Semiconductor Physics and Devices: Basic Principles, 4th edition
Chapter 1
By D. A. Neamen
Exercise Solutions
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Chapter 1
Exercise Solutions
TYU 1.2
(a) Number of atoms per (100) lattice plane
Ex 1.1
(a) Number of atoms per unit cell
Surface Density
(b) Volume Density
=
cm
(b) Number of atoms per (110) lattice plane
cm
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Ex 1.2
Intercepts of plane; p=1, q=2, s=2
Inverse;
Multiply by lowest common denominator,
plane
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Ex 1.3
(a) Number of atoms per (100) plane
Surface Density
cm
(c) Number of atoms per (111) lattice plane
Lattice plane area
where
Surface Density
cm
(b) Number of atoms per (110) plane
Surface Density
Then lattice plane area
Surface Density
cm
cm
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Test Your Understanding Solutions
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TYU 1.1
TYU 1.3
Number of atoms per unit cell
(a) For (100) planes, distance
(b) For (110) planes, distance
Volume Density
cm
Radius
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Semiconductor Physics and Devices: Basic Principles, 4th edition
Chapter 1
By D. A. Neamen
Exercise Solutions
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TYU 1.4
(a) 8 corner atoms
(b) 6 face-centered atoms
(c) 4 atoms totally enclosed
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TYU 1.5
Number of atoms in the unit cell
Volume Density
cm
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Semiconductor Physics and Devices: Basic Principles, 4th edition
Chapter 1
By D. A. Neamen
Problem Solutions
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Chapter 1
Problem Solutions
Then
1.1
(a) fcc: 8 corner atoms
atom
6 face atoms
atoms
Total of 4 atoms per unit cell
(b) bcc: 8 corner atoms
atom
1 enclosed atom
=1 atom
Total of 2 atoms per unit cell
(c) Diamond: 8 corner atoms
atom
Ratio
(d) Diamond lattice
Body diagonal
6 face atoms
atoms
4 enclosed atoms = 4 atoms
Total of 8 atoms per unit cell
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Unit cell vol
8 atoms per cell, so atom vol
1.2
(a) Simple cubic lattice:
Then
Unit cell vol
1 atom per cell, so atom vol
Ratio
Then
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Ratio
(b) Face-centered cubic lattice
1.3
(a)
; From Problem 1.2d,
Unit cell vol
Then
4 atoms per cell, so atom vol
Then
Center of one silicon atom to center of
nearest neighbor
(b) Number density
Ratio
(c) Body-centered cubic lattice
Unit cell vol
2 atoms per cell, so atom vol
cm
(c) Mass density
grams/cm
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Semiconductor Physics and Devices: Basic Principles, 4th edition
Chapter 1
By D. A. Neamen
Problem Solutions
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(a)
1.4
(a) 4 Ga atoms per unit cell
(b)
Number density
Density of Ga atoms
4 As atoms per unit cell
Density of As atoms
(b) 8 Ge atoms per unit cell
(c) A-atoms: # of atoms
cm
Density
cm
cm
B-atoms: # of atoms
Number density
Density of Ge atoms
cm
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1.5
From Figure 1.15
(a)
Density
cm
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1.9
(a)
# of atoms
(b)
Number density
cm
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Mass density
1.6
gm/cm
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(b)
# of atoms
1.7
(a) Simple cubic:
Number density
(b) fcc:
cm
(c) bcc:
(d) diamond:
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1.8
Mass density
gm/cm
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1.10
From Problem 1.2, percent volume of fcc
Semiconductor Physics and Devices: Basic Principles, 4th edition
Chapter 1
By D. A. Neamen
Problem Solutions
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atoms is 74%; Therefore after coffee is
Surface density
cm
ground,
Volume = 0.74 cm
For 1.12(a) and (b), Same material
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1.11
(b)
(b) For 1.12(a), A-atoms;
Surface density
(c) Na: Density
cm
Cl: Density
(d) Na: At. Wt. = 22.99
Cl: At. Wt. = 35.45
So, mass per unit cell
cm
cm
B-atoms;
Surface density
cm
For 1.12(b), A-atoms;
Surface density
Then mass density
cm
grams/cm
B-atoms;
Surface density
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cm
1.12
(a)
For 1.12(a) and (b), Same material
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Then
1.14
Density of A:
cm
(a) Vol. Density
Surface Density
Density of B:
cm
(b) Same as (a)
(c) Same material
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(b) Same as (a)
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1.15
(i) (110) plane
(see Figure 1.10(b))
(ii) (111) plane
(see Figure 1.10(c))
1.13
(iii) (220) plane
(a) For 1.12(a), A-atoms
Same as (110) plane and [110] direction
Surface density
(iv) (321) plane
cm
For 1.12(b), B-atoms:
Intercepts of plane at
Semiconductor Physics and Devices: Basic Principles, 4th edition
Chapter 1
By D. A. Neamen
Problem Solutions
______________________________________________________________________________________
[321] direction is perpendicular to
(321) plane
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1.16
(a)
So
Area of plane
(b)
cm
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Surface density
cm
1.17
(b) bcc
(i) (100) plane:
Intercepts: 2, 4, 3
(634) plane
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Surface density
1.18
Surface density
cm
(ii) (110) plane:
(a)
cm
(b)
(iii) (111) plane:
(c)
Surface density
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cm
(c) fcc
(i) (100) plane:
1.19
(a) Simple cubic
(i) (100) plane:
Surface density
cm
(ii) (110) plane:
Surface density
Surface density
cm
cm
(ii) (110) plane:
(iii) (111) plane:
Surface density
cm
(iii) (111) plane:
Area of plane
where
Now
Surface density
cm
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1.20
(a) (100) plane: - similar to a fcc:
Semiconductor Physics and Devices: Basic Principles, 4th edition
Chapter 1
By D. A. Neamen
Problem Solutions
______________________________________________________________________________________
=
Surface density
cm
cm
(b) (110) plane:
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Surface density
1.22
Density of silicon atoms
cm and
4 valence electrons per atom, so
Density of valence electrons
cm
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cm
(c) (111) plane:
1.23
Density of GaAs atoms
Surface density
cm
cm
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1.21
An average of 4 valence electrons per atom,
So
Density of valence electrons
cm
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1.24
(a) #/cm
(a)
cm
(b)
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(b) #/cm
cm
1.25
(a) Fraction by weight
(c)
(b) Fraction by weight
(d) # of atoms
Area of plane: (see Problem 1.19)
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1.26
Volume density
Area
So
cm
cm
cm
We have
Then
#/cm
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Semiconductor Physics and Devices: Basic Principles, 4th edition
Chapter 2
By D. A. Neamen
Exercise Solutions
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Chapter 2
Exercise Solutions
or
Ex. 2.1
eV
Then
(a)
eV,
eV,
eV
J
(b)
or
eV
(b)
J
J
or
or
eV
eV
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Then
eV
eV
Ex 2.2
(a)
eV
_______________________________________
kg-m/s
m
Ex 2.4
or
(c)
J
kg-m/s
Now
Set
=
Then
J
or
eV
_______________________________________
Ex 2.3
or
m
(a)
(a)
J
m
or
Semiconductor Physics and Devices: Basic Principles, 4th edition
Chapter 2
By D. A. Neamen
Exercise Solutions
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%
kg-m/s
(b)
m
(b)
or
%
_______________________________________
J or
eV
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Ex 2.5
(a)
m
Then
TYU 2.2
(a)
eV
s
(b)
(b) Same as part (a),
s
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TYU 2.3
(a)
Ex 2.6
From Example 2.6, we have
eV
=
meV,
meV,
meV
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Test Your Understanding
TYU 2.1
(a)
(b)
m
Semiconductor Physics and Devices: Basic Principles, 4th edition
Chapter 2
By D. A. Neamen
Exercise Solutions
______________________________________________________________________________________
m
_______________________________________
TYU 2.4
so that
m
Then
m
or
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