The semiconductor sample shown in Figure 8.1 is n-type silicon, having a rectang

Question

The semiconductor sample shown in Figure 8.1 is n-type silicon, having a rectangular cross section of 0.9 mm by 1.1 cm and a length of 1.3 cm . Assume the electron and hole mobilities are 0.13 and 0.03 m^2/V*s, respectively, at the operating temperature. Let B = 0.07 T and the electric field intensity in the direction of the current flow be 800 V/m. Find the magnitude of: (a) the voltage across the sample length: (b) the drift velocity; (c) the transverse force per coulomb of moving charge caused by B; (d) the transverse electric field intensity; (e) the Hall voltage.

The correct anwers are (a) 10.40 V (b) 104.0 m/s (c) 7.28 N/C; (d) 7.28 V/m (e) 80.1 mV

CHAPTER 8 Magnetic Forces, Materials, and Inductance 233 Figure 8.1 Equal currents directed into the material are provided by positive charges moving inward in (a) and negative charges moving outward in (b). The two cases can be distinguished by oppositely directed Hall voltages, as shown. magnetic field across it, to serve as electronic wattmeters, squaring elements, and so Returning to (4), we may therefore say that if we are considering an element of moving charge in an electron beam, the force is merely the sum of the forces on the individual electrons in that small volume element, but if we are considering an element of moving charge within a conductor, the total force is applied to the solid conductor itself. We will now limit our attention to the forces on current-carrying conductors. In Chapter 5 we defined convection current density in terms of the velocity of the volume charge density, The differential element of charge in (4) may also be expressed in terms of volume charge density, Thus or We saw in Chapter 7 that J dv may be interpreted as a differential current element; that is Remember that dv is a differential volume element and not a differential increase in velocity.

Explanation / Answer

part a)

we are given E=800 V/m

means if length is 1 m ,voltage =800 V

when length is 1.3 m, the voltage is=800*1.3 V

part b)

drift velocity=v=uE=0.13*800=(13*8) m/s

u is mobility of electron

part c)

transverse force=evB

tranverse force per Colomb=evB/e=vB=13*8*0.07 N/C

part d)

transverse electric field intensity=transverse force per coloumb=13*8*0.07 N/C

part e)

hall voltage=IB/net=AvB/t=L*t*v*B/t=LvB

I=neAv

n is no of particles per unit volume

t=thickness=0.9 mm=0.9*10-3 m

L=1.3 cm=0.013 m

v is drift velocity

B is magnetic field

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