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Frequency-determined current with a turnstile device for single electrons
Physica B 165&166 (1990) 61-62 North-Holland
FREQUENCY-DETERMINED
V.F. ANDEREGG,
CURRENT WITH A TURNSTILE DEVICE FOR SINGLE ELECTRONS
L.J. GEERLIGS,
J.E. MOOIJ
Department of Applied Physics, Delft University of Technology, P.O. Box 5046,260O GA Delft, The Netherlands
H. POTHIER, D. ESTEVE, C. URBINA, M.H. DEVORET Service de Physique du Solide et de Resonance Magnetique, Centre d’Etudes Nucleaires de Saclay 91191 Gif-Sur-Yvette, France
We have fabricated a device in which the current is to a high accuracy determined by an external frequency f as I=ef. This device consists of an array of ultrasmall tunnel junctions. An rf voltage is applied to a gate and causes the transfer of a single electron per cycle through the array. The locking of the electron transfer is obtained by using Coulomb blockade of electron tunneling.
1.
INTRODUCTION In recent years the fabrication of submicron tunnel junctions has permitted the observation of a new class of phenomena, charging effects, which are due to the discreteness of electron tunneling. These phenomena occur when the capacitance C of the ‘unctions is small enough to yield a charging energy EC = eJ2/2C larger than the thermal energie kBT. A review is given by Averin and Likharev (1). We have used the charging effects in a device in which a single electron is transferred per cycle of an externally applied rf voltage. This results in a current equal to the frequency times the electron charge. The effect is qualitatively similar to the Shapiro steps observed in “classical” (large capacitance) Josephson junctions, and seems a candidate for a standard of dc current. Together with the quantum Hall effect (V/I=RR=h/e2) and the Josephson effect (V=hf/2e) , this device with I = ef provides a metrological triangle to check these relations for inconsistencies.
T.66
3.34
5
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3.64
3
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0.07
0W 0.23
-0.77
T.16
-0.10 -0.10 T
2. CRITICAL CHARGE FOR ELECTRON TUNNELING In a voltage biased linear array of ultrasmall tunnel junctions the current-voltage characteristic exhibits zero conduction below a certain voltage, at zero temperature. This so-called Coulomb gau arises because of the discreteness of charge transfe; &I tunnel junctions. It can be conveniently described by introducing a critical charge Qc. In a junction with charge Q, no tunneling can occur for IQI
0921-4526/90/$03.50
FIGURE 1 Principle of controlled single electron transfer through a linear array of small tunnel junctions. Junctions, with capacitance C, are denoted by crossed capacitor symbols, the gate voltage V is applied via a true (non-tunneling) capacitance Cg. If $= C/2, tunneling across any junction can only occur if for at junction IQI>Qc, with Qc=e/3. The voltages and charges are indicated in units of e/C and e. l-6 indicate consecutive times in the cycle. Left: First half of the cycle, Vg=2. An elementary charge (- in a circle) ends up trapped on the central electrode. Right: Second half of the cycle, V =O. The charge can only leave on the right hand side. Ngo further tunneling can occur in the emptied array .
@ 1990 - Elsevier Science Publishers B.V. (North-Holland)
V.F. Anderegg, L.J. Geerligs, J.E. Mooij, H. Pothier, D. Esteve, C. Urbina, M.H. Devoret
62
3.
TURNSTILE
DEVICE
Our device is an array of 4 tunnel junctions of capacitance C. The gate voltage is capacitively coupled to the central island between junctions 2 and 3. If the gate capacitor C is chosen equal to C/2 all critical charges have the same va gue: Qc = e/3. The principle of our experiment is illustrated in Fig. 1. The first half of the rf cycle a bias voltage V and gate voltage Vg are applied such that the critical charge is only exceeded m the left arm of the array. An elementary charge will then tunnel across junctions 1 and 2. Once on the central island part of it will polarize the gate capacitor and the charges on the junctions will all be lower than Qc. The charge is therefore trapped on the middle island until the bias conditions are changed. We emphasize that no other tunneling event can occur after the electron has been trapped. In the next half of the cycle the gate voltage is decreased, resulting in an increase of the charges on the junctions. Because of the asymmetry caused by the bias voltage the elementary charge will tunnel through junctions 3 and 4. Cyclically changing the bias conditions by applying an alternating voltage to the gate moves one electron per cycle through the array. Electron tunneling is a stochastic process: if the tunneling is energetically favorable it will happen within a typical time RC where R is the tunneling resistance of the junction.This poses a restriction on the range of frequencies we can use. To avoid losing cycles f must be much smaller than (RC)-1. At finite temoeratures there is a urobabilitv of thermal activation outbf the middle island: This gives a second restriction to the range of frequencies: a thermally assisted transfer will be more probable for lower frequencies. These restrictions are treated quantitatively elsewhere (3). Here we only quote the result that with the smallest present-day junctions (C - lo-16 F ), for T I 75 mK and f 5 30 MHz the error in the relation I = ef is expected to be less than lo-*. 4.
MEASUREMENTS
We have fabricated a device with a lavout verv similar to Fig. 1. For this device C = 0.5 fF, R 2 340 k6hm and Cg = 0.3 fF. Cg is determined from the period of the current modulatton by a gate voltage (2). In Fig. 2 we show three I-V curves of our device. The dotted curve shows the measurement without ac gate voltage applied. The solid curves show that when a voltage of frequency 5 and 10 MHz is applied to the gate, a wide current plateau develops in the Coulomb gap at a value of I=ef. In this figure the amulitudes of the ac voltages were adjusted to ob‘iain the widest plateaus. The height of the olateau is indenendent of the amulitude. The inset of Fie. 2 ;hows that the ggreement with the relation I = ef is excel&t up to frequencies of 20 MHz. The markers give the measured current plateau versus frequency and the solid line is I = ef with e the value of the elementary charge. The measured current coincides with ef within experimental accuracy, which is around 0.3 %. We simulated the dependence of the I-V curves on ac amplitude and found very good agreement with our measurements (3).
J
‘I
0
-0.2 V
0.2
[mvl
FIGURE 2 Current-voltage characteristics without ac voltage (dotted) and with applied ac gate voltage at frequencies f equal to 5 and 10 MHz. Current plateaus are seen at I = ef. The inset shows measured current versus frequency (markers) and the line I = ef with e the elementary charge.
5.
CONCLUSIONS We have fabricated a device in which the transfer of single electrons is controlled by an externally applied ac voltage. Accuracy considerations predict that it is a promising device for a new standard of dc current. ACKNOWLEDGEMENTS This work was supported by the Dutch Foundation Fundamental Research on Matter (FOM) and Commissariat a 1’Energie Atomique (CEA). We thank Center for Submicron Technolozv (CST) in Delft for use of their nanolithographic fac&ies and P.F. Qrfila technical assistance.
for the the the for
REFERENCES (1) D.V. Averin and K.K. Likharev, Single electronics, in: Quantum Effects in Small Disordered Systems, eds B.L. Al’tshuler, P.A. Lee, and R.A. Webb (Elsevier, Amsterdam) to be published. (2) L.J. Geerligs et al., Tunneling time and offset charging in small tunnel junctions, this volume. (3) L.J. Geerligs et al., Frequency-locked turnstile device for single electrons, submitted to Phys. Rev. Lett.
FREQUENCY-DETERMINED
V.F. ANDEREGG,
CURRENT WITH A TURNSTILE DEVICE FOR SINGLE ELECTRONS
L.J. GEERLIGS,
J.E. MOOIJ
Department of Applied Physics, Delft University of Technology, P.O. Box 5046,260O GA Delft, The Netherlands
H. POTHIER, D. ESTEVE, C. URBINA, M.H. DEVORET Service de Physique du Solide et de Resonance Magnetique, Centre d’Etudes Nucleaires de Saclay 91191 Gif-Sur-Yvette, France
We have fabricated a device in which the current is to a high accuracy determined by an external frequency f as I=ef. This device consists of an array of ultrasmall tunnel junctions. An rf voltage is applied to a gate and causes the transfer of a single electron per cycle through the array. The locking of the electron transfer is obtained by using Coulomb blockade of electron tunneling.
1.
INTRODUCTION In recent years the fabrication of submicron tunnel junctions has permitted the observation of a new class of phenomena, charging effects, which are due to the discreteness of electron tunneling. These phenomena occur when the capacitance C of the ‘unctions is small enough to yield a charging energy EC = eJ2/2C larger than the thermal energie kBT. A review is given by Averin and Likharev (1). We have used the charging effects in a device in which a single electron is transferred per cycle of an externally applied rf voltage. This results in a current equal to the frequency times the electron charge. The effect is qualitatively similar to the Shapiro steps observed in “classical” (large capacitance) Josephson junctions, and seems a candidate for a standard of dc current. Together with the quantum Hall effect (V/I=RR=h/e2) and the Josephson effect (V=hf/2e) , this device with I = ef provides a metrological triangle to check these relations for inconsistencies.
T.66
3.34
5
xxx:: 0.07
3.64
3
xX0xX -0.10 -0.10
0.07
0W 0.23
-0.77
T.16
-0.10 -0.10 T
2. CRITICAL CHARGE FOR ELECTRON TUNNELING In a voltage biased linear array of ultrasmall tunnel junctions the current-voltage characteristic exhibits zero conduction below a certain voltage, at zero temperature. This so-called Coulomb gau arises because of the discreteness of charge transfe; &I tunnel junctions. It can be conveniently described by introducing a critical charge Qc. In a junction with charge Q, no tunneling can occur for IQI
0921-4526/90/$03.50
FIGURE 1 Principle of controlled single electron transfer through a linear array of small tunnel junctions. Junctions, with capacitance C, are denoted by crossed capacitor symbols, the gate voltage V is applied via a true (non-tunneling) capacitance Cg. If $= C/2, tunneling across any junction can only occur if for at junction IQI>Qc, with Qc=e/3. The voltages and charges are indicated in units of e/C and e. l-6 indicate consecutive times in the cycle. Left: First half of the cycle, Vg=2. An elementary charge (- in a circle) ends up trapped on the central electrode. Right: Second half of the cycle, V =O. The charge can only leave on the right hand side. Ngo further tunneling can occur in the emptied array .
@ 1990 - Elsevier Science Publishers B.V. (North-Holland)
V.F. Anderegg, L.J. Geerligs, J.E. Mooij, H. Pothier, D. Esteve, C. Urbina, M.H. Devoret
62
3.
TURNSTILE
DEVICE
Our device is an array of 4 tunnel junctions of capacitance C. The gate voltage is capacitively coupled to the central island between junctions 2 and 3. If the gate capacitor C is chosen equal to C/2 all critical charges have the same va gue: Qc = e/3. The principle of our experiment is illustrated in Fig. 1. The first half of the rf cycle a bias voltage V and gate voltage Vg are applied such that the critical charge is only exceeded m the left arm of the array. An elementary charge will then tunnel across junctions 1 and 2. Once on the central island part of it will polarize the gate capacitor and the charges on the junctions will all be lower than Qc. The charge is therefore trapped on the middle island until the bias conditions are changed. We emphasize that no other tunneling event can occur after the electron has been trapped. In the next half of the cycle the gate voltage is decreased, resulting in an increase of the charges on the junctions. Because of the asymmetry caused by the bias voltage the elementary charge will tunnel through junctions 3 and 4. Cyclically changing the bias conditions by applying an alternating voltage to the gate moves one electron per cycle through the array. Electron tunneling is a stochastic process: if the tunneling is energetically favorable it will happen within a typical time RC where R is the tunneling resistance of the junction.This poses a restriction on the range of frequencies we can use. To avoid losing cycles f must be much smaller than (RC)-1. At finite temoeratures there is a urobabilitv of thermal activation outbf the middle island: This gives a second restriction to the range of frequencies: a thermally assisted transfer will be more probable for lower frequencies. These restrictions are treated quantitatively elsewhere (3). Here we only quote the result that with the smallest present-day junctions (C - lo-16 F ), for T I 75 mK and f 5 30 MHz the error in the relation I = ef is expected to be less than lo-*. 4.
MEASUREMENTS
We have fabricated a device with a lavout verv similar to Fig. 1. For this device C = 0.5 fF, R 2 340 k6hm and Cg = 0.3 fF. Cg is determined from the period of the current modulatton by a gate voltage (2). In Fig. 2 we show three I-V curves of our device. The dotted curve shows the measurement without ac gate voltage applied. The solid curves show that when a voltage of frequency 5 and 10 MHz is applied to the gate, a wide current plateau develops in the Coulomb gap at a value of I=ef. In this figure the amulitudes of the ac voltages were adjusted to ob‘iain the widest plateaus. The height of the olateau is indenendent of the amulitude. The inset of Fie. 2 ;hows that the ggreement with the relation I = ef is excel&t up to frequencies of 20 MHz. The markers give the measured current plateau versus frequency and the solid line is I = ef with e the value of the elementary charge. The measured current coincides with ef within experimental accuracy, which is around 0.3 %. We simulated the dependence of the I-V curves on ac amplitude and found very good agreement with our measurements (3).
J
‘I
0
-0.2 V
0.2
[mvl
FIGURE 2 Current-voltage characteristics without ac voltage (dotted) and with applied ac gate voltage at frequencies f equal to 5 and 10 MHz. Current plateaus are seen at I = ef. The inset shows measured current versus frequency (markers) and the line I = ef with e the elementary charge.
5.
CONCLUSIONS We have fabricated a device in which the transfer of single electrons is controlled by an externally applied ac voltage. Accuracy considerations predict that it is a promising device for a new standard of dc current. ACKNOWLEDGEMENTS This work was supported by the Dutch Foundation Fundamental Research on Matter (FOM) and Commissariat a 1’Energie Atomique (CEA). We thank Center for Submicron Technolozv (CST) in Delft for use of their nanolithographic fac&ies and P.F. Qrfila technical assistance.
for the the the for
REFERENCES (1) D.V. Averin and K.K. Likharev, Single electronics, in: Quantum Effects in Small Disordered Systems, eds B.L. Al’tshuler, P.A. Lee, and R.A. Webb (Elsevier, Amsterdam) to be published. (2) L.J. Geerligs et al., Tunneling time and offset charging in small tunnel junctions, this volume. (3) L.J. Geerligs et al., Frequency-locked turnstile device for single electrons, submitted to Phys. Rev. Lett.