Determination of the Hall voltage in devices with arbitrary aspect ratio and probe position

Unconventional Measuring Transducers

“…Za mjerenje napona u praksi se sve ËeπÊe rabe otporniËki, kapacitivni i kompenzirani (RC) djelitelji [2], naponski optiËki mjerni pretvaraËi [3], [4], [5], [6], a za mjerenje struje shuntovi (tj. pad napona na otporniku) [7], strujni optiËki mjerni pretvaraËi [8], Hall sonde [9] i di/dt pretvaraËi (Rogowsky svici) [2]. »esto se, zbog teaenje prema jednostavnosti i kompaktnosti, izrauju kombinirani mjerni pretvaraËi koji u sebi ujedinjuju elemente za mjerenje napona i struje.…”

Experimental validation of a new analytical model for the position-dependent hall voltage in semiconductor devices

“…In fact, the ratio V H (y)/V H0 is slightly smaller than 1 even at y = 0, and decreases rapidly when y departs from 0. It is also worth noting that the agreement of the theory (continuous lines) with the experiments (symbols) is very good, this showing that the model of [6] is based on sound hypotheses. This is also corroborated by the fact that two devices with different sizes, but with the same aspect ratio W/L, provide exactly the same experimental behavior of V H (y)/V H0 .…”

“…A new result was shown by some of the Authors in [6], based on a more general approach to the Hall problem on devices like resistors and MOSFETs, that led to the determination of the Hall voltage as a function of the position along the y axis in the devices under test with no constraints on the W/L ratio or probe position. The usefulness of the calculation is augmented if the result is expressed in terms of normalized variables depending on purely geometrical parameters.…”

“…The boundary conditions of the problem are: ψ = 0, ψ = I/h along the insulating boundaries (x = ±W/2), with I the bias current and h the charge-layer thickness; ∂ψ/∂y = −µ H BI/(hW ) along the contact boundaries (y = ±L/2), with µ H the Hall mobility. After determining the stream function, the Hall voltage V H is calculated as reported in [6]. It reads…”

“…The usefulness of the calculation is augmented if the result is expressed in terms of normalized variables depending on purely geometrical parameters. For this reason, an analytical approach was sought in [6]. As shown in this paper, special devices have been designed and manufactured, allowing for the measuring of the Hall voltage at different positions along the channel.…”