1. Solid State Devices Avik Ghosh Electrical and Computer Engineering
University of Virginia
Fall 2010

2. Outline 1) Course Information
2) Motivation – why study semiconductor devices?
3) Types of material systems
4) Classification and geometry of crystals
5) Miller Indices
Ref: Ch1, ASF

3. Course information Books Advanced Semiconductor Fundamentals (Pierret)
Semiconductor Device Fundamentals (Pierret)
Course Website:
courseweb.html
Grader: Dincer Unluer

4. Distance Learning Info
Coordinator Rita Kostoff,
Phone:
CGEP/Collab Websites:
(UVa)
(Off-site)
(Streaming Video)
Notes:
Please press buzzer before asking questions in class
HW PDFs to or hand in class

5. Texts

6. References

7. Grading info Homeworks Wednesdays 25% 1st midterm M, Oct 05 15%
2nd midterm
W, Nov 04
Finals
S, Dec 12
35%

8. Grading Info
Homework - weekly assignments on website, no late homework accepted but lowest score dropped
Exams - three exams
Mathcad, Matlab, etc. necessary for some HWs/exams
Grade weighting:
Exam 1 ~20%
Exam 2 ~30%
Final ~30%
Homework ~20%

9. ECE 663 Class Topics Crystals and Semiconductor Materials
Where can the
electrons sit?
Crystals and Semiconductor Materials
Introduction to Quantum Mechanics (QM101)
Application to Semiconductor Crystals – Energy Bands
Carriers and Statistics
Recombination-Generation Processes
Carrier Transport Mechanisms
P-N Junctions
Non-Ideal Diodes
Metal-Semiconductor Contacts – Schottky Diodes
Bipolar Junction Transistors (BJT)
MOSFET Operation
MOSFET Scaling
Photonic Devices (photodetectors, LEDs, lasers)
Soft Cover
How are they distributed?
Semiconductors
How do they move?
Midterm1
Hard Cover
Basic Devices
Midterm2
Final

10. Why do we need this course?

11. Transistor Switches
1947
2003
A voltage-controlled resistor

12. Biological incentives
Transistors in Biology:
Ion channels in axons involve
Voltage dependent Conductances
Modeled using circuits
(Hodgkin-Huxley, ’52)

13. Economic Incentives
From Ralph Cavin, NSF-Grantees’ Meeting, Dec

14. A crisis of epic proportions: Power dissipation !
New physics needed – new kinds of computation

15. We stand at a threshold in electronics !!

16. How can we push
technology forward?

17. Better Design/architecture
Multiple Gates for superior field control

18. Better Materials? I Strained Si, SiGe Carbon Nanotubes
Bottom Gate
Source
Drain
Top Gate
Channel
Carbon Nanotubes VG VD
INSULATOR I
Silicon Nanowires
Organic Molecules

19. New Principles? SPINTRONICS Encode bits in electron’s
Spin -- Computation by
rotating spins
GMR (Nobel, 2007)
MRAMs
STT-RAMs
QUANTUM CELLULAR
AUTOMATA
Encode bits in quantum
dot dipoles
BIO-INSPIRED COMPUTING
Exploit 3-D architecture and
massive parallelism

20. Where do we stand today?

21. “Top Down” … (ECE6163) Molecular Electronics Solid State Electronics/
Mesoscopic Physics
Molecular Electronics Vd
20 µm Vd
2 nm

22. “Al-Khazneh”, Petra, Jordan
Top Down fabrication
Photolithography
Top down architecture
“Al-Khazneh”, Petra, Jordan
(6th century BC)

23. Modeling device electronics
Bulk Solid (“macro”)
(Classical
Drift-Diffusion)
~ 1023 atoms
Bottom Gate
Source
Channel
Drain
ECE 663
(“Traditional Engg”)
Clusters (“meso”)
(Semiclassical
Boltzmann
Transport)
80s ~ 106 atoms
Molecules (“nano”)
(Quantum
Transport)
Today ~ atoms
ECE 687
(“Nano Engg”)

24. “Bottom Up” ... (ECE 687) Molecular Electronics
Solid State Electronics/
Mesoscopic Physics
Molecular Electronics Vd
20 µm Vd
2 nm

25. Bottom Up fabrication Build pyramidal quantum dots from InAs atoms
Bottom up architecture
Chepren Pyramid, Giza (2530 BC)
Build pyramidal quantum dots from InAs atoms
(Gerhard Klimeck, Purdue)
ECE 587/687 (Spring)
Full quantum theory of nanodevices
Carbon nanotubes, Graphene
Atomic wires, nanowires,
Point contacts, quantum dots,
thermoelectrics,
molecular electronics
Single electron Transistors (SETs)
Spintronics

26. How can we model and
design today’s devices?

27. Need rigorous mathematical formalisms

28. Calculating current in semiconductorsV
Nonequilibrium stat mech (transport)
Drift-diffusion with Generation/
Recombination (Ch 5-6, Pierret)
I = q A n v
Quantum mech + stat mech
Effective mass, Occupation factors
(Ch 1-4, Pierret)

29. Calculating Electrons and Velocity
What are atoms made of? (Si, Ga, As, ..)
How are they arranged? (crystal structure)
How can we quantify crystal structures?
Where are electronic energy levels?

30. Solids
Metals: Gates, Interconnects

31. Solids tend to form ordered crystals
Natural History Museum, DC
(Rock salt, NaCl)

32. Describing the periodic lattices

33. Bravais Lattices Each atom has the same environment
Courtesy: Ashraf Alam, Purdue Univ
Each atom has the
same environment

34. 2D Bravais Lattices Only angles 2p/n, n=1,2,3,4,6
Courtesy: Ashraf Alam, Purdue Univ
Only angles 2p/n, n=1,2,3,4,6
(Pentagons not allowed!)

35. 2D non-Bravais Lattice – e.g. Graphene
Epitaxial growth by vapor deposition of CO/hydroC on metals (Rutter et al, NIST)
Chemical Exfoliation of HOPG
on SiO2 (Kim/Avouris)
Missing atom  not all
atoms have the same environment
Can reduce to Bravais lattice
with a basis

36. Irreducible Non-Bravais Lattices
MC Escher
“Quasi-periodic”
(Lower-D Projections
of Higher-D periodic
systems)
Early Islamic art
Penrose Tilings

37. Not just on paper... Pentagons ! (5-fold symmetry not
5-fold diffraction patterns
Pentagons !
(5-fold symmetry not
possible in a perfect Xal)
MoAl FeAl6
(Pauling, PRL ’87)

38. Pentagons allowed in 3D
Buckyball/Fullerene/C60

39. 3D Bravais Lattices
14 types

40. Describing the unit cells

41. Simple Cubic Structure
Coordination
Number (# of
nearest nbs. = ?)
# of atoms/cell
= ?
Packing fraction = ?

42. Body Centered Cubic (BCC)
Mo, Ta, W
CN = ?
# atoms/lattice = ?
Packing fraction?

43. Face Centered Cubic (FCC)
Al,Ag, Au, Pt, Pd, Ni, Cu
CN = ?
#atoms/cell = ?
Packing fraction = ?

44. Diamond Lattice C, Si, Ge a=5.43Å for Si CN = ? Packing fraction = ?
Two FCC offset
by a/4 in each
direction or
FCC lattice with
2 atoms/site

46. Web Sites That may be helpful

47. Zincblende Structure III-V semiconductors GaAs, InP, InGaAs,
InGaAsP,……..
For GaAs:
Each Ga surrounded
By 4 As, Each As
Surrounded by 4 Ga

48. Only other type common in ICs
Hexagonal Lattice
Al2O3, Ti, other metals
Hexagonal

49. Crystal Packing: FCC vs HCPX X

50. Semiconductors: 4 valence electrons
Group IV elements: Si, Ge, C
Compound Semiconductors :
III-V (GaAs, InP, AlAs)
II-VI (ZnSe, CdS)
Tertiary (InGaAs,AlGaAs)
Quaternary (InGaAsP)

51. Describing the unit cells

52. Simple Cubic Structure
Coordination
Number (# of
nearest nbs. = ?)
# of atoms/cell
= ?
Packing fraction = ?

53. Body Centered Cubic (BCC)
Mo, Ta, W
CN = ?
# atoms/lattice = ?
Packing fraction?

54. Face Centered Cubic (FCC)
Al,Ag, Au, Pt, Pd, Ni, Cu
CN = ?
#atoms/cell = ?
Packing fraction = ?

55. Diamond Lattice C, Si, Ge a=5.43Å for Si CN = ? Packing fraction = ?
Two FCC offset
by a/4 in each
direction or
FCC lattice with
2 atoms/site

57. Web Sites That may be helpful

58. Zincblende Structure III-V semiconductors GaAs, InP, InGaAs,
InGaAsP,……..
For GaAs:
Each Ga surrounded
By 4 As, Each As
Surrounded by 4 Ga

59. Only other type common in ICs
Hexagonal Lattice
Al2O3, Ti, other metals
Hexagonal

60. Semiconductors: 4 valence electrons
Group IV elements: Si, Ge, C
Compound Semiconductors :
III-V (GaAs, InP, AlAs)
II-VI (ZnSe, CdS)
Tertiary (InGaAs,AlGaAs)
Quaternary (InGaAsP)

61. Quantifying lattices:
1. Lattice Vectors for directions

62. Lattice Vectors a = (1,0,0)a b = (0,1,0)a c = (0,0,1)a
Simple cubic lattice
Three primitive vectors are ‘coordinates’ in terms of
which all lattice coordinates R can be expressed
R = ma + nb + pc (m,n,p: integers)

63. Body-centered cube a = a(½, ½, ½ ) b = a(-½,-½, ½ ) c = a(½,-½,-½ )
8x1/8 corner atom + 1 center atom gives
2 atoms per cell

64. Face-centered cube a = a(0, ½, ½) b = a(½, 0, ½) c = a(½, ½, 0)
6 face center atoms shared by 2 cubes each, 8 corners
shared by 8 cubes each, giving a total of
8 x 1/8 + 6 x 1/2 = 4 atoms/cell

65. Directions in a Crystal: Example-simple cubic
Directions expressed as
combinations of basis vectors a,b,c
Body diagonal=[111]
[ ] denotes specific direction
Equivalent directions use < >
[100],[010],[001]=<100>
These three directions are
Crystallographically equivalent

66. Quantifying lattices:
2. Miller Indices for Planes

67. Planes in a Crystal
Crystal Planes denoted by Miller Indices h,k,l

68. Miller indices of a plane
1. Determine where plane (or // plane)
intersects axes:
a intersect is 2 units
b intersect is 2 units
c intersect is infinity (is // to c axis)
2. Take reciprocals of intersects in order
(1/2, 1/2, 1 / infinity) = (1/2, 1/2, 0)
3. Multiply by smallest number to make all integers
2 * (1/2, 1/2, 0) = " (1, 1, 0) plane" b c a

69. Some prominent planes Equivalent planes denoted by {}
{100}=(100), (010), (001)
For Cubic structures:
[h,k,l]  (h,k,l)

70. Why bother naming planes?
Fabrication motivations
Certain planes cleave easier
Wafers grown and notched on specific planes
Pattern alignment
Chemical/Material Motivations
Density of electrons different on planes
Reconstruction causes different environments
Defect densities, chemical bonding depend on orientation

71. Reconstruction of surfaces
Si(100) 2x1
reconstruction
Environments, bonding, defect densities, surface bandstructures different
Important as devices scale and surfaces become important

72. Summary Current depends on charge (n) and velocity (v)
This requires knowing chemical composition and
atomic arrangement of atoms
Many combinations of materials form semiconductors.
Frequently they have tetragonal coordination and form
Bravais lattices with a basis (Si, Ge, III-V, II-VI...)
Crystals consist of repeating blocks. The symmetry helps
simplify the quantum mechanical problem of where the
electronic energy levels are (Chs. 2-3)

73. Things we learned today
Bravais Lattices
Unit cells: Coordination no.
No. of atoms/cell
Nearest neighbor distances
Lattice vectors and Miller Indices