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Single-electron tunneling in point-contact tunnel junctions
Physica B 165&166 North-Holland
(1990)
SINGLE-ELECTRON R.T.M.
Smokers,
Research Institute
P. J.M.
63-64
TUNNELING van Bentum
for Materials,
IN POINT-CONTACT
TUNNEL
JUNCTIONS
and H. van Kempen.
University
of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, the Netherlands
SET effects have been observed in point-contact tunnel junctions on surface doped Si. Changing the electromagnetic environment does not appreciably affect the junction capacitance. Furthermore the influence of a Coulomb gap on STM-spectroscopy on superconductors is discussed. 1. INTRODUCTION In small tunnel junctions
the condition
In this contribution we analyse the effect of the electromagnetic environment by tunneling into surface doped Si, at
can be reached
that the charging energy e2/2C, with C the capacitance of the junction, is comparable to, or larger than the thermal energy LBT. For low voltages across the junction Coulomb interactions strongly suppress the tunneling probability (Coulomb blockade). For the ideal case of a single current biased normal metal tunnel junction a full quantum-mechanical calculation [l] predicts an I(V) characteristic, which is parabolic near the origin, and for higher voltages approaches linear asymptotes, which are displaced from the origin by AV = e/2C. For small currents tunneling events are correlated in time, leading to oscillations of the voltage across the junction (SET-oscillations), with frequency fs~~ = I/e and
ON SURFACE
The samples in this experiment
DOPED
Si
are made on a single crys-
structures in combination with temperature variation provides a wide range of series resistances. By exposure to air an oxide layer of Y 1OA is formed. Using a low temperature STM-like set-up a tungsten tip is allowed to make mechanical contact with this oxide layer, thus forming a stable
essentially the same results. In practice stray capacitances of the leads tend to make the junction effectively voltage biased, thus suppressing the SET oscillations. Decoupling from these stray capacitances
point-contact tunnel junction. Fig.la shows an example of the I(V) characteristics of a point contact at T = 4.2K. The tunnel resistance is RT = 7.2MR. Although at this temperature the series resistance is still much smaller than RT, we find an obvious Coulomb gap. The asymptotes are offset by e/2C = 1.4mV, yielding C = 5.7 . 10-17F. At lower voltages the characteristic is clearly parabolic, as can be seen from the linear parts in the dI/dV(V) curve (fig. lb). The rounding of the dI/dV(V) curve near the origin is slightly larger than expected from temperature broadening at 4.2 K, which might be due to
can be achieved in nanofabricated planar tunnel-junction arrays [4] and in point contact tunneling through small isolated particles [5]. Solitary point-contact tunnel junctions on various materials such as Al, Sn, stainless steel, and even high-Tc superconductors such as YBazCu307_6 show clear signs of a Coulomb blockade, indicating capacitances of order 10-17F [6]. This was understood by treating the junction environment as a transmission line, assuming that only interactions in a space region cry accessible within the tunneling time
,
rr can contribute to the Coulomb blockade. A subsequent analysis [7] showed that the stray capacitance effectively interfering with the tunneling process is determined by the space region DT that can be probed by the electromagnetic field (propagation velocity u) produced by virtual tunneling events in a time span T = max(rr, At) before actual tunneling. At stems from the uncertainty relation AE . At = h with AE the energy gain of the electron after tunneling. For clean junctions Q = 10W’5s, while At z 10ml’s. For single junctions with tunnel resistance RT > RQ = h/2e2 and lead impedance S(W) << RT, I(V) is predicted to be almost linear with only a small trace of Coulomb interactions in a small conductance dip around zero bias. Measurements on a solitary planar junction [4] are in good agreement with the predictions of ref.171.
@ 1990 - Elsevier Science Publishers
2. TUNNELING
talline Si wafer by standard integrated circuit techniques. By implantation of As-ions and succesive diffusion at 1000 “C a constant dopant density of 5 8. 101scm-3 is obtained down to O.lpm below the surface. At T = 4.2K Ro Y 50kR, while at T = 1.2K Ro z 30MR. Using differently patterned
amplitude e/2C. A semi-classical approach [2,3] , based on a Fermi golden rule calculation of the tunneling probability and Monte Carlo simulation of the tunneling events, gives
0921-4526/90/$03.50
temperatures close to the metal-insulator transition. Also we investigate the influence of a Coulomb blockade in STMspectroscopy on classic and high-T, superconductors.
I
2-
s
‘=
l-15
-10
-5
V(mV) Fig.1 I(V) (a) and &/W(V) (b) curves of a point contact on a surface doped Si sample measured at 2’= 4.2K.
B.V. (North-Holland)
R. T.M. Smokers, P.J.M. van Bentum, H. van Kempen
64
-I
I
VhV)
VW) Fig.2
I(V) and
dl/dV(V) curvesof
a point contact
on a sur-
face doped Si sample measured at T = 1.5K.
modulation by stray rf signals. Extrapolations of the linear parts however do intersect the origin. C and R-’ could be increased by pushing the Fig.2 shows the I(V) junction measured at T C = 2.7. lo-r7F. Cooling to 2’ = 1.5K did not alter
tip further into the oxide layer. and dl/dV( V) curves of another = 1.5K. We find RT = 36MR and this contact down from T = 4.2K although the I(V) characteristics,
the series resistance increased up to x 2. RT. The resistance and apparent capacitance of the junction stayed roughly the
that
This suggests that it is not the high series resistance provides the decoupling from stray capacitances, but
possibly the relatively slow hopping into localised dopant states. In point-contact tunneling on other materials impurity states in the oxide or at the surface of the material probably have the same effect. 3. TUNNELING SPECTROSCOPY In STM spectroscopy one wants to distinguish between intrinsic properties of the materials under investigation, and effects associated with the nature of the tunneling process in these low capacitance point-contact tunnel junctions. In general one expects that spectroscopic features will be displaced in energy E’ = Es + e/2C and, because of the volt,age oscillations across the junction, the results are averaged over a bandwidth of order e/C IS]. Fig. 3a shows (open circles) the I(V) characteristics of a point-contact tunnel junction between a tungsten tip and a 3000 A Sn film, measured at T = 1.2K. The tip is in mechanical contact with the oxide layer of the Sn film. The Sn film was part of a planar tunnel junction with a 150 A Al film. From the tunneling characteristics of this planar junction the energy gaps of both films could be inferred. The thin line in fig.3a is the B.C.S. tunneling curve with A = 0.59meV from the measurement on the planar junction. The thick line is a Monte Carlo calculation of the I(V) curve including SET effects with the capacitance C as a single fitting parameter. We find C = 3.2. 10-16F. In fig.3b the I(V) characteristic is depicted of a tunnel
Fig.3 I(V) characteristics (circles) of point contact,s on (a) a Sn film at T = 1.2K, and (b) ceramic YBa~Cus07_~ at T = 4.2K, compared with B.C.S. curves (thin lines) and fits including SETeffects (thick lines). junction between a tungsten tip and the ceramic high-T, superconductor YBasCusOr-6, measured at T = 4.2K. The thick line is again a Monte Carlo fit, this time with both A and C as fitting parameters. We find C = 1.6. 10-17F and A = 16meV. The thin line represents the B.C.S. (T = 0) curve for this A. Material
intrinsic
effects cannot
explain
the measurement
on Sn, as they would also show up in the planar junction. Other effects such as rf pick-up or current induced nonequilibrium can explain a broadening of the gap singularity, but not the shift to higher energy. 4. CONCLUSIONS Clear manifestations of a Coulomb blockade are in STM measurements on semiconductors, metals perconductors. We find no appreciable effect of range electromagnetic environment when changing resistance from 50kR to 80MR. Decoupling from pacitances Part
may be due to tunneling
of this work was financed
Onderzoek
through
observed and suthe long the series stray ca-
impurity
by the Stichting
states.
voor Fundamenteel
der Materie (FOM).
References [I] D.V. Averin and K.K. Likharev,
J. Low Temp.
Phys.
62 (1980)
345. [2] P.J.M. van Bentum, H. van Kempen, [3] K.Mullen,
L.E.C. van de Leemput,
R.T.M.
Smokers and
Phys. Scripta T 25 (1989) 122.
E. Ben-Jacob,
R.C. Jacklevic
and Z. Schuss, Phys. Rev.
B 36 (1988) 98. [4] P. Delsing, K.K. Likharev,
L.S. Kuzmin and T. Claeson, Phys. Rev.
Lett. I33 (1989) 1180. [5] P.J.M. van Bentum, Rev. Lett.
R.T.M.
Smokers, and H. van Kempen,
Phys.
60 (1988) 2543.
[6] P.J.M. van Bentum, P.A.A. Teunissen, [7] Yu. V. Nazarov,
L.E.C. van de Leemput,
and
60 (1988) 369.
SW. Phys. JETP
[8] P.J.M. van Bentum, H. van Kempen,
H. van Kempen,
Phys. Rev. Lett.
68 (1989) 561.
H.F.C. Hoevers,
L.E.C. van de Leemput
J. Magn. Magn. Mat. 76-77
(1988) 561.
and
(1990)
SINGLE-ELECTRON R.T.M.
Smokers,
Research Institute
P. J.M.
63-64
TUNNELING van Bentum
for Materials,
IN POINT-CONTACT
TUNNEL
JUNCTIONS
and H. van Kempen.
University
of Nijmegen, Toernooiveld,
NL-6525 ED Nijmegen, the Netherlands
SET effects have been observed in point-contact tunnel junctions on surface doped Si. Changing the electromagnetic environment does not appreciably affect the junction capacitance. Furthermore the influence of a Coulomb gap on STM-spectroscopy on superconductors is discussed. 1. INTRODUCTION In small tunnel junctions
the condition
In this contribution we analyse the effect of the electromagnetic environment by tunneling into surface doped Si, at
can be reached
that the charging energy e2/2C, with C the capacitance of the junction, is comparable to, or larger than the thermal energy LBT. For low voltages across the junction Coulomb interactions strongly suppress the tunneling probability (Coulomb blockade). For the ideal case of a single current biased normal metal tunnel junction a full quantum-mechanical calculation [l] predicts an I(V) characteristic, which is parabolic near the origin, and for higher voltages approaches linear asymptotes, which are displaced from the origin by AV = e/2C. For small currents tunneling events are correlated in time, leading to oscillations of the voltage across the junction (SET-oscillations), with frequency fs~~ = I/e and
ON SURFACE
The samples in this experiment
DOPED
Si
are made on a single crys-
structures in combination with temperature variation provides a wide range of series resistances. By exposure to air an oxide layer of Y 1OA is formed. Using a low temperature STM-like set-up a tungsten tip is allowed to make mechanical contact with this oxide layer, thus forming a stable
essentially the same results. In practice stray capacitances of the leads tend to make the junction effectively voltage biased, thus suppressing the SET oscillations. Decoupling from these stray capacitances
point-contact tunnel junction. Fig.la shows an example of the I(V) characteristics of a point contact at T = 4.2K. The tunnel resistance is RT = 7.2MR. Although at this temperature the series resistance is still much smaller than RT, we find an obvious Coulomb gap. The asymptotes are offset by e/2C = 1.4mV, yielding C = 5.7 . 10-17F. At lower voltages the characteristic is clearly parabolic, as can be seen from the linear parts in the dI/dV(V) curve (fig. lb). The rounding of the dI/dV(V) curve near the origin is slightly larger than expected from temperature broadening at 4.2 K, which might be due to
can be achieved in nanofabricated planar tunnel-junction arrays [4] and in point contact tunneling through small isolated particles [5]. Solitary point-contact tunnel junctions on various materials such as Al, Sn, stainless steel, and even high-Tc superconductors such as YBazCu307_6 show clear signs of a Coulomb blockade, indicating capacitances of order 10-17F [6]. This was understood by treating the junction environment as a transmission line, assuming that only interactions in a space region cry accessible within the tunneling time
,
rr can contribute to the Coulomb blockade. A subsequent analysis [7] showed that the stray capacitance effectively interfering with the tunneling process is determined by the space region DT that can be probed by the electromagnetic field (propagation velocity u) produced by virtual tunneling events in a time span T = max(rr, At) before actual tunneling. At stems from the uncertainty relation AE . At = h with AE the energy gain of the electron after tunneling. For clean junctions Q = 10W’5s, while At z 10ml’s. For single junctions with tunnel resistance RT > RQ = h/2e2 and lead impedance S(W) << RT, I(V) is predicted to be almost linear with only a small trace of Coulomb interactions in a small conductance dip around zero bias. Measurements on a solitary planar junction [4] are in good agreement with the predictions of ref.171.
@ 1990 - Elsevier Science Publishers
2. TUNNELING
talline Si wafer by standard integrated circuit techniques. By implantation of As-ions and succesive diffusion at 1000 “C a constant dopant density of 5 8. 101scm-3 is obtained down to O.lpm below the surface. At T = 4.2K Ro Y 50kR, while at T = 1.2K Ro z 30MR. Using differently patterned
amplitude e/2C. A semi-classical approach [2,3] , based on a Fermi golden rule calculation of the tunneling probability and Monte Carlo simulation of the tunneling events, gives
0921-4526/90/$03.50
temperatures close to the metal-insulator transition. Also we investigate the influence of a Coulomb blockade in STMspectroscopy on classic and high-T, superconductors.
I
2-
s
‘=
l-15
-10
-5
V(mV) Fig.1 I(V) (a) and &/W(V) (b) curves of a point contact on a surface doped Si sample measured at 2’= 4.2K.
B.V. (North-Holland)
R. T.M. Smokers, P.J.M. van Bentum, H. van Kempen
64
-I
I
VhV)
VW) Fig.2
I(V) and
dl/dV(V) curvesof
a point contact
on a sur-
face doped Si sample measured at T = 1.5K.
modulation by stray rf signals. Extrapolations of the linear parts however do intersect the origin. C and R-’ could be increased by pushing the Fig.2 shows the I(V) junction measured at T C = 2.7. lo-r7F. Cooling to 2’ = 1.5K did not alter
tip further into the oxide layer. and dl/dV( V) curves of another = 1.5K. We find RT = 36MR and this contact down from T = 4.2K although the I(V) characteristics,
the series resistance increased up to x 2. RT. The resistance and apparent capacitance of the junction stayed roughly the
that
This suggests that it is not the high series resistance provides the decoupling from stray capacitances, but
possibly the relatively slow hopping into localised dopant states. In point-contact tunneling on other materials impurity states in the oxide or at the surface of the material probably have the same effect. 3. TUNNELING SPECTROSCOPY In STM spectroscopy one wants to distinguish between intrinsic properties of the materials under investigation, and effects associated with the nature of the tunneling process in these low capacitance point-contact tunnel junctions. In general one expects that spectroscopic features will be displaced in energy E’ = Es + e/2C and, because of the volt,age oscillations across the junction, the results are averaged over a bandwidth of order e/C IS]. Fig. 3a shows (open circles) the I(V) characteristics of a point-contact tunnel junction between a tungsten tip and a 3000 A Sn film, measured at T = 1.2K. The tip is in mechanical contact with the oxide layer of the Sn film. The Sn film was part of a planar tunnel junction with a 150 A Al film. From the tunneling characteristics of this planar junction the energy gaps of both films could be inferred. The thin line in fig.3a is the B.C.S. tunneling curve with A = 0.59meV from the measurement on the planar junction. The thick line is a Monte Carlo calculation of the I(V) curve including SET effects with the capacitance C as a single fitting parameter. We find C = 3.2. 10-16F. In fig.3b the I(V) characteristic is depicted of a tunnel
Fig.3 I(V) characteristics (circles) of point contact,s on (a) a Sn film at T = 1.2K, and (b) ceramic YBa~Cus07_~ at T = 4.2K, compared with B.C.S. curves (thin lines) and fits including SETeffects (thick lines). junction between a tungsten tip and the ceramic high-T, superconductor YBasCusOr-6, measured at T = 4.2K. The thick line is again a Monte Carlo fit, this time with both A and C as fitting parameters. We find C = 1.6. 10-17F and A = 16meV. The thin line represents the B.C.S. (T = 0) curve for this A. Material
intrinsic
effects cannot
explain
the measurement
on Sn, as they would also show up in the planar junction. Other effects such as rf pick-up or current induced nonequilibrium can explain a broadening of the gap singularity, but not the shift to higher energy. 4. CONCLUSIONS Clear manifestations of a Coulomb blockade are in STM measurements on semiconductors, metals perconductors. We find no appreciable effect of range electromagnetic environment when changing resistance from 50kR to 80MR. Decoupling from pacitances Part
may be due to tunneling
of this work was financed
Onderzoek
through
observed and suthe long the series stray ca-
impurity
by the Stichting
states.
voor Fundamenteel
der Materie (FOM).
References [I] D.V. Averin and K.K. Likharev,
J. Low Temp.
Phys.
62 (1980)
345. [2] P.J.M. van Bentum, H. van Kempen, [3] K.Mullen,
L.E.C. van de Leemput,
R.T.M.
Smokers and
Phys. Scripta T 25 (1989) 122.
E. Ben-Jacob,
R.C. Jacklevic
and Z. Schuss, Phys. Rev.
B 36 (1988) 98. [4] P. Delsing, K.K. Likharev,
L.S. Kuzmin and T. Claeson, Phys. Rev.
Lett. I33 (1989) 1180. [5] P.J.M. van Bentum, Rev. Lett.
R.T.M.
Smokers, and H. van Kempen,
Phys.
60 (1988) 2543.
[6] P.J.M. van Bentum, P.A.A. Teunissen, [7] Yu. V. Nazarov,
L.E.C. van de Leemput,
and
60 (1988) 369.
SW. Phys. JETP
[8] P.J.M. van Bentum, H. van Kempen,
H. van Kempen,
Phys. Rev. Lett.
68 (1989) 561.
H.F.C. Hoevers,
L.E.C. van de Leemput
J. Magn. Magn. Mat. 76-77
(1988) 561.
and