5.5: Problems
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5.1. Suppose that you are using a piece of semiconductor as a Hall effect device to measure a magnetic field. You supply a DC current through the device. You would like to replace the piece of semiconductor with another one that will give a larger output for the same external magnetic field. List two ways you can change the piece of semiconductor so that the output would increase. (Specify both the property and whether it would need to be increased or decreased.)
5.2. A piece of p-type semiconductor is used as a Hall effect device. The device has a thickness of dthick=1mm. It is placed in an external magnetic field of |→B|=10−5Wbcm2. A Hall voltage of 5μV is measured when a current of 3mA is applied. Calculate p, the charge (hole) concentration in units 1cm3.
5.3. A Hall effect device is used to measure the strength of an external magnetic field. The device is oriented in the way described in Fig. 5.1.1. It is made from a cube of p-type silicon with hole concentration 5⋅1015cm−3 where the length of each side of the cube is 1mm. A current of 3mA is applied through the device. The voltage measured across the device is 2.4mV. Find the strength of the external magnetic flux density, |→B|.
5.4. A Hall effect device is used to measure the strength of an external magnetic field. The device is oriented in the way described in Fig. 5.1.1. It is made from a material of length l=3mm, width w=0.5mm, and thickness dthick=0.5mm. It has a hole concentration of p=1020m−3. In an experiment, the devices was placed in an external magnetic field of |→B|=2.5Wbm2 and a voltage of 9mV was measured. What current was used in the experiment?
5.5. Two expressions were given for the Hall resistance:
RH=Bzqp⋅wl⋅dthick and RH=hq2n.
Show that both expressions have the units of ohms.