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Magnetic field sensitivity of In0.75Ga0.25As Hall nanoprobes
Materials Science and Engineering B 147 (2008) 148–151
Magnetic field sensitivity of In0.75Ga0.25As Hall nanoprobes Andrea Candini a,∗ , Franco Carillo c , Giorgio Biasiol b , Pasqualantonio Pingue c , Marco Affronte a , Lucia Sorba b,c a
CNR-INFM S3 National Research Center and Dipartimento di Fisica, Universit´a di Modena e Reggio Emilia, I-41100 Modena, Italy b CNR-INFM National Laboratory TASC, Area Science Park, I-34012 Trieste, Italy c CNR-INFM National Research Center NEST and Scuola Normale Superiore, I-56100 Pisa, Italy Received 4 July 2007; received in revised form 31 August 2007; accepted 7 September 2007
Abstract We have fabricated and characterized Hall probes on an In0.75 Al0.25 As/In0.75 Ga0.25 As two-dimensional electron gas with lateral sizes down to 100 nm. We studied the dependence of the low temperature (4 K) magnetic field sensitivity on the probe size, showing that the best flux sensitivity is achieved by devices of ≈ 200 nm, employing highly doped systems (n ∼ 1012 cm−2 ). Hall bars with sizes down to the range of 200–250 nm show a magnetic field sensitivity of a few Gauss, corresponding to a flux sensitivity equal to ≈ 10−2 Φ0 . © 2007 Elsevier B.V. All rights reserved. Keywords: Hall probes; Magnetic sensors; Semiconductor nano-devices
1. Introduction In today’s need for technology miniaturization, one of the most challenging achievements is to develop techniques for magnetic measurements at the nano-scale, capable to detect even single nano-objects [1]. Among all the experimental methods, Hall effect-based magnetometers and scanning probe microscopes (and in particular high sensitive sensors made of two-dimensional electron gas (2DEG) III/V semiconductor heterostructures) continue to attract a lot of interest, being non-invasive and operating in a very broad range of temperatures and applied magnetic fields [2–5]. Even single spin sensibility can be achieved if the size of the sensor is reduced down to the 10 nm scale, maintaining low level noise [6,7]. Unfortunately, the field sensitivity of semiconductor Hall sensors is known to rapidly deteriorate when the size is reduced to the submicron range. The best moment sensitivity achieved so far was ≈ 105 μB , employing a 600 nm size GaAs/AlGaAs Hall gradiometer [8], while the best combination of magnetic field sensitivity and small size has been obtained with
∗
Corresponding author. Tel.: +39 059 205 5678; fax: +39 059 205 5651. E-mail address: [email protected] (A. Candini).
0921-5107/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2007.09.044
GaAs/AlGaAs scanning Hall probe with effective √ active area of 0.25 m × 0.25 m and noise level of 10−7 T / Hz below 77 K [9]. Very recently, GaAs/Alx Ga1−x As 2DEG probes as small as ≈ 100 nm have been demonstrated, with sensitivity significantly improved to few Gauss (at 8 K) by tuning a gate voltage over the sensor [10]. Many research efforts are also being spent to characterize different materials that may overcome the limitations of GaAs/AlGaAs heterostructures [11–15]. We have recently shown Hall probes made of Si-doped GaAs thin films and of Au as small as 100 nm, with field sensitivity in the Gauss range at room temperature [16]. 2DEG systems, however, remain optimal candidates because of the special combination of low carrier density n and high mobility μ. Small n is desirable for a large Hall coefficient RH = 1/ne, whereas high mobility is needed for higher conductance, reducing the electrical noise. In0.75 Ga0.25 As-based heterostructures show a zero Schottky barrier and this reduce the carrier depletion at the edge of patterned wires, allowing the fabrication of etched structures as small as 80 nm [17]. Charge depletion at the edges is also considered the main responsible for the rapid increase of the noise level in small semiconductor devices. Thus In0.75 Ga0.25 As-based heterostructures can be considered a valid choice for the fabrication of sensitive Hall magnetometers at low temperature.
A. Candini et al. / Materials Science and Engineering B 147 (2008) 148–151
149
In this paper we present the characterization of In0.75 Al0.25 / In0.75 Ga0.25 As 2DEG Hall bars of various sizes, down to 100 nm. We measured the low temperature (4 K) magnetic field sensitivity of each probe as a function of the size. 2. Fabrication process The devices studied in this work were grown by molecular beam epitaxy (MBE) on GaAs(1 0 0) substrates. A sequence of Inx Al1−x As layers of increasing In content was deposited to ensure lattice matching with a 10 nm thick In0.75 Ga0.25 As quantum well [18]. Conduction electrons are provided by a Sidoping layer separated from the well by an In0.75 Al0.25 As spacer. Two different heterostructures were employed: sample A (with a 20 nm thick spacer) has a carrier density nA = 5.0 × 1011 cm−2 and a mobility μA = 1.8 × 105 cm2 /V s, while sample B (with a 10 nm thick spacer) has nB = 9.7 × 1011 cm−2 and μB = 4.5 × 104 cm2 /V s. Charge and mobility data were evaluated from Hall measurements made at 1.5 K in the dark. The first fabrication step is the deposition and annealing of Ni/AuGe/Ni/Au Ohmic contacts. Subsequently electron beam lithography followed by thermal evaporation of Ti and lift off were employed to define a Ti mask of the Hall cross geometry on the surface of the semiconductor. Reactive ion etching with CH4 /Ar/H2 was then used to transfer the mask pattern to the sample and finally Ti was removed by wet chemical etching [17]. Fig. 1 shows a scanning electron microscope image of one of the smallest devices (active area ≈ 120 nm × 120 nm) studied in this work. 3. Experimental results Low temperature (4 K) classical Hall effect measurements were carried out in a commercial Quantum Design PPM System
Fig. 1. Scanning electron microscope image of a ∼ 120 nm Hall probe.
Fig. 2. Hall response Rxy to a perpendicular magnetic field of a 250 nm size Hall bar from sample B at 4 K. The driving current was 1 A. Inset: time trace of the same signal (driving current = 10 A; applied field = 0.2 T). The vertical bar indicates the electrical noise of the device (in ): this value is then calculated into Gauss using the measured Hall coefficient and considered as the magnetic field sensitivity of the probe (Bmin ).
using the internal P400 resistivity option. An alternating (8 Hz) current of 1 A was driven in the probes while a perpendicular magnetic field was applied to measure the Hall resistance Rxy . Leaving the field switched on, the time trace of the same signal was then recorded, considering the peak to peak value as the electrical noise level of each device (in ). This can be easily expressed in terms of magnetic field using the measured Hall coefficient RH (i.e. the slope of the Hall effect curve), giving out the “field sensitivity”, that is the minimum magnetic field (Bmin ) detectable by each type of probe. In Fig. 2 the behavior of a 250 nm size Hall probe is shown as an example: the main panel exhibits the Hall effect as a function of the applied field, while in the inset the corresponding time trace (with a fixed field equal to 0.2 T) and the resulting Bmin are reported. Since the Hall resistance is given by Rxy = VHall /I, where the Hall voltage VHall = RH IB, in principle the signal to noise ratio can be improved by simply applying higher driving currents I. However, above certain limits, larger values of I can lead to heating effects that typically worsen the behavior of the probe. Optimizing the driving current is then a crucial point. For this reason, noise measurements were made at different I values: for our submicron probes optimal parameters were found in a quite broad region, between 0.5 and 10 A. We have characterized several probes with various sizes from both samples: the resulting minimum detectable fields are summarized in Fig. 3 as a function of the probe size w. As shown, higher doped devices, while showing a worse sensitivity at the 10 m scale, become superior when the size is reduced below ≈ 500 nm. Two-dimensional electron systems with higher carrier concentration are thus preferable for the fabrication of nano-sized Hall sensors. Let us now consider only the probes from sample B, and have a closer look at the variation of the noise level with the size. Smaller probes show higher noise, however Hall bars with sizes of ≈200–250 nm still have a magnetic field sensitivity of
150
A. Candini et al. / Materials Science and Engineering B 147 (2008) 148–151
Fig. 4. Time traces for three probes of different sizes from sample B. Data were taken at 4 K and are offset for clarity. The driving current was 10 A for all three Hall bars. The corresponding minimum detectable fields are 15 m: 0.6 G; 210 nm: 8 G; 115 nm: 220 G.
Fig. 3. (a) Bmin (expressed in G) for probes of different sizes, obtained after optimization of the driving √ current I. Open circles: sample A; full circles: sample B. Dashed line is ∝ RS (where RS is calculated through the Ohm’s law) normalized to the value measured for the 15 m size probe from sample B. (b) Corresponding minimum detectable flux for each probe shown in (a), expressed in units of flux quantum (Φ0 = 2.07 × 10−15 T m2 ). Φmin is given by Bmin multiplied by the active area of the Hall bar.
the order of few Gauss. More important, the flux sensitivity, that is the quantity actually measured by a Hall sensor, is at least two order of magnitude better than for 15 m sized probes, and reaches a minimum for ≈ 200 nm sized Hall bars (lower panel of Fig. 3). Down to this size, the magnetic field sensitivity approximatively follows the dashed line√depicted in the upper panel of Fig. 3. This is given by ∝ 1/ w (where w is the width of the probe) and it is normalized to the value measured for the 15 m sized Hall bar. The line actually displays the same behavior expected √ for the resistance component of the noise spectrum √ √ (NRes ∝ RS ) since RS ∝ 1/ w, if RS (i.e. the series resistance of the device) is calculated through the Ohm’s law. Below ≈ 200 nm data points fall considerably far away from the calculated line, pointing out that various sources of noise are coming into play or starting to show a different dependence with w and drastically reducing the magnetic sensitivity of the smallest devices. This is also confirmed by looking at the Hall signal time traces of three different probes shown in Fig. 4: when the lateral size is halved going from the 210 nm Hall bar to the 115 one, the height of the random jumps (i.e. the noise level) raises more than 30 times. 4. Discussion It is widely known that various sources of noise (mainly 1/f like components) play a dominant role in small semiconductor
structures, affecting the electrical conductivity. Such components are expected to generally increase with miniaturization, making the fabrication of high quality devices with sizes in the nanometer-scale a difficult task. However, the actual dependence is still fairly studied. When working at liquid helium temperature, noise from electron trapping by DX centers (deep donors levels) is frozen out [19], and the main source of fluctuations in the electrical signal is generally associated with switching processes related to remote impurities [20,21]. As recently shown by Muller et al., shrinking the probe size lowers the degree of averaging between the impurities, eventually leading to a point where only an individual trap is the dominant source of noise [22]. One could expect that the reduced ensemble averaging is going to increase the level of fluctuations and this was indeed observed [23]. Another mechanism to explain the strong size dependence of the noise could originate from the small number of electrons in the active area, i.e. the number of carriers being trapped becomes more and more relevant as the size is reduced, affecting the conductivity. Our data are consistent with the above-mentioned mechanisms, confirming a strong dependence of the Hall signal noise on the probe size, that becomes even more pronounced in the smallest devices. Finally, it is worth to draw attention to the fact that while Muller et al. found the abrupt increase in the fluctuations intensity for devices with sizes below w ∼ 0.7–0.45 m [21,22], a similar feature is observed by us only when the probe size is reduced below ∼ 0.25 m. This has to be ascribed to a lower degree of charge depletion present in our structures with respect to the GaAs/AlGaAs probes. 5. Conclusions We have fabricated Hall probes made of In0.75 Al0.25 As/ In0.75 Ga0.25 As two-dimensional electron gases as small as ≈ 100 nm and measured their magnetic field sensitivity at low temperature. We showed that, especially in the smallest devices, various sources of noise start to be activated and the intensity
A. Candini et al. / Materials Science and Engineering B 147 (2008) 148–151
of the random fluctuations in the Hall signal rapidly increases with size reduction. However, down √to ≈ 200–250 nm, the noise level approximatively scales as 1/ w, making this size optimal for the fabrication of our Hall sensors, since the flux sensitivity shows its minimum. Indeed, while the detectable field approxi√ matively scales as 1/ w, the active area is reduced as w2 . Our best flux sensitivity (Φmin ∼ 10−2 Φ0 ) is achieved for highly doped (n = 9.68 × 1011 cm−2 ) probes of ≈ 200 nm size, that show a magnetic field sensitivity of a few Gauss. Acknowledgments This work was developed within the framework of the WP4.2 activities of the EU Network of Excellence MAGMANet (contract No 515767). References [1] J.-P. Cleuziou, W. Wernsdorfer, V. Bouchiat, T. Ondracuhu, M. Monthioux, Nat. Nanotechnol. 1 (2006) 53. [2] For a comprehensive review on Hall effect sensor, see: G. Boero, M. Demierre, P.-A. Besse, R.S. Popovic, Sens. Actuators A 106 (2003) 314–320, and references therein. [3] A.D. Kent, S. von Moln´ar, S. Gider, D.D. Awschalom, J. Appl. Phys. 76 (1994) 6656–6660. [4] A.M. Chang, H.D. Hallen, L. Harriott, H.F. Hess, H.L. Kao, J. Kwo, R.E. Miller, R. Wolfe, J. van der Ziel, Appl. Phys. Lett. 61 (1992) 1974–1976. [5] A. Oral, S.J. Bending, M. Henini, Appl. Phys. Lett. 69 (1996) 1324– 1326. [6] A.K. Geim, S.V. Dubonos, J.G.S. Lok, I.V. Grigorieva, J.C. Maan, L. Theil, P.E. Lindelof, Appl. Phys. Lett. 71 (1997) 2379–2381. [7] J. Jinshuang, L. Xin-Qi, Appl. Phys. Lett. 86 (2005) 143504.
151
[8] Y. Li, P. Xiong, S. von Moln´ar, S. Wirth, Y. Ohno, H. Ohno, Appl. Phys. Lett. 80 (2002) 4644–4646. [9] A. Oral, J.C. Barnard, S.J. Bending, I.I. Kaya, S. Ooi, T. Tamegai, M. Henini, Phys. Rev. Lett. 80 (1998) 3610–3614. [10] C.W. Hicks, L. Luan, K.A. Moler, E. Zeldov, H. Strikman, Appl. Phys. Lett. 90 (2007) 133512. [11] K.S. Novoselov, S.V. Morozov, S.V. Dubonos, M. Missous, A.O. Volkov, D.A. Christian, A.K. Geim, J. Appl. Phys. 93 (2003) 10053– 10057. [12] A. Sandhu, H. Masuda, A. Oral, S.J. Bending, A. Yamada, M. Konagai, Ultramicroscopy 91 (2002) 97–101. [13] A. Pross, A.I. Crisan, S.J. Bending, V. Mosser, M. Konczykowski, J. Appl. Phys. 97 (2005) 096105. [14] D. Petit, D. Atkinson, S. Johnston, D. Wood, R.P. Cowborn, IEE Proc. Sci. Meas. Technol. 151 (2004) 127–130. [15] A. Sandhu, K. Kurosawa, M. Dede, A. Oral, Jpn. J. Appl. Phys. 43 (2004) 777–778. [16] A. Candini, G.C. Gazzadi, A. di Bona, M. Affronte, D. Ercolani, G. Biasiol, L. Sorba, Nanotechnology 17 (2006) 2105. [17] F. Carillo, G. Biasiol, D. Frustaglia, F. Giazotto, L. Sorba, F. Beltram, Physica E 32 (2006) 53–56. [18] F. Capotondi, G. Biasiol, D. Ercolani, V. Grillo, E. Carlino, F. Romanato, L. Sorba, Thin Solid Films 484 (2005) 400. [19] J.R. Kirtley, T.N. Theis, P.M. Mooney, S.L. Wright, J. Appl. Phys. 63 (1988) 1541. [20] D.H. Cobden, A. Savchenko, M. Pepper, N.K. Patel, D.A. Ritchie, J.E.F. Frost, G.A.C. Jones, Phys. Rev. Lett. 69 (1992) 502. [21] Y. Li, C. Ren, P. Xiong, S. von Moln´ar, Y. Ohno, H. Ono, Phys. Rev. Lett. 93 (2004) 246602. [22] J. Muller, S. von Moln´ar, Y. Ohno, H. Ono, Phys. Rev. Lett. 96 (2006) 186601. [23] One should look at Fig. 1 in Ref. [22], where noise spectra of a probe with size w ∼ 5 m and one with w ∼ 0.45 m are shown. In Fig. 1 of Ref. [21] a similar probe, but with an intermediate size w ∼ 0.7 m, is also presented.
Magnetic field sensitivity of In0.75Ga0.25As Hall nanoprobes Andrea Candini a,∗ , Franco Carillo c , Giorgio Biasiol b , Pasqualantonio Pingue c , Marco Affronte a , Lucia Sorba b,c a
CNR-INFM S3 National Research Center and Dipartimento di Fisica, Universit´a di Modena e Reggio Emilia, I-41100 Modena, Italy b CNR-INFM National Laboratory TASC, Area Science Park, I-34012 Trieste, Italy c CNR-INFM National Research Center NEST and Scuola Normale Superiore, I-56100 Pisa, Italy Received 4 July 2007; received in revised form 31 August 2007; accepted 7 September 2007
Abstract We have fabricated and characterized Hall probes on an In0.75 Al0.25 As/In0.75 Ga0.25 As two-dimensional electron gas with lateral sizes down to 100 nm. We studied the dependence of the low temperature (4 K) magnetic field sensitivity on the probe size, showing that the best flux sensitivity is achieved by devices of ≈ 200 nm, employing highly doped systems (n ∼ 1012 cm−2 ). Hall bars with sizes down to the range of 200–250 nm show a magnetic field sensitivity of a few Gauss, corresponding to a flux sensitivity equal to ≈ 10−2 Φ0 . © 2007 Elsevier B.V. All rights reserved. Keywords: Hall probes; Magnetic sensors; Semiconductor nano-devices
1. Introduction In today’s need for technology miniaturization, one of the most challenging achievements is to develop techniques for magnetic measurements at the nano-scale, capable to detect even single nano-objects [1]. Among all the experimental methods, Hall effect-based magnetometers and scanning probe microscopes (and in particular high sensitive sensors made of two-dimensional electron gas (2DEG) III/V semiconductor heterostructures) continue to attract a lot of interest, being non-invasive and operating in a very broad range of temperatures and applied magnetic fields [2–5]. Even single spin sensibility can be achieved if the size of the sensor is reduced down to the 10 nm scale, maintaining low level noise [6,7]. Unfortunately, the field sensitivity of semiconductor Hall sensors is known to rapidly deteriorate when the size is reduced to the submicron range. The best moment sensitivity achieved so far was ≈ 105 μB , employing a 600 nm size GaAs/AlGaAs Hall gradiometer [8], while the best combination of magnetic field sensitivity and small size has been obtained with
∗
Corresponding author. Tel.: +39 059 205 5678; fax: +39 059 205 5651. E-mail address: [email protected] (A. Candini).
0921-5107/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2007.09.044
GaAs/AlGaAs scanning Hall probe with effective √ active area of 0.25 m × 0.25 m and noise level of 10−7 T / Hz below 77 K [9]. Very recently, GaAs/Alx Ga1−x As 2DEG probes as small as ≈ 100 nm have been demonstrated, with sensitivity significantly improved to few Gauss (at 8 K) by tuning a gate voltage over the sensor [10]. Many research efforts are also being spent to characterize different materials that may overcome the limitations of GaAs/AlGaAs heterostructures [11–15]. We have recently shown Hall probes made of Si-doped GaAs thin films and of Au as small as 100 nm, with field sensitivity in the Gauss range at room temperature [16]. 2DEG systems, however, remain optimal candidates because of the special combination of low carrier density n and high mobility μ. Small n is desirable for a large Hall coefficient RH = 1/ne, whereas high mobility is needed for higher conductance, reducing the electrical noise. In0.75 Ga0.25 As-based heterostructures show a zero Schottky barrier and this reduce the carrier depletion at the edge of patterned wires, allowing the fabrication of etched structures as small as 80 nm [17]. Charge depletion at the edges is also considered the main responsible for the rapid increase of the noise level in small semiconductor devices. Thus In0.75 Ga0.25 As-based heterostructures can be considered a valid choice for the fabrication of sensitive Hall magnetometers at low temperature.
A. Candini et al. / Materials Science and Engineering B 147 (2008) 148–151
149
In this paper we present the characterization of In0.75 Al0.25 / In0.75 Ga0.25 As 2DEG Hall bars of various sizes, down to 100 nm. We measured the low temperature (4 K) magnetic field sensitivity of each probe as a function of the size. 2. Fabrication process The devices studied in this work were grown by molecular beam epitaxy (MBE) on GaAs(1 0 0) substrates. A sequence of Inx Al1−x As layers of increasing In content was deposited to ensure lattice matching with a 10 nm thick In0.75 Ga0.25 As quantum well [18]. Conduction electrons are provided by a Sidoping layer separated from the well by an In0.75 Al0.25 As spacer. Two different heterostructures were employed: sample A (with a 20 nm thick spacer) has a carrier density nA = 5.0 × 1011 cm−2 and a mobility μA = 1.8 × 105 cm2 /V s, while sample B (with a 10 nm thick spacer) has nB = 9.7 × 1011 cm−2 and μB = 4.5 × 104 cm2 /V s. Charge and mobility data were evaluated from Hall measurements made at 1.5 K in the dark. The first fabrication step is the deposition and annealing of Ni/AuGe/Ni/Au Ohmic contacts. Subsequently electron beam lithography followed by thermal evaporation of Ti and lift off were employed to define a Ti mask of the Hall cross geometry on the surface of the semiconductor. Reactive ion etching with CH4 /Ar/H2 was then used to transfer the mask pattern to the sample and finally Ti was removed by wet chemical etching [17]. Fig. 1 shows a scanning electron microscope image of one of the smallest devices (active area ≈ 120 nm × 120 nm) studied in this work. 3. Experimental results Low temperature (4 K) classical Hall effect measurements were carried out in a commercial Quantum Design PPM System
Fig. 1. Scanning electron microscope image of a ∼ 120 nm Hall probe.
Fig. 2. Hall response Rxy to a perpendicular magnetic field of a 250 nm size Hall bar from sample B at 4 K. The driving current was 1 A. Inset: time trace of the same signal (driving current = 10 A; applied field = 0.2 T). The vertical bar indicates the electrical noise of the device (in ): this value is then calculated into Gauss using the measured Hall coefficient and considered as the magnetic field sensitivity of the probe (Bmin ).
using the internal P400 resistivity option. An alternating (8 Hz) current of 1 A was driven in the probes while a perpendicular magnetic field was applied to measure the Hall resistance Rxy . Leaving the field switched on, the time trace of the same signal was then recorded, considering the peak to peak value as the electrical noise level of each device (in ). This can be easily expressed in terms of magnetic field using the measured Hall coefficient RH (i.e. the slope of the Hall effect curve), giving out the “field sensitivity”, that is the minimum magnetic field (Bmin ) detectable by each type of probe. In Fig. 2 the behavior of a 250 nm size Hall probe is shown as an example: the main panel exhibits the Hall effect as a function of the applied field, while in the inset the corresponding time trace (with a fixed field equal to 0.2 T) and the resulting Bmin are reported. Since the Hall resistance is given by Rxy = VHall /I, where the Hall voltage VHall = RH IB, in principle the signal to noise ratio can be improved by simply applying higher driving currents I. However, above certain limits, larger values of I can lead to heating effects that typically worsen the behavior of the probe. Optimizing the driving current is then a crucial point. For this reason, noise measurements were made at different I values: for our submicron probes optimal parameters were found in a quite broad region, between 0.5 and 10 A. We have characterized several probes with various sizes from both samples: the resulting minimum detectable fields are summarized in Fig. 3 as a function of the probe size w. As shown, higher doped devices, while showing a worse sensitivity at the 10 m scale, become superior when the size is reduced below ≈ 500 nm. Two-dimensional electron systems with higher carrier concentration are thus preferable for the fabrication of nano-sized Hall sensors. Let us now consider only the probes from sample B, and have a closer look at the variation of the noise level with the size. Smaller probes show higher noise, however Hall bars with sizes of ≈200–250 nm still have a magnetic field sensitivity of
150
A. Candini et al. / Materials Science and Engineering B 147 (2008) 148–151
Fig. 4. Time traces for three probes of different sizes from sample B. Data were taken at 4 K and are offset for clarity. The driving current was 10 A for all three Hall bars. The corresponding minimum detectable fields are 15 m: 0.6 G; 210 nm: 8 G; 115 nm: 220 G.
Fig. 3. (a) Bmin (expressed in G) for probes of different sizes, obtained after optimization of the driving √ current I. Open circles: sample A; full circles: sample B. Dashed line is ∝ RS (where RS is calculated through the Ohm’s law) normalized to the value measured for the 15 m size probe from sample B. (b) Corresponding minimum detectable flux for each probe shown in (a), expressed in units of flux quantum (Φ0 = 2.07 × 10−15 T m2 ). Φmin is given by Bmin multiplied by the active area of the Hall bar.
the order of few Gauss. More important, the flux sensitivity, that is the quantity actually measured by a Hall sensor, is at least two order of magnitude better than for 15 m sized probes, and reaches a minimum for ≈ 200 nm sized Hall bars (lower panel of Fig. 3). Down to this size, the magnetic field sensitivity approximatively follows the dashed line√depicted in the upper panel of Fig. 3. This is given by ∝ 1/ w (where w is the width of the probe) and it is normalized to the value measured for the 15 m sized Hall bar. The line actually displays the same behavior expected √ for the resistance component of the noise spectrum √ √ (NRes ∝ RS ) since RS ∝ 1/ w, if RS (i.e. the series resistance of the device) is calculated through the Ohm’s law. Below ≈ 200 nm data points fall considerably far away from the calculated line, pointing out that various sources of noise are coming into play or starting to show a different dependence with w and drastically reducing the magnetic sensitivity of the smallest devices. This is also confirmed by looking at the Hall signal time traces of three different probes shown in Fig. 4: when the lateral size is halved going from the 210 nm Hall bar to the 115 one, the height of the random jumps (i.e. the noise level) raises more than 30 times. 4. Discussion It is widely known that various sources of noise (mainly 1/f like components) play a dominant role in small semiconductor
structures, affecting the electrical conductivity. Such components are expected to generally increase with miniaturization, making the fabrication of high quality devices with sizes in the nanometer-scale a difficult task. However, the actual dependence is still fairly studied. When working at liquid helium temperature, noise from electron trapping by DX centers (deep donors levels) is frozen out [19], and the main source of fluctuations in the electrical signal is generally associated with switching processes related to remote impurities [20,21]. As recently shown by Muller et al., shrinking the probe size lowers the degree of averaging between the impurities, eventually leading to a point where only an individual trap is the dominant source of noise [22]. One could expect that the reduced ensemble averaging is going to increase the level of fluctuations and this was indeed observed [23]. Another mechanism to explain the strong size dependence of the noise could originate from the small number of electrons in the active area, i.e. the number of carriers being trapped becomes more and more relevant as the size is reduced, affecting the conductivity. Our data are consistent with the above-mentioned mechanisms, confirming a strong dependence of the Hall signal noise on the probe size, that becomes even more pronounced in the smallest devices. Finally, it is worth to draw attention to the fact that while Muller et al. found the abrupt increase in the fluctuations intensity for devices with sizes below w ∼ 0.7–0.45 m [21,22], a similar feature is observed by us only when the probe size is reduced below ∼ 0.25 m. This has to be ascribed to a lower degree of charge depletion present in our structures with respect to the GaAs/AlGaAs probes. 5. Conclusions We have fabricated Hall probes made of In0.75 Al0.25 As/ In0.75 Ga0.25 As two-dimensional electron gases as small as ≈ 100 nm and measured their magnetic field sensitivity at low temperature. We showed that, especially in the smallest devices, various sources of noise start to be activated and the intensity
A. Candini et al. / Materials Science and Engineering B 147 (2008) 148–151
of the random fluctuations in the Hall signal rapidly increases with size reduction. However, down √to ≈ 200–250 nm, the noise level approximatively scales as 1/ w, making this size optimal for the fabrication of our Hall sensors, since the flux sensitivity shows its minimum. Indeed, while the detectable field approxi√ matively scales as 1/ w, the active area is reduced as w2 . Our best flux sensitivity (Φmin ∼ 10−2 Φ0 ) is achieved for highly doped (n = 9.68 × 1011 cm−2 ) probes of ≈ 200 nm size, that show a magnetic field sensitivity of a few Gauss. Acknowledgments This work was developed within the framework of the WP4.2 activities of the EU Network of Excellence MAGMANet (contract No 515767). References [1] J.-P. Cleuziou, W. Wernsdorfer, V. Bouchiat, T. Ondracuhu, M. Monthioux, Nat. Nanotechnol. 1 (2006) 53. [2] For a comprehensive review on Hall effect sensor, see: G. Boero, M. Demierre, P.-A. Besse, R.S. Popovic, Sens. Actuators A 106 (2003) 314–320, and references therein. [3] A.D. Kent, S. von Moln´ar, S. Gider, D.D. Awschalom, J. Appl. Phys. 76 (1994) 6656–6660. [4] A.M. Chang, H.D. Hallen, L. Harriott, H.F. Hess, H.L. Kao, J. Kwo, R.E. Miller, R. Wolfe, J. van der Ziel, Appl. Phys. Lett. 61 (1992) 1974–1976. [5] A. Oral, S.J. Bending, M. Henini, Appl. Phys. Lett. 69 (1996) 1324– 1326. [6] A.K. Geim, S.V. Dubonos, J.G.S. Lok, I.V. Grigorieva, J.C. Maan, L. Theil, P.E. Lindelof, Appl. Phys. Lett. 71 (1997) 2379–2381. [7] J. Jinshuang, L. Xin-Qi, Appl. Phys. Lett. 86 (2005) 143504.
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[8] Y. Li, P. Xiong, S. von Moln´ar, S. Wirth, Y. Ohno, H. Ohno, Appl. Phys. Lett. 80 (2002) 4644–4646. [9] A. Oral, J.C. Barnard, S.J. Bending, I.I. Kaya, S. Ooi, T. Tamegai, M. Henini, Phys. Rev. Lett. 80 (1998) 3610–3614. [10] C.W. Hicks, L. Luan, K.A. Moler, E. Zeldov, H. Strikman, Appl. Phys. Lett. 90 (2007) 133512. [11] K.S. Novoselov, S.V. Morozov, S.V. Dubonos, M. Missous, A.O. Volkov, D.A. Christian, A.K. Geim, J. Appl. Phys. 93 (2003) 10053– 10057. [12] A. Sandhu, H. Masuda, A. Oral, S.J. Bending, A. Yamada, M. Konagai, Ultramicroscopy 91 (2002) 97–101. [13] A. Pross, A.I. Crisan, S.J. Bending, V. Mosser, M. Konczykowski, J. Appl. Phys. 97 (2005) 096105. [14] D. Petit, D. Atkinson, S. Johnston, D. Wood, R.P. Cowborn, IEE Proc. Sci. Meas. Technol. 151 (2004) 127–130. [15] A. Sandhu, K. Kurosawa, M. Dede, A. Oral, Jpn. J. Appl. Phys. 43 (2004) 777–778. [16] A. Candini, G.C. Gazzadi, A. di Bona, M. Affronte, D. Ercolani, G. Biasiol, L. Sorba, Nanotechnology 17 (2006) 2105. [17] F. Carillo, G. Biasiol, D. Frustaglia, F. Giazotto, L. Sorba, F. Beltram, Physica E 32 (2006) 53–56. [18] F. Capotondi, G. Biasiol, D. Ercolani, V. Grillo, E. Carlino, F. Romanato, L. Sorba, Thin Solid Films 484 (2005) 400. [19] J.R. Kirtley, T.N. Theis, P.M. Mooney, S.L. Wright, J. Appl. Phys. 63 (1988) 1541. [20] D.H. Cobden, A. Savchenko, M. Pepper, N.K. Patel, D.A. Ritchie, J.E.F. Frost, G.A.C. Jones, Phys. Rev. Lett. 69 (1992) 502. [21] Y. Li, C. Ren, P. Xiong, S. von Moln´ar, Y. Ohno, H. Ono, Phys. Rev. Lett. 93 (2004) 246602. [22] J. Muller, S. von Moln´ar, Y. Ohno, H. Ono, Phys. Rev. Lett. 96 (2006) 186601. [23] One should look at Fig. 1 in Ref. [22], where noise spectra of a probe with size w ∼ 5 m and one with w ∼ 0.45 m are shown. In Fig. 1 of Ref. [21] a similar probe, but with an intermediate size w ∼ 0.7 m, is also presented.