<s>
A	O
superlattice	B-General_Concept
is	O
a	O
periodic	O
structure	O
of	O
layers	O
of	O
two	O
(	O
or	O
more	O
)	O
materials	O
.	O
</s>
<s>
Superlattices	B-General_Concept
were	O
discovered	O
early	O
in	O
1925	O
by	O
Johansson	O
and	O
Linde	O
after	O
the	O
studies	O
on	O
gold-copper	O
and	O
palladium-copper	O
systems	O
through	O
their	O
special	O
X-ray	O
diffraction	O
patterns	O
.	O
</s>
<s>
The	O
increased	O
mechanical	O
hardness	O
of	O
such	O
superlattice	B-General_Concept
materials	O
was	O
confirmed	O
firstly	O
by	O
Lehoczky	O
in	O
1978	O
on	O
Al-Cu	O
and	O
Al-Ag	O
,	O
and	O
later	O
on	O
by	O
several	O
others	O
,	O
such	O
as	O
Barnett	O
and	O
Sproul	O
on	O
hard	O
PVD	O
coatings	O
.	O
</s>
<s>
If	O
the	O
superlattice	B-General_Concept
is	O
made	O
of	O
two	O
semiconductor	O
materials	O
with	O
different	O
band	O
gaps	O
,	O
each	O
quantum	O
well	O
sets	O
up	O
new	O
selection	O
rules	O
that	O
affect	O
the	O
conditions	O
for	O
charges	O
to	O
flow	O
through	O
the	O
structure	O
.	O
</s>
<s>
Since	O
the	O
1970	O
proposal	O
of	O
synthetic	O
superlattices	B-General_Concept
by	O
Esaki	O
and	O
Tsu	O
,	O
advances	O
in	O
the	O
physics	O
of	O
such	O
ultra-fine	O
semiconductors	O
,	O
presently	O
called	O
quantum	O
structures	O
,	O
have	O
been	O
made	O
.	O
</s>
<s>
The	O
concept	O
of	O
quantum	O
confinement	O
has	O
led	O
to	O
the	O
observation	O
of	O
quantum	O
size	O
effects	O
in	O
isolated	O
quantum	O
well	O
heterostructures	O
and	O
is	O
closely	O
related	O
to	O
superlattices	B-General_Concept
through	O
the	O
tunneling	O
phenomena	O
.	O
</s>
<s>
Superlattice	B-General_Concept
miniband	O
structures	O
depend	O
on	O
the	O
heterostructure	O
type	O
,	O
either	O
type	O
I	O
,	O
type	O
II	O
or	O
type	O
III	O
.	O
</s>
<s>
Type	O
III	O
superlattices	B-General_Concept
involve	O
semimetal	O
material	O
,	O
such	O
as	O
HgTe/CdTe	O
.	O
</s>
<s>
Although	O
the	O
bottom	O
of	O
the	O
conduction	O
subband	O
and	O
the	O
top	O
of	O
the	O
valence	O
subband	O
are	O
formed	O
in	O
the	O
same	O
semiconductor	O
layer	O
in	O
Type	O
III	O
superlattice	B-General_Concept
,	O
which	O
is	O
similar	O
with	O
Type	O
I	O
superlattice	B-General_Concept
,	O
the	O
band	O
gap	O
of	O
Type	O
III	O
superlattices	B-General_Concept
can	O
be	O
continuously	O
adjusted	O
from	O
semiconductor	O
to	O
zero	O
band	O
gap	O
material	O
and	O
to	O
semimetal	O
with	O
negative	O
band	O
gap	O
.	O
</s>
<s>
Another	O
class	O
of	O
quasiperiodic	O
superlattices	B-General_Concept
is	O
named	O
after	O
Fibonacci	O
.	O
</s>
<s>
A	O
Fibonacci	O
superlattice	B-General_Concept
can	O
be	O
viewed	O
as	O
a	O
one-dimensional	O
quasicrystal	O
,	O
where	O
either	O
electron	O
hopping	O
transfer	O
or	O
on-site	O
energy	O
takes	O
two	O
values	O
arranged	O
in	O
a	O
Fibonacci	B-Algorithm
sequence	I-Algorithm
.	O
</s>
<s>
Semiconductor	O
materials	O
,	O
which	O
are	O
used	O
to	O
fabricate	O
the	O
superlattice	B-General_Concept
structures	O
,	O
may	O
be	O
divided	O
by	O
the	O
element	O
groups	O
,	O
IV	O
,	O
III-V	O
and	O
II-VI	O
.	O
</s>
<s>
The	O
first	O
compositional	O
superlattice	B-General_Concept
was	O
realized	O
using	O
the	O
GaAs/AlxGa1	O
−xAs	O
material	O
system	O
.	O
</s>
<s>
The	O
superlattice	B-General_Concept
has	O
broken	O
inversion	B-Algorithm
symmetry	I-Algorithm
.	O
</s>
<s>
Superlattices	B-General_Concept
can	O
be	O
produced	O
using	O
various	O
techniques	O
,	O
but	O
the	O
most	O
common	O
are	O
molecular-beam	B-Algorithm
epitaxy	I-Algorithm
(	O
MBE	O
)	O
and	O
sputtering	O
.	O
</s>
<s>
An	O
example	O
of	O
specifying	O
a	O
superlattice	B-General_Concept
is	O
[]20	O
.	O
</s>
<s>
The	O
MBE	O
technology	O
as	O
a	O
means	O
of	O
fabricating	O
semiconductor	O
superlattices	B-General_Concept
is	O
of	O
primary	O
importance	O
.	O
</s>
<s>
In	O
addition	O
to	O
the	O
MBE	O
technology	O
,	O
metal-organic	B-Algorithm
chemical	I-Algorithm
vapor	I-Algorithm
deposition	I-Algorithm
(	O
MO-CVD	O
)	O
has	O
contributed	O
to	O
the	O
development	O
of	O
superconductor	O
superlattices	B-General_Concept
,	O
which	O
are	O
composed	O
of	O
quaternary	O
III-V	O
compound	O
semiconductors	O
like	O
InGaAsP	O
alloys	O
.	O
</s>
<s>
The	O
structural	O
quality	O
of	O
the	O
produced	O
superlattices	B-General_Concept
can	O
be	O
verified	O
by	O
means	O
of	O
X-ray	O
diffraction	O
or	O
neutron	O
diffraction	O
spectra	O
which	O
contain	O
characteristic	O
satellite	O
peaks	O
.	O
</s>
<s>
Other	O
effects	O
associated	O
with	O
the	O
alternating	O
layering	O
are	O
:	O
giant	B-General_Concept
magnetoresistance	I-General_Concept
,	O
tunable	O
reflectivity	O
for	O
X-ray	O
and	O
neutron	O
mirrors	O
,	O
neutron	O
spin	B-General_Concept
polarization	I-General_Concept
,	O
and	O
changes	O
in	O
elastic	O
and	O
acoustic	O
properties	O
.	O
</s>
<s>
Depending	O
on	O
the	O
nature	O
of	O
its	O
components	O
,	O
a	O
superlattice	B-General_Concept
may	O
be	O
called	O
magnetic	O
,	O
optical	O
or	O
semiconducting	O
.	O
</s>
<s>
The	O
schematic	O
structure	O
of	O
a	O
periodic	O
superlattice	B-General_Concept
is	O
shown	O
below	O
,	O
where	O
A	O
and	O
B	O
are	O
two	O
semiconductor	O
materials	O
of	O
respective	O
layer	O
thickness	O
a	O
and	O
b	O
(	O
period	O
:	O
)	O
.	O
</s>
<s>
As	O
and	O
are	O
periodic	O
functions	O
with	O
the	O
superlattice	B-General_Concept
period	O
d	O
,	O
the	O
eigenstates	O
are	O
Bloch	O
state	O
with	O
energy	O
.	O
</s>
<s>
By	O
definition	O
the	O
Bloch	O
functions	O
are	O
delocalized	O
over	O
the	O
whole	O
superlattice	B-General_Concept
.	O
</s>
<s>
This	O
may	O
provide	O
difficulties	O
if	O
electric	O
fields	O
are	O
applied	O
or	O
effects	O
due	O
to	O
the	O
superlattice	B-General_Concept
's	O
finite	O
length	O
are	O
considered	O
.	O
</s>
<s>
Applying	O
an	O
electric	O
field	O
F	O
to	O
the	O
superlattice	B-General_Concept
structure	O
causes	O
the	O
Hamiltonian	O
to	O
exhibit	O
an	O
additional	O
scalar	O
potential	O
eφ(z )	O
=	O
−eFz	O
that	O
destroys	O
the	O
translational	O
invariance	O
.	O
</s>
<s>
The	O
motion	O
of	O
charge	O
carriers	O
in	O
a	O
superlattice	B-General_Concept
is	O
different	O
from	O
that	O
in	O
the	O
individual	O
layers	O
:	O
mobility	O
of	O
charge	O
carriers	O
can	O
be	O
enhanced	O
,	O
which	O
is	O
beneficial	O
for	O
high-frequency	O
devices	O
,	O
and	O
specific	O
optical	O
properties	O
are	O
used	O
in	O
semiconductor	O
lasers	O
.	O
</s>
<s>
A	O
particular	O
case	O
of	O
superlattices	B-General_Concept
called	O
superstripes	O
are	O
made	O
of	O
superconducting	O
units	O
separated	O
by	O
spacers	O
.	O
</s>
<s>
Recently	O
,	O
Felix	O
and	O
Pereira	O
investigated	O
the	O
thermal	O
transport	O
by	O
phonons	O
in	O
periodic	O
and	O
quasiperiodic	O
superlattices	B-General_Concept
of	O
graphene-hBN	O
according	O
to	O
the	O
Fibonacci	B-Algorithm
sequence	I-Algorithm
.	O
</s>
<s>
Contrary	O
to	O
the	O
classical	O
superlattices	B-General_Concept
(	O
1D/3D	O
,	O
that	O
is	O
1D	O
modulation	O
of	O
electrons	O
in	O
3D	O
bulk	O
)	O
described	O
above	O
,	O
this	O
is	O
typically	O
achieved	O
by	O
treating	O
the	O
heterostructure	O
surface	O
:	O
depositing	O
a	O
suitably	O
patterned	O
metallic	O
gate	O
or	O
etching	O
.	O
</s>
<s>
If	O
the	O
amplitude	O
of	O
V(x,y )	O
is	O
large	O
(	O
as	O
an	O
example	O
)	O
compared	O
to	O
the	O
Fermi	O
level	O
,	O
,	O
the	O
electrons	O
in	O
the	O
superlattice	B-General_Concept
should	O
behave	O
similarly	O
to	O
electrons	O
in	O
an	O
atomic	O
crystal	O
with	O
square	O
lattice	O
(	O
in	O
the	O
example	O
,	O
these	O
"	O
atoms	O
"	O
would	O
be	O
located	O
at	O
positions	O
(	O
)	O
where	O
n	O
,	O
m	O
are	O
integers	O
)	O
.	O
</s>
<s>
Lattice	O
constants	O
of	O
atomic	O
crystals	O
are	O
of	O
the	O
order	O
of	O
1Å	O
while	O
those	O
of	O
superlattices	B-General_Concept
(	O
a	O
)	O
are	O
several	O
hundreds	O
or	O
thousands	O
larger	O
as	O
dictated	O
by	O
technological	O
limits	O
(	O
e.g.	O
</s>
<s>
Energies	O
are	O
correspondingly	O
smaller	O
in	O
superlattices	B-General_Concept
.	O
</s>
<s>
This	O
relation	O
is	O
only	O
a	O
rough	O
guide	O
and	O
actual	O
calculations	O
with	O
currently	O
topical	O
graphene	O
(	O
a	O
natural	O
atomic	O
crystal	O
)	O
and	O
artificial	O
graphene	O
(	O
superlattice	B-General_Concept
)	O
show	O
that	O
characteristic	O
band	O
widths	O
are	O
of	O
the	O
order	O
of	O
1	O
eV	O
and	O
10	O
meV	O
,	O
respectively	O
.	O
</s>
<s>
The	O
superlattice	B-General_Concept
of	O
palladium-copper	O
system	O
is	O
used	O
in	O
high	O
performance	O
alloys	O
to	O
enable	O
a	O
higher	O
electrical	O
conductivity	O
,	O
which	O
is	O
favored	O
by	O
the	O
ordered	O
structure	O
.	O
</s>
<s>
This	O
alloy	O
is	O
used	O
for	O
probe	O
needles	O
in	O
probe	B-Algorithm
cards	I-Algorithm
.	O
</s>
