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Image force effects on the short wavelength (UV) photoresponse of silicon Schottky barriers
I Ph,w. Chm. So/ids Vol. 42, No. 9, pp. 719-723. 1981 Printed in Great Britain.
IMAGE FORCE EFFECTS ON THE SHORT WAVELENGTH fUV) PHOTORESPONSE OF SILICON SCHOTTKY BARRIERS K. K. NC and H. C. Columbia Radiation Laboratory, (Received 26 February
CARD?
Columbia University.
NY, 10027, U.S.A.
1980; accepred in revised form 3 December 1980)
Abstract-An experimental study has been made of the short wavelength (h) response of near-ideal silicon Schottky barrier photodetectors. It is shown that the major cause of reduced quantum efficiency (Q.E.) in this range of A is the collection by the metal of majority carriers photogenera~ed within the image force maximum, in agreement with the theoretical predictions of Green. The bias-voltage dependence of the photocurrent in the near ultraviolet region is in good quantitative agreement with the image force model, with a Q.E. near unity for large reverse bias decreasing by approx. 15% at zero bias for A= 0.37pm, for example. The Q.E. under short-circuit conditions is relatively independent of A for A 2 0.45 pm, falling rapidly with decreasing A from 95% at 0.45 Frn to approx. 80% at 0.35 Wm. again in good quantitative agreement with the above theory.
INTRODUCTION
THEORY
generally assumed that the short wavelength response of Schottky barrier quantum detectors and solar cells is near-ideal, as a result of complete collection of photogenerated minority carriers right up to the surface of the semiconductor where the short A photons are absorbed. There is little recombination in this region of the semiconductor, unlike in p-n junction detectors which may exhibit dead layer effects associated with heavy surface doping. We show in this paper that, while the Schottky barrier is expected to exhibit an excellent short wavelength response, there is nevertheless a limitation on its response associated with the presence of image forces in the surface region of the semiconductor. This was first pointed out theoretically by Green[l]. In particular, for photons absorbed in the semiconductor within a distance of the image force maximum from the metal, the electric field attracts both the photogenerated majority carriers and minority carriers into the metal. These carriers can be considered to recombine in the metal, and do not contribute to the photocurrent. Since the optical absorption coefficient of the semiconductor (u) increases dramatically with decreasing wavelength (A), the above phenomenon is responsible for a decrease in quantum etliciency at short wavelengths. It is also to be noted that the p-n junction cell with passivating thermal oxide has recently been shown to have an excellent short wavelength response [24]. Experimental results for Au-n-type silicon Schottky barrier devices of the dependence of photocurrent on bias voltage (V) and on wavelength (A) are presented in the later sections of this paper and are shown to be in reasonably good agreement with calculations of the image forces present and with the dependence of the optical absorption coefficient (a) on A.
In the Mets-semiconductor structure there are two independent effects which act to reduce the quantum efficiency associated with the photogeneration and collection of charge carriers by strongly absorbed (short wavelength) photons. (i) So-called “surface recombination” which acts as a sink for photogenerated carriers. These carriers diffuse to the surface and recombine there, and the dependence of quantum efficiency on wavelength and bias voltage is determined by the transport model of the Schottky barrier interface. (ii) Image forces in the neighbourhood of the metal-semiconductor interface. Considering effect (i), we must first pin down the carrier transport model of the metal-silicon Schottky barrier. It is now well known that the thermionic emission-diffusion theory accurately predicts the transport properties of high mobility semiconductors such as silicon, and this has been verified experimentalIy for metalsilicon contacts such as those of the present paperiS]. In this model, the effective recombination velocity V,, = A*T*/qN, for an n-type semiconductor where A* is the Richardson constant for thermionic emission and N, is the effective density of states in the conduction band of the semiconductor. V,,, = 2 x IO”m/s for the samples of the present study. Greenfl] has shown that for this order of magnitude of V,, there is very little reduction in quantum efficiency at short wavelengths (~10%) and that any small reduction is very nearly independent of the wavelength of the incident illumination for h 5 4000 A. This is not the type of behavior observed in our experimental results to be described later (Fig. 5). In view of the small magnitude of this effect in comparison to that of image forces, we ignore its contribution in the remainder of this paper, and proceed now to a discussion of effect (ii). An electron near the surface of the semiconductor in a Schottky barrier experiences an attractive force towards the metal as a consequence of its image charge[6]. This
It is
tPresent address: Departmentof ElectricalEngineering,University of Manitoba,Winnipeg,CanadaR3T2N2.
719
720
K. K. NCand H. C. CARD
force is given by
As a consequence of the interfacial layer between the metal and the semiconductor, expression (4) should properly be modified to
where x is the distance from the surface and es is the permittivity of the semiconductor. The total potential energy in the semiconductor is therefore PE(x) = &
s
- q&(0)x + const . . . .
(2)
where E(O) is the electric field at the semiconductor surface as a consequence of the uncompensated donors in the semiconductor, given by E(0)= [+
(+F_
“)I”’
,I. l/4
(4)
The energy band diagram for a metal-n-type semiconductor Schottky barrier is shown in Fig. I, where the dependence of the conduction and valence band energies E, and E, on x has been modified for image forces.
! (KT,q) - V)
- d
(5)
where d is the thickness of the interfacial layer. Quantum-mechanical effects should properly be taken into account for distances of the order of x, in eqn (5), but are only of importance for carriers with energy close to E, [7]. Most carriers produced by the ultraviolet absorption have much higher energy and deBroglie wavelengths
(3)
for an n-type semiconductor. This relation is based on the depletion approximation. In forward bias there are of course many free electrons in the space-charge region, but their concentration is eNd except at the edge of this region, so that eqn (3) gives a good approximation to the surface electric field. Here JIz is the semiconductor surface potential at zero bias, Nd is the donor concentration and V is the forward bias voltage. The potential energy of the electron goes through a maximum when dPE(x)/dx = 0 in eqn (2); this occurs at x = x,,, where 4
2&Nd(@
114 1
G = F,,a exp (-ax)
(6)
where F. is the incident flux at the surface of the semiconductor. The dependence of (Yon A is given for example by Dash and Newman[8]. The number of photons absorbed between x = 0 and x = x, is given by N=
XmFoa exp (-ax) dx. I0
(7)
We now assume that all the photons included in eqn (7) give rise to electron-hole pairs in which both the electrons and the holes are collected by the metal since the electric field is attractive for both at their respective locations in the yz plane, from x = 0 to x,, as a result of image forces (Fig. I). This is discussed further below. These electron-hole pairs do not therefore contribute to the collected photocurrent. The quantum efficiency is therefore given by Q.E.=kl;
aFo exp (-ax) dx
= exp (-ax,)
> )I’ I/J
=
Fig. 1. Energy band diagram of MIS-Schottky barrier including image force effects, under optical illumination. The modifications to E<(x) and E”(x) due to image forces apply to individual free carriers at their particular location in the yz plane only, and do not imply bandgap narrowing for opiicaj absorption.
exp
2a’r,N,($:&T,q)-
V)
-d
This analysis assumes that the photons of interest are sufficiently strongly absorbed by the semiconductor that all are absorbed within a diffusion length of the surface. This is justified for the short A of interest here. The modifications to the band edges E,.(X) and E,(x) of Fig. 1 from image forces requires some explanation. With regard to the conduction band edge E,, the modified dependence on x applies only to the particular electron under consideration in the surface region. This dependence is correct only at the point in the lateral (yz) plane at which this electron exists. At another point in the yz plane there may be a hole, which induces a negative image charge in the metal only at that location, and this is what ,is represented by the modified E,(x). At any one location, there is only one value of electric field which applies to both electrons and holes at that loca-
Imageforce effects on the short wavelength (UV) photoresponse of silicon Schottky barriers
721
tion. Thus it is that the modified EC(x) and E”(x) of Fig.
to be lOA as a result of the unavoidable residual inter-
1 do not imply for example, a reduction in the energy gap (and hence increased optical absorption) since at any point in space E, maintains its normal value. If we consider an electron and hole at the same location in space, as for example at the moment of optical generation before the pair separate, the image charges exactly cancel and the image force at the time of generation is zero. Since the pair is generated by UV illumination with hv * E,, the electron and/or the hole will have a large initial kinetic energy so that the pair will rapidly separate in space. Each particle will then generate its own image charge in the metal.
facial oxide layer. The I-V characteristics of the diodes in the dark and under monochromatic illumination of two particular wavelengths are shown in Fig. 2. The light sources are provided by an argon laser (A = 0.513 pm, Spectral Physics, Model 262) and a UV black lamp (Sylvania FITS/BLB). The difference in current at any voltage between the dark and the illuminated characteristics is defined as the photocurrent &,(V). The UV response exhibits a large voltage dependence as compared to the green laser light. Experimental and theoretical values of Q.E. are compared in Fig. 3 as a function of reverse bias, and the theoretical curves are obtained from eqn (8) for
EXPERIMENTAL
RESULTS
AND DISCUSSION
n-type epitaxial silicon wafers of epi-layer thickness 40pm and donor concentration 10’5/cm3 were used in this study. The surfaces were degreased in trichloroethylene, acetone and methanol, chemically etched in HF and nitric acid solution (HF : HNOX= 1:6) and finally in 20% HF in water. Gold electrodes of circular geometry (area 0.0325cm’) were evaporated onto the wafers through an out-of-contact molybdenum mask at a base pressure of 10e6Torr. These diodes exhibit near ideal rectifying behaviour with n values = 1.05 from the (forward-bias) current-voltage characteristics exp(qV/nkT) and both current-voltage (I-V) and capacitance-voltage (C-V) measurements give the same barrier height of 0.80eV. C-V measurements are also used to obtain iVd and $P required for the calculation of x, in eqn (5) and d has been measured ellipsometrically
1.0I-
v
l
0
. -
-
v
A > 0.45pm
,,
0.9 ,
voltage(V)
Fig. 2. I-V characteristics showing the voltage dependence of photocurrent under green light (0.513km) and under UV illu-
.
W
.
1
t
A = 0.37pm
/
ti
0.8
I,
s
a = 2.6 x 105/cm
I)
ci ILo
Jzu
a
-3
0.7
0.6 /
05 0
0.4 0
-I
-2
-3 REVERSE
-4 BIAS
-5
-6
-7
-8
(V)
Fig. 3. Dependence of quantum efficiency (Q.E.) on applied reverse bias voltage, 0 experiment, - theory (eqn 8).
K. K. NC and H. C. CARD
122
the experimental Schottky barrier height of q& = 0.80eV. For the upper two curves, (Yhas been obtained from the literature[8] and the radiation flux (Fo) is obtained by fitting the data point at -8V where depletion-region recombination (discussed below) is supposed negligible. For the black light data, since the exact wavelength is unknown, (Y and F0 have been obtained by fitting the data at -4 and -8V. The discrepancies between the experimental data and the theory at low voltages are attributed to the diffusion of majority carriers, photogenerated beyond the image force maximum, into the metal as predicted by Green[l]. Equally important is a contribution from recombination in the depletion region, a process which has been analysed by Panayotatos and Card[9]. The 5% reduction in photocurrent at low voltages in Fig. 3 for longer wavelengths (A >0.45 pm) is mainly due to this latter process. The recombination is removed by the application of a reverse bias of b - 3V beyond which the photocurrent is very nearly constant. The experimental dependence of the depletion-region recombination on forward bias for a relatively long wavelength (0.513pm) is plotted vs forward bias in Fig. 4 as shown by the solid line, and is in close agreement with the analysis of Ref. [9] (dotted line). For shorter wavelengths, a larger portion of the incident radiation is absorbed within the region x = 0 to x,, and this substantially reduces the photocurrent. The spectral response of the diodes has been studied by using a monochromator (Spex Minimate, tungsten light source, bandwidth = 70 A). The short-circuit photocurrent (J,,h(OV) = J,,) has been compared to the photocurrent at large reverse bias (-8V), and this data is shown in Fig. 5. The experimental results (closed circles) indicate that even at long wavelengths (A 30.45 Fm), there is a residual loss of photocurrent of approx. 5% and that this loss
Fig. 4. Depletion-region recombination current vs forward bias. ----- indicates analytical solution from Ref. [9]. of A over the range shown. This is the loss due to depletion-region recombination as discussed above. The open circles are the experimental points after correction for this loss. The solid line is the theoretical prediction of the dependence of quantum efficiency on wavelength from the consideration of the image force effects discussed in the previous section, i.e. Q.E. (A) from eqn (8) for V = 0 and q4b = 0.80 eV. The agreement with the corrected experimental data is respectable. The calculated Q.E. due to image forces is plotted in Fig. 6 as a function of forward bias for two different barrier heights. The reduction in Q.E. due to this effect is pronounced for A S 0.4 pm. Image forces are most imis independent
, 0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
X(tLm) Fig. 5. Ratio JJJ,,,( - 8V)as a function of wavelength. lexperiment, 0 corrected for depletion-region recombination, - calculated response.
Image force effects on the short wavelength (UV) photoresponse of silicon Schottky barriers IO
CONCLUSION
-----___ 0 40pm
09-
00-
-
4+b=
0 00ev
07
-
---
q+,=
0 60eV
02
-
0
0.1 -.FORWARD
723
02
0.3 BIAS
Nd= 10'5/em3
0.4
05
(V.)
Image force effects in Schottky barrier and MIS photodetectors are responsible for a reduction in quantum efficiency (Q.E.) associated with the collection of photogenerated majority carriers near the semiconductor surface (within the image force maximum). This mechanism causes a significant decrease in Q.E. with decreasing wavelength below -0.4 pm for which case the optical absorption occurs close to the semiconductor surface. These effects are of only minor importance in applications as solar cells, but they are a major consideration in ultraviolet (UV) detection using Schottky barriers.
Acknowledgemenfs-The financial support of the Joint Services Electronics Program (U.S. Army, N&y, and Air Force) under contract DAAG-29-79-C-0079is aratefullv acknowledeed. Communications with Eric Chan, Tommy Poon and especially Pavlo Panayotatos,have been very helpful in the course of this work.
Fig. 6. Dependence of quantum efficiency (Q.E.) on forward bias voltage due to image force effects for two values of barrier height q&,. REFERENCES
portant under forward bias conditions where E(O) is reduced by the voltage and x, becomes relatively large. Image forces are nevertheless expected to play only a minor role in the reduction of photocurrents in Schottky barrier and MIS solar cells (which operate in forward bias) since very little of the optical energy in the solar spectrum corresponds to A %0.4 pm. However, for applications in UV detection, image forces can greatly influence the performance. It is clearly preferable from the considerations discussed in this paper to operate Schottky barrier UV detectors under substantial reverse bias.
I. Green
M. A., J. ,‘ippl. Phys. 47(2),547 (1976).
2. Fossum J. G., Lindholm F. A. and Shibib M. A.. IEEE Trans. Electron Deu. ED-26, 1294(1979). 3. Weaver H. T. and Nasby R. D., Int. Electron Deu. Mtg. Washington, D.C., late news paper (1979). 4. Nasby R. D. and Fossum J. G., 14thIEEE Phof. Spec. Conf. San Diego, California (1980). 5. Rhoderick E. H., .I. Phys. D.: Appl. Phys. 5, 1920(1972). 6. Sze S. M., Physics of Semiconductor Deuices. Wiley, New York (1969). 7. Crowell C. R. and Sze S. M., J. Appl. Phys. 37, 2683 (1966). 8. Dash W. C. and Newman R., Phys. Rev. 99, 1151(1955). 9. Panayotatos P. and Card H. C.. Solid Stale Electron 23. 41 (1980).
IMAGE FORCE EFFECTS ON THE SHORT WAVELENGTH fUV) PHOTORESPONSE OF SILICON SCHOTTKY BARRIERS K. K. NC and H. C. Columbia Radiation Laboratory, (Received 26 February
CARD?
Columbia University.
NY, 10027, U.S.A.
1980; accepred in revised form 3 December 1980)
Abstract-An experimental study has been made of the short wavelength (h) response of near-ideal silicon Schottky barrier photodetectors. It is shown that the major cause of reduced quantum efficiency (Q.E.) in this range of A is the collection by the metal of majority carriers photogenera~ed within the image force maximum, in agreement with the theoretical predictions of Green. The bias-voltage dependence of the photocurrent in the near ultraviolet region is in good quantitative agreement with the image force model, with a Q.E. near unity for large reverse bias decreasing by approx. 15% at zero bias for A= 0.37pm, for example. The Q.E. under short-circuit conditions is relatively independent of A for A 2 0.45 pm, falling rapidly with decreasing A from 95% at 0.45 Frn to approx. 80% at 0.35 Wm. again in good quantitative agreement with the above theory.
INTRODUCTION
THEORY
generally assumed that the short wavelength response of Schottky barrier quantum detectors and solar cells is near-ideal, as a result of complete collection of photogenerated minority carriers right up to the surface of the semiconductor where the short A photons are absorbed. There is little recombination in this region of the semiconductor, unlike in p-n junction detectors which may exhibit dead layer effects associated with heavy surface doping. We show in this paper that, while the Schottky barrier is expected to exhibit an excellent short wavelength response, there is nevertheless a limitation on its response associated with the presence of image forces in the surface region of the semiconductor. This was first pointed out theoretically by Green[l]. In particular, for photons absorbed in the semiconductor within a distance of the image force maximum from the metal, the electric field attracts both the photogenerated majority carriers and minority carriers into the metal. These carriers can be considered to recombine in the metal, and do not contribute to the photocurrent. Since the optical absorption coefficient of the semiconductor (u) increases dramatically with decreasing wavelength (A), the above phenomenon is responsible for a decrease in quantum etliciency at short wavelengths. It is also to be noted that the p-n junction cell with passivating thermal oxide has recently been shown to have an excellent short wavelength response [24]. Experimental results for Au-n-type silicon Schottky barrier devices of the dependence of photocurrent on bias voltage (V) and on wavelength (A) are presented in the later sections of this paper and are shown to be in reasonably good agreement with calculations of the image forces present and with the dependence of the optical absorption coefficient (a) on A.
In the Mets-semiconductor structure there are two independent effects which act to reduce the quantum efficiency associated with the photogeneration and collection of charge carriers by strongly absorbed (short wavelength) photons. (i) So-called “surface recombination” which acts as a sink for photogenerated carriers. These carriers diffuse to the surface and recombine there, and the dependence of quantum efficiency on wavelength and bias voltage is determined by the transport model of the Schottky barrier interface. (ii) Image forces in the neighbourhood of the metal-semiconductor interface. Considering effect (i), we must first pin down the carrier transport model of the metal-silicon Schottky barrier. It is now well known that the thermionic emission-diffusion theory accurately predicts the transport properties of high mobility semiconductors such as silicon, and this has been verified experimentalIy for metalsilicon contacts such as those of the present paperiS]. In this model, the effective recombination velocity V,, = A*T*/qN, for an n-type semiconductor where A* is the Richardson constant for thermionic emission and N, is the effective density of states in the conduction band of the semiconductor. V,,, = 2 x IO”m/s for the samples of the present study. Greenfl] has shown that for this order of magnitude of V,, there is very little reduction in quantum efficiency at short wavelengths (~10%) and that any small reduction is very nearly independent of the wavelength of the incident illumination for h 5 4000 A. This is not the type of behavior observed in our experimental results to be described later (Fig. 5). In view of the small magnitude of this effect in comparison to that of image forces, we ignore its contribution in the remainder of this paper, and proceed now to a discussion of effect (ii). An electron near the surface of the semiconductor in a Schottky barrier experiences an attractive force towards the metal as a consequence of its image charge[6]. This
It is
tPresent address: Departmentof ElectricalEngineering,University of Manitoba,Winnipeg,CanadaR3T2N2.
719
720
K. K. NCand H. C. CARD
force is given by
As a consequence of the interfacial layer between the metal and the semiconductor, expression (4) should properly be modified to
where x is the distance from the surface and es is the permittivity of the semiconductor. The total potential energy in the semiconductor is therefore PE(x) = &
s
- q&(0)x + const . . . .
(2)
where E(O) is the electric field at the semiconductor surface as a consequence of the uncompensated donors in the semiconductor, given by E(0)= [+
(+F_
“)I”’
,I. l/4
(4)
The energy band diagram for a metal-n-type semiconductor Schottky barrier is shown in Fig. I, where the dependence of the conduction and valence band energies E, and E, on x has been modified for image forces.
! (KT,q) - V)
- d
(5)
where d is the thickness of the interfacial layer. Quantum-mechanical effects should properly be taken into account for distances of the order of x, in eqn (5), but are only of importance for carriers with energy close to E, [7]. Most carriers produced by the ultraviolet absorption have much higher energy and deBroglie wavelengths
(3)
for an n-type semiconductor. This relation is based on the depletion approximation. In forward bias there are of course many free electrons in the space-charge region, but their concentration is eNd except at the edge of this region, so that eqn (3) gives a good approximation to the surface electric field. Here JIz is the semiconductor surface potential at zero bias, Nd is the donor concentration and V is the forward bias voltage. The potential energy of the electron goes through a maximum when dPE(x)/dx = 0 in eqn (2); this occurs at x = x,,, where 4
2&Nd(@
114 1
G = F,,a exp (-ax)
(6)
where F. is the incident flux at the surface of the semiconductor. The dependence of (Yon A is given for example by Dash and Newman[8]. The number of photons absorbed between x = 0 and x = x, is given by N=
XmFoa exp (-ax) dx. I0
(7)
We now assume that all the photons included in eqn (7) give rise to electron-hole pairs in which both the electrons and the holes are collected by the metal since the electric field is attractive for both at their respective locations in the yz plane, from x = 0 to x,, as a result of image forces (Fig. I). This is discussed further below. These electron-hole pairs do not therefore contribute to the collected photocurrent. The quantum efficiency is therefore given by Q.E.=kl;
aFo exp (-ax) dx
= exp (-ax,)
> )I’ I/J
=
Fig. 1. Energy band diagram of MIS-Schottky barrier including image force effects, under optical illumination. The modifications to E<(x) and E”(x) due to image forces apply to individual free carriers at their particular location in the yz plane only, and do not imply bandgap narrowing for opiicaj absorption.
exp
2a’r,N,($:&T,q)-
V)
-d
This analysis assumes that the photons of interest are sufficiently strongly absorbed by the semiconductor that all are absorbed within a diffusion length of the surface. This is justified for the short A of interest here. The modifications to the band edges E,.(X) and E,(x) of Fig. 1 from image forces requires some explanation. With regard to the conduction band edge E,, the modified dependence on x applies only to the particular electron under consideration in the surface region. This dependence is correct only at the point in the lateral (yz) plane at which this electron exists. At another point in the yz plane there may be a hole, which induces a negative image charge in the metal only at that location, and this is what ,is represented by the modified E,(x). At any one location, there is only one value of electric field which applies to both electrons and holes at that loca-
Imageforce effects on the short wavelength (UV) photoresponse of silicon Schottky barriers
721
tion. Thus it is that the modified EC(x) and E”(x) of Fig.
to be lOA as a result of the unavoidable residual inter-
1 do not imply for example, a reduction in the energy gap (and hence increased optical absorption) since at any point in space E, maintains its normal value. If we consider an electron and hole at the same location in space, as for example at the moment of optical generation before the pair separate, the image charges exactly cancel and the image force at the time of generation is zero. Since the pair is generated by UV illumination with hv * E,, the electron and/or the hole will have a large initial kinetic energy so that the pair will rapidly separate in space. Each particle will then generate its own image charge in the metal.
facial oxide layer. The I-V characteristics of the diodes in the dark and under monochromatic illumination of two particular wavelengths are shown in Fig. 2. The light sources are provided by an argon laser (A = 0.513 pm, Spectral Physics, Model 262) and a UV black lamp (Sylvania FITS/BLB). The difference in current at any voltage between the dark and the illuminated characteristics is defined as the photocurrent &,(V). The UV response exhibits a large voltage dependence as compared to the green laser light. Experimental and theoretical values of Q.E. are compared in Fig. 3 as a function of reverse bias, and the theoretical curves are obtained from eqn (8) for
EXPERIMENTAL
RESULTS
AND DISCUSSION
n-type epitaxial silicon wafers of epi-layer thickness 40pm and donor concentration 10’5/cm3 were used in this study. The surfaces were degreased in trichloroethylene, acetone and methanol, chemically etched in HF and nitric acid solution (HF : HNOX= 1:6) and finally in 20% HF in water. Gold electrodes of circular geometry (area 0.0325cm’) were evaporated onto the wafers through an out-of-contact molybdenum mask at a base pressure of 10e6Torr. These diodes exhibit near ideal rectifying behaviour with n values = 1.05 from the (forward-bias) current-voltage characteristics exp(qV/nkT) and both current-voltage (I-V) and capacitance-voltage (C-V) measurements give the same barrier height of 0.80eV. C-V measurements are also used to obtain iVd and $P required for the calculation of x, in eqn (5) and d has been measured ellipsometrically
1.0I-
v
l
0
. -
-
v
A > 0.45pm
,,
0.9 ,
voltage(V)
Fig. 2. I-V characteristics showing the voltage dependence of photocurrent under green light (0.513km) and under UV illu-
.
W
.
1
t
A = 0.37pm
/
ti
0.8
I,
s
a = 2.6 x 105/cm
I)
ci ILo
Jzu
a
-3
0.7
0.6 /
05 0
0.4 0
-I
-2
-3 REVERSE
-4 BIAS
-5
-6
-7
-8
(V)
Fig. 3. Dependence of quantum efficiency (Q.E.) on applied reverse bias voltage, 0 experiment, - theory (eqn 8).
K. K. NC and H. C. CARD
122
the experimental Schottky barrier height of q& = 0.80eV. For the upper two curves, (Yhas been obtained from the literature[8] and the radiation flux (Fo) is obtained by fitting the data point at -8V where depletion-region recombination (discussed below) is supposed negligible. For the black light data, since the exact wavelength is unknown, (Y and F0 have been obtained by fitting the data at -4 and -8V. The discrepancies between the experimental data and the theory at low voltages are attributed to the diffusion of majority carriers, photogenerated beyond the image force maximum, into the metal as predicted by Green[l]. Equally important is a contribution from recombination in the depletion region, a process which has been analysed by Panayotatos and Card[9]. The 5% reduction in photocurrent at low voltages in Fig. 3 for longer wavelengths (A >0.45 pm) is mainly due to this latter process. The recombination is removed by the application of a reverse bias of b - 3V beyond which the photocurrent is very nearly constant. The experimental dependence of the depletion-region recombination on forward bias for a relatively long wavelength (0.513pm) is plotted vs forward bias in Fig. 4 as shown by the solid line, and is in close agreement with the analysis of Ref. [9] (dotted line). For shorter wavelengths, a larger portion of the incident radiation is absorbed within the region x = 0 to x,, and this substantially reduces the photocurrent. The spectral response of the diodes has been studied by using a monochromator (Spex Minimate, tungsten light source, bandwidth = 70 A). The short-circuit photocurrent (J,,h(OV) = J,,) has been compared to the photocurrent at large reverse bias (-8V), and this data is shown in Fig. 5. The experimental results (closed circles) indicate that even at long wavelengths (A 30.45 Fm), there is a residual loss of photocurrent of approx. 5% and that this loss
Fig. 4. Depletion-region recombination current vs forward bias. ----- indicates analytical solution from Ref. [9]. of A over the range shown. This is the loss due to depletion-region recombination as discussed above. The open circles are the experimental points after correction for this loss. The solid line is the theoretical prediction of the dependence of quantum efficiency on wavelength from the consideration of the image force effects discussed in the previous section, i.e. Q.E. (A) from eqn (8) for V = 0 and q4b = 0.80 eV. The agreement with the corrected experimental data is respectable. The calculated Q.E. due to image forces is plotted in Fig. 6 as a function of forward bias for two different barrier heights. The reduction in Q.E. due to this effect is pronounced for A S 0.4 pm. Image forces are most imis independent
, 0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
X(tLm) Fig. 5. Ratio JJJ,,,( - 8V)as a function of wavelength. lexperiment, 0 corrected for depletion-region recombination, - calculated response.
Image force effects on the short wavelength (UV) photoresponse of silicon Schottky barriers IO
CONCLUSION
-----___ 0 40pm
09-
00-
-
4+b=
0 00ev
07
-
---
q+,=
0 60eV
02
-
0
0.1 -.FORWARD
723
02
0.3 BIAS
Nd= 10'5/em3
0.4
05
(V.)
Image force effects in Schottky barrier and MIS photodetectors are responsible for a reduction in quantum efficiency (Q.E.) associated with the collection of photogenerated majority carriers near the semiconductor surface (within the image force maximum). This mechanism causes a significant decrease in Q.E. with decreasing wavelength below -0.4 pm for which case the optical absorption occurs close to the semiconductor surface. These effects are of only minor importance in applications as solar cells, but they are a major consideration in ultraviolet (UV) detection using Schottky barriers.
Acknowledgemenfs-The financial support of the Joint Services Electronics Program (U.S. Army, N&y, and Air Force) under contract DAAG-29-79-C-0079is aratefullv acknowledeed. Communications with Eric Chan, Tommy Poon and especially Pavlo Panayotatos,have been very helpful in the course of this work.
Fig. 6. Dependence of quantum efficiency (Q.E.) on forward bias voltage due to image force effects for two values of barrier height q&,. REFERENCES
portant under forward bias conditions where E(O) is reduced by the voltage and x, becomes relatively large. Image forces are nevertheless expected to play only a minor role in the reduction of photocurrents in Schottky barrier and MIS solar cells (which operate in forward bias) since very little of the optical energy in the solar spectrum corresponds to A %0.4 pm. However, for applications in UV detection, image forces can greatly influence the performance. It is clearly preferable from the considerations discussed in this paper to operate Schottky barrier UV detectors under substantial reverse bias.
I. Green
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