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please dont briefly answer, explain every step of the answer. A slab of semicond

ID: 1560117 • Letter: P

Question

please dont briefly answer, explain every step of the answer.

A slab of semiconductor has a rectangular cross-section with a 10 cm width and 1 mm thickness. The slab is placed under a uniform magnetic field of 0.8 T and carries a current of I = 0.1 mA. When the potential difference between points a and b are measured, it is found that V_ab = +1mV (Hall voltage). The geometry and the directions are shown on the figure. (a) Find the electric field E due to the Hall field. (Note that there is an additional electric field along the x-direction which drives the current. Ignore this and find the Hall field only.) (b) Find the drift velocity, v_d. (c) What is the sign of the charge of the charge carriers? (d) Find the current density J. (e) Find the density of the charge carriers, n.

Explanation / Answer


a)

electric field E = Vab/ab = 1*10^-3/(0.01) = 0.1 V/m

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b)


In the slab


magnetic force = electric force

q*vd*B = E*q


vd = E/B

vd = 0.1/0.8 = 0.125 m/s


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(c)

negative charge

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(d)

current density J = I/A

J = 0.1*10^-3/(0.01*10^-3) = 10 A/m^2

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(e)

vd = I/(n*e*A)

Vd = J/(n*e)

e = charge of electron

0.125 = 10/(n*1.6*10^-19)

n = 5*10^20