1. ECE 875: Electronic Devices
Prof. Virginia Ayres
Electrical & Computer Engineering
Michigan State University

2. Part I: Semiconductor Physics
Course Content: Core:
Part I: Semiconductor Physics
Chapter 01: Physics and Properties of Semiconductors – a Review
Part II: Device Building Blocks
Chapter 02: p-n Junctions
Chapter 03: Metal-Semiconductor Contacts
Chapter 04: Metal-Insulator-Semiconductor Capacitors
Part III: Transistors
Chapter 06: MOSFETs
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3. Course Content: Beyond core:
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4. Lecture 02, 10 Jan 14
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5. Crystal Structures: Motivation:
Electronics: Transport: e-’s moving in an environment
Correct e- wave function in a crystal environment: Block function:
Y(R) = expik.a y(R) = Y(R + a)
Correct E-k energy levels versus direction of the environment: minimum = Egap
Correct concentrations of carriers n and p
Correct current and current density J: moving carriers
I-V measurement
J: Vext direction versus internal E-k: Egap direction
Fixed e-’s and holes:
C-V measurement
(KE + PE) Y = EY
x Probability f0 that energy level is occupied
q n, p velocity Area
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6. Unit cells:
A Unit cell is a convenient but not minimal volume that contains an atomic arrangement that shows the important symmetries of the crystal
Why are Unit cells like these not good enough?
Compare: Sze Pr. 01(a) for fcc versus Pr. 03
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Non-cubic

7. fcc lattice, to match Pr. 03
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8. 14 atoms needed
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9. Crystal Structures: Motivation: Electronics: Transport: e-’s moving in an environment
Correct e- wave function in a crystal environment: Block function: Y(R) = expik.a y(R) = Y(R + a)
Periodicity of the environment:
Need specify where the atoms are
Unit cell a3 for cubic systems sc, fcc, bcc, etc. OR
Primitive cell for sc, fcc, bcc, etc.
Atomic basis
Think about: need to specify:
Most atoms
Fewer atoms
Least atoms
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10. What makes a face-centered cubic arrangement of atoms unique?
A primitive Unit cell is the minimal volume that contains an atomic arrangement that shows the important symmetries of the crystal
Example:
What makes a face-centered cubic arrangement of atoms unique?
Hint: Unique means unique arrangement of atoms within an a3 cube.
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11. Answer:
Atoms on the faces
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12. Answer: Atoms on the faces
Also need two corner atoms that give maximum dimension of volume of a3 cubic Unit cell
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13. This arrangement of 8 atoms does represent the fcc primitive cell
Answer:
Atoms on the faces
Also need two corner atoms that give maximum dimension of volume of a3 cubic Unit cell
This arrangement of 8 atoms does represent the fcc primitive cell
But: specifying the arrangement of 8 atoms is a complicated description.
There is a simpler way.
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14. Switch to a simpler example:
How many atoms do you need to describe this simple cubic structure?
Want to specify:
atomic arrangement
minimal volume: a3 for this structure
Start: 8 atoms,1 on each corner.
Do you need all of them?
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15. Simpler Example:
Answer: 4 atoms and 3 vectors between them give the minimal volume = l x w x h.
4 red atoms
Specify 3 vectors:
a = l = a x + 0 y + 0 z
b = w = 0 x + a y + 0 z
c = h = 0 x + 0 y + a z
Minimal Vol = a . b x c
Specify the atomic arrangement as: one atom at every vertex of the minimal volume. h w l
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16. Return to fcc primitive cell example: 8 atoms: Simpler description:
4 atoms and 3 vectors between them give the volume of a non-orthogonal solid (parallelepiped) p.11: Volume = a . b x c
Specify the atomic arrangement as: one atom at every vertex.
rotate b c a
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17. Better picture of the fcc parallelepiped:
tilt
rotate
Ashcroft & Mermin
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18. This is what Sze does in Chp.01, Pr. 03:
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19. Picture and coordinate system for Pr. 03:
For a face centered cubic, the volume of a conventional unit cell is a3.
Find the volume of an fcc primitive cell with three basis vectors:
(000) -> (a/2,0,a/2): a = a/2 x + 0 y + a/2 z
(000) -> (a/2,a/2,0): b = a/2 x + a/2 y + 0 z
(000) -> (0,a/2,a/2): c = 0 x + a/2 y + a/2 z z c a y b
(000) x
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20. VM Ayres, ECE875, S14

21. = Volume of fcc primitive cell
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22. Sze, Chp.01, Pr. 03:
For a face centered cubic, the volume of a conventional unit cell is a3.
Find the volume of an fcc primitive cell with three basis vectors:
(000) -> (a/2,0,a/2): a = a/2 x + 0 y + a/2 z
(000) -> (a/2,a/2,0): b = a/2 x + a/2 y + 0 z
(000) -> (0,a/2,a/2): c = 0 x + a/2 y + a/2 z
a, b and c are the primitive vectors of the fcc Bravais lattice.
P. 10:
“Three primitive basis vectors a, b, and c of a primitive cell describe a crystalline solid such that the crystal structure remains invariant under translation through any vector that is the sum of integral multiples of these basis vectors. In other words, the direct lattice sites can be defined by the set
R = ma + nb + pc.”
Translational invariance is great for describing an e- wave function acknowledging the symmetries of its crystal environment: Block function: Y(R) = expik.a y(R) = Y(R + a)
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23. Formal definition of a Primitive cell, Ashcroft and Mermin:
“A volume of space that when translated through all the vectors of a Bravais lattice just fills all the space without either overlapping itself of leaving voids is called a primitive cell or a primitive Unit cell of the lattice.”
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24. 2. three vectors between them Anywhere: R = ma + nb + pc
Steps for fcc were:
1. four atoms
a = a/2 x + 0 y + a/2 z
b = a/2 x + a/2 y + 0 z
c = 0 x + a/2 y + a/2 z
2. three vectors between them
Anywhere: R = ma + nb + pc
3. minimal Vol = a3/4 (parallelepiped)
atom at each vertex of the minimal volume
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25. No! Figure 1 shows conventional Unit cells!
Typo, p. 08:
No! Figure 1 shows conventional Unit cells!
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26. Conventional Unit Cells Vol. = a3
Primitive Unit Cells:
Smaller Volumes
Vol = a3/4
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27. Primitive cell for fcc is also the primitive cell for diamond and zincblende:
Conventional cubic Unit cell
Primitive cell for:
fcc, diamond and zinc-blende
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28. P. 08: the diamond (and zinc-blende) lattices can be considered as two inter-penetrating fcc lattices.
The two interpenetrating fcc lattices are displaced (¼, ¼, ¼) x a Note: also have pairs of atoms displaced (¼, ¼, ¼) x a:
a = lattice constant
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29. P. 08: the diamond (and zinc-blende) lattices can be considered as two inter-penetrating fcc lattices.
The two interpenetrating fcc lattices are displaced (¼, ¼, ¼) x a Note: also have pairs of atoms displaced (¼, ¼, ¼) x a:
a = lattice constant
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30. Example:
What are the three primitive basis vectors for the diamond primitive cell?
(000) -> (a/2,0,a/2): a = a/2 x + 0 y + a/2 z
(000) -> (a/2,a/2,0): b = a/2 x + a/2 y + 0 z
(000) -> (0,a/2,a/2): c = 0 x + a/2 y + a/2 z
How to make it diamond: two-atom basis
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31. Picture and coordinate system for example problem:z y x
(000)
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32. Answer: Three basis vectors for the diamond primitive cell:
(000) -> (a/2,0,a/2): a = a/2 x + 0 y + a/2 z
(000) -> (a/2,a/2,0): b = a/2 x + a/2 y + 0 z
(000) -> (0,a/2,a/2): c = 0 x + a/2 y + a/2 z
Same basis vectors as fcc
Same primitive cell volume a3/4
Make it diamond by specifying the atomic arrangement as: a two-atom basis at every vertex of the primitive cell.
Pair a 2nd atom at (¼ , ¼, ¼) x a with every fcc atom in the primitive cell:
(000)
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33. Rock salt
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34. Rock salt can be also considered as two inter-penetrating fcc lattices
Rock salt can be also considered as two inter-penetrating fcc lattices. Discussion: Lec Jan 14
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35. Direct space (lattice) Direct space (lattice)
Conventional cubic Unit cell
Primitive cell for:
fcc, diamond, zinc-blende, and rock salt
Rock salt
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36. Direct space (lattice) Direct space (lattice)
Reciprocal space (lattice)
Conventional cubic Unit cell
Primitive cell for:
fcc, diamond, zinc-blende, and rock salt
Reciprocal space = first Brillouin zone for:
fcc, diamond, zinc-blende, and rock salt
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37. HW01: Direct lattice Reciprocal lattice Reciprocal lattice
Needed for describing an e- wave function in terms of the symmetries of its crystal environment: Block function: Y(R) = expik.a y(R) = Y(R + a)
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