- Email: [email protected]
Conduction of electrons on liquid helium along channels produced by multi-layer microfabrication
Physica B 249—251 (1998) 656—659
Conduction of electrons on liquid helium along channels produced by multi-layer microfabrication R.J.F. van Haren!, G. Acres", P. Fozooni!, A. Kristensen!, M.J. Lea!,*, P.J. Richardson!, A.M.C. Valkering#, R.W. van der Heijden# ! Department of Physics, Royal Holloway, University of London, Egham, TW20 0EX, UK " Department of Computer Science and Electronics, University of Southampton, SO17 1BJ, UK # Department of Physics, Eindhoven University of Technology, P.O.Box 513, 5600 MB, Eindhoven, Netherlands
Abstract We demonstrate the conduction of free electrons along an array of microchannels of liquid helium, 30 lm wide, 1 lm deep and 1.5 mm long, held by surface tension between conducting ribs. No perpendicular conduction occurs until the bulk helium level rises above the channels. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Liquid helium; Microchannels of liquid helium; One-dimensional transport
1. Introduction A major technical challenge in research into surface state electrons on liquid helium is to produce structured substrates so that the in-plane potential seen by the two-dimensional (2D) electrons can be modulated to produce 1D (or quasi-1D) channels, pinning centres, ballistic point contacts and other devices. Fractionating the surface also increases the maximum achievable electron density, compared to bulk helium, by suppressing an electrohydrodynamic instability. We demonstrate the conduction of electrons on the surface of parallel microchannels of superfluid helium, 30 lm wide ("w), 1 lm deep ("d) and * Corresponding author. Fax: #44 1784 472794; e-mail: [email protected].
1.5 mm long, using a multi-layer ribbed structure with three metal layers, which can be patterned to form gates and other control electrodes. This technique was first used by Marty [1] in a meander line electrode structure, though the conductivity was not measured. More recent experiments have used ruled optical diffraction gratings on glass [2,3] with 1.25 and 1.7 lm wide grooves, a bent dielectric foil [4] and helium films suspended between metal electrodes 300 lm apart on epoxy board [5]. 2. The structures The physical principles have been given by Marty [1]. The bulk helium surface is a distance h above (h'0) or below (h(0) the channels. For h(0 the charged helium channels have a radius of
0921-4526/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 2 8 2 - 8
R.J.F. van Haren et al. / Physica B 249–251 (1998) 656—659
657
curvature R"a/(ogDhD#n2e2/2ee ), allowing for 0 the electronic pressure, where o is the helium density. The minimum helium depth d (n) in the 0 channels is then
G
w2 n2e2 d (n)"d! ogDhD# 0 8a 2ee 0
H
(1)
for a uniform saturated electron density n. The maximum density before the helium touches the bottom of the channels (d (n )"0) is n " 0 .!9 .!9 5]1013 m~2 (for h"0). This density may also be limited by a hydrodynamic instability [1] at a critical density n "(apee /we2)1@2"1.2]1014 m~2 for c 0 w"30 lm. Calculated profiles of the helium surface are shown in Fig. 1. The devices, Fig. 2a, were made using microfabrication techniques. Two Au layers and one Al layer were deposited on a quartz substrate, separated by two insulating SiO layers. The thick (1 lm) 2 upper Al layer and the upper SiO layer were 2 reactive-ion etched to produce 1 lm deep channels between conducting ribs, with an Au base patterned by ion-beam milling. Five gold electrodes, Fig. 2b, were arranged in a Maltese cross pattern, a central electrode C (l "820 lm wide) and two C pairs of transmission and receiving electrodes (A and B on the x-axis, D and E on the y-axis; 340]500 lm). The channels run parallel to the x-axis over these electrodes to form a Sommer— Tanner [6] electrode geometry for each channel (total length ¸"1.5 mm). Ten parallel channels connect electrodes A and B. A guard electrode surrounds the measurement electrodes. Gold wires were bonded to contact pads round the perimeter of the devices.
Fig. 1. Helium surface profiles for n"0 (a), 2.5 (b) and 4.7 (c) ]1013 m~2 for h"-0.2 mm.
Fig. 2. (a) device structure; (b) the electrode geometry.
The structures were mounted in a experimental cell filled with helium whose height was monitored with a cylindrical capacitor. The channels were charged using thermionic emission from a small tungsten filament. The ribs and guard were at a negative DC potential (+!2 V) with respect to the electrodes, to confine the electrons in the channels.
3. Results and discussion Capacitively coupled electron currents were measured, parallel (electrodes A to B) and perpendicular (electrodes D to E) to the microchannels. An AC voltage » (10 or 100 mV, rms) at 10 kHz 0 was applied to electrodes A and D and the AC currents to B and E measured. Fig. 3a shows the parallel current DI D at 10 kHz , along the 10 channels as the height h is varied at ¹"1.9 K. As h rises, the channels fill with helium and conduction starts. Fig. 3b shows the perpendicular current DI D, (10~3 DI D (in the noise), an M , anisotropy better than for grooves on an insulating
658
R.J.F. van Haren et al. / Physica B 249–251 (1998) 656—659
Fig. 3. (a) The parallel current; (b) The perpendicular current.
Fig. 4. (a) The parallel current versus » ; (b) DI*D versus » . C C
substrate [3]. For h'0, as the helium surface rises above the channels, the capacitive current DI D falls , rapidly. A small perpendicular current is then observed between D and E. As h rises further, this current also falls as the capacitance to the electrons decreases. The magnitude of the measured currents is consistent with the channel geometry. At 10 kHz, for » "100 mV with d"1 lm, the capacitive current 0 should be about 100 pA/channel, compared to total measured values, for 10 channels, of up to 1200 pA. We conclude that the channels are indeed charged and that the conduction is highly anisotropic. The change in the parallel current I with the , helium height h, Fig. 3a, is interesting. For h(!0.8 mm, charging did not produce a current. For h'!0.8 mm (point X), a current flowed and the electrons remained as h changed, with no further charging. The current increased up to Y, presumably as the effective area increased. Above Y, the capacitive current decreased as the helium level
increased. At Z, the bulk helium level reached the channels. To estimate the electron density, we made the DC potential » on the central electrode C negaC tive, while measuring I , Fig. 4a. This transfers , electrons from above electrode C to above electrodes A and B,. increasing the electronic pressure on the helium over these electrodes, lowering the helium depth d , and increasing I . The change in A , the capacitive current DI*D, normalised to the value for » "0 where the depth is d (n), is, from Eq. (1) C 0 with e"DeD, dI* w2e 2l Cn, "! d» 8ad (n)2 ¸ c 0
(2)
assuming a uniform depth d (n), saturated electrons 0 and no change in the area of the electron sheet. Fig. 4b, shows plots of Eq. (2) for densities n"1 (a), 2 (b), 2.5 (c) and 3 (d)]1013 m~2. The best fit to the data gives the estimate n"2.5]1013 m~2,
R.J.F. van Haren et al. / Physica B 249–251 (1998) 656—659
659
4. Conclusions
Fig. 5. Channel switching.
compared to the value 4.1$0.6]1013 m~2 obtained by Marty [1] in channels of width 35 lm and depth 5 lm. One problem with this analysis is that the phase shift (typically 0.4 rad) of the AC current is relatively large. For n'2]1013 m~2 this would give a mobility l(0.1 m2/V s, much less than the theoretical value [7] of 0.9 m2/V s and comparable with the mobilities on very thin helium films [8]. Further experiments are in progress to resolve this. The current increases with D» D up to point Y, C corresponding to Y in Fig. 3a. The DC potential » of the electrons at saturation is %
A
B
ne ne w2n2e2 » "! (d!Dz)"! d (0)! . (3) e ee 16aee ee 0 0 0 0 As electrons are transferred from above electrode C, this becomes unstable when -ed» /dn)0 at % a helium depth of 2d (0)/3. The critical density for 0 this instability is n /J3+2.7]1013 m~2. .!9 Three types of behaviour are observed experimentally. For high starting densities, the current can suddenly vanish as D» D increases and the elecC trons are lost. Individual channel switching was also observed, as shown in Fig. 5. The total current suddenly decreased by an amount corresponding to a single channel. The electrons are not always completely lost as channels sometimes switched on again, even as D» D was increased, showing bistabilC ity. For lower densities, as in Fig. 4b, the current is reversible with » . C
We have demonstrated the conduction of electrons on an array of microchannels of liquid helium, held by surface tension. The anisotropy ratio is extremely high, with no perpendicular conduction until the bulk helium level rises above the channels. The electron density n'2.5]1013 m~2, approaching the theoretical limit of 5]1013 m~2. The advantages of these metallic multi-layers devices are (a) direct control and modulation of the in-plane potentials can be achieved (by ion-beam milling through the second Au layer), (b) higher electron densities can be reached than on bulk helium, (c) metallic substrates avoid space charge effects, (d) the electrodes give close capacitive coupling to the electrons, (e) overlapping electrodes can be fabricated and (f ) lower DC potentials are needed for a given electron density than with a thick insulating substrate. Acknowledgements We thank Yu.Z. Kovdrya, P.J.M. Peters and P.K.H. Sommerfeld for useful discussions; the EPSRC (UK) for Research Grants; the EU for support under contract number CHRXCT 930374; A.K. Betts, F. Greenough, P.A.M. Nouwens, J. Taylor and A. Wilkinson for technical assistance; A. Blackburn, G. Ensell, D. Murphy, A. Jury and other staff of the Southampton University Microelectronics Centre and the lithography unit of the Rutherford Appleton Laboratory, UK. References [1] D. Marty, J. Phys. C. 19 (1986) 6097. [2] Yu.Z. Kovdrya, V.A. Nikolaenko, Sov. J. Low. Temp. Phys. 18 (1992) 894. [3] H. Yayama, A. Tomokiyo, Czech. J. Phys. 46 - S1 (1996) 353. [4] O.I. Kirichek, Yu.P. Monarkha, Yu.Z. Kovdrya, V.N. Grigorev, Low. Temp. Phys. 19 (1993) 323. [5] A.M.C. Valkering, P.K.H. Sommerfeld, P.J. Richardson, R.W. van der Heijden, A.T.A.M. de Waele, Czech. J. Phys. 46 - S1 (1996) 321. [6] W.T. Sommer, D.J. Tanner, Phys. Rev. Lett. 27 (1971) 1345. [7] M. Saitoh, J. Phys. Soc. Japan 42 (1977) 201. [8] O. Tress, Yu.P. Monarkha, F.C. Penning, H. Bluyssen, P. Wyder, Phys. Rev. Lett. 77 (1996) 2511.
Conduction of electrons on liquid helium along channels produced by multi-layer microfabrication R.J.F. van Haren!, G. Acres", P. Fozooni!, A. Kristensen!, M.J. Lea!,*, P.J. Richardson!, A.M.C. Valkering#, R.W. van der Heijden# ! Department of Physics, Royal Holloway, University of London, Egham, TW20 0EX, UK " Department of Computer Science and Electronics, University of Southampton, SO17 1BJ, UK # Department of Physics, Eindhoven University of Technology, P.O.Box 513, 5600 MB, Eindhoven, Netherlands
Abstract We demonstrate the conduction of free electrons along an array of microchannels of liquid helium, 30 lm wide, 1 lm deep and 1.5 mm long, held by surface tension between conducting ribs. No perpendicular conduction occurs until the bulk helium level rises above the channels. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Liquid helium; Microchannels of liquid helium; One-dimensional transport
1. Introduction A major technical challenge in research into surface state electrons on liquid helium is to produce structured substrates so that the in-plane potential seen by the two-dimensional (2D) electrons can be modulated to produce 1D (or quasi-1D) channels, pinning centres, ballistic point contacts and other devices. Fractionating the surface also increases the maximum achievable electron density, compared to bulk helium, by suppressing an electrohydrodynamic instability. We demonstrate the conduction of electrons on the surface of parallel microchannels of superfluid helium, 30 lm wide ("w), 1 lm deep ("d) and * Corresponding author. Fax: #44 1784 472794; e-mail: [email protected].
1.5 mm long, using a multi-layer ribbed structure with three metal layers, which can be patterned to form gates and other control electrodes. This technique was first used by Marty [1] in a meander line electrode structure, though the conductivity was not measured. More recent experiments have used ruled optical diffraction gratings on glass [2,3] with 1.25 and 1.7 lm wide grooves, a bent dielectric foil [4] and helium films suspended between metal electrodes 300 lm apart on epoxy board [5]. 2. The structures The physical principles have been given by Marty [1]. The bulk helium surface is a distance h above (h'0) or below (h(0) the channels. For h(0 the charged helium channels have a radius of
0921-4526/98/$19.00 ( 1998 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 2 8 2 - 8
R.J.F. van Haren et al. / Physica B 249–251 (1998) 656—659
657
curvature R"a/(ogDhD#n2e2/2ee ), allowing for 0 the electronic pressure, where o is the helium density. The minimum helium depth d (n) in the 0 channels is then
G
w2 n2e2 d (n)"d! ogDhD# 0 8a 2ee 0
H
(1)
for a uniform saturated electron density n. The maximum density before the helium touches the bottom of the channels (d (n )"0) is n " 0 .!9 .!9 5]1013 m~2 (for h"0). This density may also be limited by a hydrodynamic instability [1] at a critical density n "(apee /we2)1@2"1.2]1014 m~2 for c 0 w"30 lm. Calculated profiles of the helium surface are shown in Fig. 1. The devices, Fig. 2a, were made using microfabrication techniques. Two Au layers and one Al layer were deposited on a quartz substrate, separated by two insulating SiO layers. The thick (1 lm) 2 upper Al layer and the upper SiO layer were 2 reactive-ion etched to produce 1 lm deep channels between conducting ribs, with an Au base patterned by ion-beam milling. Five gold electrodes, Fig. 2b, were arranged in a Maltese cross pattern, a central electrode C (l "820 lm wide) and two C pairs of transmission and receiving electrodes (A and B on the x-axis, D and E on the y-axis; 340]500 lm). The channels run parallel to the x-axis over these electrodes to form a Sommer— Tanner [6] electrode geometry for each channel (total length ¸"1.5 mm). Ten parallel channels connect electrodes A and B. A guard electrode surrounds the measurement electrodes. Gold wires were bonded to contact pads round the perimeter of the devices.
Fig. 1. Helium surface profiles for n"0 (a), 2.5 (b) and 4.7 (c) ]1013 m~2 for h"-0.2 mm.
Fig. 2. (a) device structure; (b) the electrode geometry.
The structures were mounted in a experimental cell filled with helium whose height was monitored with a cylindrical capacitor. The channels were charged using thermionic emission from a small tungsten filament. The ribs and guard were at a negative DC potential (+!2 V) with respect to the electrodes, to confine the electrons in the channels.
3. Results and discussion Capacitively coupled electron currents were measured, parallel (electrodes A to B) and perpendicular (electrodes D to E) to the microchannels. An AC voltage » (10 or 100 mV, rms) at 10 kHz 0 was applied to electrodes A and D and the AC currents to B and E measured. Fig. 3a shows the parallel current DI D at 10 kHz , along the 10 channels as the height h is varied at ¹"1.9 K. As h rises, the channels fill with helium and conduction starts. Fig. 3b shows the perpendicular current DI D, (10~3 DI D (in the noise), an M , anisotropy better than for grooves on an insulating
658
R.J.F. van Haren et al. / Physica B 249–251 (1998) 656—659
Fig. 3. (a) The parallel current; (b) The perpendicular current.
Fig. 4. (a) The parallel current versus » ; (b) DI*D versus » . C C
substrate [3]. For h'0, as the helium surface rises above the channels, the capacitive current DI D falls , rapidly. A small perpendicular current is then observed between D and E. As h rises further, this current also falls as the capacitance to the electrons decreases. The magnitude of the measured currents is consistent with the channel geometry. At 10 kHz, for » "100 mV with d"1 lm, the capacitive current 0 should be about 100 pA/channel, compared to total measured values, for 10 channels, of up to 1200 pA. We conclude that the channels are indeed charged and that the conduction is highly anisotropic. The change in the parallel current I with the , helium height h, Fig. 3a, is interesting. For h(!0.8 mm, charging did not produce a current. For h'!0.8 mm (point X), a current flowed and the electrons remained as h changed, with no further charging. The current increased up to Y, presumably as the effective area increased. Above Y, the capacitive current decreased as the helium level
increased. At Z, the bulk helium level reached the channels. To estimate the electron density, we made the DC potential » on the central electrode C negaC tive, while measuring I , Fig. 4a. This transfers , electrons from above electrode C to above electrodes A and B,. increasing the electronic pressure on the helium over these electrodes, lowering the helium depth d , and increasing I . The change in A , the capacitive current DI*D, normalised to the value for » "0 where the depth is d (n), is, from Eq. (1) C 0 with e"DeD, dI* w2e 2l Cn, "! d» 8ad (n)2 ¸ c 0
(2)
assuming a uniform depth d (n), saturated electrons 0 and no change in the area of the electron sheet. Fig. 4b, shows plots of Eq. (2) for densities n"1 (a), 2 (b), 2.5 (c) and 3 (d)]1013 m~2. The best fit to the data gives the estimate n"2.5]1013 m~2,
R.J.F. van Haren et al. / Physica B 249–251 (1998) 656—659
659
4. Conclusions
Fig. 5. Channel switching.
compared to the value 4.1$0.6]1013 m~2 obtained by Marty [1] in channels of width 35 lm and depth 5 lm. One problem with this analysis is that the phase shift (typically 0.4 rad) of the AC current is relatively large. For n'2]1013 m~2 this would give a mobility l(0.1 m2/V s, much less than the theoretical value [7] of 0.9 m2/V s and comparable with the mobilities on very thin helium films [8]. Further experiments are in progress to resolve this. The current increases with D» D up to point Y, C corresponding to Y in Fig. 3a. The DC potential » of the electrons at saturation is %
A
B
ne ne w2n2e2 » "! (d!Dz)"! d (0)! . (3) e ee 16aee ee 0 0 0 0 As electrons are transferred from above electrode C, this becomes unstable when -ed» /dn)0 at % a helium depth of 2d (0)/3. The critical density for 0 this instability is n /J3+2.7]1013 m~2. .!9 Three types of behaviour are observed experimentally. For high starting densities, the current can suddenly vanish as D» D increases and the elecC trons are lost. Individual channel switching was also observed, as shown in Fig. 5. The total current suddenly decreased by an amount corresponding to a single channel. The electrons are not always completely lost as channels sometimes switched on again, even as D» D was increased, showing bistabilC ity. For lower densities, as in Fig. 4b, the current is reversible with » . C
We have demonstrated the conduction of electrons on an array of microchannels of liquid helium, held by surface tension. The anisotropy ratio is extremely high, with no perpendicular conduction until the bulk helium level rises above the channels. The electron density n'2.5]1013 m~2, approaching the theoretical limit of 5]1013 m~2. The advantages of these metallic multi-layers devices are (a) direct control and modulation of the in-plane potentials can be achieved (by ion-beam milling through the second Au layer), (b) higher electron densities can be reached than on bulk helium, (c) metallic substrates avoid space charge effects, (d) the electrodes give close capacitive coupling to the electrons, (e) overlapping electrodes can be fabricated and (f ) lower DC potentials are needed for a given electron density than with a thick insulating substrate. Acknowledgements We thank Yu.Z. Kovdrya, P.J.M. Peters and P.K.H. Sommerfeld for useful discussions; the EPSRC (UK) for Research Grants; the EU for support under contract number CHRXCT 930374; A.K. Betts, F. Greenough, P.A.M. Nouwens, J. Taylor and A. Wilkinson for technical assistance; A. Blackburn, G. Ensell, D. Murphy, A. Jury and other staff of the Southampton University Microelectronics Centre and the lithography unit of the Rutherford Appleton Laboratory, UK. References [1] D. Marty, J. Phys. C. 19 (1986) 6097. [2] Yu.Z. Kovdrya, V.A. Nikolaenko, Sov. J. Low. Temp. Phys. 18 (1992) 894. [3] H. Yayama, A. Tomokiyo, Czech. J. Phys. 46 - S1 (1996) 353. [4] O.I. Kirichek, Yu.P. Monarkha, Yu.Z. Kovdrya, V.N. Grigorev, Low. Temp. Phys. 19 (1993) 323. [5] A.M.C. Valkering, P.K.H. Sommerfeld, P.J. Richardson, R.W. van der Heijden, A.T.A.M. de Waele, Czech. J. Phys. 46 - S1 (1996) 321. [6] W.T. Sommer, D.J. Tanner, Phys. Rev. Lett. 27 (1971) 1345. [7] M. Saitoh, J. Phys. Soc. Japan 42 (1977) 201. [8] O. Tress, Yu.P. Monarkha, F.C. Penning, H. Bluyssen, P. Wyder, Phys. Rev. Lett. 77 (1996) 2511.