Why there is difference between Halleffect and sensing measurement in the type of semiconductor? Example the first declare p type semiconductor while the second declare n type?
Whether the free carriers are electrons or holes determines the sign of the Hall constant (they are electrons in n-type semiconductors and holes in p-type semiconductors). For details, you may wish to consult Chapter 1 of [1], Chapters 6 and 12 of [2], and [3].
[1] NW Ashcroft, and ND Mermin, Solid State Physics (Harcourt, New York, 1976).
[2] JD Patterson, and BC Bailey, Solid State Physics: Introduction to the Theory, 3rd edition (Springer, Berlin, 2018).
[3] M Grundmann, The Physics of Semiconductors: An Introduction Including Nanophysics and Applications, 2nd edition (Springer, Berlin, 2010).
Hall effect allows us to find out whether the charge carriers in a conductor are positively or negatively charged. Beyond that, we can measure the number of such carriers per unit volume of the conductor.
A Hall potential difference V is associated with the electric field across strip width d. The magnitude of that potential difference is:
V= E.d
By connecting a voltmeter across the width (remember the voltmeter has a positive terminal and a negative one), we can measure the potential difference between the two edges of the strip. Moreover, the voltmeter can tell us which edge is at a higher potential.
When the charged particle enters the strip, due to the presence of a magnetic field it will be subject to a magnetic force and moves to one side of the strip depending on its charge. Charges will accumulate leaving the other side of the strip opp.-charge deficient. An electric field is then created and grows with the increase of accumulated charges until the force due to the electric field balances (in magnitude) the magnetic force. Depending on the reading of the voltage measuring device, if positive then the carriers are positive and if negative then the carriers are negative.
Attached below is a file with some figures that you can check.
In a magnetic field, if there is a current, there is a force
F = BIL, with
B: the magnetic field (tesla)
I : the current
L : the length.
On separate charged carriers, this becomes
F = Bvq
with v : the speed
q : the charge (elementary charge of the electron)
In a hall-effect, the force F is equibirated by the electrical field
F = Eq, or if we set E = V/W, with V the voltage over the Hall element and W the width of the
Hall element, we get:
V = BvW.
You see then, that to increase the Hall effect, it is necessary to make the speed v of the carriers in
the Hall element as large as possible. This is done by taking a material with a limited number of carriers, a N or P semiconductor. (A metal has much more conducting electrons, leading to low speed v, and low hall effect.) You also see the charge q falls out of the equation. However, for N and P semiconductors, the carriers have opposite charge, negative for N positive for P, leading to opposite speed v and different sign in Hall voltage.
Hello Bushra A Hasan ,
Can you explain what you mean by the " difference between Halleffect and sensing measurement"? Specifically, what is a sensing measurement? No one, who posed solutions to your question, mentioned anything about sensing measurements.
Regards,
Tom Cuff
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