliewer and Koehler [l] have extensively developed the theory of SDL which will underlie the basis of analyses of the present experimental data. In order to confirm the presence 0167-2738/95/$09.50 0 1995 Elsevier Science B.V. All rights reserved SSDI 0167-2738(95)00080-l
temperature;
Formation
energy
of SDL, in the experimental work a considerable amount of research has been done in silver halides [4] from the viewpoint of technical applications. As to the experimental works in alkali halides, B.L. Harris [5] has recently measured the surface potential due to SDL at room temperature. Meanwhile one of the present authors [6], by means of SIMS at ambient temperature, has observed the build-up of impurity ions toward the surface after cleaving NaCl single crystal. The purpose of the present work is to study the effect of positive ion vacancies associated with the SDL on the surface conductivity in the temperature range including an isoelectric temperature.
2. Method of measurement sults
and experimental
re-
The layout of electrodes for the measurement of dc current is shown in Fig. la. The electrodes A and B, placed on the upper surface of crystal, are to pick up the surface current i,, with electrode C located on the lower side of the overall surface. Applying a voltage to the electrodes as shown in the figure,
316
A. Fukai et al. /Solid
State Ionics 79 (1995) 315-318
temperatures while lowering the temperature at a rate of lOO”C/h. At each measurement temperature, readings of currents were performed in 20 s. after applying the voltages. Given that the current usually decreases with time, such procedures assure reproducible results. Experimental results are shown in Fig. lb. Here log cr. T is plotted against 1000/T where (+ stands for conductivity. Surface conductivity is defined here as (a/b)(i,/V), where a is the distance between electrode A and B over the crystal surface, b is the width of electrode, and V the applied voltage. It becomes, thus, necessary to divide surface conductivity by the effective thickness of surface current zAB in order to compare with bulk conductivity. Although there is no way to assess the effective thickness in which i, flows beneath the surface, the surface conductivity thus corrected must converge to almost the same as that of bulk conductivity at high temperatures. It is because the thickness of SDL becomes thinner at such a temperature. In Fig. lb, the surface conductivity is superimposed on the bulk conductivity so that they converge to the same value at high temperatures.
(a) Crystal Crystal
No.5.8(10ppm) Size(cm)
-loI
j
10100
1
700
800 500
700 400
600
3
’ ’ 2 1000/T 500
300
(K 200
)
(“C 1
(b) Fig. 1. (a). The layout of electrodes for measuring both surface and bulk conductivities. Current i, flowing into the crystal interior at electrode A consists of i, and i,. Electrode B picks up running just beneath the surface. Current i, the current i, flowing out of electrode C contributes the bulk conductivity; (b) The experimental results in cleaved-cut NaCl single crystal containing 10 ppm Ca *+ Surface conductivity, indicated by solid circles is compared with bulk conductivity after being shifted by 6d. These two conductivity curves cross at 590 K as indicated by the arrow.
makes it possible to obtain simultaneously both surface and bulk conductivities through i, and i,, respectively. The samples used in the present work were cleaved into suitable sizes from home-grown NaCl ingots. The samples were found to contain Ca2+ with the concentration as low as 10 ppm according to the SIMS analysis. Measurement procedures were as follows: after maintaining 650°C for one to two hours i, and i, were measured at predetermined
3. Analyses of the data
The following are worth mentioning from the close examination of Fig. lb: (i) The amount of upward shift, i.e. an effective thickness of current i,, is about 18 pm in this particular run. This corresponds to 1.5% of the sample thickness. (ii) Two curves seem to cross at a well defined temperature as shown by an arrow in the figure. (iii) At temperatures above the cross-over point, the surface conductivity is slightly larger than the bulk conductivity, while, at lower temperatures, the surface conductivity is considerably smaller. Before going into the detail of the analyses, the structure of SDL, as proposed by Kliewer and Koehler, is worth mentioning. Referring to Fig. 2, one sees that thickness of SDL, K-' , decreases gradually with increasing temperatures. N,.,, , the total number of excess of positive ion vacancies inside SDL varies from negative to positive through the isoelectric temperature. In other words, there are
317
A. Fukai et al./Solid State Ionics 79 (1995) 315-318
fewer charge carriers just beneath the crystal surface, below temperatures T,, which reduce the local conductivity. The total number of excess positive ion vacancies above the surface, N,.,, changes from positive to negative with increasing temperature. Judging from the considerations just mentioned above, the cross-over point of Fig. lb is suspected to correspond to an isoelectric temperature. The temperature of the cross-over point is found to be 590 K, lower by 35 K than theoretically expected temperature for NaCl with 10 ppm divalent impurity content. Since T, is dependent on the formation energy of positive ion vacancy, this means that such a formation at the surface is 0.57 eV in contrast to 0.80 eV which has been found by the experiments on the charged dislocations. It has been mentioned in Section 2 that the effective thickness of the current i, is about 18 Km. In order to understand the physical meaning of “effective thickness”, the path of i,, has been calculated with the help of distribution of line of force inside the crystal, as shown in Fig. 3a. The current i, flows through SDL with estimated thickness K- ’
-.r,,1
\
6’ /
-At
c
A
II
d
Ic i +0
(a) ‘0
.”
+b
(b)
K-’ vs.T
Nc.ex.Nc.s, Nc.ex Nc.s
.._ I
I&+&
I AS a
NaCl(C=lOppm)
K’G) Fig. 3. (al. The sideview of Fig. la. The current i, flowing into the crystal at electrode A is presumed to consist of i,, and i,,,,. The former runs above the surface, while the latter flows in the dotted region, including the surface double layer of effective thickness K-’ . (b) and (cl explain how the total conductance 5, has been calculated. In order to work out total resistance between electrode A and B, R,, the dotted region that iAB,, traverses is divided into many hollow pipes along the force lines.
600
400
I 100
I
I 300
800
I
1 500
1060
I
(K)
I 700
(“c)
Fig. 2. The temperature influence on the physical quantities relating to the structure of surface double layer in NaCl containing 10 ppm divalent impurity. The three curves have been calculated on the basis of the theory of Kliewer and Koehler. Here N,,, N,,,, and K-I are: total number of positive ion vacancy above the surface, total number of excess positive ion vacancy beneath the surface and an effective thickness of surface double layer, respectively. N,,, and N,,,, vanish at the isoelectric temperature T,.
when it passes between electrode A and B, thus carrying the information of SDL before it is picked up by electrode B. It must be noticed at this point that current i,, flows along two separate paths; one that runs over the crystal surface, i,,,, the other below the surface, iA,,,. Then “effective thickness” may be as well understood as an average depth of flow line of i,,,. By the way, i, may effectively contribute to bulk conductivity, as mentioned previously. For the purpose of calculating i,,, in detail, one has to know total conductance Gt between electrodes
318
A. Fukai et al./Solid
State lottics 79 tI995) 315-318
Comparing the calculated conductance with the experimental results shown in Fig. lb, one observes that the surface conductivity is much lower than that theoretically expected at low temperatures. The difference between these two is slight in the region of high temperatures, as expected. This situation may be explained by a smaller formation energy of positive ion vacancy, i.e. experimental value 0.57 eV is 28% smaller than 0.80 eV which has been used in calculating the total conductance. Smaller formation energy may induce greater precipitation of positive ion vacancies over the surface, causing greater deficiency of charge carriers beneath the crystal surface.
Fig. 4. the calculated total conductance 5, as a function of temperature for three different values of 6d, the maximum depth of current i,,,. In obtaining I?,, it is necessary to know the concentration of positive ion vacancies nc as a function of depth and its diffusion coefficient 0,.
A and B. The portion of electrode A from which i,,,, flows is divided into narrow strips, of width Ab, as shown in Fig. 3b. Since the concentration of positive ion vacancy charge carriers, depends on the depth from the surface, it follows that the ionic conductivity is also dependent on the depth. Fig. 3c shows how to estimate the conductance of each strip. Here pi is the specific resistivity at the distance xi along the line of force. The expression shown below the figure gives the total conductance of a strip with width of unity. Fig. 4 shows the calculated conductance for three different ad, maximum depth of line of force (refer to Fig. 3c), which may be varied by reducing the crystal thickness. Total conductance is plotted in arbitrary unit against 1000/T. Physical quantities in working out these curves are as follows: formation energy of positive ion vacancy 0.8 eV -3.1 kT, activation energy of diffusion of positive ion vacancy 0.8 eV. 6d can be taken as an effective thickness of i,,,,. It is seen in this figure that the effect of SDL becomes noticeable for the thickness as thin as 0.15 pm, i.e. about 200 times the thickness of SDL.
4. Conclusions (i) Both surface and bulk conductivities have been simultaneously measured in the temperature range of 200°C up to 650°C for cleaved-cut NaCl single crystals. (ii) The corrected surface conductivity intersects with the bulk conductivity at a well defined temperature which may correspond to an isoelectric temperature of the surface double layer. The temperature thus obtained gives 0.57 eV as formation energy of positive ion vacancy at the surface, 28% smaller than that at the dislocation. (iii) It seems that the deficiency of positive ion vacancies below the surface is greater than that so far reported.
References [l] K. KIiewer and J. Koehler, Phys. Rev. 140 (1965) A1226, A1241. [2] 1. Lifshitz, A. Kosevich and Ya. Geguzin, J. Phys. Chem. Solids 28 (1967) 78. [3] R. Poeppel and J. Blakely, Surface Sci. 15 (1969) 507. [4] M.E. van HuIIe and W. Maenhout-van der Vorst, Phys. Status Solidi (a) 39 (1977) 253. [5] L.B. Harris, Radiat. Eff. Defects Solids, 119-121 (1991) 481. f6] A. Fukai, Y. Sato, T. Shimoide and H. Usuki in: Secondary Ion Mass Spectrometry SIMS IX, eds. A. Benninghoven, R. Shimizu, M. Nihei and H.W. Werner (Wiley, Chichester, 1994) p. 480.