ECE 875: Electronic Devices

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ECE 875Electronic Devices

• Prof. Virginia Ayres
• Electrical Computer Engineering
• Michigan State University
• ayresv_at_msu.edu

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Lecture 03, 13 Jan 14
Chp. 01 Crystals Direct space primitive
cells Reciprocal space Brillouin zones
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Ref. Dissertation Enzo Ungersbock, Advanced
modeling of strained CMOS technology
Only shows one of the four inside atoms
c
a
b
Diamond can be considered as two
inter-penetrating fcc lattices. Same basis
vectors as fcc 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 Same primitive cell volume a3/4 Make it
diamond by putting a two-atom basis at each
vertex of the fcc primitive cell. Pair a 2nd atom
at (¼ , ¼ , ¼) x a with every fcc atom in the
primitive cell
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Rock salt can be also considered as two
inter-penetrating fcc lattices.
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Rock salt can be also considered as two
inter-penetrating fcc lattices.
Ref http//sunlight.caltech.edu/chem140a/Ch1aCrys
tals1.pdf
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Rock salt can be also considered as two
inter-penetrating fcc lattices.
Ref http//sunlight.caltech.edu/chem140a/Ch1aCrys
tals1.pdf
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Rock salt can be also considered as two
inter-penetrating fcc lattices.
Ref http//sunlight.caltech.edu/chem140a/Ch1aCrys
tals1.pdf
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Rock salt can be also considered as two
inter-penetrating fcc lattices.
Ref http//sunlight.caltech.edu/chem140a/Ch1aCrys
tals1.pdf
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Rock salt can be also considered as two
inter-penetrating fcc lattices.
Ref http//sunlight.caltech.edu/chem140a/Ch1aCrys
tals1.pdf
The two interpenetrating fcc lattices are
displaced (½, ½ , ½) x aNote also have pairs
of atoms displaced (½, ½, ½) x a
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Rock salt can be also considered as two
inter-penetrating fcc lattices.
Ref http//www.theochem.unito.it/crystal_tuto/mss
c2008_cd/tutorials/surfaces/surfaces_tut.html
MgO crystallizes in the Rock salt structure
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MgO crystallizes in the Rock salt structure
Rock salt can be also considered as two
inter-penetrating fcc lattices. Same basis
vectors as fcc 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 Same primitive cell volume a3/4 Make it Rock
salt by putting a two-atom basis at each vertex
of the fcc primitive cell. Pair a 2nd atom at (½
, ½, ½) x a with every fcc atom in the primitive
cell
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6 conventional cubic Unit cells 4/6 have same
fcc primitive cell and basis vectors fcc single
atom basis Diamond/zb two atom basis, fcc atoms
paired with atoms at (¼, ¼ , ¼ ) x a Rock salt
two atom basis, fcc atoms paired with atoms at
(½, ½ , ½) x a
Wurtzite two interpenetrating hcp
lattices Same tetrahedral bonding as
diamond/zincblende
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The bcc and fcc lattices are reciprocals of each
other Pr. 06.
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Easier modelling Also crystal similarities can
enable heterostructures and biphasic
homostructures
Wurtzite two interpenetrating hcp
lattices Same tetrahedral bonding as
diamond/zincblende
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Gallium Nitride
Plan view
Refs Jacobs, Ayres, et al, NanoLett, 07 05
(2007) Jacobs, Ayres, et al, Nanotech. 19
405706 (2008)
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Gallium Nitride
Cross section view
Refs Jacobs, Ayres, et al, NanoLett, 07 05
(2007) Jacobs, Ayres, et al, Nanotech. 19
405706 (2008)
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Reciprocal space (Reciprocal lattice)
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HW01
C-C
Find Miller indices in a possibly non-standard
direction Miller indices describe a general
direction k. Miller indices describe a plane
(hkl). The normal to that plane describes the
direction. In an orthogonal system direction
hx ky lz In a non-orthogonal system
direction ha kb lc
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Example Streetman and Banerjee Pr. 1.3 Label
the planes illustrated in fig. P1-3
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Answer Cubic system Orthogonal standard plane
and direction in Reciprocal space
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Answer Cubic system Orthogonal non-standard
plane and direction in Reciprocal space
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HW01
C-C
Si cubic orthogonal Find Miller indices in a
possibly non-standard direction Hint check
intercept values versus the value of the lattice
constant a for Si (Sze Appendix G)
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HW01
Find Miller indices in a possibly non-standard
direction Miller indices describe a general
direction k. Miller indices describe a plane
(hkl). The normal to that plane describes the
direction. In an orthogonal system direction
hx ky lz In a non-orthogonal system
direction ha kb lc
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Non-orthogonal, non-standard directions in
Reciprocal space
P. 10 for a given set of direct primitive cell
basis vectors, a set of reciprocal k-space
lattice vectors a, b, c are defined
P. 11 the general reciprocal lattice vector is
defined G ha kb lc
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For 1.5(a)
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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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For 1.5(b) Find the volume of k-space
corresponding to the reciprocal space vectors a,
b and c
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Note pick up factors of (2p)3
1 a. b x c
1 primitive cell volume Sze Vc Vcrystal

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HW01
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Given direct space basis vectors a, b, and c for
bcc. Find reciprocal space basis vectors a, b,
and c for bcc Compare the result to direct space
a, b, and c for fcc
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