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Tunneling processes across the CdS-electrolyte interface
J. Phys. Chenr. Solids
Pergamon
Printed in Great Britain.
Press 1965. Vol. 26, pp. 587-593.
•T~~~ELI~~ PROCESSES ACROSS THE CdS-ELECTROLYTE INTERFACE* A. MANY-f RCA Laboratories, (&ccked
Princeton,
New Jersey
25 Augtrst 1964)
Abstract-The high-field behavior of the irnterface between a canducting CdS crystal and a bIocking electrolyte contact is studied by the use of pulse techniques, The method employed is very suitable for determiniig the characteristics of the space-charge region at the crystal surface. In contrast to the case of d-c. measurements, where breakdown of the blocking contact is not apparent up to fields of at least 2 x f06 V/cm, large transient currents through the interface are observed in the. range 5 x 106-10s V/cm. These currents are ascribed to field emission from surface states into the conduction band of the CdS crystal. The surface states are shown to be intimate$ correlated with electrolytically deposited sulphur.
INTR0DUCTI0N
previous paper(l) a contact-fess method using Mylar blocking electrodes and pulsemeasurements has been described for the study of highfield effects in insulating cadmium sulphide crystals. This method completely suppresses field emission from the end electrodes, but the range of fields attained so far does not exceed about 3 x 105 V/cm. Considerably higher fields can be obtained by the use of an electrolyte solution as a blocking contact on a conducting (n-type) CdS crystal.(s) Biasing the electrolyte negatively with respect to the crystal permits fields as high as 2 x 10s V/em to be established across a carrier-free depletion or Schottky barrier formed within the crystal adjacent to the interface.@) D.C. measurements carried out by WILLIAMS(~)show that under steady-state conditions, neither field emission across the interface nor impact ionization within the depletion layer take place up to a field of about 2 x 106 V/cm, at which field tunneling from the valence into the conduction band of the CdS crystal sets in. IN THE
* The research reported in this paper was sponsored by the US, Army Research Office (Durham) under Contract Number DA 31-124-ARC)(D)-84 and RCA I&oratories, Princeton, New Jersey. T Permanent address : The Hebrew University, Jerusalem, Israel. 587
The measurements reported in the present paper are similar tu those described by W~L~~~,~~~ except that the current-voltage characteristics are taken under pulsed conditions. In contrast to the de. case, very large transient currents are observed at field intensities well below those required for tunneling across the gap. These currents are ascribed to field emission from surface states at the electrolyte-CdS interface, situated about O-8 eV below the conduction-band edge. The states are shown to be correlated with electrolytically deposited sulfur. The pulse technique used permits a direct and easy determination of the characteristics of the depletion layer. It is established that in all the conducting CdS samples studied a true Schottky barrier is formed near the surface. EXPERIMENTAL METHOD A schematic diagram of the crystal mounting and measuring circuit is shown in Fig, I. The crystal slab is glued by Glyptol cement to the walls of a glass tube. A gallium contact is apphed to the crystal face inside the tube while the other face is in contact with the electrolyte solution. The crystal samples studied were wpourgrown slabs with resistivities ranging from O-2 to 2 a-cm. The pulse is applied between 8 platinum electrode dipped into the electroiyte and the gallium contact, the electrolyte contact being negative in all cases. A smatf series resistor fi is used to measure the transient current, while the total charge flowing into the space-charge region of
588
A.
MANY
GALLIUM
OR
KCI
FIG. 1. Schematic
diagram of the crystal mounting circuit.
the crystal as a result of the applied pulse is determined by means of the large series capacitor C. RESULTS
AND
Qac = (2~rakTna)~/~[exp( -qV,/KT) 111’2.
(1)
Here K is the dielectric constant of the semiconductor, la the permittivity of free space, no the ionized donor concentration (= free carrier density in the bulk) and V, the absolute magnitude of the barrier height at the surface. For qV, g kT, the exponential term as well as the unity inside the second brackets can be neglected, and equation (1) reduces to:
Q)se = (2!cEoq)%~w~‘?
and measuring
If we express no in units of cm-s, and V, in volts, we obtain for CdS Qse zz 5.7 x lO-I6+aI/l!a.
DISCUSSION
A number of measurements were performed in order to ascertain that a Schottky barrier is formed when the electrolyte is biased negatively with respect to the crystal. The conditions that a depletion layer would constitute a true Schottky barrier are the absence of minority-carriers (either in the bulk or at the surface) and complete ionization of the donor or acceptor impurities. Under these conditions the space-charge layer is composed of fixed ionized impurities plus whatever majority-carriers that have not been completely depleted from the surface. For an extrinsic n-type sample, the total charge density per unit surface area contained in a Schottky barrier is given by:@)
+qV,/kT-
CONTACT
(2)
Qsc in C/cm2 = 11.8) :
(K
s
(3)
The absolute magnitude b, of the field intensity at the surface is obtained from Gauss’s law: &s = lO=Q,,
= 5.7x
lo-“nl,sVl’s,
(4)
where Qse is expressed in C/ems, as before, and &, is in V/cm. The experimental determination of Qse vs. V, would be straightforward if no barrier existed at the surface (V, = 0) prior to the application of the external voltage. In this case V, would be just equal to the pulse amplitude and Qs to the charge collected at the series capacitor C (Fig. 1) following the application of the pulse. In reality it is found, however, that a depletion layer already exists at the surface in the absence of the external voltage. If we denote by VOthe absolute magnitude of the equilibrium barrier height associated with this layer, then clearly V = V,-- VO and AQse = Qssc(Vs) -Qsc( VO), where V is the pulse amplitude and AQsc is the measured charge collected at C. In order to verify the square-root dependence of Qsc on V, characteristic of a Schottky barrier, it is therefore necessary to determine VO as well. This can be done by trial and error procedures: AQsc is plotted as a function of ( V+T)~/~ and 7 is adjusted until the points are collinear, when q is taken
TUNNELING
PROCESSES
as equal to Vs. (It should value of 77affects only the is, when V is comparable procedure,(s) however, is
ACROSS
be noted that the precise low-voltage results, that to Ve.) A more elegant as follows:
- V’d”), A&,, = A( V’“8’” where A =
equations
(5)
CdS-ELECTROLYTE
589
INTERFACE
using the value of 300 ems/V-set for the electron mobility). Before discussing the high-field behavior of the CdSjelectrolyte interface it would be of interest to consider the characteristics of the charging current flowing to form the Schottky barrier at the
Hence:
(~KEo~?zo)~/~.
I’ = I’,-- Vo = (AQ&)(Vys+ Combining
THE
V;‘2).
(6)
(5) and (6) we obtain:
V/AQ,, = AQscjA2+(2/A)V~2.
(7)
Thus, if the depletion layer is a Schottky barrier, the plot of V/AQse vs. A&,, (both quantities being directly measureable) should yield a straight line. This is indeed found to be the case for all CdS samples studied, as illustrated in Fig. 2. From the slope of the line and its intersection’with the ordinate (AQ,, = 0) one can readily calculate both VO and A. Once VO has been determined, it is possible to replot the data as AQsc vs. (I’#/2 = (V+ V0)1/2. This is shown in Fig. 3 for three samples of different resistivity. In all cases the points are collinear, with VO lying between about 1.7 and 2 V. The slopes of the straight lines are consistent with the values of the free-electron densities (as determined from the resistivities,
0
1
2
3
5
6
l/(V+Vo)(W”) FIG. 3. A plot of the measured change in space-charge density as a function of applied voltage for three conducting samples. The equilibrium barrier height 5’0 in each case was determined by the procedure of Fig. 2.
l----T7
crystal surface. It can be shown@) that if the initial barrier height (VO) is zero, then the current following the onset of the voltage pulse (t = 0) is given approximately by : 4 exp( - t/7) i(t) = -IL Rs [l + exp( - t/~)]~
I
I
I
I
I
I
I
0123456799 AC&x 10’ FE.
(cod/cm
2)
2. A plot of VlAQ~c VS. AQ, for a conducting CdS sample (see equation 7).
I
(8)
where V is the pulse amplitude, and R, is the crystal resistance between the ohmic contact and the interface plus whatever series resistance may be present in the circuit. The time constant -r is given by: r = +RsCsc. (9) Here Csc is the so-called space-charge capacitance when steady-state conditions have been reached and is given by Qsc/Vs multiplied by the interface area. It should be noted that equation (8) does not
590
A.
MANY
represent a simple exponential decay, as might have been expected on the basis of qualitative considerations. The value of R, in ,the experimental arrangement used is normally several hundred ohms (consisting mostly of the electrolyte resistance), while C,, is typically 10-s pF. Thus 7 is of the order of O-1 p set, a value that is considerably smaller than the available experimental resolution time. Accordingly, the charging of the spacecharge region is completed, and the steady-state Schottky barrier is established, well before any current reading is taken. All subsequent references to the phrase ‘onset of the voltage pulse’ or to ‘t = 0’ will refer to conditions just following the charging time. Equation (8) can be checked experimentally by artificially increasing R, through the use of a large series resistance, so as to make 7 fall in a convenient range. The time dependence of the charging current under such conditions is shown in Fig. 4. The pulse amplitude has been taken sufficiently large to ensure that any deviations from equation (8) due to the fact that Vs is not zero would be negligible. The theoretical curve representing equation (8) fits quite well the experimental data.
\
0.02 t
TIME()rsec) FIG. 4. The time dependence of the current charging the depletion layer in the presence of a large external series resistance.
We turn now to current-voltage measurements at high applied voltages. At low pulse amplitudes, no current flows through the system (apart from the rapid charging current discussed above), the electrolyte contact being completely blocking. As the voltage is raised, however, a transient current is observed, which decays after several milliseconds to zero. The initial current j is found to increase very rapidly with applied voltage. In the highvoltage range, j can be expressed as: j = const. exp( - x/&~),
(10)
where b, is the absolute magnitude of the field at the surface associated with the Schottky barrier. This field is evaluated from equation (4) using the measured values of AQsc. Typical results of j vs. l/g8 obtained with a NaCl electrolyte solution are shown in Fig. 5. The four curves were taken on the same CdS sample, but following different surface treatments, consisting of illumination of the interface under short-circuit conditions for different periods. As can be seen, such prior treatment has a profound effect on the current-field characteristics. In all cases, however, the data can be fitted by expressions of the type of equation (IO), the main difference being in the values of a. Since the range of fields studied (0.5 to 1 x 10s V/cm) is below that for which tunneling across the gap becomes significant(s) ( > 2 x 105 V/cm), one concludes that the observed currents must be due to breakdown of the blocking contact. The transient character of the current indicates that it arises from tunneling from some sort of interface states of limited density, into the conduction band of the crystal. Attempts were made to measure the overall charge associated with the tunneling current. The series capacitor in Fig. 1 was used again for this purpose. At low fields the total charge transported was found to be of the order of 1Ol5 electronic charges per ems, corresponding to a surface-state density comparable to the atomic density in a monolayer. Larger charge densities apparently flow across the interface at higher fields, but their measurement is made impossible by the irrecoverable damage they introduce into the crystal surface. A single measurement of this sort, where. time must be allowed for a complete decay of the tunneling current (milliseconds), may completely alter the current-voltage characteristics taken on the next run. The measurement of the initial
I
&n-cm
FOLLWING
8
ASSEMBLY
I
in space-charge density vs. applied with a KC1 and a NaCl electrolyte solutions.
C -15
C-8
ELECTROLYTE
CdS
ELECTROLYTE
FIG. 6. Change voltage obtained
MCI
KC1
p=O8
CONDUCTING CdS
I
(V/cm) ,
58
KC!
.
ELECTROLYl
p=o65ohm-Cl
CONDLUING CdS C-i
I
FS
z D ._
I” ;: 0
Eld
5x10-
sx’o
5
5X10
t
I
10
I
C-24
I
M
,
0
ELECTROLYTE
JMI+~S ohm-cm
CdS
6/Fs W’cm)
N
NaCl
CONDUCTING
FIG. 7. A plot of the initial current vs. l/l* obtained with a KC1 and a NaCl electrolyte solutions. The lower curve in each case corresponds to a surface freshly dipped into the respective electrolyte and was taken immediately following assembly of the system. The upper curves were obtained after prolonged illumination of the interfaces under short-circuit conditions.
I
TUNNELING
PROCESSES
ACROSS
THE
likely that the lowering of the barrier height Vo and the decrease in Aa, brought about by the illumination treatment, are closely interrelated. The former increases the equilibrium density of shallower surface states which can then become effective in the field emission processes. On this basis AEt should be expected to be approximately equal to gYo, since both quantities represent in effect the energetic distance between the conduction-band edge at the surface and the Fermi level. Whereas A& and qV0 do indeed change in the same direction by the illumination treatment, their magnitudes do not exactly match. In surfaces freshly dipped into the electrolyte, for example, AEe lies in the range 0.7 to 043 eV while Vo is usually found to be larger than 1 V. This discrepancy, however, is probably due to inaccuracies in the measurement of Vo by the charging technique. The large density of surface states that can be discharged by tunneling ( 2 101s cm-z) is rather surprising. It appears as if each sulfur atom in one or several monolayers may become ionized in this process. It is possible that one should not discuss the tunneling process under such conditions in
CdS-ELECTROLYTE
INTERFACE
593
terms of discrete surface states but rather as field emission from the valence band of sulphur into the conduction band of the CdS crystal. Acknotuledgements-The
author wishes to express his
thanks to severa members of this laboratory, especially to Drs. A. ROSE and R. W~LLIPUMS for many helpful discussions. Thanks are also extended to A. WILLIS for his very skillful contribution to the experimental work. REFl2EtENCES 1. MANV A., preceding paper [J. Phs. Chm. Solids 26, 5751. 2. WILLIAMS R., Phys. Rev. 123, 1645 (1961). 3. WILLIAMS R., Phys. Rev. 125,850 (1962). 4. See, for example, MANY A., GOLDSTEIN Y. and GROVER N. B., Semiconductor Srcrfaces. North Holland, Amsterdam t1965). 5. This procedure has been pointed out to the author by A. KP~TZIRof the Physics Department of the Hebrew University. 6. MANY A., GOLDSTEINY. and GROVERN. B., Sewiconductor Surfaces, p. 233-237. North Holland, Amsterdam (1965). FRAXZ W., Ann. Phys. 11. 17 (19521. HOPFIELD J. J. and %.%o&s D‘. G.,‘Php. Rev. 122, 35 (1961). 9. WILLIAMS R., J. C&em. Phys. 32, 1505 (1960).
5:
Pergamon
Printed in Great Britain.
Press 1965. Vol. 26, pp. 587-593.
•T~~~ELI~~ PROCESSES ACROSS THE CdS-ELECTROLYTE INTERFACE* A. MANY-f RCA Laboratories, (&ccked
Princeton,
New Jersey
25 Augtrst 1964)
Abstract-The high-field behavior of the irnterface between a canducting CdS crystal and a bIocking electrolyte contact is studied by the use of pulse techniques, The method employed is very suitable for determiniig the characteristics of the space-charge region at the crystal surface. In contrast to the case of d-c. measurements, where breakdown of the blocking contact is not apparent up to fields of at least 2 x f06 V/cm, large transient currents through the interface are observed in the. range 5 x 106-10s V/cm. These currents are ascribed to field emission from surface states into the conduction band of the CdS crystal. The surface states are shown to be intimate$ correlated with electrolytically deposited sulphur.
INTR0DUCTI0N
previous paper(l) a contact-fess method using Mylar blocking electrodes and pulsemeasurements has been described for the study of highfield effects in insulating cadmium sulphide crystals. This method completely suppresses field emission from the end electrodes, but the range of fields attained so far does not exceed about 3 x 105 V/cm. Considerably higher fields can be obtained by the use of an electrolyte solution as a blocking contact on a conducting (n-type) CdS crystal.(s) Biasing the electrolyte negatively with respect to the crystal permits fields as high as 2 x 10s V/em to be established across a carrier-free depletion or Schottky barrier formed within the crystal adjacent to the interface.@) D.C. measurements carried out by WILLIAMS(~)show that under steady-state conditions, neither field emission across the interface nor impact ionization within the depletion layer take place up to a field of about 2 x 106 V/cm, at which field tunneling from the valence into the conduction band of the CdS crystal sets in. IN THE
* The research reported in this paper was sponsored by the US, Army Research Office (Durham) under Contract Number DA 31-124-ARC)(D)-84 and RCA I&oratories, Princeton, New Jersey. T Permanent address : The Hebrew University, Jerusalem, Israel. 587
The measurements reported in the present paper are similar tu those described by W~L~~~,~~~ except that the current-voltage characteristics are taken under pulsed conditions. In contrast to the de. case, very large transient currents are observed at field intensities well below those required for tunneling across the gap. These currents are ascribed to field emission from surface states at the electrolyte-CdS interface, situated about O-8 eV below the conduction-band edge. The states are shown to be correlated with electrolytically deposited sulfur. The pulse technique used permits a direct and easy determination of the characteristics of the depletion layer. It is established that in all the conducting CdS samples studied a true Schottky barrier is formed near the surface. EXPERIMENTAL METHOD A schematic diagram of the crystal mounting and measuring circuit is shown in Fig, I. The crystal slab is glued by Glyptol cement to the walls of a glass tube. A gallium contact is apphed to the crystal face inside the tube while the other face is in contact with the electrolyte solution. The crystal samples studied were wpourgrown slabs with resistivities ranging from O-2 to 2 a-cm. The pulse is applied between 8 platinum electrode dipped into the electroiyte and the gallium contact, the electrolyte contact being negative in all cases. A smatf series resistor fi is used to measure the transient current, while the total charge flowing into the space-charge region of
588
A.
MANY
GALLIUM
OR
KCI
FIG. 1. Schematic
diagram of the crystal mounting circuit.
the crystal as a result of the applied pulse is determined by means of the large series capacitor C. RESULTS
AND
Qac = (2~rakTna)~/~[exp( -qV,/KT) 111’2.
(1)
Here K is the dielectric constant of the semiconductor, la the permittivity of free space, no the ionized donor concentration (= free carrier density in the bulk) and V, the absolute magnitude of the barrier height at the surface. For qV, g kT, the exponential term as well as the unity inside the second brackets can be neglected, and equation (1) reduces to:
Q)se = (2!cEoq)%~w~‘?
and measuring
If we express no in units of cm-s, and V, in volts, we obtain for CdS Qse zz 5.7 x lO-I6+aI/l!a.
DISCUSSION
A number of measurements were performed in order to ascertain that a Schottky barrier is formed when the electrolyte is biased negatively with respect to the crystal. The conditions that a depletion layer would constitute a true Schottky barrier are the absence of minority-carriers (either in the bulk or at the surface) and complete ionization of the donor or acceptor impurities. Under these conditions the space-charge layer is composed of fixed ionized impurities plus whatever majority-carriers that have not been completely depleted from the surface. For an extrinsic n-type sample, the total charge density per unit surface area contained in a Schottky barrier is given by:@)
+qV,/kT-
CONTACT
(2)
Qsc in C/cm2 = 11.8) :
(K
s
(3)
The absolute magnitude b, of the field intensity at the surface is obtained from Gauss’s law: &s = lO=Q,,
= 5.7x
lo-“nl,sVl’s,
(4)
where Qse is expressed in C/ems, as before, and &, is in V/cm. The experimental determination of Qse vs. V, would be straightforward if no barrier existed at the surface (V, = 0) prior to the application of the external voltage. In this case V, would be just equal to the pulse amplitude and Qs to the charge collected at the series capacitor C (Fig. 1) following the application of the pulse. In reality it is found, however, that a depletion layer already exists at the surface in the absence of the external voltage. If we denote by VOthe absolute magnitude of the equilibrium barrier height associated with this layer, then clearly V = V,-- VO and AQse = Qssc(Vs) -Qsc( VO), where V is the pulse amplitude and AQsc is the measured charge collected at C. In order to verify the square-root dependence of Qsc on V, characteristic of a Schottky barrier, it is therefore necessary to determine VO as well. This can be done by trial and error procedures: AQsc is plotted as a function of ( V+T)~/~ and 7 is adjusted until the points are collinear, when q is taken
TUNNELING
PROCESSES
as equal to Vs. (It should value of 77affects only the is, when V is comparable procedure,(s) however, is
ACROSS
be noted that the precise low-voltage results, that to Ve.) A more elegant as follows:
- V’d”), A&,, = A( V’“8’” where A =
equations
(5)
CdS-ELECTROLYTE
589
INTERFACE
using the value of 300 ems/V-set for the electron mobility). Before discussing the high-field behavior of the CdSjelectrolyte interface it would be of interest to consider the characteristics of the charging current flowing to form the Schottky barrier at the
Hence:
(~KEo~?zo)~/~.
I’ = I’,-- Vo = (AQ&)(Vys+ Combining
THE
V;‘2).
(6)
(5) and (6) we obtain:
V/AQ,, = AQscjA2+(2/A)V~2.
(7)
Thus, if the depletion layer is a Schottky barrier, the plot of V/AQse vs. A&,, (both quantities being directly measureable) should yield a straight line. This is indeed found to be the case for all CdS samples studied, as illustrated in Fig. 2. From the slope of the line and its intersection’with the ordinate (AQ,, = 0) one can readily calculate both VO and A. Once VO has been determined, it is possible to replot the data as AQsc vs. (I’#/2 = (V+ V0)1/2. This is shown in Fig. 3 for three samples of different resistivity. In all cases the points are collinear, with VO lying between about 1.7 and 2 V. The slopes of the straight lines are consistent with the values of the free-electron densities (as determined from the resistivities,
0
1
2
3
5
6
l/(V+Vo)(W”) FIG. 3. A plot of the measured change in space-charge density as a function of applied voltage for three conducting samples. The equilibrium barrier height 5’0 in each case was determined by the procedure of Fig. 2.
l----T7
crystal surface. It can be shown@) that if the initial barrier height (VO) is zero, then the current following the onset of the voltage pulse (t = 0) is given approximately by : 4 exp( - t/7) i(t) = -IL Rs [l + exp( - t/~)]~
I
I
I
I
I
I
I
0123456799 AC&x 10’ FE.
(cod/cm
2)
2. A plot of VlAQ~c VS. AQ, for a conducting CdS sample (see equation 7).
I
(8)
where V is the pulse amplitude, and R, is the crystal resistance between the ohmic contact and the interface plus whatever series resistance may be present in the circuit. The time constant -r is given by: r = +RsCsc. (9) Here Csc is the so-called space-charge capacitance when steady-state conditions have been reached and is given by Qsc/Vs multiplied by the interface area. It should be noted that equation (8) does not
590
A.
MANY
represent a simple exponential decay, as might have been expected on the basis of qualitative considerations. The value of R, in ,the experimental arrangement used is normally several hundred ohms (consisting mostly of the electrolyte resistance), while C,, is typically 10-s pF. Thus 7 is of the order of O-1 p set, a value that is considerably smaller than the available experimental resolution time. Accordingly, the charging of the spacecharge region is completed, and the steady-state Schottky barrier is established, well before any current reading is taken. All subsequent references to the phrase ‘onset of the voltage pulse’ or to ‘t = 0’ will refer to conditions just following the charging time. Equation (8) can be checked experimentally by artificially increasing R, through the use of a large series resistance, so as to make 7 fall in a convenient range. The time dependence of the charging current under such conditions is shown in Fig. 4. The pulse amplitude has been taken sufficiently large to ensure that any deviations from equation (8) due to the fact that Vs is not zero would be negligible. The theoretical curve representing equation (8) fits quite well the experimental data.
\
0.02 t
TIME()rsec) FIG. 4. The time dependence of the current charging the depletion layer in the presence of a large external series resistance.
We turn now to current-voltage measurements at high applied voltages. At low pulse amplitudes, no current flows through the system (apart from the rapid charging current discussed above), the electrolyte contact being completely blocking. As the voltage is raised, however, a transient current is observed, which decays after several milliseconds to zero. The initial current j is found to increase very rapidly with applied voltage. In the highvoltage range, j can be expressed as: j = const. exp( - x/&~),
(10)
where b, is the absolute magnitude of the field at the surface associated with the Schottky barrier. This field is evaluated from equation (4) using the measured values of AQsc. Typical results of j vs. l/g8 obtained with a NaCl electrolyte solution are shown in Fig. 5. The four curves were taken on the same CdS sample, but following different surface treatments, consisting of illumination of the interface under short-circuit conditions for different periods. As can be seen, such prior treatment has a profound effect on the current-field characteristics. In all cases, however, the data can be fitted by expressions of the type of equation (IO), the main difference being in the values of a. Since the range of fields studied (0.5 to 1 x 10s V/cm) is below that for which tunneling across the gap becomes significant(s) ( > 2 x 105 V/cm), one concludes that the observed currents must be due to breakdown of the blocking contact. The transient character of the current indicates that it arises from tunneling from some sort of interface states of limited density, into the conduction band of the crystal. Attempts were made to measure the overall charge associated with the tunneling current. The series capacitor in Fig. 1 was used again for this purpose. At low fields the total charge transported was found to be of the order of 1Ol5 electronic charges per ems, corresponding to a surface-state density comparable to the atomic density in a monolayer. Larger charge densities apparently flow across the interface at higher fields, but their measurement is made impossible by the irrecoverable damage they introduce into the crystal surface. A single measurement of this sort, where. time must be allowed for a complete decay of the tunneling current (milliseconds), may completely alter the current-voltage characteristics taken on the next run. The measurement of the initial
I
&n-cm
FOLLWING
8
ASSEMBLY
I
in space-charge density vs. applied with a KC1 and a NaCl electrolyte solutions.
C -15
C-8
ELECTROLYTE
CdS
ELECTROLYTE
FIG. 6. Change voltage obtained
MCI
KC1
p=O8
CONDUCTING CdS
I
(V/cm) ,
58
KC!
.
ELECTROLYl
p=o65ohm-Cl
CONDLUING CdS C-i
I
FS
z D ._
I” ;: 0
Eld
5x10-
sx’o
5
5X10
t
I
10
I
C-24
I
M
,
0
ELECTROLYTE
JMI+~S ohm-cm
CdS
6/Fs W’cm)
N
NaCl
CONDUCTING
FIG. 7. A plot of the initial current vs. l/l* obtained with a KC1 and a NaCl electrolyte solutions. The lower curve in each case corresponds to a surface freshly dipped into the respective electrolyte and was taken immediately following assembly of the system. The upper curves were obtained after prolonged illumination of the interfaces under short-circuit conditions.
I
TUNNELING
PROCESSES
ACROSS
THE
likely that the lowering of the barrier height Vo and the decrease in Aa, brought about by the illumination treatment, are closely interrelated. The former increases the equilibrium density of shallower surface states which can then become effective in the field emission processes. On this basis AEt should be expected to be approximately equal to gYo, since both quantities represent in effect the energetic distance between the conduction-band edge at the surface and the Fermi level. Whereas A& and qV0 do indeed change in the same direction by the illumination treatment, their magnitudes do not exactly match. In surfaces freshly dipped into the electrolyte, for example, AEe lies in the range 0.7 to 043 eV while Vo is usually found to be larger than 1 V. This discrepancy, however, is probably due to inaccuracies in the measurement of Vo by the charging technique. The large density of surface states that can be discharged by tunneling ( 2 101s cm-z) is rather surprising. It appears as if each sulfur atom in one or several monolayers may become ionized in this process. It is possible that one should not discuss the tunneling process under such conditions in
CdS-ELECTROLYTE
INTERFACE
593
terms of discrete surface states but rather as field emission from the valence band of sulphur into the conduction band of the CdS crystal. Acknotuledgements-The
author wishes to express his
thanks to severa members of this laboratory, especially to Drs. A. ROSE and R. W~LLIPUMS for many helpful discussions. Thanks are also extended to A. WILLIS for his very skillful contribution to the experimental work. REFl2EtENCES 1. MANV A., preceding paper [J. Phs. Chm. Solids 26, 5751. 2. WILLIAMS R., Phys. Rev. 123, 1645 (1961). 3. WILLIAMS R., Phys. Rev. 125,850 (1962). 4. See, for example, MANY A., GOLDSTEIN Y. and GROVER N. B., Semiconductor Srcrfaces. North Holland, Amsterdam t1965). 5. This procedure has been pointed out to the author by A. KP~TZIRof the Physics Department of the Hebrew University. 6. MANY A., GOLDSTEINY. and GROVERN. B., Sewiconductor Surfaces, p. 233-237. North Holland, Amsterdam (1965). FRAXZ W., Ann. Phys. 11. 17 (19521. HOPFIELD J. J. and %.%o&s D‘. G.,‘Php. Rev. 122, 35 (1961). 9. WILLIAMS R., J. C&em. Phys. 32, 1505 (1960).
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