The Hall effect finds important application in the electronics industry. It is u

Question

The Hall effect finds important application in the electronics industry. It is used to find the sign and density of the carriers of electric current in semiconductor chips. The arrangement is shown in Figure P22.66. A semiconducting block of thickness t and width d carries a current I in the x direction. A uniform magnetic field B is applied in the y direction. If the charge carriers are positive, the magnetic force deflects them in the z direction. Positive charge accumulates on the top surface of the sample and negative charge on the bottom surface, creat- ing a downward electric field. In equilibrium, the downward electric force on the charge carriers balances the upward mag- netic force and the carriers move through the sample without deflection. The Hall voltage %u0394VH 5 Vc 2 Va between the top and bottom surfaces is measured, and the density of the charge carriers can be calculated from it. (a) Demonstrate that if the charge carriers are negative the Hall voltage will be negative. Hence, the Hall effect reveals the sign of the charge carriers, so the sample can be classified as p-type (with positive majority charge carriers) or n-type (with negative). (b) Determine the number of charge carriers per unit volume n in terms of I, t, B, %u0394VH, and the magnitude q of the carrier charge.

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The Hall effect finds important application in the electronics industry. It is u

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