- Email: [email protected]
High electric fields in sodium chloride
J. Phys.
Chem. Solids
Pergamon
Press 1964, Vol. 25, pp. 853-858.
Printed in Great Britain.
HIGH ELECTRIC FIELDS IN SODIUM CHLORIDE RICHARD
WILLIAMS
RCA Laboratories, (Received
Princeton,
6 December
N. J.
1963)
Abstract-Space charge polarization measurements have been done with NaCl single crystals, made photoconducting through F centers. Either a silver or an electrolyte electrode is a blocking electrode for the flow of electrons into the crystal. As current flows, a space charge appears near the cathode, due to immobile ionized F centers. If the terminals of the crystal are then connected together, there is a current flow in the opposite direction within the crystal as the accumulated space charge is neutralized. Integrating the current which flows during this process gives the total polarization charge for a given applied voltage. A Schottky barrier is formed at the cathode. The experimental data give the magnitude of the field and its distribution within the crystal for any applied voltage. When the silver electrode is the cathode, the field in the crystal cannot be increased beyond the value of 1.5 x lo6 V/cm. At this field a current begins to flow through the blocking electrode which is apparently due to field emission of electrons. When the cathode is an electrolyte solution, the field may be made as high as 4.4 x 10s V/cm before the apparent field emission current begins. This field is substantially. higher than the accepted value of the dielectric breakdown field for NaCI. 1. INTRODUCTION STUDY of high electric fields in solids has been greatly facilitated by use of structures such as the p-n junction and the Schottky barrier. By concentrating an applied voltage across a space charge region of ionized donors or acceptors such structures provide a very small effective specimen thickness. Under favorable conditions, undesirable injection of carriers into the high field region is avoided up to fields where intrinsic breakdown of the material occurs. P-N junctions have been used by CHYNOWETHand others to study avalanche breakdown in Ge, Si, GaAs and GaP.(l-4) The Schottky barrier formed by an electrolyte contact to conducting CdS has recently been used to study dielectric breakdown.(s* s) VON HIPPEL et uZ.(7) found that, under illumination, an additively colored crystal of KBr with evaporated gold electrodes behaves an an n-type semiconductor and forms Schottky barriers at the electrodes.@) They found a limiting current, attributed to field emission of electrons from the cathode, which, in one case limited the field which could be applied to 3 -7 x 1O5V/cm. In this work it has been found that a Schottky barrier may be formed by illuminating additively 853
colored crystals of sodium chloride. The effect has been studied with two different electrodes, one a metallic contact of silver paste and the other an electrolyte electrode consisting of a saturated water solution of sodium chloride. With the metal contact, the results are similar to those reported by von Hippel et al. for KBr. A Schottky barrier is formed at low fields and at high fields there is a current, apparently due to field emission from the metal cathode, which limits the magnitude of field which can be applied. Using an electrolyte electrode as the cathode it is possible to obtain substantially higher fields. 2. EXPERIMENTAL PROCEDURE Experiments were designed to establish whether or not given contacts form a Schottky barrier which can be used as a tool for further high field studies. The quantities measured were current during charge and discharge of a specimen, and the integrated charge passed during discharge. A schematic drawing of the crystal mounting and measuring circuit are shown in Fig. 1. The crystal specimens used were Harshaw cleavage plates 1-O cm square and about 1 mm thick. They were additively colored by heating in sodium vapor
854
RICHARD
under nitrogen atmosphere in a quartz tube, followed by quenching, during which the tube was plunged into cold water. Visual examination showed the crystals to be uniformly colored and the intensity of coloration(s) indicated that the concentration of F-centres was in the range 1015-101s cmW3. Each crystal had one electrolyte electrode and one silver paste electrode. Either electrode could be made the blocking electrode, at which the Schottky barrier should form, by connecting it to the negative terminal of the external voltage source. Thus, either contact LIGHT LUCITE ,
444
BOX
NaCl SOLUTION
ELECTRODE
t %
I--’ ELECTROMETER INTEGRATING CAPACITOR
AND
FIG. 1. Schematic drawing showing crystal mounting and circuit for measuring current and integrated charge. permits conduction electrons to leave the crystal but neither permits conduction electrons to enter the crystal. This property is an important feature of the model adopted by VON HIPPEL(‘) in discussing similar experiments on KBr. Several other features of his model are also assumed to be true for the present work. These are that the principal conductivity is due to electrons, that these are primarily liberated from F-centers by light absorption, and that conduction by ions and holes is negligible. The assumption that electrons may leave the crystal at either electrode but may not enter requires some qualification. Results indicate that it is a good approximation for a period of time not longer than a few minutes. If a crystal has been polarized by removing electrons then, if the two
WILLIAMS
terminals are connected together, and the crystal is illuminated for half an hour or longer the polarization may be removed, indicating that electrons enter the crystal from the electrodes under these conditions. To measure current during the charge and discharge of the barrier, the following procedure was used. Voltage was applied with the crystal in the dark. The crystal was exposed to light from a focused microscope lamp and, at the same time, a pen recorder was started which recorded the current as a function of time. The voltage and light were left on till the current reached a small limiting value. The RC time constant for the specimens used was of the order of 60 sec. Then the light and the voltage were switched off and the crystal was again illuminated. The reverse current due to discharge of the space charge polarization within the crystal was then recorded as a function of time. For measurements of the integrated polarization charge within the specimen a similar procedure was followed. The crystal was charged by applying a voltage with the light on and the electrometer input shorted. The voltage was left on for a time, empirically determined, sufficient to charge the crystal completely for the given voltage. This time is the RC time constant for the bulk resistance of the crystal in series with the capacitance of the space charge barrier region at the electrode. Then the light was removed and the voltage was removed. Following this the crystal was again illuminated and the charge flowing was collected on a known capacitor connected across the input of an electrometer. For both these measurements and the current measurements a Keithley 610 electrometer was used. 3. RESULTS Recorder tracings of current vs. time are shown in Fig. 2. These tracings are for the silver paste electrode as the blocking electrode (negative). Nearly identical tracings are obtained for the same crystal when the electrolyte is the blocking contact except that the noisy limiting current seen in Fig. 2(b) does not begin until more than 4000 Vs are applied. Traces in Fig. 2(a) are typical of low field results. Those in Fig. 2(b) are high field results. In Fig. 2(a) it can be seen that charge and discharge curves are identical except for a small
HIGH
ELECTRIC
FIELDS
IN
residual current after long times on the charging curve. This current is apparently a leakage around the crystal which it wa6 not possible to eliminate. It is enhanced by the light since this make6 the crystal conducting. The residual current doe6 not contribute to the space charge which is stored and recovered during the discharge. If the residual current is allowed to flow ten times as long as the length of the illustrated trace, the discharge curve is the same as that shown here. Thus the charging current is superimposed on a base line due to the
Time,
CHLORIDE
855
paste electrode a6 the blocking electrode. As the charging approaches completion the trace becomes noisy. This noise is not seen during the discharge nor is it seen when the electrolyte is the blocking electrode until several thousand volts are applied. This is interpreted as a noisy field emission of electrons from the silver cathode similar to that reported in reference (7). Evidence for this statement is provided by the measurements of integrated. charge. It should be noted that the noise in Fig. 2(b) does not appear at the beginning of the charging trace but only after several seconds. At the beginning of the trace the field within the crystal is relatively small and only builds up a6 positive space charge accumulates near the cathode. It is then that the noise appears. Result6 of integrating current during the discharge of a charged crystal are given in Fig. 3. Integration of the current passed during charging was complicated by the presence of the residual
SIC
Vi,
J
40 Time,
SODIUM
sac
FIG. 2. Recorder tracings showing currents vs. time for charging and discharging at two different voltages. Electrode area = 0.38 ems. Top traces 625 V applied. Bottom traces 1500 V applied.
residual current which is independent of time. When this is taken into account the charge and discharge curve6 are identical. This indicate6 a blocking contact which permits storage of positive charge in ionized F-centres near the surface of the crystal. These are the essential requirements for a Schottky barrier. Figure 2(b) shows charge and discharge traces for a higher applied voltage, again with the silver
(volts)f
FIG. 3. Total charge collected on discharge of a charged crystal under illumination plotted against the square root of voltage applied during charging. 0 0 O-electrolyte blocking. + + +-silver blocking electrode. Both electrodes are on the same crystal. Note that the actual charge collected is plotted but this is multiplied by two to obtain the surface field given on the right vertical axis (see Discussion).
current mentioned above. This current was absent when there was no applied voltage so the integration of current during the discharge provided a true measure of the total polarization charge in the crystal. Collected charge is plotted against the square root of the applied voltage. This plot should give a straight line for a Schottky barrier in a crystal with a uniform distribuion of ionized
8.56
RICHARD
donors. This will be amplified in the discussion. For low fields a straight line is obtained with either electrode as the blocking electrode. With the silver electrode there is a maximum amount of charge which can be stored which does not increase as the voltage is increased farther. Since the stored charge and the surface electric field are directly related by Coulomb’s law(ls) this means that the field does not increase beyond a certain value. This is interpreted to mean that at this field there is field emission from the silver and the resulting current transfers further voltage increases to the bulk of the crystal as an RI drop. The field at which the curve in Fig. 3 levels off is in good agreement with that at which the noise appears in Fig. 2(b). With the electrolyte contact as the blocking electrode substantially higher fields are obtained without breakdown of the contact. 4. DISCUSSION
The experiments will first be interpreted by simple band picture potential diagrams and then by quantitative electrostatic equations. For the diagrams, the common convention is used in which the energy of an electron is plotted on the vertical scale, increasing upward, and
(d) FIG. 4. Band picture diagrams giving the potential distribution within the crystal during the various stages of the experiment as described in the test. Band picture representation of the electrodes has been omitted for simplicity.
WILLIAMS
position within the crystal is plotted on the horizontal scale. Figure 4 shows the potential distribution within the crystal at several stages of the experiments. Figure 4(a) shows an insulator with an applied voltage whose negative terminal goes to the left side. This represents the potential distribution in the dark before any light has reached the crystal and also the crystal at the instant the light is turned on. At this time the current flow is governed simply by the resistance of the illuminated crystal which may be obtained from the initial currents of Fig. 2. As current flows, electrons leave behind a positive space charge of ionized F-centers next to the cathode. Electrons do not enter at the cathode except at high fields. Thus the applied field becomes concentrated across a thin layer, the Schottky barrier. The negative charge may be present either as electrons when the metal electrode is used or as ions when the electrolyte electrode is used. In either case the negative charge is located in a plane on or very near the surface of the crystal and the lines of force terminate on the ionized Fcentres which are assumed uniformly distributed and which extend from the surface into the interior for a distance which depends on the applied voltage but may be as large as 10-s cm. When equilibrium is reached all of the applied voltage is across the space charge region and current flow ceases. This condition is illustrated by Fig. 4(b). The transient leading to this condition is analysed in reference (7) but will not be considered in detail here. To measure the charge contained in the space charge region the light is first shut off, after which the situation remains as shown in Fig. 4(b). Then the crystal is connected to the integrating standard capacitor which is, in turn, connected to the electrometer. This brings both ends of the crystal to the same potential as shown in Fig. 4(c). To give a more quantitative picture of the field in the space charge region as compared to that in the bulk, it may be remembered that the space charge region is about 10-s cm thick and the crystal is about 10-r cmthick. The integration of chargenow begins when the light is turned on. Again, during this process, no electrons enter the crystal but electrons flow within the crystal from right to left as long as there is any field remaining within the bulk. This builds up a positive space charge of ionized F-centres at
HIGH
ELECTRIC
FIELDS
IN SODIUM
CHLORIDE
857
the right boundary which continues to grow until Here e is the electronic charge, K, is the dielectric there is the same potential drop across both space constant of the crystal and the units are cgs electrocharge regions. At this point there is no longer a static units. The diffusion voltage term has been field in the interior of the crystal and current omitted from the equation given in reference (11) flow ceases. This condition is illustrated in Fig. because it is small compared to V. The quantity plotted in Fig. 3 is twice the 4(d). Both space charge regions are now identical and together they contain the same total positive measured charge obtained on discharge of a charge which was originally contained in one space charged barrier and is therefore equal to Cv charge region as shown in Fig. 4(b). Thus the discussed above, From equation (l), integrated charge collected on going from Fig. 4(c) to (d) is half the charge contained in the space cv = charge region of Fig. 4(b). To obtain the total 2n charge, which is required to calculate the field for The linear relation between CV and VlJz shown the confi~ration in Fig. 4(b), the measured in Fig. 3 is therefore characteristic of a Schottky charge must be multiplied by two. barrier with a uniform distribution of donors. If the original voltage is now applied with the From the slope of the line and equation (2), it is same polarity and the crystal is illuminated the inferred that the density of F-centers, N, is 1.9 potential distribution will go from that in Fig. x 1015,/ems.This agrees with qualitative observa4(d) to that in Fig. 4(b) and the total charge tions on the intensity of coloration of the crystals. passing in the external circuit will be equal to that On another crystal a similar plot of CV vs. W2 on going from Fig. 4(c) to (d). It is this sequence gave an equally good straight line indicating which is illustrated by the current-time plots in 1.9 x 101s donorsjcms. Fig. 2, where charging and discharing currents are For the plane parallel geometry of the barrier identical except for the small constant leakage in these experiments the maximum field is at the current during charging. It is clear that twice as surface within the crystal and is of magnitude, much total charge is passed on going from Fig. 4(a) to (b) as is passed on going from Fig. 4(d) to j+-j (3) fb). This is observed, approximately. If a crystal is used which has been illuminated for a long period of time with its end electrodes connected E is the field at the surface and o is the surface together, the current-time relation during the charge density in e.s.u. Using this relation the first charging is different from that during dis- scale of field strength was constructed which charge, and also from that during subsequent appears on the right hand vertical axis of Fig. 3. charging. The initial current at zero time is the It will be noted that when the silver electrode same in all cases since this is determined by the forms the Schottky barrier the field goes no higher series resistance of the bulk crystal under illumi- than about 1.5 x 10s V/cm. When the electrolyte nation. The time constant of the current decay is is at the Schottky barrier the field rises to at least larger for the first charging than it is for subse- 2.2 x 10s V/cm. In the other crystal specimen quent charging and roughly twice as much charge mentioned above which had a higher density of passes. The current-time curves cannot be fitted donors a field of 4.4 x 10s V/cm was established by an exponential with a single time constant so using the electrolyte contact, at which point the charging current began to show considerable noise no quantitative analysis of this has been made. as in Fig. Z(b). 5. QUANTITATIVE CONSIDERATIONS Very near the electrode the field is somewhat The capacitance per unit area, C, of a Schottky smaller than that given by equation (3) due to the barrier in a crystal having a uniform distribution image field, Earn. This is giver+) by the equation: of donors with a concentration, N, is given as a function of applied voltage, V, by the equation:(rl) Etm = 4Kx2
(NeKv >l/J2
c = -_(NeK 11/Z &TV
-!7.-
(1)
Here x is the distance from the electrode. When x
858
RICHARD
is greater than 30 A the image field is negligible compared with that given by equation (3) for high applied fields as studied here. Since the total thickness of the Schottky barrier is N 10-3 cm, it is correctly described by neglecting the image field. CONCLUSION
The results indicate that a good approximation to the Schottky barrier is provided by additively colored crystals of NaCl with either metal or electrolyte electrodes. Substantially higher fields may be established with electrolyte electrodes than with silver electrodes. With the silver eiectrode there is a noisy current, apparently due to tunneling of electrons from the metal into the crystal. Similar behavior was reported by VON HIPPEL(~) and others for KBr. It is interesting to note that the field strength at which this occurs in these experiments is 1.5 x 10s V/cm. This is the accepted value for the dielectric breakdown field strength for NaCl.(lQ It is frequently cited(ls) in support of calculations of the intrinsic dielectric breakdown field strength based on the mechanism of electron impact ionization. The present results suggest that a contact phenomenon rather than an electron avalanche may be dominant. Recent experiments on the breakdown field strength of thin specimens of NaCl in which electrolyte electrodes were used have been reported by KOSTRYGIN.(~~) Thin specimens were obtained by machining to small dimensions. The breakdown field strength was a function of thickness, being large for small thicknesses, over the thickness range 3 x 10-4-16 x 10-a cm. Breakdown field strengths ranged from 2.7 x 106-7 x 106 V/cm. The present value of 4.4 x 10s V/cm is in good agreement with Kostrygin’s value for a specimen of the same thickness. For specimen thickness in this work the thickness of the space charge region
WILLIAMS has been taken. Kostrygin interpreted his results as breakdown by impact ionization. For a thicker specimen he obtained similar values for the breakdown field using powdered graphite electrodes and electrolyte electrodes, so it is not certain whether the high values are due to the electrode materials or to the use of thin specimens.
Acknowledgement-The author is indebted to A. ROSE and A. MANY for valuable advice and discussions during the course of this work. The research reported in this paper was sponsored by the U.S. Army Research Office (Durham) under Contract Number DA 31-124-ARO-(D)-84.
REFERENCES 1. MCKAY K. G. and MCAFEE K. B., Phys. Rev. 91, 1079 (1953). 2. MCKAY K. G., Phys. Rev. 94, 877 (1954). 3. LOGAN R. A. and CHYNOWETH A. G., J. Appl. Pkys. 33, 1649 (1962). 4. LOGANR. A., CHYNOWETHA. G. and COHEN B. G., Phys. Rev. 128, 2518 (1962). 5. WILLIAMS R., J. Phys. Chem. Solids 22, 129 (1961). 6. WILLIAMS R., Phys. Rev. 125, 850 (1962). 7. VON HIPPEL A., GROSS E. P., JELATISJ. G. and GELLERM., Phys. Rev. 91, 568 (1953). Electronic Semiconductors, p. 74. 8. SPENKE E., McGraw-Hill, New York (1958). 9. SCHULMAN J. H. and COMPTON W. D.. Color Centers in Solids, p. 55. Macmillan Co., New York (1962). IO. JEANSJ. H., Electricity and Magnetism. Cambridge Univ. Press, New York. Semiconductor Contacts, Il. HENISCH H. K., Rectifying p, 214. Oxford Univ. Press, New York (1957). 12. VON HIPPEL A., 2. Physik 75, 145 (1932). and GU~EY R. W., Electronic 13. MOTT N. F. Processes in Ionic Crystals (2nd ed.), p. 201. Oxford Univ. Press, New Yolk. WHITEHEAD S.. Dielectric Breakdown of Solids. p. 61. Oxford Univ. Press, New York (lb53). Tela 2, 1664 14. KOSTRYGIN V. A., Fiz. Tverdogo (1960).
Chem. Solids
Pergamon
Press 1964, Vol. 25, pp. 853-858.
Printed in Great Britain.
HIGH ELECTRIC FIELDS IN SODIUM CHLORIDE RICHARD
WILLIAMS
RCA Laboratories, (Received
Princeton,
6 December
N. J.
1963)
Abstract-Space charge polarization measurements have been done with NaCl single crystals, made photoconducting through F centers. Either a silver or an electrolyte electrode is a blocking electrode for the flow of electrons into the crystal. As current flows, a space charge appears near the cathode, due to immobile ionized F centers. If the terminals of the crystal are then connected together, there is a current flow in the opposite direction within the crystal as the accumulated space charge is neutralized. Integrating the current which flows during this process gives the total polarization charge for a given applied voltage. A Schottky barrier is formed at the cathode. The experimental data give the magnitude of the field and its distribution within the crystal for any applied voltage. When the silver electrode is the cathode, the field in the crystal cannot be increased beyond the value of 1.5 x lo6 V/cm. At this field a current begins to flow through the blocking electrode which is apparently due to field emission of electrons. When the cathode is an electrolyte solution, the field may be made as high as 4.4 x 10s V/cm before the apparent field emission current begins. This field is substantially. higher than the accepted value of the dielectric breakdown field for NaCI. 1. INTRODUCTION STUDY of high electric fields in solids has been greatly facilitated by use of structures such as the p-n junction and the Schottky barrier. By concentrating an applied voltage across a space charge region of ionized donors or acceptors such structures provide a very small effective specimen thickness. Under favorable conditions, undesirable injection of carriers into the high field region is avoided up to fields where intrinsic breakdown of the material occurs. P-N junctions have been used by CHYNOWETHand others to study avalanche breakdown in Ge, Si, GaAs and GaP.(l-4) The Schottky barrier formed by an electrolyte contact to conducting CdS has recently been used to study dielectric breakdown.(s* s) VON HIPPEL et uZ.(7) found that, under illumination, an additively colored crystal of KBr with evaporated gold electrodes behaves an an n-type semiconductor and forms Schottky barriers at the electrodes.@) They found a limiting current, attributed to field emission of electrons from the cathode, which, in one case limited the field which could be applied to 3 -7 x 1O5V/cm. In this work it has been found that a Schottky barrier may be formed by illuminating additively 853
colored crystals of sodium chloride. The effect has been studied with two different electrodes, one a metallic contact of silver paste and the other an electrolyte electrode consisting of a saturated water solution of sodium chloride. With the metal contact, the results are similar to those reported by von Hippel et al. for KBr. A Schottky barrier is formed at low fields and at high fields there is a current, apparently due to field emission from the metal cathode, which limits the magnitude of field which can be applied. Using an electrolyte electrode as the cathode it is possible to obtain substantially higher fields. 2. EXPERIMENTAL PROCEDURE Experiments were designed to establish whether or not given contacts form a Schottky barrier which can be used as a tool for further high field studies. The quantities measured were current during charge and discharge of a specimen, and the integrated charge passed during discharge. A schematic drawing of the crystal mounting and measuring circuit are shown in Fig. 1. The crystal specimens used were Harshaw cleavage plates 1-O cm square and about 1 mm thick. They were additively colored by heating in sodium vapor
854
RICHARD
under nitrogen atmosphere in a quartz tube, followed by quenching, during which the tube was plunged into cold water. Visual examination showed the crystals to be uniformly colored and the intensity of coloration(s) indicated that the concentration of F-centres was in the range 1015-101s cmW3. Each crystal had one electrolyte electrode and one silver paste electrode. Either electrode could be made the blocking electrode, at which the Schottky barrier should form, by connecting it to the negative terminal of the external voltage source. Thus, either contact LIGHT LUCITE ,
444
BOX
NaCl SOLUTION
ELECTRODE
t %
I--’ ELECTROMETER INTEGRATING CAPACITOR
AND
FIG. 1. Schematic drawing showing crystal mounting and circuit for measuring current and integrated charge. permits conduction electrons to leave the crystal but neither permits conduction electrons to enter the crystal. This property is an important feature of the model adopted by VON HIPPEL(‘) in discussing similar experiments on KBr. Several other features of his model are also assumed to be true for the present work. These are that the principal conductivity is due to electrons, that these are primarily liberated from F-centers by light absorption, and that conduction by ions and holes is negligible. The assumption that electrons may leave the crystal at either electrode but may not enter requires some qualification. Results indicate that it is a good approximation for a period of time not longer than a few minutes. If a crystal has been polarized by removing electrons then, if the two
WILLIAMS
terminals are connected together, and the crystal is illuminated for half an hour or longer the polarization may be removed, indicating that electrons enter the crystal from the electrodes under these conditions. To measure current during the charge and discharge of the barrier, the following procedure was used. Voltage was applied with the crystal in the dark. The crystal was exposed to light from a focused microscope lamp and, at the same time, a pen recorder was started which recorded the current as a function of time. The voltage and light were left on till the current reached a small limiting value. The RC time constant for the specimens used was of the order of 60 sec. Then the light and the voltage were switched off and the crystal was again illuminated. The reverse current due to discharge of the space charge polarization within the crystal was then recorded as a function of time. For measurements of the integrated polarization charge within the specimen a similar procedure was followed. The crystal was charged by applying a voltage with the light on and the electrometer input shorted. The voltage was left on for a time, empirically determined, sufficient to charge the crystal completely for the given voltage. This time is the RC time constant for the bulk resistance of the crystal in series with the capacitance of the space charge barrier region at the electrode. Then the light was removed and the voltage was removed. Following this the crystal was again illuminated and the charge flowing was collected on a known capacitor connected across the input of an electrometer. For both these measurements and the current measurements a Keithley 610 electrometer was used. 3. RESULTS Recorder tracings of current vs. time are shown in Fig. 2. These tracings are for the silver paste electrode as the blocking electrode (negative). Nearly identical tracings are obtained for the same crystal when the electrolyte is the blocking contact except that the noisy limiting current seen in Fig. 2(b) does not begin until more than 4000 Vs are applied. Traces in Fig. 2(a) are typical of low field results. Those in Fig. 2(b) are high field results. In Fig. 2(a) it can be seen that charge and discharge curves are identical except for a small
HIGH
ELECTRIC
FIELDS
IN
residual current after long times on the charging curve. This current is apparently a leakage around the crystal which it wa6 not possible to eliminate. It is enhanced by the light since this make6 the crystal conducting. The residual current doe6 not contribute to the space charge which is stored and recovered during the discharge. If the residual current is allowed to flow ten times as long as the length of the illustrated trace, the discharge curve is the same as that shown here. Thus the charging current is superimposed on a base line due to the
Time,
CHLORIDE
855
paste electrode a6 the blocking electrode. As the charging approaches completion the trace becomes noisy. This noise is not seen during the discharge nor is it seen when the electrolyte is the blocking electrode until several thousand volts are applied. This is interpreted as a noisy field emission of electrons from the silver cathode similar to that reported in reference (7). Evidence for this statement is provided by the measurements of integrated. charge. It should be noted that the noise in Fig. 2(b) does not appear at the beginning of the charging trace but only after several seconds. At the beginning of the trace the field within the crystal is relatively small and only builds up a6 positive space charge accumulates near the cathode. It is then that the noise appears. Result6 of integrating current during the discharge of a charged crystal are given in Fig. 3. Integration of the current passed during charging was complicated by the presence of the residual
SIC
Vi,
J
40 Time,
SODIUM
sac
FIG. 2. Recorder tracings showing currents vs. time for charging and discharging at two different voltages. Electrode area = 0.38 ems. Top traces 625 V applied. Bottom traces 1500 V applied.
residual current which is independent of time. When this is taken into account the charge and discharge curve6 are identical. This indicate6 a blocking contact which permits storage of positive charge in ionized F-centres near the surface of the crystal. These are the essential requirements for a Schottky barrier. Figure 2(b) shows charge and discharge traces for a higher applied voltage, again with the silver
(volts)f
FIG. 3. Total charge collected on discharge of a charged crystal under illumination plotted against the square root of voltage applied during charging. 0 0 O-electrolyte blocking. + + +-silver blocking electrode. Both electrodes are on the same crystal. Note that the actual charge collected is plotted but this is multiplied by two to obtain the surface field given on the right vertical axis (see Discussion).
current mentioned above. This current was absent when there was no applied voltage so the integration of current during the discharge provided a true measure of the total polarization charge in the crystal. Collected charge is plotted against the square root of the applied voltage. This plot should give a straight line for a Schottky barrier in a crystal with a uniform distribuion of ionized
8.56
RICHARD
donors. This will be amplified in the discussion. For low fields a straight line is obtained with either electrode as the blocking electrode. With the silver electrode there is a maximum amount of charge which can be stored which does not increase as the voltage is increased farther. Since the stored charge and the surface electric field are directly related by Coulomb’s law(ls) this means that the field does not increase beyond a certain value. This is interpreted to mean that at this field there is field emission from the silver and the resulting current transfers further voltage increases to the bulk of the crystal as an RI drop. The field at which the curve in Fig. 3 levels off is in good agreement with that at which the noise appears in Fig. 2(b). With the electrolyte contact as the blocking electrode substantially higher fields are obtained without breakdown of the contact. 4. DISCUSSION
The experiments will first be interpreted by simple band picture potential diagrams and then by quantitative electrostatic equations. For the diagrams, the common convention is used in which the energy of an electron is plotted on the vertical scale, increasing upward, and
(d) FIG. 4. Band picture diagrams giving the potential distribution within the crystal during the various stages of the experiment as described in the test. Band picture representation of the electrodes has been omitted for simplicity.
WILLIAMS
position within the crystal is plotted on the horizontal scale. Figure 4 shows the potential distribution within the crystal at several stages of the experiments. Figure 4(a) shows an insulator with an applied voltage whose negative terminal goes to the left side. This represents the potential distribution in the dark before any light has reached the crystal and also the crystal at the instant the light is turned on. At this time the current flow is governed simply by the resistance of the illuminated crystal which may be obtained from the initial currents of Fig. 2. As current flows, electrons leave behind a positive space charge of ionized F-centers next to the cathode. Electrons do not enter at the cathode except at high fields. Thus the applied field becomes concentrated across a thin layer, the Schottky barrier. The negative charge may be present either as electrons when the metal electrode is used or as ions when the electrolyte electrode is used. In either case the negative charge is located in a plane on or very near the surface of the crystal and the lines of force terminate on the ionized Fcentres which are assumed uniformly distributed and which extend from the surface into the interior for a distance which depends on the applied voltage but may be as large as 10-s cm. When equilibrium is reached all of the applied voltage is across the space charge region and current flow ceases. This condition is illustrated by Fig. 4(b). The transient leading to this condition is analysed in reference (7) but will not be considered in detail here. To measure the charge contained in the space charge region the light is first shut off, after which the situation remains as shown in Fig. 4(b). Then the crystal is connected to the integrating standard capacitor which is, in turn, connected to the electrometer. This brings both ends of the crystal to the same potential as shown in Fig. 4(c). To give a more quantitative picture of the field in the space charge region as compared to that in the bulk, it may be remembered that the space charge region is about 10-s cm thick and the crystal is about 10-r cmthick. The integration of chargenow begins when the light is turned on. Again, during this process, no electrons enter the crystal but electrons flow within the crystal from right to left as long as there is any field remaining within the bulk. This builds up a positive space charge of ionized F-centres at
HIGH
ELECTRIC
FIELDS
IN SODIUM
CHLORIDE
857
the right boundary which continues to grow until Here e is the electronic charge, K, is the dielectric there is the same potential drop across both space constant of the crystal and the units are cgs electrocharge regions. At this point there is no longer a static units. The diffusion voltage term has been field in the interior of the crystal and current omitted from the equation given in reference (11) flow ceases. This condition is illustrated in Fig. because it is small compared to V. The quantity plotted in Fig. 3 is twice the 4(d). Both space charge regions are now identical and together they contain the same total positive measured charge obtained on discharge of a charge which was originally contained in one space charged barrier and is therefore equal to Cv charge region as shown in Fig. 4(b). Thus the discussed above, From equation (l), integrated charge collected on going from Fig. 4(c) to (d) is half the charge contained in the space cv = charge region of Fig. 4(b). To obtain the total 2n charge, which is required to calculate the field for The linear relation between CV and VlJz shown the confi~ration in Fig. 4(b), the measured in Fig. 3 is therefore characteristic of a Schottky charge must be multiplied by two. barrier with a uniform distribution of donors. If the original voltage is now applied with the From the slope of the line and equation (2), it is same polarity and the crystal is illuminated the inferred that the density of F-centers, N, is 1.9 potential distribution will go from that in Fig. x 1015,/ems.This agrees with qualitative observa4(d) to that in Fig. 4(b) and the total charge tions on the intensity of coloration of the crystals. passing in the external circuit will be equal to that On another crystal a similar plot of CV vs. W2 on going from Fig. 4(c) to (d). It is this sequence gave an equally good straight line indicating which is illustrated by the current-time plots in 1.9 x 101s donorsjcms. Fig. 2, where charging and discharing currents are For the plane parallel geometry of the barrier identical except for the small constant leakage in these experiments the maximum field is at the current during charging. It is clear that twice as surface within the crystal and is of magnitude, much total charge is passed on going from Fig. 4(a) to (b) as is passed on going from Fig. 4(d) to j+-j (3) fb). This is observed, approximately. If a crystal is used which has been illuminated for a long period of time with its end electrodes connected E is the field at the surface and o is the surface together, the current-time relation during the charge density in e.s.u. Using this relation the first charging is different from that during dis- scale of field strength was constructed which charge, and also from that during subsequent appears on the right hand vertical axis of Fig. 3. charging. The initial current at zero time is the It will be noted that when the silver electrode same in all cases since this is determined by the forms the Schottky barrier the field goes no higher series resistance of the bulk crystal under illumi- than about 1.5 x 10s V/cm. When the electrolyte nation. The time constant of the current decay is is at the Schottky barrier the field rises to at least larger for the first charging than it is for subse- 2.2 x 10s V/cm. In the other crystal specimen quent charging and roughly twice as much charge mentioned above which had a higher density of passes. The current-time curves cannot be fitted donors a field of 4.4 x 10s V/cm was established by an exponential with a single time constant so using the electrolyte contact, at which point the charging current began to show considerable noise no quantitative analysis of this has been made. as in Fig. Z(b). 5. QUANTITATIVE CONSIDERATIONS Very near the electrode the field is somewhat The capacitance per unit area, C, of a Schottky smaller than that given by equation (3) due to the barrier in a crystal having a uniform distribution image field, Earn. This is giver+) by the equation: of donors with a concentration, N, is given as a function of applied voltage, V, by the equation:(rl) Etm = 4Kx2
(NeKv >l/J2
c = -_(NeK 11/Z &TV
-!7.-
(1)
Here x is the distance from the electrode. When x
858
RICHARD
is greater than 30 A the image field is negligible compared with that given by equation (3) for high applied fields as studied here. Since the total thickness of the Schottky barrier is N 10-3 cm, it is correctly described by neglecting the image field. CONCLUSION
The results indicate that a good approximation to the Schottky barrier is provided by additively colored crystals of NaCl with either metal or electrolyte electrodes. Substantially higher fields may be established with electrolyte electrodes than with silver electrodes. With the silver eiectrode there is a noisy current, apparently due to tunneling of electrons from the metal into the crystal. Similar behavior was reported by VON HIPPEL(~) and others for KBr. It is interesting to note that the field strength at which this occurs in these experiments is 1.5 x 10s V/cm. This is the accepted value for the dielectric breakdown field strength for NaCl.(lQ It is frequently cited(ls) in support of calculations of the intrinsic dielectric breakdown field strength based on the mechanism of electron impact ionization. The present results suggest that a contact phenomenon rather than an electron avalanche may be dominant. Recent experiments on the breakdown field strength of thin specimens of NaCl in which electrolyte electrodes were used have been reported by KOSTRYGIN.(~~) Thin specimens were obtained by machining to small dimensions. The breakdown field strength was a function of thickness, being large for small thicknesses, over the thickness range 3 x 10-4-16 x 10-a cm. Breakdown field strengths ranged from 2.7 x 106-7 x 106 V/cm. The present value of 4.4 x 10s V/cm is in good agreement with Kostrygin’s value for a specimen of the same thickness. For specimen thickness in this work the thickness of the space charge region
WILLIAMS has been taken. Kostrygin interpreted his results as breakdown by impact ionization. For a thicker specimen he obtained similar values for the breakdown field using powdered graphite electrodes and electrolyte electrodes, so it is not certain whether the high values are due to the electrode materials or to the use of thin specimens.
Acknowledgement-The author is indebted to A. ROSE and A. MANY for valuable advice and discussions during the course of this work. The research reported in this paper was sponsored by the U.S. Army Research Office (Durham) under Contract Number DA 31-124-ARO-(D)-84.
REFERENCES 1. MCKAY K. G. and MCAFEE K. B., Phys. Rev. 91, 1079 (1953). 2. MCKAY K. G., Phys. Rev. 94, 877 (1954). 3. LOGAN R. A. and CHYNOWETH A. G., J. Appl. Pkys. 33, 1649 (1962). 4. LOGANR. A., CHYNOWETHA. G. and COHEN B. G., Phys. Rev. 128, 2518 (1962). 5. WILLIAMS R., J. Phys. Chem. Solids 22, 129 (1961). 6. WILLIAMS R., Phys. Rev. 125, 850 (1962). 7. VON HIPPEL A., GROSS E. P., JELATISJ. G. and GELLERM., Phys. Rev. 91, 568 (1953). Electronic Semiconductors, p. 74. 8. SPENKE E., McGraw-Hill, New York (1958). 9. SCHULMAN J. H. and COMPTON W. D.. Color Centers in Solids, p. 55. Macmillan Co., New York (1962). IO. JEANSJ. H., Electricity and Magnetism. Cambridge Univ. Press, New York. Semiconductor Contacts, Il. HENISCH H. K., Rectifying p, 214. Oxford Univ. Press, New York (1957). 12. VON HIPPEL A., 2. Physik 75, 145 (1932). and GU~EY R. W., Electronic 13. MOTT N. F. Processes in Ionic Crystals (2nd ed.), p. 201. Oxford Univ. Press, New Yolk. WHITEHEAD S.. Dielectric Breakdown of Solids. p. 61. Oxford Univ. Press, New York (lb53). Tela 2, 1664 14. KOSTRYGIN V. A., Fiz. Tverdogo (1960).