Semiconductor Sensors & Hall-Effect Devices

Semiconductors as sensors. Learn the Hall effect (Lorentz force, Hall voltage, Hall coefficient and carrier-type determination), linear Hall sensors, Hall switches/latches, current sensing and position/speed sensing, other magnetic sensors (AMR/GMR/TMR overview); temperature sensors (diode/PTAT, thermistors NTC/PTC, silicon resistive), piezoresistive pressure/strain sensors and MEMS, photodetectors and image sensors, gas sensors (metal-oxide, FET-based), radiation detectors (PIN, Si drift, CdTe/CZT) — covering physical effect, structure, output, sensitivity, temperature effects, conditioning and applications — with Python computing Hall voltages, piezoresistive bridge output and PTAT/diode temperature signals.

Semiconductor properties depend on magnetic field, temperature, stress, light, chemistry and radiation — each dependence is a sensor. Integrated with CMOS signal processing, they form the smart sensors in cars, phones and factories.

The Hall effect is both a measurement technique (carrier type, density and mobility) and one of the most widely used sensors.

An analogy

In a Hall sensor, electrons flowing through a strip are like cars on a road with a crosswind (magnetic field): they drift to one side, piling up and creating a sideways 'height difference' (Hall voltage) proportional to the wind.

Hall-effect sensors

Device types:

Temperature sensors

Silicon diodes and bipolar transistors (−2 mV/K, PTAT ΔV_BE for accurate on-chip sensors with digital outputs), NTC thermistors (large negative TC, nonlinear — Steinhart-Hart), silicon PTC 'spreading-resistance' sensors (KTY), and thermocouples/RTDs interfaced by semiconductor front ends. On-chip sensors protect processors and power devices from overheating.

Pressure, MEMS, gas and radiation

Piezoresistive silicon (π ≈ 72 × 10⁻¹¹ Pa⁻¹ for p-type ⟨110⟩) on thin diaphragms makes MAP, tyre and medical pressure sensors; capacitive MEMS make accelerometers, gyros and microphones. Metal-oxide (SnO₂) gas sensors change resistance with adsorbed gases; ISFETs sense pH. Reverse-biased PIN, silicon drift and CdTe/CZT detectors count and measure ionising radiation for medical imaging and physics.

Signal conditioning and errors

Sensor outputs are small and temperature-sensitive: offsets, sensitivity drift, nonlinearity, mechanical stress on packages and 1/f noise. Integrated sensors use chopping/spinning current, on-chip temperature compensation, trimming and digital calibration; outputs are ratiometric analogue, PWM, SENT, or I²C/SPI digital.

Formulas

Worked example: Carrier density from Hall

Given: V_H 5 mV, I 1 mA, B 0.5 T, t 100 µm

Find: n.

Answer: 6.2 × 10²¹ m⁻³ = 6.2 × 10¹⁵ cm⁻³

Worked example: PTAT slope

Given: N = 4

Find: dΔV_BE/dT.

Answer: 119 µV/K

Worked example: NTC

Given: 10 kΩ at 25 °C, B 3950 K

Find: R at 50 °C.

Answer: ≈ 3.6 kΩ

Hall plate

            B (into page) ⊗
     ┌──────────────────────────┐   + + + + (holes/deficit side)
  I →│  electrons deflected ↑   │→  V_H measured across width
     └──────────────────────────┘   − − − − (electrons pile up)
  V_H = IB/(qnt): thin plate (small t), low n → large signal; sign reveals carrier type
  Spinning-current technique cancels offset; integrated flux concentrators boost B

The Lorentz force pushes moving carriers sideways until the resulting transverse field balances it. Thin, lightly doped (or low-carrier, high-mobility) films give large Hall voltages. Integrated Hall sensors use spinning-current offset cancellation, temperature compensation and digital calibration.

Hall, piezoresistive and temperature sensor signals

import math
# Hall sensor, piezoresistive pressure bridge, diode/PTAT temperature sensors
q = 1.602e-19
n, t, I, B = 1e16 * 1e6, 10e-6, 1e-3, 0.1       # n in m^-3, thickness 10 um, 1 mA, 100 mT
VH = I * B / (q * n * t)
print(f"Si Hall plate (n 1e16 cm^-3, 10 um): VH = {VH*1e3:.2f} mV at 100 mT; sensitivity {VH/B/I:.0f} V/(A*T)")
n2 = 2e16 * 1e6                                # thin InSb film: n ~ 2e16 cm^-3, 1 um thick (high mobility, low offset)
print(f"InSb film (n 2e16 cm^-3, 1 um thick): VH = {I*B/(q*n2*1e-6)*1e3:.1f} mV; Hall coefficient of the Si plate = {1/(q*n):.2e} m^3/C")
pi_l, sigma = 72e-11, 50e6                      # longitudinal piezoresistive coefficient (1/Pa), stress 50 MPa
dR = pi_l * sigma
print(f"piezoresistor: dR/R = pi*sigma = {dR*100:.2f}% -> full-bridge output {3.3*dR*1e3:.0f} mV from 3.3 V")
VT = 0.02585
print(f"PTAT: two diodes at 8:1 current density: dVBE = VT*ln8 = {VT*math.log(8)*1e3:.2f} mV at 300 K ({8.617e-5*math.log(8)*1e6:.0f} uV/K)")
print(f"single diode at 100 uA: about -2 mV/K -> 50 K change gives {-2*50} mV")
# Si Hall plate (n 1e16 cm^-3, 10 um): VH = 6.24 mV at 100 mT; sensitivity 62 V/(A*T)
# InSb film (n 2e16 cm^-3, 1 um thick): VH = 31.2 mV; Hall coefficient of the Si plate = 6.24e-04 m^3/C
# piezoresistor: dR/R = pi*sigma = 3.60% -> full-bridge output 119 mV from 3.3 V
# PTAT: two diodes at 8:1 current density: dVBE = VT*ln8 = 53.75 mV at 300 K (179 uV/K)
# single diode at 100 uA: about -2 mV/K -> 50 K change gives -100 mV

A 10 µm silicon Hall plate gives ~6 mV at 100 mT with 1 mA — tens of mV/T, which is why integrated Hall ICs need amplification and offset cancellation; thin InSb films give ~5× more. A silicon piezoresistor sees a 3.6% change at 50 MPa (a full bridge gives ~120 mV from 3.3 V). PTAT sensing uses the precisely known ΔV_BE = V_T ln 8 ≈ 54 mV at 300 K (179 µV/K).

Common mistakes

Applications

Key takeaways

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