Geometrical Magnetoresistance in Multi-Gate FDSOI Structures
Magnetoresistance is a direct consequence of carrier deflection by a magnetic field. When carriers do not follow the shortest path from source to drain, the channel resistance increases. The relation between the resistances obtained when the magnetic field is present or not yields:
RB = R0 ( 1 + μMR2 B2 )
The carrier deviation by the Lorentz force is shown in Fig. 1a. The deviation is modulated by the device geometry. If the transistor is long and narrow (W/L < 1) the Hall field opposes to the Lorentz force and the magnetoresistance is weak. However, when the sample is wide and short (W/L >> 1) the Hall field is short-circuited by the end contacts and the Lorentz force is not compensated. Hence, carriers are deviated and the magnetoresistance is maximum. Fig. 2 illustrates the simulated electron mobility against the aspect ratio (W/L) for several magnetic field orientations. The magnetoresistance is much higher for normal magnetic fields (and W/L > 5) than for transversal fields as fully documented by experimental data .
On the other hand, in double-gate FinFETs (Fig. 1b), the magnetoresistance is high even in narrow samples (W ~ L). This surprising result was explained by the lateral gate action which cancels the Hall voltage so preventing the compensation of the Lorentz force and resulting in the magnetoresistance .
TCAD numerical simulations  were carried out to clarify the carrier deflection and magnetoresistance mobility in FinFETs. The impact of the device architecture, thicknesses, gate biasing scheme, and magnetic field orientation is documented and explained.
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 Synopsys TCAD, Sentaurus Workbench Advanced, Version H-2013.10, Synopsys, Inc.