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Surface states in electroluminescent MIS diodes of zinc selenide
Solid-State Electronics. 1911,Vol. 20. pp. 343-347.
Pergamon Press.
Printed in Great Britain
SURFACE STATES IN ELECTROLUMINESCENT MIS DIODES OF ZINC SELENIDE
Department
M. E. &SAN and J. WOODS of Applied Physics and Electronics, University of Durham South Road, Durham DHI 3LE, England
(Received I June 1976; in revised form 6 October 1976) Abstract-Measurements of the shunt conductance of electroluminescent MIS diodes of zinc selenide show that the density of surface states in a device in which the metal (gold) electrode was deposited on an etched surface, was of the order of 4 x IO” cm-‘eV’. When the gold was evaporated on to cleaved surfaces the surface state density was reduced to about 5 x lOlo cm-’ eV_‘. The low density of surface states means that donor densities calculated in the normal way from standard C-V measurements are only 6% too high if the measurements are made at IO0 kHz and 2% too high if 200 kHz is used.
Burr and Woods[3]. The preparation of the diodes has already been described in detail in the earlier paper[l]. The conductance method as a means of investigating surface states relies on the fact that their time constant, r, gives rise to a shunt conductance G, = C/r, as the distribution of charge in the surface states lags behind the measuring signal. Here C, is the capacitance associated with the interface states. Assuming a simple single discrete set of surface states, the equivalent circuit of a diode, which is regarded as an MIS (metal-insulator-semiconductor) device is shown in Fig. 1. C, and C, are the insulator and depletion layer capacitances and R, is the resistance representing the loss mechanism due to the surface states at the interface. The parallel branch of this circuit can be regarded as a frequency dependent capacitance, C,, with an equivalent parallel conductance, G,, where
1. INTRODUCTION
In a recent publication[l], the authors described the yellow-orange electroluminescence which is obtained when a Schottky diode based on manganese-doped zinc selenide is operated in reverse bias. The nature of the potential barrier was investigated by making measurements of the junction capacitance as a function of bias and of the spectral distribution of the short-circuit photocurrent. Gold was used as the Schottky contact and two types of diode were investigated. In the first the gold was deposited on to a surface of zinc selenide which had previously been etched in a solution of bromine-inmethanol. In the second the gold was evaporated on to a cleaved surface. The cleaving had been performed in air. The measurements of capacitance and photo-effect were interpreted to indicate that the diodes prepared on cleaved crystals contained a semi-insulating layer under the gold which was about 14 8, thick, while the diodes prepared on the etched crystals contained semi-insulating layers up to 200 A thick. In the earlier work we ignored the possible existence of surface states at the boundary between the zinc selenide and the interfacial layer, and considered the measured capacitance to be the series combination of the capacitance of the semi-insulator and the depletion region. We have now used an improved experimental arrangement which has allowed us to determine the shunt conductance of our devices. Thus we have been able to exploit the technique described by Nicollian and Goetzberger[2] and have been able to show that the mid-gap density of surface states on a cleaved surface of zinc selenide is of the order of 5 x 10”’cm-* eV I. With etched zinc selenide the surface state density is about 4 *: IO” cm2 eV’. Since both these values are very low the conclusions drawn previously[l] from the earlier C-V measurements are not seriously in error.
C,=G+&i G,,/o =
C,WT
i-Km+
In practice the input admittance is measured, and by making appropriate allowance for the capacitance of the insulator Ci, the values of C, and G, can be extracted. It is of course necessary to know C; and this is found by measuring the input capacitance in the region of strong accumulation at high foward bias. The technique consists of measuring G,/w as a function of o and noting that it assumes a maximum value when w7 = 1. The maximum value (G,,/w),,,.%. - C/2, and once C, is known the density of surface states can be calculated. In order to obtain an order of magnitude estimate of the density of surface states, N,, cm-*eV’, we have put C, = eAN,,, where A is the contact area of the device. N,, then refers to the density of surface states in the vicinity of the Fermi level. This procedure is only approximate since the insulator/semiconductor interface is likely to contain a continuum of surface states distributed through the band gap and such states might well exhibit a large
2. EXPERIMENTAL
The Schottky diodes were fabricated from single crystals of zinc selenide which were grown in this laboratory using the vapour phase technique employed by 343
344
M. E.
X
~ZSAN
Y
Fig. 1. The equivalent circuit of an MIS ZnSe device assuming a single level interface state. C, is the capacitance of the semiinsulator, C, is the depletion layer capacitance and C. that of the interface states. R, is the electron capture resistance. variation in their time constants. This situation prevails at the Si-SiO, interface and it is this system which has been discussed extensively by Nicollian and Goetzberger. However with the present stage of understanding of the MIS barrier in zinc selenide, the procedure adopted here is quite adequate for the present. 3. EXPERIMENTAL
RESULTS
3.1 Conductance measurements The input admittance (Y, = G,,,+ jwC,) of our devices was measured using an automatic G/C - V plotter designed in this laboratory by Martin[41. With the samples in the dark, measurements were made as a function of bias with frequency as a parameter. The range of frequencies examined extended from 1 to 300 kHz. Typical plots of the input capacitance C,,,, and conductance G,, of the two types of diode used in this work are shown in Fig. 2. These particular measurements were made at 200 kHz. The conductance curves illustrate a feature which was common to all the zinc selenide diodes examined here, namely that G,,, increased rapidly with forward biases in excess of OSV. This prevented us from measuring the input capacitance under conditions of high accumulation when C,,, is expected to saturate at the value of insulator
and J.
WOODS
capacitance C,. We were unable, therefore, to detect any saturation in C,,,, and as a first approximation the variation of G,/w with w was examined by ignoring C,, i.e. G,, was taken as equal to G,. Curves showing the variation of G,,/w as a function of w with the applied bias as a parameter are shown in Fig. 3 for a diode prepared on a single crystal of zinc selenide containing diffused-in aluminium. This device was formed by depositing gold on one face of a chemically etched cube of zinc selenide. The indium ohmic contact had previously been applied to the opposite face. The remaining four faces of the cube had their surface layers removed by cleaving so as to eliminate the effects of the semi-insulating layers on these faces. This procedure usually led to a small reduction in the measured conductance. The plots of GJw as a function of w, Fig. 3, were all broad curves with maxima at an angular frequency of about 100kHz, independently of the bias. If the shunt conductance is associated with surface states with a single time constant, the shape of the curves should be described by eqn (2). The broken curve in Fig. 3 is a plot of this equation with 7 = 12psec. Clearly this theoretical curve is substantially narrower than the experimental curves. The value of (GJw)~~~ at zero bias was 3.5 x 10‘“‘F which leads to a density of surface states of 3.6 x 10” cm ’ eV near the middle of the forbidden gap. The long wavelength photoelectric threshold shows that at zero bias the Fermi level at the interface lies 1.65eV below the conduction band. The full-line curves in Fig. 4 are plots of G,,/w against o obtained for a Schottky diode prepared by depositng gold on a {1IO}cleaved surface of a crystal. With cleaved diodes the curves were narrower and the maxima all occurred at an angular frequency near 700 kHz. This corresponds to a response time T = 4psec. The broken curve in Fig. 4 is in fact a plot of eqn (2) using this time constant. With zero bias the value of (G,,/w),,, was 3.7 x IO“’ F which corresponds to a surface state density
0.2 .
/
-h
--’
----
____-_--3
-2 APPLIED
-_ -1 BIAS
0 [Volts
Fig. 2. Measured values of conductance and capacitance as functions chemically etched diode, G’ and
0
1 1 +
of bias for a cleaved, G and C, and a
C’.
345
Surface states in electroluminescent MIS diodes of zinc selenide
vf=o.5
v
/I/\
cl
\
v=ov
v,=l
:.:-4--,
\ /
v
/
0 \
\O \
O\ \
y=2v
\ \
vr=3v
\ 0
pQz<\
‘\\ a
10
\
lo3
lo* ANGULAR
FREQUENCY,
w
I kHz1
-
Fig. 3. Plots of G,/w as a function of angular frequency, with bias as a parameter, for a device formed on chemically etched ZnSe. The broken curve is that expected theoretically for a single interface state with a time constant of 121*sec.
ANGULAR
FREQUENCY
, W [ktizl
-
Fig. 4. Plots of G,/o as a function of angular frequency, with bias as a parameter, for a device formed on a cleaved surface of ZnSe. The broken curve is that expected theoretically for a single interface state with a time constant of 1.4wsec.
of 4.6 X 10” cmm2eV’, some 1.36eV below the conduction band. (With cleaved diodes the photoelectric threshold occurs at 1.36eV). 3.2 Thickness of the intetfacial layer In their previous paper [ 11, the authors obtained some
estimates of the thicknesses of the interfacial layers in the various zinc selenide diodes. This was done by comparing the photoelectric threshold with the voltage intercept of the plot of C-* against V and using the ideas described by Cowley [5]. In this earlier work the possible existence of surface states was ignored. When the same
346
M. E.
&SAh
analysis was applied to the diode for which the conductance curves of Fig. 3 were obtained, the thickness of the insulating layer was calculated to be 200 A, assuming that it was composed of zinc oxide with a dielectric constant of 8.5. The parameters used to obtain this estimate of the thickness of the interfacial layer were: photoelectric threshold, $BN= 1.63 eV; voltage intercept in C ’ - V plots, V, = 2.06 eV; depth of Fermi level in the bulk = 0.08 eV; uncompensated donor concentration, N,! = 8.44 X 10lhcm-’ and effective density of states in the conduction band at 295 K, N, = 1.7x 10’”cm-‘. Cowley[S] also gave an expression which allows surface states to be taken into account when calculating the thickness of the interfacial layer. When the surface state density of 3.6 x IO” cm-‘Eve’ which was measured for this diode was used with the foregoing parameters, the thickness of the interfacial layer was calculated to be 240 instead of 2OOA. Similar calculations with the cleaved diode show that the thickness of the interfacial layer appeared to be 14 A when surface states were totally ignored, but when the measured density of 4.6 x IO”’cm ’ eV ’ was taken into account the calculated thickness of the insulating layer became 27 A. It is worth mentioning that the thickness of the interfacial layer can also be found from the C-V measurements in a rather different way. Thus the capacitance of the insulating layer C, can be calculated from the measured capacitance when C, and C, are known. The value of the capacitance of the depletion layer can be estimated if the diffusion potential and the concentration of uncompensated donors is known. The diffusion potenital can be calculated if the photoelectric barrier height is known and the donor concentration can be obtained from C-V measurements made at high frequency. C, is obtained from the measured value of (G,,/w),.,,. Using the values of Cd and C, obtained in these ways, we calculated the capacitance of the insulating layer in our chemically etched diode to be 2.8 x 10--F cm-‘, which means that it was 260 A thick. One further point to mention is that having obtained a value of C, indirectly, it was then possible to extract a more accurate value of G,/w from the measured value of G,,,/w. It will be recalled that since it was not possible to measure the capacitance of our devices in the high accumulation region, a direct measure of C, could not be obtained. At a first approximation therefore it was assumed that G, = G,,,. When due allowance was made for a value of C, = 2.8 x IO-‘F cm -’ the curves of G,,/w were displaced vertically to lower values by a factor of up to two, so that we conclude that the concentrations of surface states reported above may be too high, but the error does not exceed a factor of two. Another possible source of error would arise if any appreciable conductivity were associated with the semiinsulating layer. This situation would be most apparent at the highest frequencies used, where it can be demonstrated that an error of greater than 10% in the value of C, could be introduced if the resistivity of the semiinsulating layer, p,, were less than 10’ ohm cm. We believe, however, that the consistency of the slopes of the corrected C-‘-V plots at different frequencies (see
and .I. WOOD&
below) indicates that p, > IO’ ohm cm. If p, were too low, the effect of the calculated density of surface states would be that the value would approach that obtained by ignoring C, altogether. The effects of the surface states on the C ‘-V plots at high frequencies are negligible. This is because C, = C,, when w7 * 1 (see eqn I). However the discrepancies in the plots which arise from ignoring the surface states can be calculated. These of course become larger at lower frequencies. First the contribution from C, is allowed for, and C,, is calculated from the measured capacitance C,,,. Once the plots of G&o vs w have been made, and C, and T determined from the magnitude and location of the maxima, the second term on the right hand side of eqn (1) can be calculated for each value of the bias at which the conductance measurements were made. The true value of Cd can then be extracted from eqn (I). This is the correct capacitance to use in a plot of C 2against V. When this was done for the diodes described here. the slopes of the new C ‘-V lines at 200 kHz gave values of (N,,-N,) which were some 2% lower than those obtained using uncorrected values of C,,. The corresponding error at 100 kHz was about 6% and at IO kHz it was approximately 50%. The correction of C ‘-V plots for the effects of surface states is well illustrated by the results of some measurements made at 10 and 100 kHz on a chemically etched diode. The uncorrected capacitances led to values of (N,,-N,,) of 5.0 x IO” cm ’ (IOOkHz) and 7.0 x IO” cm ’ (IO kHz), while the corrected capacitances led to values of (N,,-N,,) of 4.67 x IO” (100 kHz) and 4.60 x 10” (IO kHz). Use of the corrected values of capacitance also led to lines with lower and constant voltage intercepts of 1.60 V. The excellent agreement between the values of (Nd-N,) calculated from the corrected capacitances measured at frequencies differing by an order of magnitude confirms that the procedure adopted here is correct, as does the agreement between the corrected voltage intercept (1.60V) and the photoelectric threshold (I.63 eV). 4. DISCUSSION In their original paper[l] the authors discussed the electroluminescent and the electrical properties of zinc selenide devices which were described as Schottky diodes. In fact it was obvious that the devices were metal-insulator-semiconductor (MIS) capacitors with a semi-insulating layer which consisted mostly of zinc and oxygen lying between the gold (metal) electrode and the zinc selenide (semiconductor). The possible existence of surface states at the surface of the selenide was ignored in the earlier paper, but nonetheless the results were interpreted to show that the semi-insulating oxide layer could be up to 200 A thick if the selenide had previously been etched in bromine-in-methanol, whereas if the gold was deposited on a cleaved surface of the selenide, the resultant semi-insulating layer was only about 14 A thick. The work described in the present paper was done in an attempt to make the existence of surface states into account, Measurements of the equivalent parallel conductance of the MIS electrollminescent diodes have
Surface
states in electroluminescentMIS diodes of zinc selenide
shown that the density of surface states lying near the middle of the band of zinc selenide is very low. With diodes prepared on cleaved crystals the measured surface state density was 4.6 x 10”’cm-’ eV-‘. The thickness of the semi-insulating layer in our particular devices was recalculated to be 27 w instead of 14A when the surface states were taken into account. With devices formed on etched crystals the insulating layers were found to be of the order of 240-260A thick instead of 2OOA which is calculated when surface states are ignored. The density of surface states with such crystals is slightly larger, but still small, at 3.6 x 10” cm-’ eV_‘. One result of the low density of surface states is that straightforward C-V measurements do not introduce serious error into the derived values of voltage intercept and uncompensated donor density provided the measurements are made at sufficiently high frequency. We estimate an error of 6% in Nd if the measurements are made at 100kHz falling to 2% when the measuring frequency is increased to 200 kHz. Finally one should mention that the magnitude of the surface state densities reported here is totally inadequate to pin the Fermi level at the free surface of the selenide; a density of about 10” cm-? is required for that purpose. As far as we are aware there are no reports of measurements of surface state densitites on zinc
347
selenide. However in the Appendix to Mead’s paper [6] on surface states on II-VI compounds, the photoelectric barrier heights are recorded for diodes formed by depositing various metals on zinc selenide and zinc sulphide in uhv. With both compounds the measured barrier heights vary linearly with the difference in electronegativities of zinc and the metal in question. Clearly no pinning of the Fermi level occurred and this is taken to indicate that surface states were virtually non-existent in the middle of the band gaps of zinc selenide and zinc sulphide. This of course is in complete agreement with our observations on zinc selenide. It is interesting to note that although cadmium sulphide also contains very few surface states, cadmium selenide does have sufficient of them to exhibit Fermi-level pinning, i.e. barrier heights in that compound are independent of the metal used[6].
REFERENCES
1. M. E. dzsan and J. Woods, Solid-St. Electron. 18, 519 (1975). 2. E. H. Nicollian and A. Goetzberger, Bell Syst. Tech. J. 46, 1055 ((1%7). 3. K. F. Burr and J. Woods, J. Cryst. Growth 9, 183 (1971). 4. P. Martin, MSc. Thesis, University of Durham (1970). 5. A. M. Cowley, J. Appl. Phys. 37, 3024 (1966). 6. C. A. Mead, Solid-St. Electron. 9, 1023 (1%6).
Pergamon Press.
Printed in Great Britain
SURFACE STATES IN ELECTROLUMINESCENT MIS DIODES OF ZINC SELENIDE
Department
M. E. &SAN and J. WOODS of Applied Physics and Electronics, University of Durham South Road, Durham DHI 3LE, England
(Received I June 1976; in revised form 6 October 1976) Abstract-Measurements of the shunt conductance of electroluminescent MIS diodes of zinc selenide show that the density of surface states in a device in which the metal (gold) electrode was deposited on an etched surface, was of the order of 4 x IO” cm-‘eV’. When the gold was evaporated on to cleaved surfaces the surface state density was reduced to about 5 x lOlo cm-’ eV_‘. The low density of surface states means that donor densities calculated in the normal way from standard C-V measurements are only 6% too high if the measurements are made at IO0 kHz and 2% too high if 200 kHz is used.
Burr and Woods[3]. The preparation of the diodes has already been described in detail in the earlier paper[l]. The conductance method as a means of investigating surface states relies on the fact that their time constant, r, gives rise to a shunt conductance G, = C/r, as the distribution of charge in the surface states lags behind the measuring signal. Here C, is the capacitance associated with the interface states. Assuming a simple single discrete set of surface states, the equivalent circuit of a diode, which is regarded as an MIS (metal-insulator-semiconductor) device is shown in Fig. 1. C, and C, are the insulator and depletion layer capacitances and R, is the resistance representing the loss mechanism due to the surface states at the interface. The parallel branch of this circuit can be regarded as a frequency dependent capacitance, C,, with an equivalent parallel conductance, G,, where
1. INTRODUCTION
In a recent publication[l], the authors described the yellow-orange electroluminescence which is obtained when a Schottky diode based on manganese-doped zinc selenide is operated in reverse bias. The nature of the potential barrier was investigated by making measurements of the junction capacitance as a function of bias and of the spectral distribution of the short-circuit photocurrent. Gold was used as the Schottky contact and two types of diode were investigated. In the first the gold was deposited on to a surface of zinc selenide which had previously been etched in a solution of bromine-inmethanol. In the second the gold was evaporated on to a cleaved surface. The cleaving had been performed in air. The measurements of capacitance and photo-effect were interpreted to indicate that the diodes prepared on cleaved crystals contained a semi-insulating layer under the gold which was about 14 8, thick, while the diodes prepared on the etched crystals contained semi-insulating layers up to 200 A thick. In the earlier work we ignored the possible existence of surface states at the boundary between the zinc selenide and the interfacial layer, and considered the measured capacitance to be the series combination of the capacitance of the semi-insulator and the depletion region. We have now used an improved experimental arrangement which has allowed us to determine the shunt conductance of our devices. Thus we have been able to exploit the technique described by Nicollian and Goetzberger[2] and have been able to show that the mid-gap density of surface states on a cleaved surface of zinc selenide is of the order of 5 x 10”’cm-* eV I. With etched zinc selenide the surface state density is about 4 *: IO” cm2 eV’. Since both these values are very low the conclusions drawn previously[l] from the earlier C-V measurements are not seriously in error.
C,=G+&i G,,/o =
C,WT
i-Km+
In practice the input admittance is measured, and by making appropriate allowance for the capacitance of the insulator Ci, the values of C, and G, can be extracted. It is of course necessary to know C; and this is found by measuring the input capacitance in the region of strong accumulation at high foward bias. The technique consists of measuring G,/w as a function of o and noting that it assumes a maximum value when w7 = 1. The maximum value (G,,/w),,,.%. - C/2, and once C, is known the density of surface states can be calculated. In order to obtain an order of magnitude estimate of the density of surface states, N,, cm-*eV’, we have put C, = eAN,,, where A is the contact area of the device. N,, then refers to the density of surface states in the vicinity of the Fermi level. This procedure is only approximate since the insulator/semiconductor interface is likely to contain a continuum of surface states distributed through the band gap and such states might well exhibit a large
2. EXPERIMENTAL
The Schottky diodes were fabricated from single crystals of zinc selenide which were grown in this laboratory using the vapour phase technique employed by 343
344
M. E.
X
~ZSAN
Y
Fig. 1. The equivalent circuit of an MIS ZnSe device assuming a single level interface state. C, is the capacitance of the semiinsulator, C, is the depletion layer capacitance and C. that of the interface states. R, is the electron capture resistance. variation in their time constants. This situation prevails at the Si-SiO, interface and it is this system which has been discussed extensively by Nicollian and Goetzberger. However with the present stage of understanding of the MIS barrier in zinc selenide, the procedure adopted here is quite adequate for the present. 3. EXPERIMENTAL
RESULTS
3.1 Conductance measurements The input admittance (Y, = G,,,+ jwC,) of our devices was measured using an automatic G/C - V plotter designed in this laboratory by Martin[41. With the samples in the dark, measurements were made as a function of bias with frequency as a parameter. The range of frequencies examined extended from 1 to 300 kHz. Typical plots of the input capacitance C,,,, and conductance G,, of the two types of diode used in this work are shown in Fig. 2. These particular measurements were made at 200 kHz. The conductance curves illustrate a feature which was common to all the zinc selenide diodes examined here, namely that G,,, increased rapidly with forward biases in excess of OSV. This prevented us from measuring the input capacitance under conditions of high accumulation when C,,, is expected to saturate at the value of insulator
and J.
WOODS
capacitance C,. We were unable, therefore, to detect any saturation in C,,,, and as a first approximation the variation of G,/w with w was examined by ignoring C,, i.e. G,, was taken as equal to G,. Curves showing the variation of G,,/w as a function of w with the applied bias as a parameter are shown in Fig. 3 for a diode prepared on a single crystal of zinc selenide containing diffused-in aluminium. This device was formed by depositing gold on one face of a chemically etched cube of zinc selenide. The indium ohmic contact had previously been applied to the opposite face. The remaining four faces of the cube had their surface layers removed by cleaving so as to eliminate the effects of the semi-insulating layers on these faces. This procedure usually led to a small reduction in the measured conductance. The plots of GJw as a function of w, Fig. 3, were all broad curves with maxima at an angular frequency of about 100kHz, independently of the bias. If the shunt conductance is associated with surface states with a single time constant, the shape of the curves should be described by eqn (2). The broken curve in Fig. 3 is a plot of this equation with 7 = 12psec. Clearly this theoretical curve is substantially narrower than the experimental curves. The value of (GJw)~~~ at zero bias was 3.5 x 10‘“‘F which leads to a density of surface states of 3.6 x 10” cm ’ eV near the middle of the forbidden gap. The long wavelength photoelectric threshold shows that at zero bias the Fermi level at the interface lies 1.65eV below the conduction band. The full-line curves in Fig. 4 are plots of G,,/w against o obtained for a Schottky diode prepared by depositng gold on a {1IO}cleaved surface of a crystal. With cleaved diodes the curves were narrower and the maxima all occurred at an angular frequency near 700 kHz. This corresponds to a response time T = 4psec. The broken curve in Fig. 4 is in fact a plot of eqn (2) using this time constant. With zero bias the value of (G,,/w),,, was 3.7 x IO“’ F which corresponds to a surface state density
0.2 .
/
-h
--’
----
____-_--3
-2 APPLIED
-_ -1 BIAS
0 [Volts
Fig. 2. Measured values of conductance and capacitance as functions chemically etched diode, G’ and
0
1 1 +
of bias for a cleaved, G and C, and a
C’.
345
Surface states in electroluminescent MIS diodes of zinc selenide
vf=o.5
v
/I/\
cl
\
v=ov
v,=l
:.:-4--,
\ /
v
/
0 \
\O \
O\ \
y=2v
\ \
vr=3v
\ 0
pQz<\
‘\\ a
10
\
lo3
lo* ANGULAR
FREQUENCY,
w
I kHz1
-
Fig. 3. Plots of G,/w as a function of angular frequency, with bias as a parameter, for a device formed on chemically etched ZnSe. The broken curve is that expected theoretically for a single interface state with a time constant of 121*sec.
ANGULAR
FREQUENCY
, W [ktizl
-
Fig. 4. Plots of G,/o as a function of angular frequency, with bias as a parameter, for a device formed on a cleaved surface of ZnSe. The broken curve is that expected theoretically for a single interface state with a time constant of 1.4wsec.
of 4.6 X 10” cmm2eV’, some 1.36eV below the conduction band. (With cleaved diodes the photoelectric threshold occurs at 1.36eV). 3.2 Thickness of the intetfacial layer In their previous paper [ 11, the authors obtained some
estimates of the thicknesses of the interfacial layers in the various zinc selenide diodes. This was done by comparing the photoelectric threshold with the voltage intercept of the plot of C-* against V and using the ideas described by Cowley [5]. In this earlier work the possible existence of surface states was ignored. When the same
346
M. E.
&SAh
analysis was applied to the diode for which the conductance curves of Fig. 3 were obtained, the thickness of the insulating layer was calculated to be 200 A, assuming that it was composed of zinc oxide with a dielectric constant of 8.5. The parameters used to obtain this estimate of the thickness of the interfacial layer were: photoelectric threshold, $BN= 1.63 eV; voltage intercept in C ’ - V plots, V, = 2.06 eV; depth of Fermi level in the bulk = 0.08 eV; uncompensated donor concentration, N,! = 8.44 X 10lhcm-’ and effective density of states in the conduction band at 295 K, N, = 1.7x 10’”cm-‘. Cowley[S] also gave an expression which allows surface states to be taken into account when calculating the thickness of the interfacial layer. When the surface state density of 3.6 x IO” cm-‘Eve’ which was measured for this diode was used with the foregoing parameters, the thickness of the interfacial layer was calculated to be 240 instead of 2OOA. Similar calculations with the cleaved diode show that the thickness of the interfacial layer appeared to be 14 A when surface states were totally ignored, but when the measured density of 4.6 x IO”’cm ’ eV ’ was taken into account the calculated thickness of the insulating layer became 27 A. It is worth mentioning that the thickness of the interfacial layer can also be found from the C-V measurements in a rather different way. Thus the capacitance of the insulating layer C, can be calculated from the measured capacitance when C, and C, are known. The value of the capacitance of the depletion layer can be estimated if the diffusion potential and the concentration of uncompensated donors is known. The diffusion potenital can be calculated if the photoelectric barrier height is known and the donor concentration can be obtained from C-V measurements made at high frequency. C, is obtained from the measured value of (G,,/w),.,,. Using the values of Cd and C, obtained in these ways, we calculated the capacitance of the insulating layer in our chemically etched diode to be 2.8 x 10--F cm-‘, which means that it was 260 A thick. One further point to mention is that having obtained a value of C, indirectly, it was then possible to extract a more accurate value of G,/w from the measured value of G,,,/w. It will be recalled that since it was not possible to measure the capacitance of our devices in the high accumulation region, a direct measure of C, could not be obtained. At a first approximation therefore it was assumed that G, = G,,,. When due allowance was made for a value of C, = 2.8 x IO-‘F cm -’ the curves of G,,/w were displaced vertically to lower values by a factor of up to two, so that we conclude that the concentrations of surface states reported above may be too high, but the error does not exceed a factor of two. Another possible source of error would arise if any appreciable conductivity were associated with the semiinsulating layer. This situation would be most apparent at the highest frequencies used, where it can be demonstrated that an error of greater than 10% in the value of C, could be introduced if the resistivity of the semiinsulating layer, p,, were less than 10’ ohm cm. We believe, however, that the consistency of the slopes of the corrected C-‘-V plots at different frequencies (see
and .I. WOOD&
below) indicates that p, > IO’ ohm cm. If p, were too low, the effect of the calculated density of surface states would be that the value would approach that obtained by ignoring C, altogether. The effects of the surface states on the C ‘-V plots at high frequencies are negligible. This is because C, = C,, when w7 * 1 (see eqn I). However the discrepancies in the plots which arise from ignoring the surface states can be calculated. These of course become larger at lower frequencies. First the contribution from C, is allowed for, and C,, is calculated from the measured capacitance C,,,. Once the plots of G&o vs w have been made, and C, and T determined from the magnitude and location of the maxima, the second term on the right hand side of eqn (1) can be calculated for each value of the bias at which the conductance measurements were made. The true value of Cd can then be extracted from eqn (I). This is the correct capacitance to use in a plot of C 2against V. When this was done for the diodes described here. the slopes of the new C ‘-V lines at 200 kHz gave values of (N,,-N,) which were some 2% lower than those obtained using uncorrected values of C,,. The corresponding error at 100 kHz was about 6% and at IO kHz it was approximately 50%. The correction of C ‘-V plots for the effects of surface states is well illustrated by the results of some measurements made at 10 and 100 kHz on a chemically etched diode. The uncorrected capacitances led to values of (N,,-N,,) of 5.0 x IO” cm ’ (IOOkHz) and 7.0 x IO” cm ’ (IO kHz), while the corrected capacitances led to values of (N,,-N,,) of 4.67 x IO” (100 kHz) and 4.60 x 10” (IO kHz). Use of the corrected values of capacitance also led to lines with lower and constant voltage intercepts of 1.60 V. The excellent agreement between the values of (Nd-N,) calculated from the corrected capacitances measured at frequencies differing by an order of magnitude confirms that the procedure adopted here is correct, as does the agreement between the corrected voltage intercept (1.60V) and the photoelectric threshold (I.63 eV). 4. DISCUSSION In their original paper[l] the authors discussed the electroluminescent and the electrical properties of zinc selenide devices which were described as Schottky diodes. In fact it was obvious that the devices were metal-insulator-semiconductor (MIS) capacitors with a semi-insulating layer which consisted mostly of zinc and oxygen lying between the gold (metal) electrode and the zinc selenide (semiconductor). The possible existence of surface states at the surface of the selenide was ignored in the earlier paper, but nonetheless the results were interpreted to show that the semi-insulating oxide layer could be up to 200 A thick if the selenide had previously been etched in bromine-in-methanol, whereas if the gold was deposited on a cleaved surface of the selenide, the resultant semi-insulating layer was only about 14 A thick. The work described in the present paper was done in an attempt to make the existence of surface states into account, Measurements of the equivalent parallel conductance of the MIS electrollminescent diodes have
Surface
states in electroluminescentMIS diodes of zinc selenide
shown that the density of surface states lying near the middle of the band of zinc selenide is very low. With diodes prepared on cleaved crystals the measured surface state density was 4.6 x 10”’cm-’ eV-‘. The thickness of the semi-insulating layer in our particular devices was recalculated to be 27 w instead of 14A when the surface states were taken into account. With devices formed on etched crystals the insulating layers were found to be of the order of 240-260A thick instead of 2OOA which is calculated when surface states are ignored. The density of surface states with such crystals is slightly larger, but still small, at 3.6 x 10” cm-’ eV_‘. One result of the low density of surface states is that straightforward C-V measurements do not introduce serious error into the derived values of voltage intercept and uncompensated donor density provided the measurements are made at sufficiently high frequency. We estimate an error of 6% in Nd if the measurements are made at 100kHz falling to 2% when the measuring frequency is increased to 200 kHz. Finally one should mention that the magnitude of the surface state densities reported here is totally inadequate to pin the Fermi level at the free surface of the selenide; a density of about 10” cm-? is required for that purpose. As far as we are aware there are no reports of measurements of surface state densitites on zinc
347
selenide. However in the Appendix to Mead’s paper [6] on surface states on II-VI compounds, the photoelectric barrier heights are recorded for diodes formed by depositing various metals on zinc selenide and zinc sulphide in uhv. With both compounds the measured barrier heights vary linearly with the difference in electronegativities of zinc and the metal in question. Clearly no pinning of the Fermi level occurred and this is taken to indicate that surface states were virtually non-existent in the middle of the band gaps of zinc selenide and zinc sulphide. This of course is in complete agreement with our observations on zinc selenide. It is interesting to note that although cadmium sulphide also contains very few surface states, cadmium selenide does have sufficient of them to exhibit Fermi-level pinning, i.e. barrier heights in that compound are independent of the metal used[6].
REFERENCES
1. M. E. dzsan and J. Woods, Solid-St. Electron. 18, 519 (1975). 2. E. H. Nicollian and A. Goetzberger, Bell Syst. Tech. J. 46, 1055 ((1%7). 3. K. F. Burr and J. Woods, J. Cryst. Growth 9, 183 (1971). 4. P. Martin, MSc. Thesis, University of Durham (1970). 5. A. M. Cowley, J. Appl. Phys. 37, 3024 (1966). 6. C. A. Mead, Solid-St. Electron. 9, 1023 (1%6).