Modelling and fabrication of wide temperature range Al0.24Ga0.76As/GaAs Hall magnetic sensors

Hua Fan, Huichao Yue, Jiangmin Mao, Ting Peng, Siming Zuo, Quanyuan Feng,Qi Wei, and Hadi Heidari

1State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China,Chengdu 610054, China

2Chengdu HiWafer Semiconductor Co., Ltd., Chengdu 610225, China

3James Watt School of Engineering, University of Glasgow, G12 8QQ, Glasgow, UK

4Southwest Jiaotong University, Chengdu 611756, China

5Department of Precision Instrument, Tsinghua University, Beijing 100084, China 6Institute of Electronic and Information Engineering of UESTC in Guangdong, University of Electronic Science and Technology of China,Dongguan 523878, China

Abstract: Silicon Hall-effect sensors have been widely used in industry and research fields due to their straightforward fabrication process and CMOS compatibility. However, as their material property limitations, technicians usually implement complex CMOS circuits to improve the sensors’ performance including temperature drift and offset compensation for fitting tough situation, but it is no doubt that it increases the design complexity and the sensor area. Gallium arsenide (GaAs) is a superior material of Hall-effect device because of its large mobility and stable temperature characteristics. Concerning there is no specified modelling of GaAs Hall-effect device, this paper investigated its modelling by using finite element method (FEM) software Silvaco TCAD? to help and guide GaAs Hall-effect device fabrication. The modeled sensor has been fabricated and its experimental results are in agreement with the simulation results. Comparing to our previous silicon Hall-effect sensor, the GaAs Hall-effect sensor demonstrates potential and reliable benchmark for the future Hall magnetic sensor developments.

Key words: Hall-effect sensors; GaAs Hall sensor; GaAs semiconductor device

1.Introduction

Hall-effect sensors have dominated most markets of magnetic sensors over the past several decades because of their high performance, small physical size and low cost. Their various applications such as electronic compass, position detecting, current sensing, and contactless switching have made them the most popular type of magnetic devices. This is even truer since silicon Hall sensors are easily integrated on complementary metal oxide technology (CMOS) wafers with the readout electronics[1?4]. Generally, the Hall sensors enjoy wide detection range from 10μT to 20 T, high spatial resolution smaller than 1μm, and a wide band-width from DC to over 1 MHz[5]. However, with the increased use of Hall-effect sensors both in industry and research fields, studying higher performance materials and fabrication process for Hall-effect sensors becomes super important.

We have previously demonstrated a high-performance Hall sensor in CMOS technology with its integrated readout circuit[2]. According to our experience on CMOS hall sensors, the mobility is a critical material parameter of Hall-effect device,because large mobility Hall-effect device always means large sensitivity and low power consumption. Table 1 shows the electron mobility and energy gap of four common materials of Hall-effect devices and gallium nitride (GaN) studied recently for Hall-effect devices[6,7]. In mobility, Si < GaN < GaAs

Table 1. Comparison of five materials of Hall-effect devices.

Fig. 1. (Color online) GaAs Hall-effect sensor layers structures.

In addition, other benefits of GaAs based Hall sensors include: (a) a high Hall constant about 6250 cm3/C with an electron concentration of 1015cm?3; (b) a high thermal conductivity about 0.81 W/(cm·K), utilizing an advantage of the heat released in the epitaxial layer; (c) almost any custom shape can be achieved in photolithographic nanofabrication process; (e)an excellent temperature stability due to the 1.4 eV energy gap of GaAs at 300 K; (d) a high resistivity about 105Ω?cm;and (e) an ultra-thin thickness without changing desired properties of the bulk materials.

Considering there is no specified modelling of GaAs Halleffect device, in this paper, a constant voltage bias modelling of GaAs Hall-effect device is presented by using commercial finite element method (FEM) software Silvaco TCAD?to guide and further study the GaAs Hall-effect sensor. The device has been fabricated, and its experimental results of sensitivity performance and temperature performance are compared with simulation results. The important thing is that this model can also be used for the simulation of Hall sensors made of materials such as Si, Ga and InSb. In the design process, we can choose different types of materials, and we can also choose the corresponding electron mobility according to different manufacturing processes.

The layer structure of our Hall magnetic sensor is shown in Fig. 1. The 300 nm N+GaAs with 1017cm?3uniform Si doping is the active layer to induce Hall output, and it is also used to form ohmic-contact with metal wire. AlGaAs has a larger band gap than GaAs, which can form a barrier to prevent the migration of electrons. The 20 nm Al0.24Ga0.76As is used as the barrier layer to make electron be restricted in N+GaAs space. Periodic Al0.24Ga0.76As and GaAs form a superlattice structure which is used as a buffer layer and to produce periodic barriers for further preventing current flowing away from the substrate. The bottom layer is the GaAs substrate which is to provide mechanical strength and grow high quality GaAs epilayer.

2.Hall-effect modelling

The Hall-effect sensor is based on the physical effect produced by a current-carrying semiconductor in a magnetic field. Its output voltage is directly proportional to the magnetic field strength. Currently, the cross-shaped model is widely employed as an optimum geometry to achieve the highest sensitivity and lowest offset[2]. In addition, such symmetric geometry can dramatically decrease the mismatch resulting from the fabrication process[11]. In our model, a conventional constant voltage bias Hall sensor is adopted, which can reduce the design complexity of bias circuit[7]. A constant voltage supply (Vbias) is utilized to bias the Hall-effect sensor and then an output voltage (Vhall) as a result of an external magnetic field is measured at terminals. The Hall voltage with a voltage biasing can be expressed as[11]

whereμHdenotes the Hall mobility of majority carriers,WandLrepresent the width and length of the sensor respectively,Bis the external magnetic field vertical to the device surface,GHis the geometrical correction factor of Hall voltages.GHis usually determined by the actual sensor structure and the shape of the contact pole, and the value range is 0

whereθHdenotes the Hall angle. Reducing the width-tolength ratioW/Lof the Hall device can improve the device geometrical correction factor, which will also improve the sensor performance. However, as the width of the Hall device increases, the area of the sensor increases accordingly. Therefore, it is necessary to compromise the aspect ratio of the device within an appropriate range. For a cross-type horizontal Hall sensor,GHvalue can usually reach approximately 1. In addition, the absolute sensor sensitivity can be defined from the Eq. (3). The sensitivity depending on the voltage output quantity can be given by[12]:

which represents the capability of the sensor to convert the magnetic field into a Hall voltage. For eliminating the influence of bias voltage on device sensitivity, the relative sensitivity is finally defined as the Eq. (4) dividing by the bias voltage, shown below[12]:

Fig. 2. (Color online) (a) Fully symmetrical cross-shaped Hall element.(b) The Hall voltage of the fully symmetrical cross Hall element changes with the shape.

Fig. 3. (Color online) (a) Narrow cross-shaped Hall element. (b) The Hall voltage of the narrow cross Hall element varies with the width of the output port.

whereμminandμmaxrepresent the mobility saturation at the highest and lowest doping concentrate respectively,N0denotes the doping concentrate at which mobility reduces to half ofμmaxvalue,Ndenotes the concentration of ionized donors.TLdenotes the lattice temperature.α, β, γ, δare adjustment parameters[14].

In Caughey-Thomas mobility model of Silvaco,μmin= 500 cm2/(V·s),μmax= 8600 cm2/(V·s),α= 0,β= –2.1,γ= –1.182,δ=0.394,N0= 6 × 1016cm–3. In Ref. [14],μmin= 500 cm2/(V·s),μmax=9400 cm2/(V·s),α= 0,β=?2.1,γ=?1.182,δ= 0.394,N0= 6 ×1016cm–3, meaning they use the Hall mobility and assumeμ～μH.

3.Simulation and experimental results

Fig. 4. (Color online) GaAs Hall-effect sensor built in Silvaco TCAD.

COMSOL Multiphysics is a multiphysics simulation software based on finite element analysis methods, which can simulate and analyze actual engineering problems involved in many fields including electromagnetics, structural mechanics,acoustics, fluid mechanics, and thermals. Because the COMSOL finite element simulation software has a parameter scanning function, COMSOL is used to explore the geometric factors of the Hall element. The shape of the fully symmetrical cross Hall element is shown in Fig. 2(a). The input and output ports have the same lengthLand widthW. When studying this structure, the ratio ofWandhis more commonly used instead of lengthLand widthWas the abscissa of the coordinate axis. The simulation result is shown in Fig. 2(b). At the beginning, the Hall voltage increases withW/h. WhenW/his about 3, the sensitivity of the fully symmetrical crossshaped Hall disk is the greatest. WhenW/his greater than 3,the Hall voltage tends to decrease. The narrow cross-shaped Hall element studied in this paper is shown in Fig. 3(a), which is similar in shape to a fully symmetrical cross-shaped Hall plate, but the output interface is narrower. Because the width and length of the output port have a small effect on the input resistance, it has a small effect on the static operating point of the Hall element. Therefore, this paper studies the influence of the changes in the widthW’and lengthL’of the output port of the narrow cross-shaped Hall element on the Hall voltage. Based on the fully symmetrical cross-shaped Hall plate when theW/his about 3 and the Hall voltage output is the maximum. Take the fully symmetrical cross-shaped Hall element at the maximumW/hof 3 Hall voltage output as the reference. By changing the width of the output port of the reference Hall element, the Hall voltage of the narrow cross Hall element in Fig. 3(b) varies with the width of the output port. It can be concluded that the smaller the output port, the greater the Hall voltage. WhenW’/W= 0.5, that is, when the output port is half of the input port, the Hall voltage output growth tends to slow down asW’/Wdecreases.

Numerical simulation of the Hall-effect sensor is performed using Silvaco TCAD?. Previous simulations of Hall sensors are summarized in Ref. [15]. Fig. 4 shows our proposed structure of the Hall-effect sensor. The color legend indicates the surface potential distribution by applying a magnetic field of 100 mT. The model geometry of the Hall sensor has been simulated without any mismatch. The ground and supply voltage are added to cathode and anode of Hall-effect sensor.

Fig. 5. (Color online) (a) The 2D vertical cut-plane of Hall-effect sensor. GaAs layer (bottle green) is the doping layer and AlxGa1?xAs/GaAs (green)is the channel layer. (b) Electrons distribution of 2DEG GaAs Hall-effect sensor in 1D when a 5 V supply voltage is added. (c) Simulated output voltage of AlxGa1?xAs/GaAs Hall sensor.

Fig. 6. (Color online) Fabricated AlxGa1?xAs/GaAs Hall sensor microphotograph.

Fig. 7. (Color online) (a) Simulated sensitivity of the voltage-mode Hall sensor. (b) Dependence of temperature on output voltage. (c) Simulated offset with different misalignment of output contacts.

The 2D and 1D electrons distribution of vertical cutplane are demonstrated in Figs. 5(a) and 5 (b). Although Al0.24Ga0.76As is just below the N+doping epilayer, it almost has no carrier because of its larger energy gap barrier which stops carriers in GaAs flowing to AlxGa1–xAs. So the electrons are inside the potential well. Electrons are restricted in the thin N+GaAs channel, which forms the two-dimensional electron gas (2DEG) structure confined in the potential well near AlxGa1–xAs/GaAs interface. The final output voltage of the Hall sensor is demonstrated in Fig. 5(c). The value ofy-axis represents the Hall voltage. It is noted that the output is linearly increased by changing the magnetic field from 0 to 100 mT.The voltage response is very linear, and the maximum output voltage of 0.25 V is obtained. The sensitivity of the Hall effect device is 0.51 V/(V·T) .

Fig. 6 illustrates the microphotograph of the Hall-effect sensor. The red line cross-shape represents the active region of dthe evice, but the effective region of the device doesn’t include pads in white color, and its maximum width and length are 110 and 90μm, respectively. The sensor manufacture is compatible with pHEMT processing technology[9]. There are 4 main steps in its manufacture. Firstly, isolating the device through implant Boron. Secondly, Au/Pt/Ti metals are grown on N+GaAs epilayer, which is used to form Ohmic contact—a classic contact for avoiding forming nonlinearI–Vrelationship between the metal and the semiconductor. Thirdly, Si3N4is deposited on the wafer surface and etched in the pad to protect the device. Finally, a metal wire is grown for its connection to circuits.

During the experiment, electromagnet Helmholtz coil is used inducing magnetic field. Hall-effect sensor is put in the center of Helmholtz coil for obtaining a relatively constant magnetic field, and there has no consideration for shielding geomagnetic, because it induces the Hall voltage less than 0.1 mV. Guassmeter HT208 (0.1μT resolution) from Hengtong Inc. is used to measure the induced magnetic fields from the coils. In terms of temperature performance, temperature chamber CST842T from Hhtesting Inc. is used to generate temperature from?75 to 200 °C, providing a constant temperature environment. The measured sensitivity at room temperature is shown in Fig. 7(a). The average is 0.28 V/(V·T),which is in the same order of magnitude as the simulation result, but it still has large mismatch, so the model resolution should be improved, which will be further discussed.

Fig. 8. (Color online) Combining 2 types of epilayer structure and 2 physical models, 4 simulation results are presented. Experiment results are added for comparison with (a, b) magnetic field and (c, d) temperature (50 mT).

Moreover, the temperature dependence of the final output voltages is shown in Fig. 7(b), with the temperature ranging from?40 to 150 °C at 50 mT vertical magnetic field. The highest measured value of the Hall voltage isVH= 72.5 mV at?40 °C. In addition, it is clearly noticed that the output signal slightly drops as the temperature increases. It is worth mentioning that the increasing temperature brings about the raise of carrier scattering, which leads the decrease of carrier mobility of Hall sensor. Therefore, the higher the temperature, the smaller the carrier mobility, which results in the lower Hall output voltage.

Finally, Fig. 7(c) performs the offset with different misalignment of output contacts from?300 to 300 nm to find the lowest offset. The measurement is at room temperature and the external applied magnetic field is zero. Ideally, non-misalignment of output contacts will obtain zero output voltage.However, non-ideal factors of piezoelectric effect and discontinuity of material will result in an asymmetry of the device property and then generate offset voltage. It can be alleviated by misaligning output contacts. The offset is equal to 5 mV when the misalignment is 0. When there is 100 nm mismatch, the device approximately has the lowest zero offset.Subsequently, a standard CMOS-based analogue front-end circuit comprises of an operational amplifier and a low-pass filter could achieve on-chip noise and offset suppression.

If only using the Shockley-Read-Hall Recombination model, a common model in semiconductor, it can obtain 0.44 V/(V·T) sensitivity, which leads to large error compared with 0.28 V/(V·T) in experimental results. Aiming at narrowing the difference between the simulation and experimental results,models need to be improved. Considering the Eq. (5), carrier mobilityμmust be corrected. It is higher in previous simulation work. Carrier mobility is always related with the temperature and the doping concentrate, so analytic physical model is used to correct the device modelling. The quantity relationship of analytic physical model is defined in 6, whereμ1, μ2,α, β, γ, δ, N0are constant parameters related to material property and they can be obtained in the datasheet.TLandNare lattice temperature and carrier concentration, respectively,which are related to the user defined doping concentration and temperature. On the other hand, the simulation model of Hall device is specified into 3 sub-models according to its epilayers. Single GaAs layer simulation, GaAs and AlxGa1?xAs two-layer simulation, and all epilayers simulation are built for studying the model pithily, effectively and accurately.

Table 2. The comparison of simulation results and experimental results at 300 K.

Figs. 8(a) and 8(b) show the new simulation results of Hall outputs. In order to explore the difference between GaAs Hall sensor and Al0.24Ga0.76As/GaAs Hall sensors, we further conducted some tests on individual GaAs Hall devices to explore the influence of Al0.24Ga0.76As layer on the sensor. The experimental results are also added for comparison. The two different epilayer simulations show slight differences. That means only GaAs channel layer needs to be considered, which can effectively reduce the simulation complexity and time. It also shows AlxGa1?xAs is a suitable barrier material to form 2DEG.After considering analytic physical model, the simulation results are highly in consistent with the experimental results.The simulated sensitivity is also 0.28 V/(V·T). Furthermore, simulation results are shown in Fig. 8(b), which are in consistent with the experimental results after using analytic physical mode.

Table 2 summaries and compares simulation results using the Caughey-Thomas model with different parameters and our experimental results at 300 K. Regarding the mobility and Hall mobility, Refs. [16, 13] are relatively low. We used the Caughey-Thomas mobility model provided inRef. [13] and got a voltage sensitivity of 0.24 V/(V·T). We used another Caughey-Thomas mobility model provided by Dr Hadi Heidari in Ref. [16] and got a voltage sensitivity of 0.26 V/(V·T). If only using the common model in semiconductor, it can obtain 0.44 V/(V·T) sensitivity, but it leads to large error compared with 0.28 V/(V·T) in experimental results. It can be seen that we have obtained more accurate sensitivity after we have corrected the mobility model.

Table 3. The comparison of different types of Hall-effect devices.

Table 3 summaries specifications of our fabricated Al0.24Ga0.76As/GaAs Hall-effect sensor and compares with other works in terms of the sensitivity, offset, and input/output resistances. From the experimental results of our developed Hall sensor, four times higher sensitivity has been achieved compared to the state-of-the-art Hall sensors based on Si[15]and GaN[7]. It operates at the highest absolute sensitivity of 1.38 V/T. Also, it achieves a relatively low offset compared with the GaAs Hall-effect device in Ref. [18].

The simulation results are highly consistent with the experimental output.μmin= 500 cm2/(V·s),μmax= 8600 cm2/(V·s),α= 0,β=?2.1,γ=?1.182,δ= 0.394,N0= 6 × 1016cm–3are adopted for fitting the experimental data.

4.Conclusions

We have developed a GaAs based Hall sensor and its constant voltage-bias modelling. We used the COMSOL multiphysics simulation tool to study the influence of geometry on the Hall voltage. It is found that the sensitivity of the fully symmetrical Hall element is optimal whenW/his equal to 3. Studies have found that the sensitivity of the narrow cross is better than that of a fully symmetrical Hall element, and it is optimal when the length of the long contact port is twice the length of the short contact port. The cross-shaped Hall sensor has been simulated using Silvaco TCAD?to investigate the sensitivity and temperature performance. Simulation results are highly in consistent with the experimental results. The high sensitivity of 0.28 V/(V·T) is obtained from the experiment with a low offset of 5 mV. A high absolute sensitivity of 1.38 V/T is achieved at 5 V bias voltage. Moreover, the temperature dependence of the Hall sensor is investigated for the maximum Hall voltage of 72.5 mV and the sensitivity of 0.275 V/(V·T) at ?40 °C. The future work will focus on the design and implementation of a whole Hall microsystem with readout circuits using standard CMOS technology.

Acknowledgements

The work of Hua Fan was supported by the National Natural Science Foundation of China (NSFC) under Grant 61771111, supported by Sichuan Provincial Science and Technology Important Projects under Grant 22ZDYF2805, supported by the Open Foundation of the State Key Laboratory of Electronic Thin Films and Integrated Devices under Grant KFJJ202006, and supported by Intelligent Terminal Key Laboratory of Sichuan Province under Grant SCITLAB-1001.

The work of Quanyuan Feng was supported by Major Project of the National Natural Science Foundation of China under Grant 62090012.