Microscopic 2DEG linear Hall probe arrays

Superlattices and Microstructures, Vol. 24, No. 3, 1998 Article No. sm960364

Microscopic 2DEG linear Hall probe arrays V. C AMBEL , B. O LEJN´I KOV A´ , P. E LI A´ Sˇ , ´ , M. K U Cˇ ERA ´ , J. N OV AK R. K UDELA Institute of Electrical Engineering, Slovak Academy of Sciences, D´ubravsk´a cesta 9, 842 39 Bratislava, Slovakia (Received 15 July 1996) The technology, preparation and first characterization of a microscopic 2DEG Hall probe array are presented. The vertical heterostructure of the array based on InGaP/InGaAs/ GaAs has been prepared by MOCVD. The active area of the array is placed on the top of a mesa 40 µm above the planar contact level. A physical model of the heterostructure including a self-consistent description of coupled Schr¨odinger and Poisson equations has been solved to better understand the influence of the heterostructure design on its electronic properties. The first device characterization exhibits a sensitivity of 470 V /AT in the magnetic field range ±0.4 T at 77 K. c 1998 Academic Press

Key words: Hall sensors, arrays, semiconductor devices, Al-free heterostructures.

1. Introduction Semiconductor magnetic field sensors with a Hall element made of InSb, GaAs and Si are widely used for practical applications. In these 3D devices the condition to obtain high sensitivity and low thermal drift at room temperature appears contradictory. Fortunately, at present it is possible to fabricate high-quality III–V heterostructures using sophisticated growth techniques. The use of a 2D electron gas (2DEG) in a quantum well (QW) as the active layer of a Hall element seems to be an effective method of achieving high electron mobility, low sheet electron density and reduced temperature sensitivity. A number of such sensors based on GaAlAs/GaAs [1], GaAlAs/GaInAs/GaAs [2], and InAlAs/InGaAs/InP [3] have recently been proposed. In this paper a series of monolithically integrated and highly sensitive linear Hall probe arrays based on an InGaP/InGaAs/GaAs QW heterostructure with a selectively δ-doped barrier [4] prepared by MOCVD is presented. This Al-free material is used to avoid the creation of DX centres and the structure degradation in high-power conditions, the problems encountered in lasers based on Al compositions. The smallest array consists of eight in-line sensors with an active area of 2 µm × 2 µm and a 4 µm centre-to-centre separation. The sensor is developed for the measurement of spatial inhomogeneities and/or time dynamics of the magnetic field near the surface of high temperature and standard superconductors [5–7] in the temperature range 4.2–77 K. Supporting electronics has also been developed to control these arrays [8]. To allow close contact with a superconductor sample tested, the active area of the array is formed on the top of a 40 µm high structure. 0749–6036/98/090181 + 08

$30.00/0

c 1998 Academic Press

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Microscopic dimensions, heterostructure design and lowered operating temperature are conditions which determine the final sensitivity of a Hall probe. The influence of the heterostructure design on the sensor properties is the aim of this study. For this purpose a physical model of the structure including a self-consistent solution of coupled Schr¨odinger and Poisson equations is used. The heterostructure was characterized by transport measurements at 77 K and by photoluminescence at 6 K. The energy spectrum measured was explained using the theoretical model. Finally, the array was characterized in the magnetic field interval ±0.4 T at 300 and 77 K.

2. Theory of operation Let us consider a microscopic Hall probe, in which only a limited power P can be dissipated. The Hall voltage Vh = Vh (P) can be written as [9]: Vh = rn (µn w/qntl)1/2 GBP1/2 , where µn is the electron mobility at the electron concentration n in the active layer, rn is the Hall scattering factor (rn ∼ 1), G is the geometrical correction factor (G ∼ 1), B is the magnetic field, q is the elementary charge, and l, w, and t are the length, width and thickness of the active layer, respectively. From the relation we see that for a Hall probe of a defined geometry, and for a dissipated power P at a magnetic field B, the square of the induced Hall voltage is proportional to the Hall mobility and inversely proportional to the sheet carrier concentration nt. For a good sensor a high sensitivity and independence on operating conditions (temperature, bias current) are desired, i.e. both the electron mobility and concentration have to be constant. Active layers with the constant sheet concentration of a 2DEG can be prepared by MOCVD almost without problems. However, a problem is achieving a constant value of µn . In the temperature range 4.2–77 K the mobility of carriers in a 2DEG is strongly enhanced in comparison with the one at room temperature due to suppressed electron–polar optical phonon interaction. Other scattering mechanisms become more important and the resulting mobility strongly depends on the heterostructure design and operating conditions. The mobility is a complicated function of the shape of the Fermi–Dirac distribution function [10], the shape of the electron wavefunction in the QW [11], electron interaction with screened Coulomb remote and background centres [12], and with the alloy potential [13]. In conditions under which alloy scattering is the dominant scattering mechanism, the mobility becomes temperature independent in the temperature range mentioned. Decreasing the lateral dimensions of the Hall sensor to a micrometre level brings about other physical and technological problems. The operating electric field applied parallel to the 2DEG at 4.2–77 K can cause warm electron transport in the active layer [14], which lowers the electron mobility due to increased electron–optical phonon scattering. Also, when higher electric fields are applied, the real space transfer of hot electrons from the active layer is possible if the quantum structure is not designed properly. Another problem is that for small dimensions the bias current density is large (for a Hall probe with the width w = l µm, the QW thickness t = 10 nm, and bias current 1 mA, the current density J = 107 A cm−2 ). Only limited power can be used to avoid heterostructure heating and the device degradation. The use of current pulse mode by special supporting electronics [8] is one method to lower P for DC measurements while maintaining an unchanged level of sensitivity. Further problems connected with lithographic mask misalignment and etching fluctuations in the case of microscopic Hall arrays are discussed in [8].

3. Device fabrication The technology of the 2DEG Hall probe arrays consists of three basic steps. The vertical structure containing an InGaAs active layer is grown within the first step. The Hall probe arrays are then defined

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cap lnGap : 50 nm δ-Si : 9.2 × 1011 cm–2 spacer lnGaP : 5 nm QW lnGaAs : 12.5 nm

buffer GaAs : 95 nm

substrate S.I. GaAs

Fig. 1. Schematic cross section of a grown heterostructure.

and electrically isolated in the vertical semiconductor structure. The purpose of the third step is to shape the layers of the vertical structure and part of the GaAs substrate into a mesa by means of deep etching to make possible the measurement of the magnetic field within a distance less than 10 µm from an object measured. The heterostructure was grown in a low-pressure MOCVD equipment AIX 200 on (100)-oriented semiinsulating GaAs substrates with unintentional misorientation up to 0.2◦ . Trimethylgallium, trimethylindium, arsine, phosphine and silane were used as precursors and hydrogen as a carrier gas. The growth procedure consisted of heating the GaAs substrate in an overpressure of AsH3 , epitaxial growth at the total reactor pressure 50 mbar, and the cooling phase in an overpressure of PH3 . This growth pressure of 50 mbar was found optimal for the surface morphology and uniformity of the layers grown. The corresponding flow velocity inside the reactor was new 0.8 m s−1 . Typical mole fractions of TMGa, TMIn were of the order of 10−5 . The corresponding growth rates, depending on the material grown, ranged from 0.6 to 1.2 µm h−1 . The growth temperature was 640 ◦ C. The vertical semiconductor structure consisted of a 95 nm GaAs buffer layer, a 12.5 nm In0.2 Ga0.8 As quantum well active layer, a 5 nm In0.49 Ga0.51 P spacer, and Si δ-layer, and a 50 nm In0.49 Ga0.51 P cap layer (see Fig. 1). The sheet carrier concentration in this structure measured at 77 K was 9.2 × 1011 cm−2 . An Au–Sn metal film for ohmic contact was evaporated onto the InGaP cap layer through an AZ5214-E resist mask and defined by the standard lift-off technique. The ohmic contact was made by alloying the metal film at 420 ◦ C for 4 min in flowing N2 . The topology of planar Hall probe arrays was then defined and isolated by means of a 1 µm deep wet etch through another AZ5214-E resist mask. The etching of the GaInP, InGaAs, and GaAs layers of the vertical structure was carried out using 1HC1 : 10CH3 COOH : 3.5H2 02 at 20 ◦ C [15]. Deep mesa etching into the GaAs substrate makes it possible to place Au connecting wires under the level of the active area of the array. The mesa etch must be at least 40 µm deep with all four sides smooth, moderately slanted, and without sharp edges. Au contact metallization is then formed to connect the active area on the top of the high mesa with contact pads situated at the bottom of the mesa. Therefore, it is necessary to use an etchant with similar etching properties in all directions of the h110i type to obtain

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a symmetrical mesa. Also, the etchant should have the same etching velocity in the h111i and h111i directions to prevent the creation of sharp pikes at the top edge of the mesa. This can be successfully fulfilled using the 1HF : 8.5H2 O2 : 50H2 O etchant [16]. The etching rate of this mixture for semi-insulating GaAs substrate is near to 1 µm min−1 at room temperature. All four sides of the mesa are approximately slanted at 45◦ . This angle can be lowered by increasing the water component in the mixture, however, the resulting sides are rougher.

4. Experimental and heterostructure modelling To optimize the design of the heterostructure of the Hall probe arrays for operation at 77 K, a model involving a self-consistent system of Schr¨odinger and Poisson equations including the Fermi–Dirac statistics has been solved. In thermodynamical equilibrium the Fermi level has to be constant in the entire heterostructure. At the semi-insulating GaAs/GaAs interface the Fermi level should coincide with the Fermi level in the GaAs substrate, which lies approximately in the middle of the gap. Within the model the shape of wavefunctions, the energy levels in the InGaAs QW, and their population were computed. The doping level (electron sheet density), the QW, spacer and buffer thicknesses were chosen to set the Fermi energy just between the energy levels E 1 and E 2 and to achieve the complete transfer of carriers from the δ-plane into the quantum well. If the occupation of both of the energy levels is comparable, a mobility drop in the QW due to intersubband electron scattering occurs [10]. An incomplete depletion of the δ-plane should make sheet concentration in the QW temperature dependent and also sensitive to parallel operating voltage applied to the heterostructure. The distance between E 1 and E 2 in the energy space is engineered by the well thickness. The carrier concentration is controlled by the concentration of Si atoms in the δ-plane. In our case we chose 20% In composition in the InGaAs alloy, which sets the conduction band discontinuities at 383 meV and 143 meV at 77 K for InGaP/InGaAs and InGaAs/GaAs interfaces, respectively [17]. Other parameters used in the model were as follows. The effective electron mass m ∗e = 0.059 m e , the relative material permitivity εr (InGaP) = 11.8, εr (InGaAs) = 13.2, the quantum well thickness t = 12.5 nm, the spacer thickness L sp = 5 nm, and the electron concentration n s = 9.2 × 1011 cm−2 . Figure 2 shows the electric potential in the structure and the calculated electron wavefunctions. The energy E 1 at the bottom of the first subband is 88.6 meV with the subband occupation 9.13 × 1011 cm−2 , the confinement energy E 2 of the second subband is 147 meV with the occupation 6.35 × 109 cm−2 , and the Fermi energy is at 125.6 meV. The energy levels E 3 and E 4 are less occupied by several orders, so it is possible to neglect them in further assumptions. The structure under study was characterized by PL measurements. A 20 mW HeNe laser beam (652.8 nm) focused by a cylindrical lens was used for excitation. Samples measured were placed in an optical cryostat and cooled by flowing He vapours to 6 K. The PL radiation was filtered by a quarter-meter monochromator (spectral bandwidth set to 0.6 meV) and detected by an Si photodiode. A standard lock-in technique was used to read the photodiode signal. Figure 3 shows the PL spectra achieved. Three peaks are evident: E GaAs at 1490 meV, corresponding to the GaAs conduction band–acceptor transition, the second one at 1345 meV, related to the recombination of electrons at the energy level E 2 with heavy holes HH1 , and the third one at 1291 meV, which corresponds to the recombination of electrons at the energy level E 1 with heavy holes HH1 . These values are in good agreement with the self-consistent solution of the Schr¨odinger and Poisson equations. The shape of the potential during the PL measurement differs slightly in comparison with the one without illumination. At the beginning of a PL measurement the photogenerated electrons and holes are separated due to the band bending in GaAs, further electrons are caught by the well, and holes are repelled into the substrate. The bands become flat as a result of the formation of an electric field and the holes can diffuse into the well—the luminescence from the QW appears. As the electron sheet concentration in the well increased,

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400

Energy (meV)

300

200 E2 EF

100

E1

0

–100

0

–10

10 Distance (nm)

20

30

Fig. 2. The electric potential in the structure and the calculated electron wavefunctions. The energy E 1 at the bottom of the first subband is 88.6 meV, the confinement energy E 2 of the second subband is 147 meV, the Fermi energy is 125.6 meV.

PL signal (au)

12

8

4

0

1.1

1.2

1.4 1.3 Energy (eV)

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1.6

Fig. 3. PL spectra of the heterostructure depicted in Fig. 1 measured at 6 K. Three main peaks are at 1490 meV (GaAs conduction band–acceptor transition), at 1345 meV (E 2 –HH1 transition) and at 1291 meV (E 1 –HH1 transition).

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2.5 T = 300 K I BIAS = 10 µA 2.0

UH (mV)

1.5

1.0

0.5

0.0

0.0

0.1

0.2

0.3

B (T) Fig. 4. The Hall voltage of the selected probe of the 5 µm × 5 µm Hall sensor versus magnetic field for bias current IBIAS = 10 µm at 300 K.

the Fermi level is shifted above the energy level E 2 . At 6 K the bottom of the second subband is occupied just enough to produce a high luminescence peak E 2 –HH1 , which is shown in Fig. 3. When the laser source is switched off, the Fermi energy in the heterostructure is again restored to its equilibrium position between E 1 and E 2 . 4.1. Device calibration The 2DEG Hall probe arrays were calibrated in a calibrated magnet in the magnetic field range ±0.4 T at 77 K. As the characteristics of all probes of an array were similar for a good device, characteristics of one selected probe of a 5 µm × 5 µm sensor are presented in this paper. Figure 4 shows the linear dependence of the Hall voltage of the probe on the magnetic field for bias current IBIAS = 10 µA. Figure 5 shows the linear dependence of the Hall voltage of the probe on bias current for magnetic fields 66 mT, 92 mT, 200 mT, and 400 mT at 77 K. In comparison with our previously published results with a Hall probe array based on a GaAs epitaxial layer [8], the sensitivity of the sensor based on the 2DEG active layer increased from 20 V/AT to 470 V/AT at 77 K.

5. Conclusion In this paper we have presented the results of the preparation and characterization of novel microscopic linear 2DEG Hall probe arrays based on an Al-free InGaP/InGaAs/GaAs heterostructure. The results can be summarized as follows. • Problems related to lowered dimensions, enlarged power density and lowered temperature performance are discussed.

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10 T = 77 K

400 mT

200 mT

UH (mV)

8

6

92 mT

4

66 mT

2

0 0.00

0.02

0.04

0.06

0.08

0.10

IBIAS (mA) Fig. 5. The Hall voltage of the selected probe of the 5 µm × 5 µm sensor versus bias current for magnetic fields 66 mT, 92 mT, 200 mT, and 400 mT at 77 K.

• In accordance with the physical model, the InGaP/InGaAs/GaAs heterostructure with a 2DEG was prepared by MOCVD. The analysis of the PL signal measured is in good agreement with the calculated energy structure. • A deep mesa etch was realized to place Au connection wires under the level of the active area of the array and to make possible close contact with a superconductor sample tested. • The arrays realized were characterized for various bias currents at the magnetic field range ±0.4 T at 300 K and 77 K. In the near future these microscopic Hall probe arrays will be used for measurements with standard and high-temperature superconductors. Acknowledgements—The authors wish to thank Martin Moˇsko for helpful discussion. This work was supported by Project No. 2/1090/96-VEGA.

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