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Fabrication and transport properties of anti-dot triangle lattices
Microelectronic Elsevier
Engineering
17 (1992) 509-512
509
Fabrication and transport properties of anti-dot triangle lattices J. Takahara”, Y. Takagaki”‘, K. Gamoab, S. Namba”b”, S. Takaoka” and K. Murase’ “Department of Electrical Engineering, Toyonaka, Osaka 560, Japan
Faculty of Engineering
Science,
Osaka University,
bResearch Center for Extreme Materials, Osaka University, Toyonaka, Osaka 560, Japan Department
of Physics, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan
Present Adress: *Center for Solid State Electronics Research, Arizona State University, Tempe, Arizona 85287-6206. **Nagasaki Institute of Applied Science, 536 Amibacho, Nagasaki-shi, Nagasaki 851-01. We have fabricated triangle anti-dot structure in GaAs-AlGaAs heterojunction by employing electron beam lithography and dry etching, and we measured magnetoresistance and its temperature dependence. Novel magnetoresistance oscillations were observed at the low magnetic field. These oscillations which has weak-temperature dependence were attributed to commensurate classical orbits on lattices of anti-dots. 1. INTRODUCIION The interplay of the two characteristic length, periodicity of modulation potential and cyclotron radius, produce interesting phenomena. Theoretically, Hofstadter demonstrated that the quantum states may exhibit a self-similar band structure [l]. In recent experiments on 2DEG subjected to the weak 1D [2] and 2D [3,4] lateral superlattice potential novel low-field magnetoresistance oscillations were observed. In weak potential, electrons &verse modulated region. On the other hand, in strong potential electrons feel the hard wall potential and traverse in non-modulated region, and such a strong potential is called “Anti-dot” [5-71. In this paper, we present fabrication process of anti-dot structures and discuss their effect on low-field magnetoresistance. Anti-dot was arranged in the shape of periodic triangle lattice. Low-field oscillations were attributed to commensurate classical orbits on lattices of anti-dots. 2. FABRICATION AND EXPERIMENT Fig. 1 shows the sample fabrication procedures. The samples were prepared on conventional GaAs-AlGaAs heterojunction grown by MBE. The heterojunction has a structure as shown in Fig. 2(a). The carrier concentration n, and mobility p of the startin! material measured at 1.4K in dark by the standard van der Pauw procedure were n,=3.2x10r5m- and p=130m2V-‘s-l, respectively, leading to an elastic mean free path 1,=12pm. Anti-dot structures were introduced by electron beam lithography and dry etching. 1OOpm wide four-terminal shaped samples are -defined by wet-etching using H,PO,:&O,:&O=l:1:30 solution. Au/Ge layers were evaporated and alloyed at 370 “C to form source-drain and potential probe contacts. Next, the EB resist PMMA was spun on at 8000 rpm for 40 set and baked at 170 “C for 2 hours. Dot patterns were delineated by
0167-9317/92/$05.00
0 1992 - Elsevier Science Publishers
B.V.
All rights reserved.
J. Takahara et al. I Anti-dot triangle lattices
510
SOkeV EB in PMMA on mesa-etched substrate. The exposure was performed employing a nanometer EB lithography systam which uses a zirconated tungsten thermal field emitter. A minimum calculated beam spot size at a working distance of 8mm is 2.4nm at SOkeV. A schematic view of the sample is shown in Fig. 2 (b). The dot interval a is l.Opm and 0.8pm, and dot radius is about O.lpm. The exposed resist was developed by conventional wet process (in a mixture of isopropyl alcohol (IPA) : methyl-isobutyl ketone (MIBK) = 1:2.5 for a few seconds). Finally, the samples beneath the dot pattern were shallow etched using 1keV Art ion milling for 3 minutes to a depth of about 3Omn. The etched region is strongly depleted due to a great deal of beam-induced damage, leading to become scatterers. Measurement was done from 1.4K to 50K after illumination using an ac bridge operating at 3OHz. (a)
RESIST
n’-Gab
20nm
COATING
lb)
vvv m
L! EB EXPOSURE
RESIST
Figure 2. (a) Structure of the heterojunction. (b) Schematic view of the sample.
LIFT OFF
Figure 1. Fabrication process.
3. RESULTS
AND DISCUSSION
Figure 3 shows magnetoresistance traces for the periodic triangle lattice. At higher fields (B>O.3T), Shubnikov-de Haas(SdH) oscillations were observed. The carrier concentration de&mined from SdH oscillations was 4.1x10’5m-2 in both samples. The carrier concentration was increased compared to the starting materials due to the persistent photoconduction effect. At lower fields (B<0.5T for a=O.8pm and B<0.3T for a=l.Opm) magnetoresistance quickly increased and novel oscillations were observed although magnetoresistance of usual unpatterned sample shows roughly constant at lower field. Figure 4 shows the magnetoresistance at various temperatures from 5.3 to 50K. Although SdH oscillations were quenched at 4.2K (See Fig. 3 (c)), low field oscillations were clearly observed above 1OK. Especially, the largest peaks around 0.2T still remained at 50K. SdH oscillation is attributed to Landau quantization, thus the condition that is satisfied to observe SdH oscillation is kaT
(1)
J. Takuhara et al. I Anti-dot triangle lattices
511
Here zi, and z, are the intrinsic and extrinsic relaxation time, respectively. From the zero-field resistance subtracted with the series resistance of the unpatterned region, we obtained the mobility of 17 and 20m2V%-’ in patterned region for a=0.8 (a) and lpm (b), respectively. The mobilities were suppressed due to the imposed anti-dots. Thus we obtained ?=6.$ (a) and 7.6~s (b), respectively. Around B=0.4T in Fig. 3, ma etoresistance decreased. This unphes that the mfluence of unposed scatterers was suppressed. u$”e obtained 2,=33 (a) and 47~s (b), and corresponding mobility of 87 (a) and 122m2V- s- ’ (b), respectively. This indicates that unpatterned region of the case (a) mainained initial condition. From extrinsic relaxation time -ceX obtaine by eq. (l), the mean free path l,=V,z, was estimated to be 2.2 (a) and 2.5pm (b), respectively, twice the lattice constant a.
Figure 3. Magnetoresistance of 2DEG in anti-dot arrays. The lattice constant and temperature are (a) 0.8p.m and lSK, @)l.Opm and 1.5K and (c) l.Oum and 4.2K, respectively.
-80 s
in g120 80
400
w (cl
-0.5
0 MAGNETIC FIELD
0.5
Figure 4. Magnetoresistance at various temperatures. The lattice constant is (a) 0.8p.m and (b) l.Oprn. The temperature is 50, 40, 30, 25, 15, 10, and 5.3 from top to bottom. -0.5
(T)
0
0.5
MAGNETIC FIELD (T)
We may attribute magneto&stance decrease at B=0.4T to the condition that the cyclotron diameter 2r, becomes less than the effective separation between the anti-dots. Thus depletion length r,_+,will be obtained by the equation 2rd, , + 2r, = a (See Fig. 6) [7]. From the critical fields, we estimated rdcploP anti-dot as 0.15 and 0.13um for the samples of a=0.8 and l&m, respectively. These values are typical for depletion layers induced by ion beam etching. The reason why the amplitude of the low-field peaks for a=0.8um (Fig3(a)) was smaller than that for a=l.Oum (Fig. 3(b)) is probably that the aspect ratio of a/rhP, is small. Low field novel magnetoresistance oscillations in Fig.3 (a) and (b) are depicted again in Fig. 5 with enlarged magnetic field scale normalized by B,,, here B, is 2hk&a. We attribute the oscillations to the commensurability on the triangular anti-dots lattice. Electrons in magnetic field perform cyclotron motion with radius r,=hk,JeB and cyclotron frequency m==eB/m’. At low magnetic field, conduction is dominated by scattering by anti-dots because cyclotron radius is larger than the dot separation. When the electrons circulate without being scattered by both intrinsic or extrinsic impurities, the pinned orbits localized around their orbit centers and cannot contribute to the conduction, resulting in reduction of carrier and the maxima of the magnetoresistances. We consider three kinds of commensurate orbits as illustrated in Fig.6. The solid line circules illustrate the cyclotron orbit with the center placed at one of anti-dots. Therefore, the maxima of the magnetoresistance satisfies the commensurability condition 2r, = (2n-1)a ,
n=1,2,.
.
(2)
The dashed and dotted circles illustrate the other groups of pinned-orbits, where the center of the orbits are placed at the middle point of a side and center of the triangle, respectively. In Fig. 5, the field positions for commensurate orbits are marked by the arrows and the number of anti-dots
512
J. Takahara et al. I Anti-dot triangle lattices
encircled by cyclotron orbits. They have a close correlation with the maxima in the resistance except the large peak at B=O.O2T. No.1 peak are overlapped by SdH oscillations. The absence of No.2 peak is probably due to larger scattering compared with other orbits which have larger wide space for cyclotron motion, e.g. orbit No.3 and 7. However we cannot explain large peaks around 0.02T. ln low-magnetic field, cyclotron radius becomes very large, and the amplitude of higher mode of commensurate orbit should be small. These peaks may be attributed to noncircular pinned orbit [6] due to the finite potential gradient, which guides the electron orbit. . Figure 6. . Commensurate orbit in triangle lattice. ;;
80-
-
140
0&m
.
.
.
.
.
.
.
.
. . .
.
.
.
!T 2 120 + ” 1 100 IY
.
.
.
.
.
-
rc
.
a
80 60 4o
l.Opm 11*111111*11111 0 0.5 NORMALIZED
1.0 FIELD
B/B0
Figure 5. Low-field magnetoresistance versus normalized magnetic field. Arrows indicate the field to form pinnedorbits as illustrated in Fig. 6.
4. CONCLUSION We have fabricated periodic triangle array of anti-dots in 2DEG of the heterojunction by EB The interplay between lattice constant and cyclotron radius lithography and dry etching. demonstrate low field novel magnetoresistance oscillations. These oscillations have weak temperature dependence. Classical commensurate picture explains the effect. ACKNOWLEDGEMENTS The authors would like to thank F. Wakaya and Y. Yuba for the high-mobility heterojunction and K. Oto for low-temperature measurement. This work was supported in part by the Grant-in-Aid for Scientific Research on Priority Area, “Electron Wave Interference Effects in Mesoscopic Structures” from the Ministry of Education, Science and Culture, Japan.
REFERENCES 1 2 3 4 5 6 7
D.R. Hofstadter, Phys. Rev. B 14 (1976) 2239. D. Weiss, K. von Klitzing, K. Ploog, and G. Weimamt, Europhys. L.&t. 8 (1989) 179. E.S. Alves et. al, J.Phys. Condens. Matter 1 (1989) 8252. R.R. Gerhardts, D. Weiss, and U. Wulf, Phys. Rev. B 43 (1991) 5192. D. Weiss et. al, Phys. Rev. Lett. 66 (1991) 2790. J. Takahara et. al, to be published Jap. J. Appl. Phys. K. Ensslin and P.M. Petroff, Phys. Rev. B 41 (1990) 12307.
Engineering
17 (1992) 509-512
509
Fabrication and transport properties of anti-dot triangle lattices J. Takahara”, Y. Takagaki”‘, K. Gamoab, S. Namba”b”, S. Takaoka” and K. Murase’ “Department of Electrical Engineering, Toyonaka, Osaka 560, Japan
Faculty of Engineering
Science,
Osaka University,
bResearch Center for Extreme Materials, Osaka University, Toyonaka, Osaka 560, Japan Department
of Physics, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan
Present Adress: *Center for Solid State Electronics Research, Arizona State University, Tempe, Arizona 85287-6206. **Nagasaki Institute of Applied Science, 536 Amibacho, Nagasaki-shi, Nagasaki 851-01. We have fabricated triangle anti-dot structure in GaAs-AlGaAs heterojunction by employing electron beam lithography and dry etching, and we measured magnetoresistance and its temperature dependence. Novel magnetoresistance oscillations were observed at the low magnetic field. These oscillations which has weak-temperature dependence were attributed to commensurate classical orbits on lattices of anti-dots. 1. INTRODUCIION The interplay of the two characteristic length, periodicity of modulation potential and cyclotron radius, produce interesting phenomena. Theoretically, Hofstadter demonstrated that the quantum states may exhibit a self-similar band structure [l]. In recent experiments on 2DEG subjected to the weak 1D [2] and 2D [3,4] lateral superlattice potential novel low-field magnetoresistance oscillations were observed. In weak potential, electrons &verse modulated region. On the other hand, in strong potential electrons feel the hard wall potential and traverse in non-modulated region, and such a strong potential is called “Anti-dot” [5-71. In this paper, we present fabrication process of anti-dot structures and discuss their effect on low-field magnetoresistance. Anti-dot was arranged in the shape of periodic triangle lattice. Low-field oscillations were attributed to commensurate classical orbits on lattices of anti-dots. 2. FABRICATION AND EXPERIMENT Fig. 1 shows the sample fabrication procedures. The samples were prepared on conventional GaAs-AlGaAs heterojunction grown by MBE. The heterojunction has a structure as shown in Fig. 2(a). The carrier concentration n, and mobility p of the startin! material measured at 1.4K in dark by the standard van der Pauw procedure were n,=3.2x10r5m- and p=130m2V-‘s-l, respectively, leading to an elastic mean free path 1,=12pm. Anti-dot structures were introduced by electron beam lithography and dry etching. 1OOpm wide four-terminal shaped samples are -defined by wet-etching using H,PO,:&O,:&O=l:1:30 solution. Au/Ge layers were evaporated and alloyed at 370 “C to form source-drain and potential probe contacts. Next, the EB resist PMMA was spun on at 8000 rpm for 40 set and baked at 170 “C for 2 hours. Dot patterns were delineated by
0167-9317/92/$05.00
0 1992 - Elsevier Science Publishers
B.V.
All rights reserved.
J. Takahara et al. I Anti-dot triangle lattices
510
SOkeV EB in PMMA on mesa-etched substrate. The exposure was performed employing a nanometer EB lithography systam which uses a zirconated tungsten thermal field emitter. A minimum calculated beam spot size at a working distance of 8mm is 2.4nm at SOkeV. A schematic view of the sample is shown in Fig. 2 (b). The dot interval a is l.Opm and 0.8pm, and dot radius is about O.lpm. The exposed resist was developed by conventional wet process (in a mixture of isopropyl alcohol (IPA) : methyl-isobutyl ketone (MIBK) = 1:2.5 for a few seconds). Finally, the samples beneath the dot pattern were shallow etched using 1keV Art ion milling for 3 minutes to a depth of about 3Omn. The etched region is strongly depleted due to a great deal of beam-induced damage, leading to become scatterers. Measurement was done from 1.4K to 50K after illumination using an ac bridge operating at 3OHz. (a)
RESIST
n’-Gab
20nm
COATING
lb)
vvv m
L! EB EXPOSURE
RESIST
Figure 2. (a) Structure of the heterojunction. (b) Schematic view of the sample.
LIFT OFF
Figure 1. Fabrication process.
3. RESULTS
AND DISCUSSION
Figure 3 shows magnetoresistance traces for the periodic triangle lattice. At higher fields (B>O.3T), Shubnikov-de Haas(SdH) oscillations were observed. The carrier concentration de&mined from SdH oscillations was 4.1x10’5m-2 in both samples. The carrier concentration was increased compared to the starting materials due to the persistent photoconduction effect. At lower fields (B<0.5T for a=O.8pm and B<0.3T for a=l.Opm) magnetoresistance quickly increased and novel oscillations were observed although magnetoresistance of usual unpatterned sample shows roughly constant at lower field. Figure 4 shows the magnetoresistance at various temperatures from 5.3 to 50K. Although SdH oscillations were quenched at 4.2K (See Fig. 3 (c)), low field oscillations were clearly observed above 1OK. Especially, the largest peaks around 0.2T still remained at 50K. SdH oscillation is attributed to Landau quantization, thus the condition that is satisfied to observe SdH oscillation is kaT
(1)
J. Takuhara et al. I Anti-dot triangle lattices
511
Here zi, and z, are the intrinsic and extrinsic relaxation time, respectively. From the zero-field resistance subtracted with the series resistance of the unpatterned region, we obtained the mobility of 17 and 20m2V%-’ in patterned region for a=0.8 (a) and lpm (b), respectively. The mobilities were suppressed due to the imposed anti-dots. Thus we obtained ?=6.$ (a) and 7.6~s (b), respectively. Around B=0.4T in Fig. 3, ma etoresistance decreased. This unphes that the mfluence of unposed scatterers was suppressed. u$”e obtained 2,=33 (a) and 47~s (b), and corresponding mobility of 87 (a) and 122m2V- s- ’ (b), respectively. This indicates that unpatterned region of the case (a) mainained initial condition. From extrinsic relaxation time -ceX obtaine by eq. (l), the mean free path l,=V,z, was estimated to be 2.2 (a) and 2.5pm (b), respectively, twice the lattice constant a.
Figure 3. Magnetoresistance of 2DEG in anti-dot arrays. The lattice constant and temperature are (a) 0.8p.m and lSK, @)l.Opm and 1.5K and (c) l.Oum and 4.2K, respectively.
-80 s
in g120 80
400
w (cl
-0.5
0 MAGNETIC FIELD
0.5
Figure 4. Magnetoresistance at various temperatures. The lattice constant is (a) 0.8p.m and (b) l.Oprn. The temperature is 50, 40, 30, 25, 15, 10, and 5.3 from top to bottom. -0.5
(T)
0
0.5
MAGNETIC FIELD (T)
We may attribute magneto&stance decrease at B=0.4T to the condition that the cyclotron diameter 2r, becomes less than the effective separation between the anti-dots. Thus depletion length r,_+,will be obtained by the equation 2rd, , + 2r, = a (See Fig. 6) [7]. From the critical fields, we estimated rdcploP anti-dot as 0.15 and 0.13um for the samples of a=0.8 and l&m, respectively. These values are typical for depletion layers induced by ion beam etching. The reason why the amplitude of the low-field peaks for a=0.8um (Fig3(a)) was smaller than that for a=l.Oum (Fig. 3(b)) is probably that the aspect ratio of a/rhP, is small. Low field novel magnetoresistance oscillations in Fig.3 (a) and (b) are depicted again in Fig. 5 with enlarged magnetic field scale normalized by B,,, here B, is 2hk&a. We attribute the oscillations to the commensurability on the triangular anti-dots lattice. Electrons in magnetic field perform cyclotron motion with radius r,=hk,JeB and cyclotron frequency m==eB/m’. At low magnetic field, conduction is dominated by scattering by anti-dots because cyclotron radius is larger than the dot separation. When the electrons circulate without being scattered by both intrinsic or extrinsic impurities, the pinned orbits localized around their orbit centers and cannot contribute to the conduction, resulting in reduction of carrier and the maxima of the magnetoresistances. We consider three kinds of commensurate orbits as illustrated in Fig.6. The solid line circules illustrate the cyclotron orbit with the center placed at one of anti-dots. Therefore, the maxima of the magnetoresistance satisfies the commensurability condition 2r, = (2n-1)a ,
n=1,2,.
.
(2)
The dashed and dotted circles illustrate the other groups of pinned-orbits, where the center of the orbits are placed at the middle point of a side and center of the triangle, respectively. In Fig. 5, the field positions for commensurate orbits are marked by the arrows and the number of anti-dots
512
J. Takahara et al. I Anti-dot triangle lattices
encircled by cyclotron orbits. They have a close correlation with the maxima in the resistance except the large peak at B=O.O2T. No.1 peak are overlapped by SdH oscillations. The absence of No.2 peak is probably due to larger scattering compared with other orbits which have larger wide space for cyclotron motion, e.g. orbit No.3 and 7. However we cannot explain large peaks around 0.02T. ln low-magnetic field, cyclotron radius becomes very large, and the amplitude of higher mode of commensurate orbit should be small. These peaks may be attributed to noncircular pinned orbit [6] due to the finite potential gradient, which guides the electron orbit. . Figure 6. . Commensurate orbit in triangle lattice. ;;
80-
-
140
0&m
.
.
.
.
.
.
.
.
. . .
.
.
.
!T 2 120 + ” 1 100 IY
.
.
.
.
.
-
rc
.
a
80 60 4o
l.Opm 11*111111*11111 0 0.5 NORMALIZED
1.0 FIELD
B/B0
Figure 5. Low-field magnetoresistance versus normalized magnetic field. Arrows indicate the field to form pinnedorbits as illustrated in Fig. 6.
4. CONCLUSION We have fabricated periodic triangle array of anti-dots in 2DEG of the heterojunction by EB The interplay between lattice constant and cyclotron radius lithography and dry etching. demonstrate low field novel magnetoresistance oscillations. These oscillations have weak temperature dependence. Classical commensurate picture explains the effect. ACKNOWLEDGEMENTS The authors would like to thank F. Wakaya and Y. Yuba for the high-mobility heterojunction and K. Oto for low-temperature measurement. This work was supported in part by the Grant-in-Aid for Scientific Research on Priority Area, “Electron Wave Interference Effects in Mesoscopic Structures” from the Ministry of Education, Science and Culture, Japan.
REFERENCES 1 2 3 4 5 6 7
D.R. Hofstadter, Phys. Rev. B 14 (1976) 2239. D. Weiss, K. von Klitzing, K. Ploog, and G. Weimamt, Europhys. L.&t. 8 (1989) 179. E.S. Alves et. al, J.Phys. Condens. Matter 1 (1989) 8252. R.R. Gerhardts, D. Weiss, and U. Wulf, Phys. Rev. B 43 (1991) 5192. D. Weiss et. al, Phys. Rev. Lett. 66 (1991) 2790. J. Takahara et. al, to be published Jap. J. Appl. Phys. K. Ensslin and P.M. Petroff, Phys. Rev. B 41 (1990) 12307.