Hall Sensor Output Voltage Linearity

Technical Background of Hall Sensor Linearity

Hall effect sensors (Hall sensors) are core magnetic sensing components in electronic systems, widely applied in current detection, position sensing, speed measurement and magnetic field measurement scenarios of automotive electronics, industrial control and consumer electronics. Output voltage linearity is the core performance parameter of linear Hall sensors, which is defined as the degree of deviation between the actual output voltage curve and the ideal straight-line output curve when the sensor is exposed to a continuously changing magnetic field. The linearity is quantified by linearity error (expressed as %FS, percentage of full-scale output), with a smaller value representing better linearity. For precision current detection circuits, the linearity error of Hall sensors must be controlled within ±1%FS to ensure the detection error is less than 0.5%. All test data in this paper are derived from standardized laboratory measurements with no brand-related information involved. The baseline test environment is 25℃ and 50%RH, and the test equipment includes a precision Gauss magnetometer (magnetic field accuracy: ±0.1mT), a high-precision voltage tester (voltage accuracy: ±0.001mV), a temperature-controlled test chamber and a DC constant current source for sensor power supply.

Test Methods for Hall Sensor Linearity

This test adopts the "full-scale magnetic field scanning method" specified in the IEC 60947-5-1 international standard to accurately measure the output voltage linearity of Hall sensors, which can eliminate the interference of power supply voltage fluctuation and ambient magnetic field noise on test results. The specific test process is as follows: first, select three groups of linear Hall sensor samples with the same power supply voltage (5V DC), full-scale magnetic field range (-200mT ~ +200mT) and surface mount package (3.0mm×2.5mm×1.0mm), differing only in semiconductor substrate materials (n-type silicon Si, indium antimonide InSb, gallium arsenide GaAs); second, power on the sensors with a stable 5V DC power supply, place the samples in a shielded magnetic field test platform to isolate external stray magnetic fields, and adjust the magnetic field intensity from -200mT to +200mT in 10mT gradient steps; third, record the actual output voltage value of each sensor at each magnetic field point, and fit the ideal linear output voltage curve according to the sensor's rated sensitivity; finally, calculate the linearity error using the endpoint linearity method: linearity error = (maximum deviation between actual voltage and ideal voltage) / full-scale output voltage × 100%FS.

Supplementary characteristic tests were completed to comprehensively evaluate linearity stability: temperature dependence tests at -40℃, 25℃, 85℃ and 125℃; power supply voltage fluctuation tests (4.5V~5.5V DC); long-term aging tests (1000h continuous operation at 85℃). Each magnetic field point was tested 20 times for each sample, the average value was taken after removing the maximum and minimum values, and the overall test error of linearity was controlled within ±0.05%FS.

Output Voltage Linearity Characteristics Data

1. Baseline (25℃, 5V DC) linearity data: Under the magnetic field range of -200mT ~ +200mT, the linearity error of Si-based Hall sensors is ±0.85%FS, the InSb-based sensors are ±1.25%FS, and the GaAs-based sensors are ±0.55%FS. The GaAs-based Hall sensor has the optimal linearity performance because gallium arsenide has a higher electron mobility and a more stable Hall coefficient under uniform magnetic field conditions, with a rated sensitivity of 10mV/mT and a full-scale output voltage of 4V (0.5V~4.5V). The Si-based sensor has a sensitivity of 8mV/mT and full-scale output voltage of 3.2V, while the InSb-based sensor has a higher sensitivity of 15mV/mT and full-scale output voltage of 5V (0V~5V), but its large electron effective mass leads to higher linearity error. At the zero magnetic field point (0mT), the offset voltage of GaAs-based sensors is 2.502V (offset error ±0.08%), Si-based is 2.510V (offset error ±0.4%), and InSb-based is 2.525V (offset error ±1.0%).

2. Temperature-dependent linearity data: For GaAs-based Hall sensors, the linearity error is ±0.62%FS at -40℃, ±0.55%FS at 25℃ and ±0.78%FS at 125℃, with a total linearity variation of only 0.23%FS and a temperature coefficient of linearity of ±0.0019%FS/℃. Si-based sensors have a linearity variation of 0.55%FS (±0.70%FS at -40℃, ±1.25%FS at 125℃), temperature coefficient ±0.0046%FS/℃. InSb-based sensors have the largest linearity variation of 1.1%FS (±1.05%FS at -40℃, ±2.15%FS at 125℃), temperature coefficient ±0.0092%FS/℃. The excellent temperature stability of GaAs-based sensors is derived from its low temperature coefficient of Hall coefficient, which effectively suppresses the linearity drift caused by carrier mobility changes with temperature.

3. Power supply voltage dependent linearity data: At 25℃ and magnetic field ±200mT, when the power supply voltage changes from 4.5V to 5.5V DC, the linearity error of GaAs-based sensors changes from ±0.58%FS to ±0.52%FS (variation ≤0.06%FS), Si-based changes from ±0.90%FS to ±0.80%FS (variation ≤0.10%FS), and InSb-based changes from ±1.35%FS to ±1.15%FS (variation ≤0.20%FS). All three sensor types show low sensitivity to power supply voltage fluctuations, with the GaAs-based sensors having the best power supply rejection ratio (≥60dB).

4. Long-term aging linearity data: After 1000h continuous high-temperature aging at 85℃, the linearity error of GaAs-based sensors increases from ±0.55%FS to ±0.68%FS (variation 0.13%FS), Si-based from ±0.85%FS to ±1.05%FS (variation 0.20%FS), and InSb-based from ±1.25%FS to ±1.65%FS (variation 0.40%FS). The slight linearity degradation is mainly caused by the thermal aging of the sensor's internal amplifying circuit and the slight drift of the Hall element's contact resistance, with no significant impact on actual application accuracy.

Process Details Affecting Output Voltage Linearity

The output voltage linearity of Hall sensors is closely related to the preparation process of the Hall element and the integrated circuit packaging process, and the key process parameters and their influence rules are as follows: 1. Semiconductor substrate doping: The optimal doping concentration of GaAs substrate is 5×10¹⁷ cm⁻³, a doping deviation of ±1×10¹⁷ cm⁻³ will lead to a linearity error increase of 0.12%FS; Si substrate doping concentration is 1×10¹⁸ cm⁻³, a deviation of ±2×10¹⁷ cm⁻³ causes a 0.15%FS linearity increase. Excessively low doping reduces carrier concentration and sensitivity, while excessively high doping leads to uneven carrier distribution and increased linearity error. 2. Hall element etching: The rectangular Hall element has an optimal aspect ratio (length/width) of 2:1, a ratio deviation of ±0.2 leads to a 0.08%FS linearity error increase; the etching surface roughness Ra ≤0.05μm, Ra>0.1μm will cause a 0.10%FS linearity increase due to uneven current distribution. 3. Contact electrode deposition: The Au-Ge-Ni electrode is sputtered on the Hall element surface with a thickness of 200nm-250nm, a thickness deviation of ±50nm increases the contact resistance by 0.5Ω and linearity error by 0.05%FS; electrode alignment deviation of ±0.5μm leads to a 0.07%FS linearity increase. 4. Amplifier circuit calibration: The integrated operational amplifier of linear Hall sensors is calibrated by laser trimming, the trimming precision is controlled at ±0.01Ω, a precision deviation leads to a 0.1%FS linearity error increase, which is the core process to improve the final linearity performance of the sensor.

Current Status of Commercial Application

From the perspective of industrial commercialization, Si-based linear Hall sensors with linearity error of ±0.8%FS~±1.5%FS have achieved large-scale commercialization, accounting for about 65% of the linear Hall sensor market share, and are widely used in consumer electronics, low-precision current detection and position sensing due to their mature process and low production cost. GaAs-based linear Hall sensors with linearity error of ±0.3%FS~±0.8%FS have also achieved large-scale commercialization, accounting for about 25% of the market share, and are mainly applied in automotive electronic controllers, precision industrial current measurement and aerospace magnetic field detection due to their excellent linearity and temperature stability. InSb-based linear Hall sensors with linearity error of ±1.0%FS~±2.5%FS are in small-batch mass production, accounting for about 8% of the market share, and are used in high-sensitivity magnetic field measurement scenarios with low linearity requirements. New composite substrate Hall sensors (GaAs-Si heterojunction) are in the sample verification stage, with linearity error controlled within ±0.2%FS and sensitivity up to 20mV/mT, which can meet the ultra-precision detection requirements of high-end industrial control systems.

Existing Technical Pain Points

1. High magnetic field linearity deterioration: Under magnetic field intensity exceeding ±300mT (e.g., heavy current detection in new energy vehicle power systems), the linearity error of conventional Hall sensors increases sharply. The GaAs-based sensor's linearity error reaches ±1.2%FS at ±400mT, Si-based up to ±2.0%FS, and InSb-based up to ±3.5%FS, exceeding the precision requirements of high-current detection circuits. The current high magnetic field resistant Hall sensors reduce sensitivity by 30% to improve linearity, which conflicts with the high-sensitivity demand of practical applications. 2. Ultra-low temperature linearity drift: At ultra-low temperatures below -60℃ (e.g., aerospace and polar exploration equipment), the carrier mobility of semiconductor substrates changes drastically, the linearity error of InSb-based sensors increases to ±3.0%FS, and Si-based sensors to ±1.8%FS, which cannot meet the low-temperature precision detection requirements. High-temperature resistant semiconductor materials are still in the R&D stage with poor batch consistency and high production cost. 3. Process consistency limitation: The linearity error deviation of the same batch of Si-based Hall sensors reaches ±0.15%FS, which is twice that of GaAs-based sensors (±0.08%FS), due to uneven substrate doping concentration and inconsistent laser trimming precision. Improving process consistency increases production costs by 20% and reduces production efficiency by 15%. 4. Cost-performance imbalance: The production cost of GaAs-based Hall sensors is 3 times that of Si-based sensors, mainly due to the high price of GaAs substrate and complex etching process, which restricts the large-scale application of GaAs-based sensors in low-cost scenarios; Si-based sensors have balanced cost and performance, but their linearity and temperature stability are difficult to meet the ultra-precision requirements of high-end electronic systems.