Hall bar curve. The following features are readily apparent. .... [2] Ismail K, Arafa M, Saenger K L, Chu J O and Meyerson B S. 1995 Appl. Phys. Lett. 66 1077â9.
INSTITUTE OF PHYSICS PUBLISHING
NANOTECHNOLOGY
Nanotechnology 12 (2001) 132–135
www.iop.org/Journals/na
PII: S0957-4484(01)21091-5
Investigation of SiGe-heterostructure nanowires E Giovine1 , A Notargiacomo1 , L Di Gaspare1 , E Palange1 , F Evangelisti1 , R Leoni2 , G Castellano2 , G Torrioli2 and V Foglietti2 1
Unit`a INFM, Dipartimento di Fisica ‘E. Amaldi’, Universit`a di Roma TRE, Via Vasca Navale 84, 00146 Roma, Italy 2 Istituto di Elettronica dello Stato Solido, IESS-CNR, Via Cineto Romano 42, 00156 Roma, Italy
Received 18 January 2001, in final form 24 April 2001 Abstract Transport characterizations of wires obtained by electron beam lithography and etching of (100) Si/SiGe heterostructures with a high-mobility two-dimensional electron gas are reported. Depending on the wire width, two different regimes for the electrical transport are found. Wires with a width larger than ∼200 nm exhibit metallic behaviour in the quasi-ballistic regime. The conductance dependence on the wire width reveals the presence of a depletion layer, ∼100 nm thick, on each etched side of the wire. The wires of width smaller than 200 nm have very large resistance and two different behaviours. The first kind of wires exhibit a zero-current region, compatible with a Coulomb blockade effect involving multiple tunnel junctions or with a space-charge limited current. Other wires are insulating up to applied voltages larger than 5–6 V and their I –V characteristics can be fitted by the functional dependence of voltage-induced tunnelling of Fowler–Nordheim type.
1. Introduction Presently there is widespread interest in establishing the potentiality of Si-based quantum devices in nanoelectronics, in particular for single-electron memory applications. Therefore, it is of great importance to investigate mesoscopic physics in systems, such as SiGe heterostructures, compatible with Si technology. Indeed, the capability of depositing good quality SiGe epitaxial layers on Si(100) has resulted in twodimensional (2D) systems [1–3] that can be used for the realization of mesoscopic devices, in particular high-mobility quantum wires [4]. As a step toward the realization of single-electron devices on silicon, in this paper we have produced and characterized wires obtained by electron beam lithography and etching.
2. Experimental In order to realize 2D electron gases, a virtual substrate was obtained by growing a compositionally graded Si1−x Gex buffer layer on a Si(001) wafer, followed by a thick relaxed layer of x = 0.19 fixed composition. The 2DEGs were obtained by depositing on the virtual substrate the following sequence 0957-4484/01/020132+04$30.00
© 2001 IOP Publishing Ltd
of layers: (i) a strained Si channel layer 10 nm thick, (ii) a Si0.81 Ge0.19 spacer layer 5 nm thick with x = 0.19 and (iii) an n-doped Si0.81 Ge0.19 layer 5 nm thick. The structures were completed by a second, 35 nm thick, Si0.81 Ge0.19 spacer layer and, finally, a 15 nm Si cap layer. The 2DEG has a carrier density of 8.8 × 1011 cm−2 and a low-field mobility of 0.9 × 105 cm2 V−1 s−1 . Mesas were defined to delimit an area of the 2DEG containing the contact pads used for electrical measurements. In the inner region of the mesa, as shown in figure 1(a), 4 µm long wires were fabricated by electron beam lithography followed by reactive ion etching. The wire-width ranges from 100 to 1300 nm. A SEM micrograph of a 100 nm wire is presented in figure 1(b). In order to correct for contact non-ohmicity, a fourprobe configuration was adopted for the electrical transport characterization.
3. Electrical transport measurements Typical four-probe I –V characteristics are shown in figure 2 for three wires of different width W together with the 2DEG Hall bar curve. The following features are readily apparent. At
Printed in the UK
132
Investigation of SiGe-heterostructure nanowires 1,2x10-3 1,0x10 -3
G[S]
8,0x10-4 6,0x10-4 4,0x10 -4 2,0x10 -4 0,0 0
200
400
600 800 W[nm]
1000
1200
1400
Figure 3. Conductance as a function of the wire width at low field measured at 4.2 K. A width offset (∼200 nm) due to damages introduced by fabrication processes is apparent.
Figure 1. (a) Mesa delimiting the conducting 2DEG region with the EBL pattern for wire definition visible in the centre; (b) SEM micrograph of a 100 nm wire.
quite low in the narrower wires. Eventually, at still higher voltages, the current increases abruptly exhibiting an s-shaped characteristic in some cases (figure 2(b)). In the following we discuss, in more detail, the different behaviours. 3.1. Wide wires In figure 3 the low-field conductance is reported as a function of the wire width. We see that the dependence is linear and that there is an offset on the horizontal axis, indicating that the width must exceed a threshold value WC of about 200 nm for the wires to be conducting. Indeed, narrower wires exhibit a very high resistance at low field, as discussed later on. A zeroconductance offset is a common finding in etched wires [4, 5] and points to the presence of a band bending inducing a depletion of electrons in the region close to the wire lateral surfaces. The defect states induced by the etching process are likely to pin the Fermi level at the gap centre and trap the electrons at the wire lateral surfaces. Numerical simulations of the effect confirm that a surface state density of 1014 eV−1 cm−2 is required for producing the observed depletion width [6]. Considering now the high-field regime where current saturation occurs, the saturation drift velocity was determined by normalizing for the effective wire width. It was found that in all conducting wires the drift velocity saturates at a value vs = 6.5 × 106 cm s−1 , corresponding to a critical field Fc = 300 V cm−1 compatible with the phonon scattering process [7, 8]. 3.2. Narrow wires
Figure 2. (a) I –V curves for wire of 120, 330, 1300 nm measured at 4.2 K; (b) s-shaped characteristic exhibited at higher applied voltage.
low applied voltages (figure 2(a)) wider wires (W > ∼200 nm) are conducting while narrower wires (W < ∼200 nm) have very large resistance. At intermediate voltages (0.2–2 V) the current tends to saturate in the wider wires whereas it remains
The wires narrower than the critical width WC (∼200 nm) exhibit I –V characteristics of the kind reported in figure 4, with a central region of the curve where almost no current flows and the conduction starting when a positive/negative threshold voltage VT is reached. The conductance of the central region decreases as the temperature is reduced, i.e. the wires exhibit ‘insulating’ behaviour at small source–drain bias. We find that VT can have rather different values not correlated to the wire width, as exemplified by the two characteristics shown in figure 4 for two wires of similar width. We found that, roughly speaking, the samples can be grouped in two categories, one having VT in the tenths of a volt range (figure 4(a)) and the other 133
E Giovine et al
(a)
20
I [nA]
10
0 − 10 I = AV2 fit
− 20 − 0,8
− 0,4
(b)
0,0 V[V]
0,4
0,8
600
Figure 5. Schematic of the barrier potential along a wire narrower than WC : (a) small potential fluctuations and (b) large potential fluctuations.
400
I [nA]
200 0 − 200 − 400 − 600 −8
I = AV2 exp ( − B/V) fit −4
0 V[V]
4
8
Figure 4. I –V curves measured at 4.2 K for wire widths smaller than ∼200 nm. The main feature is an insulating behaviour: (a) till a few tenths of a volt or (b) several volts are applied. The wires are 115 and 110 nm wide, respectively.
with VT of several volts (figure 4(b)). The natural explanation for the ‘insulating’ behaviour is that, due to the lateral band bending, the wires narrower than Wc have the conduction band energy Ec higher than the Fermi level EF , as shown schematically in figure 5(a), and are completely depleted of electrons. Consequently, a barrier is present anywhere at the border between the 2DEG and the wire. Furthermore, it is very likely that the potential fluctuates along the wire, giving rise to a small ripple on the Ec profile as schematically depicted in figure 5. Potential fluctuations can originate from three kinds of disorder: fluctuation of the wire width, fluctuation of the dopant density and fluctuation of the surface defect density created by the wire etching process. In this model the difference of VT in similar wires is attributed to different barrier heights at the interface (2 DEG)/wire, which result from a possible variation, from wire to wire, of the density of defects at the lateral surfaces, induced by the etching process. This assumption is confirmed by the functional dependence of the two I – V characteristics of figure 4. Curve a is satisfactorily fitted by the I = AV 2 function typical of a spacecharge limited current and is, therefore, compatible with a negligibly small barrier height. Curve b is well reproduced by I = AV 2 exp(−B/V ) functional dependence, typical of the voltage-induced tunnelling of Fowler–Nordheim type. The estimated barrier is about 15 meV. An alternative explanation for the characteristics displayed in figure 4(a) could be in terms of Coulomb blockade 134
effects. Indeed, if the potential fluctuations along the wire are strong, regions where Ec < Ef can also be present, giving rise to an alternation of small metallic islands separated by potential barriers, as schematically depicted in figure 5(b). Similar models were proposed for III–V semiconductor quantum devices [9, 10] and for interpreting transport results in highly doped Si wires [11] in terms of the Coulomb blockade effect. The region V < VT would represent a Coulomb gap, resulting from the charging of the small islands present in the wires as a consequence of disorder. However, the amplitude of the non-conducting region is too large for a single-island Coulomb gap and should be explained as a tunnelling process through multiple islands [12]. In order to distinguish between the two alternative explanations it is necessary to apply a gate to the wires. We are presently working on this project.
4. Conclusions We have measured the I –V characteristics in the quasi-ballistic regime of wires fabricated on (100) Si/SiGe heterostructures with a high mobility 2D electron gas. A depletion layer has been found determining a critical width WC ∼ 200 nm. Wires wider than WC are metallic with a linear dependence of conductance on the wire width. Wires narrower than WC are insulating and exhibit a threshold voltage for conduction VT , which varies considerably from wire to wire and is attributed to a barrier present at the (2 DEG)/wire interface. The zero-current region of wires exhibiting small VT values is compatible with a Coulomb blockade effect involving multiple tunnel junctions or with a space-charge limited current. The I –V characteristics of large-VT wires can be fitted by the functional dependence of voltage-induced tunnelling of Fowler–Nordheim type.
References [1] Sch¨affler F 1997 Semicond. Sci. Technol. 12 1515–49 [2] Ismail K, Arafa M, Saenger K L, Chu J O and Meyerson B S 1995 Appl. Phys. Lett. 66 1077–9 [3] Churchill A C, Robbins D J, Wallis D J, Griffin N, Paul D L and Pidduck A J 1997 Semicond. Sci. Technol. 12 943–6 [4] Koester S J, Ismail K, Lee K Y and Chu J O 1996 Phys. Rev. B 54 10604–8
Investigation of SiGe-heterostructure nanowires
[5] Beaumont S P et al 1992 Phys. Scr. T 45 196 [6] Iannaccone G, Macucci M, Gennai S and Pellegrini B unpublished [7] Miyatsuji K, Ueda D, Masaki K, Yamakawa S and Hamaguchi C 1994 Semicond. Sci. Technol. 9 772–4 [8] Madhavi S, Venkataraman V, Sturm J C and Xie Y H 2000 Phys. Rev. B 61 16807–18
[9] Nixon J A and Davies J H 1990 Phys. Rev. B 41 7929–32 [10] Nixon J A, Davies J H and Baranger H U 1991 Phys. Rev. B 43 12638–41 [11] Ng V, Ahmed H and Shimada T 1998 Appl. Phys. Lett. 73 972–4 [12] Ng V, Ahmed H and Shimada T 1999 J. Appl. Phys. 86 6931–9
135
