D3 Hall Effect

Topic

When an electric current flows through a sample of semiconductor material while an applied magnetic field also passes through it—in a direction perpendicular to the current—a transverse Hall voltage is induced across the sample. The Lorentz force exerted by the applied magnetic field on the majority charge carriers constituting the current deflects them toward one of the sample's lateral edges. These deflected majority charge carriers accumulate at that edge until the resulting transverse electric field exactly balances the Lorentz force; this balanced transverse electric field constitutes the transverse Hall voltage measured between the sample's two lateral edges. A stronger applied magnetic field acting on the current increases the Lorentz force, thereby increasing the resulting transverse Hall voltage.

This transverse Hall voltage determines the Hall coefficient of the semiconductor sample. The sign of the Hall coefficient directly reveals the type of majority charge carrier: it is positive if holes are deflected and accumulate at the lateral edge, and negative if electrons do so. Meanwhile, the magnitude of the Hall coefficient reveals the concentration of these majority charge carriers; the magnitude is lower when the concentration is higher, because a higher concentration of majority charge carriers distributes the current among more individual carriers, thereby reducing the net deflection that produces the transverse Hall voltage. Consequently, a lower concentration of majority charge carriers results in a higher transverse Hall voltage—and a larger Hall coefficient magnitude—for a given electric current and applied magnetic field. Therefore, this model—which began with the transverse Hall voltage and the Hall coefficient—combines that Hall coefficient with the sample's conductivity (measured separately) to determine the Hall mobility of the majority charge carriers; this combination allows the Hall mobility to be obtained without requiring any additional tests beyond the two already performed on the sample. The fact that the Hall coefficient—determined here from the transverse Hall voltage—is greater in magnitude for a given measured conductivity means that the Hall mobility of the majority charge carriers is consequently higher as well.

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