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Formation and characteristics of 100-nm scale GaAs quantum wires by selective area MOVPE
Applied Surface Science 216 (2003) 402–406
Formation and characteristics of 100-nm scale GaAs quantum wires by selective area MOVPE H. Takahashi*, Y. Miyoshi, F. Nakajima, P. Mohan, J. Motohisa, T. Fukui Research Center for Integrated Quantum Electronics (RCIQE), Hokkaido University, North 13 West 8, Sapporo 060-8628, Japan
Abstract We fabricated quantum wires (QWRs) with sub-micron wire width using GaAs/AlGaAs selectively doped structures grown by selective area metalorganic vapor phase epitaxy (SA-MOVPE) on (0 0 1) masked GaAs substrates partially covered by SiON. From the measurement of a two-terminal conductance as a function of geometrical wire width, QWRs with effective channel width <100 nm are formed without application of any gate bias. The magnetoresistance measurement at 1.7 K also suggests the formation of narrow QWRs, although it also indicates a presence of potential fluctuation along the QWRs. The effective channel width of present QWRs are much narrower than the previously reported values (300 nm) of those formed by SA-MOVPE. # 2003 Published by Elsevier Science B.V. Keywords: Single electron transistor; SA-MOVPE; Quantum dot; Quantum wire; GaAs; Magnetoresistance
1. Introduction Recently, new electron devices with quantum nanostructures such as single electron transistors (SETs) and single electron memories have attracted much attention. One of the key issues for their realization is formation of high quality quantum nano-structures with strong quantum confinement in a size- and site-controlled fashion. Various kinds of approaches have been reported and attempted for the formation of extremely small quantum nano-structures, including self-assemble formation InGaAs quantum dots on GaAs substrates [1–3] and growth on patterned substrates [4–8]. Among these, selective area metalorganic vapor phase epitaxy (SA-MOVPE) is a promising method because it enables *
Corresponding author. Tel.: þ81-11-706-7172; fax: þ81-11-716-6004. E-mail address: [email protected] (H. Takahashi).
us to realize semiconductor nano-structure fabrication without any processing damage or contamination, and gives us the size reduction as the growth proceeds owing to the formation of crystallographic facets [4,7,8]. Our group has successfully fabricated SETs by SA-MOVPE. However, our demonstrations are still limited to the devices or circuits operating at very low temperatures, and further reduction of the size of quantum dots (QDs) and quantum wires (QWRs) is required for their high temperature operation. In addition, the QD and tunneling barriers in SETs are defined mainly by side-wall depletions controlled by Schottky gates, and it is difficult to realize strong confinement and high tunneling barriers, which is also required for high temperature operation. In general, mesa structures are formed due to the evolution of side-wall facets in SA-MOVPE when the growth is carried out in masked substrates with wire openings. The top width of the mesa structure is
0169-4332/03/$ – see front matter # 2003 Published by Elsevier Science B.V. doi:10.1016/S0169-4332(03)00458-6
H. Takahashi et al. / Applied Surface Science 216 (2003) 402–406
narrower than the initial mask opening, W, and becomes narrower and narrower as the growth proceeds. If the growth further proceeds, it ends up with self-limited ridge structures [4,9]. Therefore, we can reduce the size of QWRs formed on the top of the mesa or ridge structures simply by reducing the initial opening, W, or increasing the amount of the growth. This means, however, the wire becomes close to the top surface, and a difficulty in growing overlayers, which is particularly important to have sufficiently thick carrier supplying layer of selectively doped structures. To compromise the reduction of wire size and insufficient thickness of doping layer, we previously proposed a doping scheme where the selective doping is carried out in the AlGaAs layer beneath the channel [8], which we hereafter refer to the bottomside selective doping. In this paper, we report on the formation and characterization of GaAs QWRs using SA-MOVPE. By adopting the bottom-side selectively doped structure and based on the conductivity and magnetoresistance measurement, we will show that the effective channel width of QWRs can be an order of 100 nm, which is much narrower than the similar wire structures formed by SA-MOVPE.
403
2. Experimental We carry out SA-MOVPE of GaAs/AlGaAs selectively doped double heterostructures on (0 0 1)GaAs substrates partially covered by SiON. Fig. 1 shows a mask pattern of the substrate. Wire-like openings are formed along the [1 1 0] direction by electron beam lithography and wet chemical etching. The width of the openings W is ranging from 500 to 1300 nm (which are measured after the fabrication of masked substrates), and their length L is 1 mm. Wide opening areas attached at the both end are for the source and drain contacts. A low-pressure, horizontal reactor MOVPE system is used for the growth. We use Trimethylgallium (TMGa), trimethylaluminum (TMAl) and arsine (AsH3) as source materials. Purified hydrogen (H2) is used as a carrier gas. The working pressure of 0.1 atm is automatically controlled. The partial pressure of TMGa and TMAl are 3:8 106 atm and 6:3 107 atm, respectively, and the corresponding growth rate of GaAs and AlGaAs on planar substrates is 0.23 and 0.32 nm/s, respectively. The growth rates on the masked substrates are larger by about 10%, as described later. AsH3 partial pressure is 1:3 104 atm for GaAs buffer layer, and
Fig. 1. (a) Schematic illustration of a SiON mask pattern formed on GaAs(0 0 1) substrate. Typical SEM image of: (b) sample A; and (c) sample B. (d) Schematic cross-section of the sample B.
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H. Takahashi et al. / Applied Surface Science 216 (2003) 402–406
6:7 104 atm for Al0.3Ga0.7As to obtain better crystal quality. We grow two types of samples by SA-MOVPE. The first one (sample A) is to check the geometrical width of QWR channel, and a 256-nm thick GaAs and a 154nm thick AlGaAs layres are grown. The other (sample B) is for the bottom-side selectively doped double heterostructures with the following layer sequence: a 390 nm buffer layer, a 110 nm Al0.3Ga0.7As layer, a 28 nm n-doped Al0.3Ga0.7As layer, a 16 nm AlGaAs spacing layer, a 16 nm quantum well layer, a 160 nm Al0.3Ga0.7As layer, and a 10 nm GaAs capping layer. The growth temperature is 700 8C. For latter structures, Ge/Au/Ni/Au Ohmic contacts at the source and drain are formed by the lift-off method after the growth, and two-terminal conductance and magnetoresistance measurements are carried out at low temperatures. Typical values of electron mobility and sheet carrier concentration of two-dimensional electron gas (2D EG) on a reference planar substrate are 18,000 cm2/Vs and 5:5 1012 cm2 at 77 K, respectively.
3. Experimental results and discussions 3.1. Selective area growth Fig. 1(b) shows a typical scanning electron microscope (SEM) image of the sample A. Here, the initial opening with W of the wire is measured to be 890 nm. As mentioned in the beginning, the structure after the SA-MOVPE on (0 0 1)GaAs substrates with wire openings is a mesa structure or a triangular ridge wire structure. In the case of sample A, the total growth thickness, t, is 410 nm and the mesa structures consisting of (0 0 1) top surface and {1 1 1}B side-wall facets are obtained for all W used in the study. We note that the height of the mesa structures is slightly higher than the thickness of the GaAs/AlGaAs layers on planar substrates (380 nm). This is due to the diffusion of growth species from masked areas to the top surface and side-wall facets. On the other hand, a ridge wire structure having a triangular cross-section facet is obtained for sample B, as shown in the SEM image of Fig. 1(c) and its schematic cross-section of Fig. 1(d). For this SEM image, W is 760 nm and the total thickness, t, for the growth is 730 nm. We note that
most of the sample B turned out to be ridge wire structures, except for the sample with widest W used in the present study. This indicates that the ridge structures are self-limited [8], i.e. the growth hardly proceeds after the completion of wire structures with triangular cross-section. For this reason, we cannot directly estimate the geometrical width, Wch, of the GaAs channel of QWRs from the SEM images of sample B. In turn, the channel widths of sample B was estimated based on the results for sample A as follows. Fig. 2 shows the top width, Wtop, of the wire structure after the growth, plotted as a function of W. The open circles represent the results for sample A with total thickness, t, of 410 nm. Wtop increases linearly with W, as normally expected. If we assume Wtop becomes narrower in proportional to t and selflimited growth in ridge wire structures, Wtop for t ¼ 730 nm, which corresponds to the total thickness of sample B, would be given by the dotted line in Fig. 2. In this estimation, the top (0 0 1) surface disappears if W < 1010 nm. This estimation gives reasonable agreement with the results for sample B (closed symbols). Therefore, considering the thickness of GaAs and AlGaAs layers beneath the GaAs channel (see Fig. 1(d)), the channel width is expected to follow the thick dashed line in Fig. 2. Results of measured mask opening width W and estimated QWR channel width Wch is summarized in Table 1. As one can see, the channel width is almost zero for W ¼ 640 and 760 nm. Rigorously speaking, the top width is always finite (30 nm) due to the self-limiting mechanism [4,9]. In
Fig. 2. Measured top width of sample A (open circles) and sample B (closed circles). Solid line represents a linear fit to the data for sample A, and dotted line estimated top width for sample B based on the linear extrapolation of the results of sample A. Dashed line represents an estimated with of GaAs channel for sample B.
H. Takahashi et al. / Applied Surface Science 216 (2003) 402–406 Table 1 Summary of measured width of initial mask opening, W, estimated channel width, Wch, and effective wire width, Weff, of sample B W (nm)
Wch (nm)
Weff (nm)
640 760 870 950 1040 1150
0 0 90 165 260 365
Pinch-off Pinch-off Pinch-off 75 170 275
addition, the linear relationship between W and Wch, or between Wch and t, is not applicable due to the diffusion of growth spices from masked regions to top (0 0 1) surfaces [9,10]. Thus, Wch would be much narrower than the estimation based on the linear relationship. However, these facts do not alter our main conclusion as discussed later.
405
[11], Yamada et al. [12], and Fukui et al. [13] reported the fabrication of quantum wires by SA-MOVPE, and they reported that the effective width of wires formed on the top of (0 0 1) surface was Weff ¼ 300 nm. Our group also reported the fabrication of similar quantum wires [7], and the effective wire width could be reduced to about 76 nm by applying gate voltage. In comparison with these previous results, we can reasonably say that our present QWR structures is the narrowest among QWRs formed by SA-MOVPE, and we could realize much narrower wires by using Schottky gate to wrap over the wires which is left for future study. Fig. 4(a) shows magnetoresistance (MR) of the sample B with three different Weff (¼ Wch Wdep) measured at 1.7 K. We can see clear MR oscillations for samples width Weff ¼ 170 and 275 nm. The oscillations are periodic in inverse of magnetic field, 1/B, as shown in the Landau plot of Fig. 4(b). The direction of
3.2. Transport properties Fig. 3 shows a relationship between two-terminal conductance and Wch of quantum wires measured at 120 and 1.7 K. From this result, it is concluded that the wires become pinched-off for Wch < 90 nm. This is due to the depletion from side walls. Therefore, the effective wire width Weff is expected to be much narrower than Wch. The depletion width Wdep from the side wall is estimated to be 90 nm from this plot. By subtracting the total depletion width, we can say that the QWRs with Weff ¼ 75 and 170 nm are formed for W ¼ 165 and 260 nm, respectively. This is summarized in Table 1. Note that these values are achieved without application of any gate bias voltage. Asai et al.
Fig. 3. Conductance vs. Wch characteristics of sample B.
Fig. 4. (a) Magnetoresistance of samples for Weff ¼ 75, 170 and 275 nm; and (b) their plot. Arrows in (a) indicate the position of magnetoresistance peaks used for the Landau plot of the sample with Weff ¼ 75 nm.
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magnetic field B is perpendicular to samples. This indicates the two-dimensional nature of the electrons in the channel of these samples. On the other hand, somewhat aperiodic but reproducible MR oscillation is observed for the wires with Weff ¼ 75 nm. The aperiodic oscillation is superimposed on the negative magnetoresistance in the low field. At high field (B > 3T), the amplitude of the aperiodic oscillations becomes smaller and it seems that the oscillations become dominated by that periodic in 1/B, as we can see in the Landou plot of Fig. 4(b). It also seems that the oscillations appearing at 1/B 0.5 seems to be deviates from the linear behavior, which is expected when there is a lateral confinement as QWRs [14]. However, this deviation is not so clear at the moment due to the aperiodic part of the oscillations, and requires more careful investigation. We think that the aperiodic magnetioresistance oscillation and its suppression at high magnetic field is explained by universal conductance fluctuation in the semiconductor wires [15]. Negative magnetoresistance is also explained within the framework of weak localization in one-dimensional systems [16]. These results also suggest that there are still large potential fluctuations along QWRs in the present samples. Considering the lower electron mobility in the present bottom-side selectively doped structure than that in conventional structures typically (about 7:2 104 cm2/Vs [8]), this would be partly due to the lower quality of the bottom-side selectively doped structures. The lower quality would originate from the lower quality of so-called bottom (GaAs-on-AlGaAs) interfaces, as compared to the top (AlGaAs-on-GaAs) interface of the channel, and segregation of impurity from doped AlGaAs layers to GaAs channel. Optimization of the growth conditions is required to realize high-quality quantum nanostructures utilizing bottom-side selectively doped structures.
4. Conclusion We demonstrated the fabrication of very narrow GaAs QWRs formed by SA-MOVPE. Based on the estimation of geometrical wire width and two-terminal conductivity measurement, we concluded that QWRs
with effective wire width <75 nm was realized by adopting bottom-side selective doped structures. which is narrowest among conducting QWRs formed by SA-MOVPE. Although the improvements in the quality of grown layers are still required, bottom-side selective doping scheme is effective to realize quantum nanostructures with extremely small size.
Acknowledgements The authors are grateful for stimulating discussions with Prof. Hasegawa. This work is partly financially supported by a Grant-in-Aid for Scientific Research by Japan Society of Promotion of Science.
References [1] J. Tenmyo, E. Kuramochi, M. Sugo, T. Nishiya, R. Ntzel, T. Tamamura, Electron. Lett. 31 (1995) 209. [2] D. Bimberg, N.N. Ledentsov, M. Grundmann, N. Kirstaedter, O.G. Schmidt, M.N. Mao, V.M. Ustinov, A.Yu. Egorov, A.E. Zhukov, P.S. Kopev, Zh.I. Alferov, S.S. Ruvimov, U.G. Sele, J. Heydenreich, Jpn. J. Appl. Phys. 35 (1996) 1311. [3] D. Leonard, M. Krishnamurthy, C.M. Reaves, S.P. Denbaars, P.M. Petroff, Appl. Phys. Lett. 63 (1993) 3203. [4] K. Kumakura, K. Nakakoshi, J. Motohisa, T. Fukui, H. Hasegawa, Jpn. J. Appl. Phys. Part 1 34 (1995) 4387. [5] M. Digler, R.J. Haug, K. Eberl, K. von Klitzing, Semicond. Sci. Technol. 11 (1996) 1493. [6] A. Hartmann, Y. Ducommun, L. Loubies, K. Leifer, E. Kapon, Appl. Phys. Lett. 73 (1998) 2322. [7] K. Kumakura, J. Motohisa, T. Fukui, Physica E2 (1998) 809. [8] F. Nakajima, Y. Ogasawara, J. Motohisa, T. Fukui, J. Appl. Phys. 90 (2001) 2606. [9] Y. Aritsuka, T. Umeda, J. Motohisa, T. Fukui, Mater. Res. Soc. Symp. Proc. 97 (1999) 570. [10] K. Kumakura, K. Nakakoshi, J. Motohisa, T. Fukui, H. Hasegawa, J. Cryst. Growth 145 (1994) 308. [11] H. Asai, S. Yamada, T. Fukui, Appl. Phys. Lett. 51 (1987) 1518. [12] S. Yamada, H. Asai, Y. Fukai, T. Fukui, Phys. Rev. B 39 (1989) 11199. [13] Y. Fukai, S. Yamada, H. Nakano, Appl. Phys. Lett. 56 (1990) 2123. [14] K.F. Berggren, G. Roos, H. van Houten, Phys. Rev. B 37 (1988) 10118. [15] C.W.J. Beenakker, H. van Houten, Phys. Rev. B 37 (1988) 6544. [16] B.L. Altshuler, A.G. Aronov, JETP Lett. 33 (1981) 499.
Formation and characteristics of 100-nm scale GaAs quantum wires by selective area MOVPE H. Takahashi*, Y. Miyoshi, F. Nakajima, P. Mohan, J. Motohisa, T. Fukui Research Center for Integrated Quantum Electronics (RCIQE), Hokkaido University, North 13 West 8, Sapporo 060-8628, Japan
Abstract We fabricated quantum wires (QWRs) with sub-micron wire width using GaAs/AlGaAs selectively doped structures grown by selective area metalorganic vapor phase epitaxy (SA-MOVPE) on (0 0 1) masked GaAs substrates partially covered by SiON. From the measurement of a two-terminal conductance as a function of geometrical wire width, QWRs with effective channel width <100 nm are formed without application of any gate bias. The magnetoresistance measurement at 1.7 K also suggests the formation of narrow QWRs, although it also indicates a presence of potential fluctuation along the QWRs. The effective channel width of present QWRs are much narrower than the previously reported values (300 nm) of those formed by SA-MOVPE. # 2003 Published by Elsevier Science B.V. Keywords: Single electron transistor; SA-MOVPE; Quantum dot; Quantum wire; GaAs; Magnetoresistance
1. Introduction Recently, new electron devices with quantum nanostructures such as single electron transistors (SETs) and single electron memories have attracted much attention. One of the key issues for their realization is formation of high quality quantum nano-structures with strong quantum confinement in a size- and site-controlled fashion. Various kinds of approaches have been reported and attempted for the formation of extremely small quantum nano-structures, including self-assemble formation InGaAs quantum dots on GaAs substrates [1–3] and growth on patterned substrates [4–8]. Among these, selective area metalorganic vapor phase epitaxy (SA-MOVPE) is a promising method because it enables *
Corresponding author. Tel.: þ81-11-706-7172; fax: þ81-11-716-6004. E-mail address: [email protected] (H. Takahashi).
us to realize semiconductor nano-structure fabrication without any processing damage or contamination, and gives us the size reduction as the growth proceeds owing to the formation of crystallographic facets [4,7,8]. Our group has successfully fabricated SETs by SA-MOVPE. However, our demonstrations are still limited to the devices or circuits operating at very low temperatures, and further reduction of the size of quantum dots (QDs) and quantum wires (QWRs) is required for their high temperature operation. In addition, the QD and tunneling barriers in SETs are defined mainly by side-wall depletions controlled by Schottky gates, and it is difficult to realize strong confinement and high tunneling barriers, which is also required for high temperature operation. In general, mesa structures are formed due to the evolution of side-wall facets in SA-MOVPE when the growth is carried out in masked substrates with wire openings. The top width of the mesa structure is
0169-4332/03/$ – see front matter # 2003 Published by Elsevier Science B.V. doi:10.1016/S0169-4332(03)00458-6
H. Takahashi et al. / Applied Surface Science 216 (2003) 402–406
narrower than the initial mask opening, W, and becomes narrower and narrower as the growth proceeds. If the growth further proceeds, it ends up with self-limited ridge structures [4,9]. Therefore, we can reduce the size of QWRs formed on the top of the mesa or ridge structures simply by reducing the initial opening, W, or increasing the amount of the growth. This means, however, the wire becomes close to the top surface, and a difficulty in growing overlayers, which is particularly important to have sufficiently thick carrier supplying layer of selectively doped structures. To compromise the reduction of wire size and insufficient thickness of doping layer, we previously proposed a doping scheme where the selective doping is carried out in the AlGaAs layer beneath the channel [8], which we hereafter refer to the bottomside selective doping. In this paper, we report on the formation and characterization of GaAs QWRs using SA-MOVPE. By adopting the bottom-side selectively doped structure and based on the conductivity and magnetoresistance measurement, we will show that the effective channel width of QWRs can be an order of 100 nm, which is much narrower than the similar wire structures formed by SA-MOVPE.
403
2. Experimental We carry out SA-MOVPE of GaAs/AlGaAs selectively doped double heterostructures on (0 0 1)GaAs substrates partially covered by SiON. Fig. 1 shows a mask pattern of the substrate. Wire-like openings are formed along the [1 1 0] direction by electron beam lithography and wet chemical etching. The width of the openings W is ranging from 500 to 1300 nm (which are measured after the fabrication of masked substrates), and their length L is 1 mm. Wide opening areas attached at the both end are for the source and drain contacts. A low-pressure, horizontal reactor MOVPE system is used for the growth. We use Trimethylgallium (TMGa), trimethylaluminum (TMAl) and arsine (AsH3) as source materials. Purified hydrogen (H2) is used as a carrier gas. The working pressure of 0.1 atm is automatically controlled. The partial pressure of TMGa and TMAl are 3:8 106 atm and 6:3 107 atm, respectively, and the corresponding growth rate of GaAs and AlGaAs on planar substrates is 0.23 and 0.32 nm/s, respectively. The growth rates on the masked substrates are larger by about 10%, as described later. AsH3 partial pressure is 1:3 104 atm for GaAs buffer layer, and
Fig. 1. (a) Schematic illustration of a SiON mask pattern formed on GaAs(0 0 1) substrate. Typical SEM image of: (b) sample A; and (c) sample B. (d) Schematic cross-section of the sample B.
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H. Takahashi et al. / Applied Surface Science 216 (2003) 402–406
6:7 104 atm for Al0.3Ga0.7As to obtain better crystal quality. We grow two types of samples by SA-MOVPE. The first one (sample A) is to check the geometrical width of QWR channel, and a 256-nm thick GaAs and a 154nm thick AlGaAs layres are grown. The other (sample B) is for the bottom-side selectively doped double heterostructures with the following layer sequence: a 390 nm buffer layer, a 110 nm Al0.3Ga0.7As layer, a 28 nm n-doped Al0.3Ga0.7As layer, a 16 nm AlGaAs spacing layer, a 16 nm quantum well layer, a 160 nm Al0.3Ga0.7As layer, and a 10 nm GaAs capping layer. The growth temperature is 700 8C. For latter structures, Ge/Au/Ni/Au Ohmic contacts at the source and drain are formed by the lift-off method after the growth, and two-terminal conductance and magnetoresistance measurements are carried out at low temperatures. Typical values of electron mobility and sheet carrier concentration of two-dimensional electron gas (2D EG) on a reference planar substrate are 18,000 cm2/Vs and 5:5 1012 cm2 at 77 K, respectively.
3. Experimental results and discussions 3.1. Selective area growth Fig. 1(b) shows a typical scanning electron microscope (SEM) image of the sample A. Here, the initial opening with W of the wire is measured to be 890 nm. As mentioned in the beginning, the structure after the SA-MOVPE on (0 0 1)GaAs substrates with wire openings is a mesa structure or a triangular ridge wire structure. In the case of sample A, the total growth thickness, t, is 410 nm and the mesa structures consisting of (0 0 1) top surface and {1 1 1}B side-wall facets are obtained for all W used in the study. We note that the height of the mesa structures is slightly higher than the thickness of the GaAs/AlGaAs layers on planar substrates (380 nm). This is due to the diffusion of growth species from masked areas to the top surface and side-wall facets. On the other hand, a ridge wire structure having a triangular cross-section facet is obtained for sample B, as shown in the SEM image of Fig. 1(c) and its schematic cross-section of Fig. 1(d). For this SEM image, W is 760 nm and the total thickness, t, for the growth is 730 nm. We note that
most of the sample B turned out to be ridge wire structures, except for the sample with widest W used in the present study. This indicates that the ridge structures are self-limited [8], i.e. the growth hardly proceeds after the completion of wire structures with triangular cross-section. For this reason, we cannot directly estimate the geometrical width, Wch, of the GaAs channel of QWRs from the SEM images of sample B. In turn, the channel widths of sample B was estimated based on the results for sample A as follows. Fig. 2 shows the top width, Wtop, of the wire structure after the growth, plotted as a function of W. The open circles represent the results for sample A with total thickness, t, of 410 nm. Wtop increases linearly with W, as normally expected. If we assume Wtop becomes narrower in proportional to t and selflimited growth in ridge wire structures, Wtop for t ¼ 730 nm, which corresponds to the total thickness of sample B, would be given by the dotted line in Fig. 2. In this estimation, the top (0 0 1) surface disappears if W < 1010 nm. This estimation gives reasonable agreement with the results for sample B (closed symbols). Therefore, considering the thickness of GaAs and AlGaAs layers beneath the GaAs channel (see Fig. 1(d)), the channel width is expected to follow the thick dashed line in Fig. 2. Results of measured mask opening width W and estimated QWR channel width Wch is summarized in Table 1. As one can see, the channel width is almost zero for W ¼ 640 and 760 nm. Rigorously speaking, the top width is always finite (30 nm) due to the self-limiting mechanism [4,9]. In
Fig. 2. Measured top width of sample A (open circles) and sample B (closed circles). Solid line represents a linear fit to the data for sample A, and dotted line estimated top width for sample B based on the linear extrapolation of the results of sample A. Dashed line represents an estimated with of GaAs channel for sample B.
H. Takahashi et al. / Applied Surface Science 216 (2003) 402–406 Table 1 Summary of measured width of initial mask opening, W, estimated channel width, Wch, and effective wire width, Weff, of sample B W (nm)
Wch (nm)
Weff (nm)
640 760 870 950 1040 1150
0 0 90 165 260 365
Pinch-off Pinch-off Pinch-off 75 170 275
addition, the linear relationship between W and Wch, or between Wch and t, is not applicable due to the diffusion of growth spices from masked regions to top (0 0 1) surfaces [9,10]. Thus, Wch would be much narrower than the estimation based on the linear relationship. However, these facts do not alter our main conclusion as discussed later.
405
[11], Yamada et al. [12], and Fukui et al. [13] reported the fabrication of quantum wires by SA-MOVPE, and they reported that the effective width of wires formed on the top of (0 0 1) surface was Weff ¼ 300 nm. Our group also reported the fabrication of similar quantum wires [7], and the effective wire width could be reduced to about 76 nm by applying gate voltage. In comparison with these previous results, we can reasonably say that our present QWR structures is the narrowest among QWRs formed by SA-MOVPE, and we could realize much narrower wires by using Schottky gate to wrap over the wires which is left for future study. Fig. 4(a) shows magnetoresistance (MR) of the sample B with three different Weff (¼ Wch Wdep) measured at 1.7 K. We can see clear MR oscillations for samples width Weff ¼ 170 and 275 nm. The oscillations are periodic in inverse of magnetic field, 1/B, as shown in the Landau plot of Fig. 4(b). The direction of
3.2. Transport properties Fig. 3 shows a relationship between two-terminal conductance and Wch of quantum wires measured at 120 and 1.7 K. From this result, it is concluded that the wires become pinched-off for Wch < 90 nm. This is due to the depletion from side walls. Therefore, the effective wire width Weff is expected to be much narrower than Wch. The depletion width Wdep from the side wall is estimated to be 90 nm from this plot. By subtracting the total depletion width, we can say that the QWRs with Weff ¼ 75 and 170 nm are formed for W ¼ 165 and 260 nm, respectively. This is summarized in Table 1. Note that these values are achieved without application of any gate bias voltage. Asai et al.
Fig. 3. Conductance vs. Wch characteristics of sample B.
Fig. 4. (a) Magnetoresistance of samples for Weff ¼ 75, 170 and 275 nm; and (b) their plot. Arrows in (a) indicate the position of magnetoresistance peaks used for the Landau plot of the sample with Weff ¼ 75 nm.
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magnetic field B is perpendicular to samples. This indicates the two-dimensional nature of the electrons in the channel of these samples. On the other hand, somewhat aperiodic but reproducible MR oscillation is observed for the wires with Weff ¼ 75 nm. The aperiodic oscillation is superimposed on the negative magnetoresistance in the low field. At high field (B > 3T), the amplitude of the aperiodic oscillations becomes smaller and it seems that the oscillations become dominated by that periodic in 1/B, as we can see in the Landou plot of Fig. 4(b). It also seems that the oscillations appearing at 1/B 0.5 seems to be deviates from the linear behavior, which is expected when there is a lateral confinement as QWRs [14]. However, this deviation is not so clear at the moment due to the aperiodic part of the oscillations, and requires more careful investigation. We think that the aperiodic magnetioresistance oscillation and its suppression at high magnetic field is explained by universal conductance fluctuation in the semiconductor wires [15]. Negative magnetoresistance is also explained within the framework of weak localization in one-dimensional systems [16]. These results also suggest that there are still large potential fluctuations along QWRs in the present samples. Considering the lower electron mobility in the present bottom-side selectively doped structure than that in conventional structures typically (about 7:2 104 cm2/Vs [8]), this would be partly due to the lower quality of the bottom-side selectively doped structures. The lower quality would originate from the lower quality of so-called bottom (GaAs-on-AlGaAs) interfaces, as compared to the top (AlGaAs-on-GaAs) interface of the channel, and segregation of impurity from doped AlGaAs layers to GaAs channel. Optimization of the growth conditions is required to realize high-quality quantum nanostructures utilizing bottom-side selectively doped structures.
4. Conclusion We demonstrated the fabrication of very narrow GaAs QWRs formed by SA-MOVPE. Based on the estimation of geometrical wire width and two-terminal conductivity measurement, we concluded that QWRs
with effective wire width <75 nm was realized by adopting bottom-side selective doped structures. which is narrowest among conducting QWRs formed by SA-MOVPE. Although the improvements in the quality of grown layers are still required, bottom-side selective doping scheme is effective to realize quantum nanostructures with extremely small size.
Acknowledgements The authors are grateful for stimulating discussions with Prof. Hasegawa. This work is partly financially supported by a Grant-in-Aid for Scientific Research by Japan Society of Promotion of Science.
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