(b) What is the number of free electrons per copper atom? - ECE360

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fig_18_04

18.1
(a)

Compute the electrical conductivity of a 5.1
-
mm diameter cylindrical
silicon specimen 51 mm long in which a current of 0.1 A passes in an axial
direction. A voltage of 12.5 V is measured across two probes that are separated
by 38 mm.


(b)

Compute the resistance over the entire 51 mm of the specimen.




18.10
(a)

Calculate the drift velocity of electrons in germanium at room temperature and
when the magnitude of the electric field is 1000 V/m. (b) Under these circumstances,
how long does it take an electron to traverse a 25
-
mm length of crystal?


(mobility of electrons in Ge is 0.38 m2/v
-
s)


18.11
At room temperature the electrical conductivity and the electron mobility
for copper are 6.0


10
7

(ohm
-
m)
-
1 and 0.0030 m2/V
-
s, respectively. (a) Compute the
number of free electrons per cubic meter for copper at room temperature. (b) What is the
number of free electrons per copper atom? Assume a density of 8.9 g/cm3.


= 1.25


10
29

m
-
3

(b)

In

order

to

calculate

the

number

of

free

electrons

per

copper

atom,

we

must

first

determine

the

number

of

copper

atoms

per

cubic

meter,

N
Cu
.

From

Equation

4
.
2

(and

using

the

atomic

weight

value

for

Cu

found

inside

the

front

cover

viz
.

63
.
55

g/mol)

= 8.43


10
28

m
-
3

And, finally, the number of
free electrons per aluminum
atom is just
n/N
Cu


18.18
(a)

Using the data presented in Figure 18.16, determine the number of free
electrons per atom for intrinsic germanium and silicon at room temperature (298 K). The
densities for Ge and Si are 5.32 and 2.33 g/cm3, respectively.


(b)

Now explain the difference in these free
-
electron
-
per
-
atom values.

Intrinsic Semiconduction

table_18_03

Extrinsic Semiconduction

*18.21 At room temperature the electrical conductivity of PbTe
(Lead telluride) is 500 (Ω
-
m)

1
, whereas the electron and
hole mobilities are 0.16 and 0.075 m
2
/V
-
s, respectively.
Compute the intrinsic carrier concentration for PbTe at room
temperature.

*18.25
An n
-
type semiconductor is known to have an electron
concentration of 3


10
18 m
-
3. If the electron drift velocity is 100
m/s in an electric field of 500 V/m, calculate the conductivity of
this material.


18.30
Germanium to which 5


10
22

m
-
3 Sb atoms have been added is an extrinsic
semiconductor at room temperature, and virtually all the Sb atoms may be thought of as
being ionized (i.e., one charge carrier exists for each Sb atom). (a) Is this material n
-
type or p
-
type? (b) Calculate the electrical conductivity of this material, assuming
electron and hole mobilities of 0.1 and 0.05 m2/V
-
s, respectively.


= 800 (

-
m)
-
1

The Temperature Dependence of Carrier Concentration



18.32
Calculate the conductivity of intrinsic silicon at 100
°
C.

10

Intrinsic Semiconductors: Conductivity vs
T

• Data for
Pure Silicon
:


--



increases with
T


--

opposite to metals

Adapted from Fig. 18.16,
Callister & Rethwisch 8e.


material


Si


Ge


GaP


CdS

band gap (eV)


1.11


0.67


2.25


2.40

Selected values from Table 18.3,
Callister & Rethwisch 8e.


Factors That Affect Carrier Mobility



18.38

Calculate the room
-
temperature electrical conductivity of
silicon that has been doped with 2
×

10
23

m

3 of arsenic atoms.