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InP Hall sensor at 77 K
Microelectronic Engineering 51–52 (2000) 333–342 www.elsevier.nl / locate / mee
Approaching the pT range with a 2DEG InGaAs / InP Hall sensor at 77 K ´ Cambel a , *, Goran Karapetrov b , Peter Elias ´ˇ a , Stanislav Hasenohrl ¨ a, Vladimır b c d ´ Manka ˇ Wai-Kwong Kwok , Jochen Krause , Jan a
b
Institute of Electrical Engineering, Slovak Academy of Sciences, 842 39 Bratislava, Slovak Republic Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USA c ¨ ¨ , Julich , Germany Research Centre Julich d Institute of Measurement Science, Slovak Academy of Sciences, Bratislava, Slovak Republic
Abstract The noise of two-dimensional electron gas InGaAs / InP Hall sensors of various dimensions was studied. In the first part of the work we show that for large-scale sensors ( . 0.2 mm linear dimension) at 77 K and at 1 kHz, a sensitivity better then 1 nT can be achieved. The second part of present work deals with the noise measurements of 2 and 10 mm sensors dependent on bias current, frequency, applied magnetic field and temperature. It was found that the low-frequency noise of the 10 mm sensor rapidly increased for applied magnetic field, but the noise of the 2 mm sensor is a complicated function of temperature and magnetic field: for low temperatures and fields 1–3 T is the low-frequency noise of the sensor suppressed. 2000 Elsevier Science B.V. All rights reserved. Keywords: 2DEG Hall sensor; InGaAs / InP heterostructure; 1 /f noise
1. Introduction During the recent period Hall sensors based on III–V heterostructures have shown increased importance in magnetometry experiments [1–3] as well as in standard applications (CD controllers). Heterostructures, such as InGaAs / InP, exhibit excellent properties due to the spatial separation of the two-dimensional electron gas (2DEG) channel and the electron-supplying layer. In such structures, if prepared carefully, the limiting factor is low-frequency noise (LF). The origin of LF or 1 /f noise has not yet been fully understood [4]. For years it was thought that 1 /f noise was a problem stemming from semiconductor technology, and thus it was expected that improved technology should yield devices with lower noise. However, using small metallic samples, it was found later that 1 /f noise is present also in metals. Thirty years ago Hooge proposed the relation which collects a lot of experimental data on 1 /f noise: *Corresponding author. 0167-9317 / 00 / $ – see front matter PII: S0167-9317( 99 )00491-8
2000 Elsevier Science B.V. All rights reserved.
334
V. Cambel et al. / Microelectronic Engineering 51 – 52 (2000) 333 – 342
Ss 5 s 2 aH /( f N), where Ss is noise in a sample due to conductivity, s is the conductivity of the sample, f is the frequency, N is the number of electrons that contribute to the conductivity, and aH is the Hooge parameter (a normalized measure for the relative noise in different materials). From the relation 1 /f noise is independent on electron concentration, sample dimensions, and frequency range, and it is caused by conductivity fluctuations. But conductivity depends on electron concentration and mobility, and therefore conductivity fluctuations can be assumed to occur either as the consequence of mobility fluctuations (typical 1 /f or flicker noise) or as the result of a number of fluctuations of free carriers, produced by generation–recombination processes at levels in the forbidden band. During recent years a lot of work has been done on 1 /f noise in homogeneously doped bulk material. Using Matthiessen’s rule, the total Hooge parameter aH,tot can be divided into parts due to different scattering mechanisms, i.e., aH,phon is the part due to phonon scattering, aH,imp is the part due to impurity scattering. For materials of excellent quality the Hooge parameter aH,phon was determined at room temperatures. Crystals of poorer quality have always higher values of aH,phon . The Hooge parameter aH,imp expresses the noise contribution of the impurity scattering, and it is proportional to the dopant concentration [5]. In contrast to the bulk material, the 1 /f noise of 2DEG structures with undoped channels has not yet been so systematically studied, although some works have appeared recently [6]. Also, experimental study of the noise behaviour of 2DEG samples at low temperatures is missing. Moreover, the influence of external magnetic field on the 1 /f noise of such structures at low temperatures has not been studied yet. The aim of this work is 2-fold: first, to study the possibility for the preparation of large-area highly sensitive magnetic field 2DEG Hall sensors with a resolution better than 1 nT at 77 K for metallic construction integrity control and, second, to study experimentally the influence of external magnetic field on the 1 /f noise of micro-Hall sensors for various frequencies and operating currents at low temperatures (4.2–80 K).
2. Sensor preparation Two-dimensional electron gas (2DEG) Hall sensors of dimensions 2–1000 mm based on an InGaAs / InP heterostructure have been prepared and characterized. To reduce their noise, one has to suppress all the noise sources usually present in the semiconductor sensors [7]. Thermal noise is effectively suppressed in the 2DEG sensors by lowering the temperature to 77 K (2DEG mobility increases). Shot noise, caused by electrons crossing the potential barrier, is in our sensors completely eliminated by the preparation of high quality Au–Sn ohmic contacts. The quality of the contacts has been tested down to 4.2 K. To avoid generation–recombination noise, the 2DEG must be far enough apart from the surface and the heterostructure interface must have low density of traps (case of InGaAs / InP [8]). Special wafer cleaning has been used to avoid parallel conducting channels in the sensors. The presence of such parallel channels can be easily tested in the quantum Hall regime at 4.2 K. 1 /f noise is minimized by selecting an appropriate heterostructure — the InGaAs / InP interface has very low density of traps compared with other materials [8], by adjusting the 2DEG concentration (only one sub-band occupied), and by the increase of sensor dimensions (more electrons present in the system).
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Fig. 1. Heterostructure for the InGaAs / InP Hall probes.
The heterostructure was grown on (100) semi-insulating Fe-doped InP substrate at 6408C using low-pressure MOCVD equipment (AIXTRON 200). The active layer of the Hall sensor is formed by a triangular InGaAs quantum well. The heterostructure consists of a semi-insulating InP substrate, a 300 nm buffer layer, a 10 nm Si-doped InP layer, a 20 nm InP spacer, and a 160 nm active1cap InGaAs layer (Fig. 1). The 2DEG of a sheet concentration 5310 11 cm 22 at 4.2 K is created at the InGaAs / InP heterointerface. An Au–AuSn system was used for the ohmic and contact metallization of the sensors. Their topology was defined in the form of either a simple Greek cross of various active area (Fig. 2), or ladder-like arrays [9]. The sensors were electrically isolated by wet etching. Bias current was applied through current terminals, and the noise was measured differentially between voltage terminals A and B.
3. Results and discussion We first tested the noise properties using a set of samples with linear dimensions from 2 mm to 1 mm. The samples of dimensions 0.5 and 1 mm were not ideal from the topological point of view —
Fig. 2. Topology of the Hall probes. Dashed square is the active area; ohmic contacts are shown in dark grey.
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the length of the cross arms were only half of the length of the active area. The noise spectral density of the Hall terminals at 10 Hz, 1 kHz at 300 K and 77 K is expressed in THz 21 / 2 in Fig. 3; the voltage noise is converted to the magnetic field noise using the sensor sensitivity. The figure shows that: • 1 /N behaviour of the magnetic noise spectral density is confirmed in the probes for both temperatures 300 and 77 K; • noise is lower than 1 nT Hz 21 / 2 at 1 kHz and 77 K in probes with the active area of 2003200 mm; • in the probes with non-ideal Hall probe topology (sensors$0.5 mm) the 1 /f noise of the Hall terminals is increased — they ‘feel’ the noise of the current terminals; • in the smallest sensor the 1 /f noise is increased probably as the result of reduced real active area of the sensor (due to under-etching) as well as electron capture and emission at the 2DEG boundary.
Fig. 3. Dependence of the noise of the sensors vs. sensor linear dimension for 10 Hz, 1 kHz at 300 K, reps. 77 K.
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From the measured data Hooge parameter aH,tot , can also be evaluated for the set of probes. The results for temperatures 300 and 77 K are summarized in Fig. 4: • 300 K values of aH are above the Hooge parameter given by Handel’s quantum 1 /f noise theory developed for the calculation of the Hooge parameter in homogeneous bulk material (|2310 25 for InGaAs) [10]; • for the non-ideal Hall probe topology aH,tot of the Hall terminals increased drastically at 300 K as well as 77 K; • for Hall sensors at 77 K the value of aH,tot is slightly lower (|5310 26 ) than the value given by 25 Handel’s quantum 1 /f theory for bulk material (10 ). In comparison with Ref. [6] our aH,tot is higher at 300 K. In agreement with Ref. [6] we have tried to prepare an optimized InGaAs / InP heterostructure to minimize the noise. In our structure only one sub-band is occupied. On the other hand the penetration depth of the electron wave function is not
Fig. 4. Measured Hooge parameter aH tot meas vs. Hall sensor linear dimension for 300 and 77 K.
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minimized in the structure as we use the lattice matched heterostructure with a 53% content of In. Our minimum value of aH,tot at 300 K was achieved for the 3-mm sensor (4310 25 ), and at 77 K the minimum was achieved for the 200 mm sensor (5310 26 ). It has to be mentioned that the role of dimensionality has not yet been sufficiently clarified in the present 1 /f theories. More experimental and theoretical work has to be done in this field in the near future. To conclude this part, we have found that the pT region can be achieved using large-area cryogenic 2DEG InGaAs / InP sensors. In the following we will discuss the noise of micro-Hall sensors, which is important for all types of micromagnetometry experiment in which 2DEG Hall sensors are often used to evaluate very weak magnetic fields at low temperatures [1–3]. In the second part we discuss the noise properties of the 2 and 10 mm Hall probes in external magnetic fields at low temperatures. We have found a great difference in the behaviours of these two sensors at low temperatures.
4. Noise properties of 2 and 10 mm Hall sensors The galvanomagnetic characterisation of the 10 mm sensor has shown the typical behaviour of the InGaAs / InP 2DEG systems (Fig. 5). The electron concentration is approximately constant in the temperature interval investigated — in the entire interval all donors are ionizied and the electrons are captured by the quantum well. The electron mobility is limited due to alloy scattering (always present
Fig. 5. Mobility and electron concentration versus temperature for a 10 mm Hall sensor characterized.
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in ternary semiconductors) at lower temperatures, and for higher temperatures it is limited by polar optical phonons. The power spectral density (PSD) of the sensors was measured using a fast Fourier noise analyzer SR 760. The signal was first amplified using a low-noise preamplifier SR 560, and all the experimental conditions (temperature, bias current, magnetic field) were computer-controlled using a LabView program. During the measurement a lot of data have been collected. The PSD was taken for 2 and 10 mm Hall sensors for 10 various bias currents at magnetic fields 0, 0.1, 0.2, 0.5 1, 2, 3.1 and 5 T, all this at temteratures from 4.2–90 K with the steps 4 or 8 K. Moreover, at certain temperatures data for magnetic fields 0–5 T were taken with the step 0.2 T. In this paper only a part of the results is discussed.
5. Results and discussion All PSD measurements show that for both sensor dimensions, at a given temperature and magnetic field, the LF noise depends linearly on bias current through the sensor, except for very high currents, for which the LF noise increases rapidly. This rapid noise jump for large currents can be interpreted by the real space transfer of the heated electrons from the channel to the surface of the structure. Another dependence that was found is the slope of a noise spectrum that changes from 21 to 21.5, when the temperature of the sensor is decreased from |80 to |40 K. Fig. 6 shows a summary of the temperature dependence of the noise for a 10 mm sensor at 5 Hz for bias current 500 mA (the dependence is similar for lower currents). Here, the applied external magnetic field was a parameter. The noise of the sensor rapidly increases for increased magnetic field, and it is temperature independent for 4.2–30 K. This noise increase with magnetic field limits the dynamic range of the sensor. On the other hand, for temperatures higher than 30 K the magnetic-field dependence is similar but a rapid increase of the noise also with temperature is observed. Polar optical phonons emitted and absorbed by the 2DEG are probably responsible for this noise increase. The PSD of a 2 mm Hall sensor showed that its noise is a complicated function of temperature, frequency, and magnetic field applied. In the PSD there are strong oscillations that are suppressed by the magnetic field. The slope of the noise spectra changes from 21 (92 K) to 21.5 (48 K), which supports the idea that 1 /f spectra are partially caused also by trapping centres at the InGaAs boundary and not only by mobility fluctuations. Fig. 7 is a summarizing figure, like Fig. 6, but for a 2 mm Hall sensor with a 80 mA bias current applied (current density similar to the 10 mm sensor). The high-temperature part of the dependence follows the characteristics from the previous figure — there is evident a rapid increase of noise with increased temperature, which can be interpreted again by an enhanced emission and absorption of polar optical phonons. The only difference is that the magnetic field applied has much weaker influence on the noise of the 2 mm Hall sensor, and it increases the noise only for magnetic fields higher than 1 T. At low temperatures and for magnetic fields |1–3 T the role of the magnetic field is the opposite — the low frequency noise is suppressed for all bias currents supplied to the sensor. This unusual behaviour can be explained considering classical 1D transport of electrons in our structure. If the electron mean free path is comparable with the channel width, and if we assume that the noise is caused by the interaction of electrons with the channel boundary, then the magnetic field can lower the probability of the interaction of 2DEG with trapping centres at the boundary, the electron mean
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Fig. 6. Low-frequency noise (5 Hz) of the 10 mm Hall sensor versus temperature for bias current 500 mA, the magnetic field applied is the parameter.
free path can be increased and therefore the overall low frequency noise in the structure is suppressed. This surprising result can be utilized in magnetometry experiments in the future — the application of background magnetic field can be used to reduce the noise in such systems. But to confirm this assumption more experimental and theoretical work has to be done. Fig. 8 summarizes the noise data for the 2 mm Hall sensor versus magnetic field at 12 K. Bias current was in this case 120 mA. The noise at various frequencies is depicted here. The resulting noise characteristics of the sensor support the surprising behaviour of the LF part of the noise from Fig. 7 — the LF noise is suppressed for magnetic fields of 1–3 T. For higher frequencies the noise increases exponentially with applied magnetic field, and for 5 T the noise is in one order of magnitude higher than without applied magnetic field.
6. Conclusions In this work a study is presented on the noise of 2DEG InGaAs / InP Hall sensors of various dimensions. In the first part of the work we have shown that for the large-scale sensors (0.2 mm linear dimension) at 77 K and at 1 kHz a sensitivity better than 1 nT can be achieved.
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Fig. 7. Low-frequency noise of a 2 mm Hall sensor versus temperature at 5 Hz for bias current 80 mA, the magnetic field applied is the parameter.
The second part of the work deals with the noise properties of 2 and 10 mm sensors dependent on bias current, frequency, applied magnetic field and temperature. It was found that the LF noise depends linearly on bias current, for very high currents, increases rapidly — 2DEG reaches surface (observed for all temperatures). It was found that the LF noise of the 10 mm sensor rapidly increases for applied magnetic field, but the LF noise of the 2 mm sensor is a complicated function of temperature and magnetic field: for low temperatures and fields of |1–3 T the noise of the sensor is suppressed. In the near future more experimental and theoretical work has to be done in the field of noise properties of 2DEG micro-Hall sensors in external magnetic fields at low temperatures.
Acknowledgements This work was supported by project NATO SfP-972399 Magnetic Microscopy. The authors wish to ˇ for helpful discussions. thank Dr M. Mosko
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Fig. 8. Noise versus magnetic field applied for the 2 mm Hall sensor for 120 mA current at 12 K.
References [1] S.T. Stoddart, S.J. Bending et al., Phys. Rev. Lett. 71 (1993) 3854. [2] G. Karapetrov, V. Cambel, W.K. Kwok, R. Nikolova, G.W. Crabtree, H. Zheng, B.W. Veal, Contactless characterization of melt-textured superconducting junctions using micro hall sensor arrays, J. Appl. Phys. 86 (1999) 6282. [3] A. Oral, S.J. Bending, R.G. Humphreys, M. Henini, Superconduct. Sci. Technol. 10 (1997) 17. [4] C.M. Van Vliet, A survey of results and future prospects on quantum 1 / f noise and 1 / f noise in general, Solid-State Electronics 34 (1991) 1. [5] F.N. Hooge, 1 / f noise sources, IEEE Trans. Electron Devices 41 (1994) 1926. [6] J. Berntgen, K. Heime, W. Daumann, U. Auer, F.-J. Tegude, A. Matulionis, The 1 / f noise of InP based 2DEG devices and its dependence on mobility, IEEE Trans. Electron Devices 46 (1999) 194. [7] A. van der Ziel, A.D. van Rheenen, in: Noise in Electronic Circuits, Encyclopedia of Physical Science and Technology, Vol. 10, Academic Press, New York, 1992. [8] P. Viktorovitch, P. Rojo-Romeo, J.L. Leclercq, X. Letartre, J. Tardy, M. Oustric, M. Gendry, Low frequency noise sources in InAlAs / InGaAs MODFET’s, IEEE Trans. Electron Devices 43 (1996) 2085. ˇ Mozolova, ´ˇ R. Kudela, ´ ´ B. Olejnıkova, ´ ´ Z. ´ M. Majoros, ˇ J. Kvitkovic, ˇ P. Hudek, [9] V. Cambel, P. Elias, J. Novak, Preparation, characterization and application of microscopic Hall probe arrays, Sol. State Electron. 42 (1998) 247. [10] A. Van der Ziel, P.H. Handel, X. Zhu, K.H. Duh, A theory of the Hooge parameters in solid-state devices, IEEE Trans. Electron Devices 32 (1985) 667.
Approaching the pT range with a 2DEG InGaAs / InP Hall sensor at 77 K ´ Cambel a , *, Goran Karapetrov b , Peter Elias ´ˇ a , Stanislav Hasenohrl ¨ a, Vladimır b c d ´ Manka ˇ Wai-Kwong Kwok , Jochen Krause , Jan a
b
Institute of Electrical Engineering, Slovak Academy of Sciences, 842 39 Bratislava, Slovak Republic Materials Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, USA c ¨ ¨ , Julich , Germany Research Centre Julich d Institute of Measurement Science, Slovak Academy of Sciences, Bratislava, Slovak Republic
Abstract The noise of two-dimensional electron gas InGaAs / InP Hall sensors of various dimensions was studied. In the first part of the work we show that for large-scale sensors ( . 0.2 mm linear dimension) at 77 K and at 1 kHz, a sensitivity better then 1 nT can be achieved. The second part of present work deals with the noise measurements of 2 and 10 mm sensors dependent on bias current, frequency, applied magnetic field and temperature. It was found that the low-frequency noise of the 10 mm sensor rapidly increased for applied magnetic field, but the noise of the 2 mm sensor is a complicated function of temperature and magnetic field: for low temperatures and fields 1–3 T is the low-frequency noise of the sensor suppressed. 2000 Elsevier Science B.V. All rights reserved. Keywords: 2DEG Hall sensor; InGaAs / InP heterostructure; 1 /f noise
1. Introduction During the recent period Hall sensors based on III–V heterostructures have shown increased importance in magnetometry experiments [1–3] as well as in standard applications (CD controllers). Heterostructures, such as InGaAs / InP, exhibit excellent properties due to the spatial separation of the two-dimensional electron gas (2DEG) channel and the electron-supplying layer. In such structures, if prepared carefully, the limiting factor is low-frequency noise (LF). The origin of LF or 1 /f noise has not yet been fully understood [4]. For years it was thought that 1 /f noise was a problem stemming from semiconductor technology, and thus it was expected that improved technology should yield devices with lower noise. However, using small metallic samples, it was found later that 1 /f noise is present also in metals. Thirty years ago Hooge proposed the relation which collects a lot of experimental data on 1 /f noise: *Corresponding author. 0167-9317 / 00 / $ – see front matter PII: S0167-9317( 99 )00491-8
2000 Elsevier Science B.V. All rights reserved.
334
V. Cambel et al. / Microelectronic Engineering 51 – 52 (2000) 333 – 342
Ss 5 s 2 aH /( f N), where Ss is noise in a sample due to conductivity, s is the conductivity of the sample, f is the frequency, N is the number of electrons that contribute to the conductivity, and aH is the Hooge parameter (a normalized measure for the relative noise in different materials). From the relation 1 /f noise is independent on electron concentration, sample dimensions, and frequency range, and it is caused by conductivity fluctuations. But conductivity depends on electron concentration and mobility, and therefore conductivity fluctuations can be assumed to occur either as the consequence of mobility fluctuations (typical 1 /f or flicker noise) or as the result of a number of fluctuations of free carriers, produced by generation–recombination processes at levels in the forbidden band. During recent years a lot of work has been done on 1 /f noise in homogeneously doped bulk material. Using Matthiessen’s rule, the total Hooge parameter aH,tot can be divided into parts due to different scattering mechanisms, i.e., aH,phon is the part due to phonon scattering, aH,imp is the part due to impurity scattering. For materials of excellent quality the Hooge parameter aH,phon was determined at room temperatures. Crystals of poorer quality have always higher values of aH,phon . The Hooge parameter aH,imp expresses the noise contribution of the impurity scattering, and it is proportional to the dopant concentration [5]. In contrast to the bulk material, the 1 /f noise of 2DEG structures with undoped channels has not yet been so systematically studied, although some works have appeared recently [6]. Also, experimental study of the noise behaviour of 2DEG samples at low temperatures is missing. Moreover, the influence of external magnetic field on the 1 /f noise of such structures at low temperatures has not been studied yet. The aim of this work is 2-fold: first, to study the possibility for the preparation of large-area highly sensitive magnetic field 2DEG Hall sensors with a resolution better than 1 nT at 77 K for metallic construction integrity control and, second, to study experimentally the influence of external magnetic field on the 1 /f noise of micro-Hall sensors for various frequencies and operating currents at low temperatures (4.2–80 K).
2. Sensor preparation Two-dimensional electron gas (2DEG) Hall sensors of dimensions 2–1000 mm based on an InGaAs / InP heterostructure have been prepared and characterized. To reduce their noise, one has to suppress all the noise sources usually present in the semiconductor sensors [7]. Thermal noise is effectively suppressed in the 2DEG sensors by lowering the temperature to 77 K (2DEG mobility increases). Shot noise, caused by electrons crossing the potential barrier, is in our sensors completely eliminated by the preparation of high quality Au–Sn ohmic contacts. The quality of the contacts has been tested down to 4.2 K. To avoid generation–recombination noise, the 2DEG must be far enough apart from the surface and the heterostructure interface must have low density of traps (case of InGaAs / InP [8]). Special wafer cleaning has been used to avoid parallel conducting channels in the sensors. The presence of such parallel channels can be easily tested in the quantum Hall regime at 4.2 K. 1 /f noise is minimized by selecting an appropriate heterostructure — the InGaAs / InP interface has very low density of traps compared with other materials [8], by adjusting the 2DEG concentration (only one sub-band occupied), and by the increase of sensor dimensions (more electrons present in the system).
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Fig. 1. Heterostructure for the InGaAs / InP Hall probes.
The heterostructure was grown on (100) semi-insulating Fe-doped InP substrate at 6408C using low-pressure MOCVD equipment (AIXTRON 200). The active layer of the Hall sensor is formed by a triangular InGaAs quantum well. The heterostructure consists of a semi-insulating InP substrate, a 300 nm buffer layer, a 10 nm Si-doped InP layer, a 20 nm InP spacer, and a 160 nm active1cap InGaAs layer (Fig. 1). The 2DEG of a sheet concentration 5310 11 cm 22 at 4.2 K is created at the InGaAs / InP heterointerface. An Au–AuSn system was used for the ohmic and contact metallization of the sensors. Their topology was defined in the form of either a simple Greek cross of various active area (Fig. 2), or ladder-like arrays [9]. The sensors were electrically isolated by wet etching. Bias current was applied through current terminals, and the noise was measured differentially between voltage terminals A and B.
3. Results and discussion We first tested the noise properties using a set of samples with linear dimensions from 2 mm to 1 mm. The samples of dimensions 0.5 and 1 mm were not ideal from the topological point of view —
Fig. 2. Topology of the Hall probes. Dashed square is the active area; ohmic contacts are shown in dark grey.
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the length of the cross arms were only half of the length of the active area. The noise spectral density of the Hall terminals at 10 Hz, 1 kHz at 300 K and 77 K is expressed in THz 21 / 2 in Fig. 3; the voltage noise is converted to the magnetic field noise using the sensor sensitivity. The figure shows that: • 1 /N behaviour of the magnetic noise spectral density is confirmed in the probes for both temperatures 300 and 77 K; • noise is lower than 1 nT Hz 21 / 2 at 1 kHz and 77 K in probes with the active area of 2003200 mm; • in the probes with non-ideal Hall probe topology (sensors$0.5 mm) the 1 /f noise of the Hall terminals is increased — they ‘feel’ the noise of the current terminals; • in the smallest sensor the 1 /f noise is increased probably as the result of reduced real active area of the sensor (due to under-etching) as well as electron capture and emission at the 2DEG boundary.
Fig. 3. Dependence of the noise of the sensors vs. sensor linear dimension for 10 Hz, 1 kHz at 300 K, reps. 77 K.
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From the measured data Hooge parameter aH,tot , can also be evaluated for the set of probes. The results for temperatures 300 and 77 K are summarized in Fig. 4: • 300 K values of aH are above the Hooge parameter given by Handel’s quantum 1 /f noise theory developed for the calculation of the Hooge parameter in homogeneous bulk material (|2310 25 for InGaAs) [10]; • for the non-ideal Hall probe topology aH,tot of the Hall terminals increased drastically at 300 K as well as 77 K; • for Hall sensors at 77 K the value of aH,tot is slightly lower (|5310 26 ) than the value given by 25 Handel’s quantum 1 /f theory for bulk material (10 ). In comparison with Ref. [6] our aH,tot is higher at 300 K. In agreement with Ref. [6] we have tried to prepare an optimized InGaAs / InP heterostructure to minimize the noise. In our structure only one sub-band is occupied. On the other hand the penetration depth of the electron wave function is not
Fig. 4. Measured Hooge parameter aH tot meas vs. Hall sensor linear dimension for 300 and 77 K.
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minimized in the structure as we use the lattice matched heterostructure with a 53% content of In. Our minimum value of aH,tot at 300 K was achieved for the 3-mm sensor (4310 25 ), and at 77 K the minimum was achieved for the 200 mm sensor (5310 26 ). It has to be mentioned that the role of dimensionality has not yet been sufficiently clarified in the present 1 /f theories. More experimental and theoretical work has to be done in this field in the near future. To conclude this part, we have found that the pT region can be achieved using large-area cryogenic 2DEG InGaAs / InP sensors. In the following we will discuss the noise of micro-Hall sensors, which is important for all types of micromagnetometry experiment in which 2DEG Hall sensors are often used to evaluate very weak magnetic fields at low temperatures [1–3]. In the second part we discuss the noise properties of the 2 and 10 mm Hall probes in external magnetic fields at low temperatures. We have found a great difference in the behaviours of these two sensors at low temperatures.
4. Noise properties of 2 and 10 mm Hall sensors The galvanomagnetic characterisation of the 10 mm sensor has shown the typical behaviour of the InGaAs / InP 2DEG systems (Fig. 5). The electron concentration is approximately constant in the temperature interval investigated — in the entire interval all donors are ionizied and the electrons are captured by the quantum well. The electron mobility is limited due to alloy scattering (always present
Fig. 5. Mobility and electron concentration versus temperature for a 10 mm Hall sensor characterized.
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in ternary semiconductors) at lower temperatures, and for higher temperatures it is limited by polar optical phonons. The power spectral density (PSD) of the sensors was measured using a fast Fourier noise analyzer SR 760. The signal was first amplified using a low-noise preamplifier SR 560, and all the experimental conditions (temperature, bias current, magnetic field) were computer-controlled using a LabView program. During the measurement a lot of data have been collected. The PSD was taken for 2 and 10 mm Hall sensors for 10 various bias currents at magnetic fields 0, 0.1, 0.2, 0.5 1, 2, 3.1 and 5 T, all this at temteratures from 4.2–90 K with the steps 4 or 8 K. Moreover, at certain temperatures data for magnetic fields 0–5 T were taken with the step 0.2 T. In this paper only a part of the results is discussed.
5. Results and discussion All PSD measurements show that for both sensor dimensions, at a given temperature and magnetic field, the LF noise depends linearly on bias current through the sensor, except for very high currents, for which the LF noise increases rapidly. This rapid noise jump for large currents can be interpreted by the real space transfer of the heated electrons from the channel to the surface of the structure. Another dependence that was found is the slope of a noise spectrum that changes from 21 to 21.5, when the temperature of the sensor is decreased from |80 to |40 K. Fig. 6 shows a summary of the temperature dependence of the noise for a 10 mm sensor at 5 Hz for bias current 500 mA (the dependence is similar for lower currents). Here, the applied external magnetic field was a parameter. The noise of the sensor rapidly increases for increased magnetic field, and it is temperature independent for 4.2–30 K. This noise increase with magnetic field limits the dynamic range of the sensor. On the other hand, for temperatures higher than 30 K the magnetic-field dependence is similar but a rapid increase of the noise also with temperature is observed. Polar optical phonons emitted and absorbed by the 2DEG are probably responsible for this noise increase. The PSD of a 2 mm Hall sensor showed that its noise is a complicated function of temperature, frequency, and magnetic field applied. In the PSD there are strong oscillations that are suppressed by the magnetic field. The slope of the noise spectra changes from 21 (92 K) to 21.5 (48 K), which supports the idea that 1 /f spectra are partially caused also by trapping centres at the InGaAs boundary and not only by mobility fluctuations. Fig. 7 is a summarizing figure, like Fig. 6, but for a 2 mm Hall sensor with a 80 mA bias current applied (current density similar to the 10 mm sensor). The high-temperature part of the dependence follows the characteristics from the previous figure — there is evident a rapid increase of noise with increased temperature, which can be interpreted again by an enhanced emission and absorption of polar optical phonons. The only difference is that the magnetic field applied has much weaker influence on the noise of the 2 mm Hall sensor, and it increases the noise only for magnetic fields higher than 1 T. At low temperatures and for magnetic fields |1–3 T the role of the magnetic field is the opposite — the low frequency noise is suppressed for all bias currents supplied to the sensor. This unusual behaviour can be explained considering classical 1D transport of electrons in our structure. If the electron mean free path is comparable with the channel width, and if we assume that the noise is caused by the interaction of electrons with the channel boundary, then the magnetic field can lower the probability of the interaction of 2DEG with trapping centres at the boundary, the electron mean
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Fig. 6. Low-frequency noise (5 Hz) of the 10 mm Hall sensor versus temperature for bias current 500 mA, the magnetic field applied is the parameter.
free path can be increased and therefore the overall low frequency noise in the structure is suppressed. This surprising result can be utilized in magnetometry experiments in the future — the application of background magnetic field can be used to reduce the noise in such systems. But to confirm this assumption more experimental and theoretical work has to be done. Fig. 8 summarizes the noise data for the 2 mm Hall sensor versus magnetic field at 12 K. Bias current was in this case 120 mA. The noise at various frequencies is depicted here. The resulting noise characteristics of the sensor support the surprising behaviour of the LF part of the noise from Fig. 7 — the LF noise is suppressed for magnetic fields of 1–3 T. For higher frequencies the noise increases exponentially with applied magnetic field, and for 5 T the noise is in one order of magnitude higher than without applied magnetic field.
6. Conclusions In this work a study is presented on the noise of 2DEG InGaAs / InP Hall sensors of various dimensions. In the first part of the work we have shown that for the large-scale sensors (0.2 mm linear dimension) at 77 K and at 1 kHz a sensitivity better than 1 nT can be achieved.
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Fig. 7. Low-frequency noise of a 2 mm Hall sensor versus temperature at 5 Hz for bias current 80 mA, the magnetic field applied is the parameter.
The second part of the work deals with the noise properties of 2 and 10 mm sensors dependent on bias current, frequency, applied magnetic field and temperature. It was found that the LF noise depends linearly on bias current, for very high currents, increases rapidly — 2DEG reaches surface (observed for all temperatures). It was found that the LF noise of the 10 mm sensor rapidly increases for applied magnetic field, but the LF noise of the 2 mm sensor is a complicated function of temperature and magnetic field: for low temperatures and fields of |1–3 T the noise of the sensor is suppressed. In the near future more experimental and theoretical work has to be done in the field of noise properties of 2DEG micro-Hall sensors in external magnetic fields at low temperatures.
Acknowledgements This work was supported by project NATO SfP-972399 Magnetic Microscopy. The authors wish to ˇ for helpful discussions. thank Dr M. Mosko
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Fig. 8. Noise versus magnetic field applied for the 2 mm Hall sensor for 120 mA current at 12 K.
References [1] S.T. Stoddart, S.J. Bending et al., Phys. Rev. Lett. 71 (1993) 3854. [2] G. Karapetrov, V. Cambel, W.K. Kwok, R. Nikolova, G.W. Crabtree, H. Zheng, B.W. Veal, Contactless characterization of melt-textured superconducting junctions using micro hall sensor arrays, J. Appl. Phys. 86 (1999) 6282. [3] A. Oral, S.J. Bending, R.G. Humphreys, M. Henini, Superconduct. Sci. Technol. 10 (1997) 17. [4] C.M. Van Vliet, A survey of results and future prospects on quantum 1 / f noise and 1 / f noise in general, Solid-State Electronics 34 (1991) 1. [5] F.N. Hooge, 1 / f noise sources, IEEE Trans. Electron Devices 41 (1994) 1926. [6] J. Berntgen, K. Heime, W. Daumann, U. Auer, F.-J. Tegude, A. Matulionis, The 1 / f noise of InP based 2DEG devices and its dependence on mobility, IEEE Trans. Electron Devices 46 (1999) 194. [7] A. van der Ziel, A.D. van Rheenen, in: Noise in Electronic Circuits, Encyclopedia of Physical Science and Technology, Vol. 10, Academic Press, New York, 1992. [8] P. Viktorovitch, P. Rojo-Romeo, J.L. Leclercq, X. Letartre, J. Tardy, M. Oustric, M. Gendry, Low frequency noise sources in InAlAs / InGaAs MODFET’s, IEEE Trans. Electron Devices 43 (1996) 2085. ˇ Mozolova, ´ˇ R. Kudela, ´ ´ B. Olejnıkova, ´ ´ Z. ´ M. Majoros, ˇ J. Kvitkovic, ˇ P. Hudek, [9] V. Cambel, P. Elias, J. Novak, Preparation, characterization and application of microscopic Hall probe arrays, Sol. State Electron. 42 (1998) 247. [10] A. Van der Ziel, P.H. Handel, X. Zhu, K.H. Duh, A theory of the Hooge parameters in solid-state devices, IEEE Trans. Electron Devices 32 (1985) 667.