Consider a short cylinder with its axis parallel to the drift velocity. Ithas a cross-sectional area A, a length vd At, and a volume Avd At. If thereare n charge carriers per volume, each of charge q, the charge in thatcylinder is(charge)(carriers/volume)(volume), orAQ = (q)(n)(Avd At).Now we substitute this expression for AQ = Iat. The current density isJ=nqvd. If there is more than one type of charge carrier, we simply add the%3Dcurrent densities for eeach type of charge carrier to find the total currentdensity. Silicon is doped with aluminum until it has 5.0 x 1023 holes/m3 asits positive charge carriers and almost no free electrons. If the currentdensity in the doped silicon is 16.0 A/m- î calculate the drift velocity of theholes. UseI and q= 1.6 x10-19Cnq8.0 x 10-4m/s5.0 x 10 23m/sre2.0 x 10-4m/sO.1.6 x 10-19m/s

Answered: Now we substitute this expression for…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Consider a short cylinder with its axis parallel to the drift velocity. It
has a cross-sectional area A, a length vd At, and a volume Avd At. If there
are n charge carriers per volume, each of charge q, the charge in that
cylinder is
(charge)(carriers/volume)(volume), or
AQ = (q)(n)(Avd At).
Now we substitute this expression for AQ = Iat. The current density is
J=nqvd. If there is more than one type of charge carrier, we simply add the
%3D
current densities for eeach type of charge carrier to find the total current
density. Silicon is doped with aluminum until it has 5.0 x 1023 holes/m3 as
its positive charge carriers and almost no free electrons. If the current
density in the doped silicon is 16.0 A/m- î calculate the drift velocity of the
holes. Use
I and q= 1.6 x10-19C
nq
8.0 x 10-4m/s
5.0 x 10 23m/s
re
2.0 x 10-4m/s
O.
1.6 x 10-19m/s

Expert Solution

Step 1

We consider a short cylinder with an axis parallel to the drift velocity and it has a cross-sectional area A and length v_d^{$∆ t$ and a volume Av}d ^{$∆ t$}

if there are n charge per unit volume, each charge q the change in that cylinder is

$∆ Q = qn ({Av}_{d} ∆ t) and ∆ Q = I ∆ t We also know that J = {nqv}_{d}$

Now If there is more than one type of charge carrier, we simply add the current densities for each type of charge carrier to find the total current density.

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