Direct Energy, 2018a

100 5.6 Problems
5.6 Problems
5.1. Suppose that you are using a piece of semiconductor as a Hall eect
device to measure a magnetic eld. 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
eld. 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 eect device. The
device has a thickness of d thick =1mm. It is placed in an external
magnetic eld of | −→ −5
B | =10 Wb
cm . A Hall voltage of 5 μV is measured
2
when a current of 3 mA is applied. Calculate p, the charge (hole)
1
concentration in units cm . 3
5.3. A Hall eect device is used to measure the strength of an external
magnetic eld. The device is oriented in the way described in Fig.
5.1. It is made from a cube of p-type silicon with hole concentration
5 · 10 15 cm −3 where the length of each side of the cube is 1 mm. A
current of 3 mA is applied through the device. The voltage measured
across the device is 2.4 mV. Find the strength of the external magnetic
ux density, | −→ B |.
5.4. A Hall eect device is used to measure the strength of an external
magnetic eld. The device is oriented in the way described in Fig.
5.1. It is made from a material of length l =3mm, width w =0.5
mm, and thickness d thick =0.5 mm. It has a hole concentration of
p =10 20 m −3 . In an experiment, the devices was placed in an external
magnetic eld of ∣ −→ B ∣ =2.5 Wb m and a voltage of 9 mV was measured.
2
What current was used in the experiment?
5.5. Two expressions were given for the Hall resistance:
R H = B z · w
qp l·d thick
and R H = h . q 2 n
Show that both expressions have the units of ohms.