Embed Size (px)
Citation preview
spri
nger
Ser
ies
in S
olid
-Sta
te S
cien
ces
Edi
tors
: M
.Ca
rdo
na
P.F
uld
e K
.von
Kli
tzin
g H
.-J.
Qu
eiss
er
4U S
cak
oa
da
clo
r P
h)w
s A
n In
trod
uct
ion
3rd
Edi
tion
B
y K
S
ecg
er
41
Th
e L
MT
O
Met
hod
M
uff
in-T
in O
rbit
als
an
d E
lect
ron
ic S
tru
ctu
re
By
H
L.
Sk
rive
r
42
Cry
eUl O
pik
s w
ith
Sp
atia
l D
isp
ersi
on,
and
Eid
loH
B
y V
M
. A
gra
no
vich
an
d V
.L.
Gin
zbu
rg
43
Rei
oaan
t N
onli
nea
r In
tera
ctio
ns
of
Lif
hl
wit
h M
att
er
By
V
S.
Bu
tylk
in,
A.E
. K
ap
lan
,
Yu
. G
. K
hro
no
pu
lo,
and
E.I
. Y
ak
ub
ovi
ch
44
Ela
stic
Med
u w
ith
Mic
rost
mct
Hrc
U
Th
ree-
Dim
ensi
on
al
Mo
del
s
By
I. A
. K
un
in
45
Ele
ctro
nic
Pro
per
ties
o
f D
oped
S
emic
ond
uct
ors
By
B.I
. S
hk
lovs
kii
an
d A
.L.
Efr
os
46
Top
olog
ical
Dis
ord
er i
n C
ond
ense
d M
atte
r E
dito
rs:
F.
Yo
ncz
aw
a an
d T
. N
inom
iya
47
Su
tks
and
Dyn
amic
s of
Non
Un
car
Sys
tem
s
Edi
tors
: G
. B
encd
ek,
H.
Bil
z, a
nd
R.
Zcy
hcr
48
Mag
net
ic
Ph
ase
Tra
nsi
tion
s E
dito
rs:
M.
Au
sio
osa
nd
R.J
. E
llio
tt
49
Org
anic
Mol
ecu
lar
Agg
rega
tes,
E
lect
ron
ic
Exc
itat
ion
and
Inte
ract
ion
Pro
cess
es
Edi
tors
: P
. R
ein
eker
, H
. H
ak
en,
and
H.C
. W
olf
50 M
alti
ple
Dil
Tra
ctio
n o
f X
-Ra
ys
in C
ryst
als
By
Sh
ih-L
in C
han
g
51
Ph
onon
Sca
tter
ing
in C
ond
ense
d M
atte
r E
dito
rs:
W.
Eis
enm
enge
r,
K.
La
Bm
an
n,
and
S. D
ott
ing
er
52
Sap
erco
nd
nct
ivit
y in
Mag
net
ic
and
Exo
tic
Mat
eria
ls
Edi
tors
: T
. M
atsu
bara
an
d A
. K
ota
ni
53 T
wo-
Dim
ensi
onal
Sys
tem
s,
Het
eros
tmct
iire
s,
ami
Sap
eria
ttk
es
Edi
tors
: G
. B
au
er,
P.
Ku
cha
r, a
nd
H.
Hei
nri
ch
54
Mag
nct
k E
xch
atk
Mis
an
d F
luct
uat
ion
s E
dito
rs:
S.
Lov
esey
, U
. B
alu
can
i, F
. B
orsa
,
and
V.
To
gn
etti
55 T
he
Th
eory
of
Mag
net
ism
II
Th
erm
od
yna
mic
s an
d S
tati
stic
al
Mec
han
ics
By
D
C.
Ma
ttis
56 S
pin
Flu
ctu
atio
ns
in I
tin
eran
t E
lect
ron
Mag
net
ism
B
y T
. M
oriy
a
57
Pol
ycry
stal
Un
e S
emic
ond
uct
ors,
P
hys
ical
Pro
pert
ies
and
Ap
pli
cati
on
s E
dit
or:
G
. H
arb
eke
58 T
he
Rec
urs
ion
Met
hod
an
d It
s A
pp
lica
tion
s
Ed
ito
rs:
D.
Pet
tifo
r an
d D
. W
eair
e
59 D
ynam
ical
Pro
cess
es
and
Ord
erin
g on
Sol
id S
urf
aces
Edi
tors
: A
. Y
osh
imo
ri a
nd
M.
Tsu
kada
60
Exc
iton
ic P
roce
sses
in
Sol
ids
By
M.
Uet
a,
H.
Ka
nza
ki.
K
Ko
ba
yash
i.
Y.
To
yoza
wa
, an
d E
. H
an
am
ura
61
Loc
aliz
atio
n,
Inte
ract
ion
, an
d T
ran
spor
t P
hen
omen
a
Edi
tors
: B
. K
ram
er,
G.
Ber
gm
an
n,
and
Y.
Bru
ynse
raed
c
62 T
heo
ry o
f H
eavy
F
erm
ion
s
and
Val
ence
F
luct
uat
ion
s E
dito
rs:
T.
Kas
uya
an
d T
. S
aso
63
Ele
ctro
nic
Pro
per
ties
of
P
olym
eis
and
Rel
ated
C
omp
oun
ds
Edi
tors
: H
. K
uzm
an
y, M
. M
ehri
ng,
an
d S.
R
oth
64 S
ymm
etri
es i
n P
hys
ics,
Gro
up
Th
eory
A
pp
lied
to
Ph
ysic
al
Pro
ble
ms
By
W.
Lu
dwig
65
Ph
onon
s: T
heo
ry a
nd
Exp
erim
ents
II
Ex
per
imen
ts a
nd
Inte
rpre
tati
on
of
Ex
per
imen
tal
Res
ult
s B
y P
. B
riie
sch
66
Ph
onon
s: T
heo
ry a
nd
Exp
erim
ents
III
By
P.
Bri
iesc
h
67 T
wo-
Dim
ensi
onal
Sys
tem
s:
Ph
ysic
s an
d N
ew D
evic
es
Ed
ito
rs:
G.
Ba
uer
, F
. K
uch
ar,
an
d H
. H
ein
rich
Vol
um
es 1
-39
are
list
ed o
n th
e b
ack
insi
de c
over
Tw
o-D
imen
sion
al S
yste
ms
Phy
sics
and
New
Dev
ices
Pro
ceed
ings
of
the
In
tern
atio
nal
Win
ter
Sch
ool
Mau
tern
dorf
, A
ust
ria,
Feb
ruar
y 2
4-2
8,1
98
6
Edi
tors
:
G.
Bau
er,
F.
Kuc
har,
and
H. H
einr
ich
Wit
h 2
01
Fig
ure
s
Spri
nger
-Ver
lag
Ber
lin
Hei
del
ber
g N
ew Y
ork
Lon
don
P
aris
Tok
yo
Res
onan
t T
un
nel
ing
Dev
ices
an
d O
pto
elec
tron
ic
Ge/
Si
Su
per
latt
ice
Str
uct
ure
s
S. Luryi and F. Capsisso
ATkT
B
ell
Lab
orat
orie
s, M
urr
ay
Hil
l, N
J 0
79
74
, U
SA
Th
is
pa
pe
r w
ill
rev
iew
tw
o cl
ass
es
of
sem
ico
nd
uc
tor
dev
ices
:
(1)
reso
na
nt-
tun
ne
lin
g d
iod
es
an
d tr
an
sist
ors
, a
nd
(2)
infr
are
d d
etec
tors
o
n
a si
lic
on
ch
ip.
Th
e o
nly
c
on
ne
cti
on
be
twe
en
the
se
top
ics
is
tha
t b
oth
cla
sse
s o
f d
evic
es
em
plo
y h
ete
roju
nc
tio
ns.
1.
Re
son
an
t T
unne
ling
De
vice
s
].]
Intr
oduc
tion
Re
ce
ntl
y,
a n
um
be
r o
f w
ork
ers
h
av
e d
em
on
stra
ted
a n
eg
ati
ve
dif
fere
nti
al
resi
sta
nc
e (N
DR
) a
nd
a m
icro
wa
ve
ac
tiv
ity
in
do
ub
le-b
arr
ier
(DB
) q
ua
ntu
m-w
ell
(QW
) st
ruc
ture
s.
Fig
. 1
. S
inc
e th
e p
ion
ee
rin
g w
or
k o
f T
SU
, E
SA
KI,
a
nd
CH
AN
G
[1]
on
tun
ne
lin
g in
D
BQ
W
stru
ctu
res,
th
e m
ate
ria
l q
ua
lity
h
as
imp
ro
ve
d to
th
e
po
int
tha
t n
eg
ati
ve
dif
fere
nti
al
resi
sta
nc
e (N
DR
) ca
n b
e o
bse
rve
d [2
,3]
dir
ec
tly
in
the
cu
rre
nt-
vo
lta
ge
cha
ract
eris
tics
a
t 77
K
, as
o
pp
ose
d to
th
e d
eri
va
tiv
e o
f th
e
7^
mm
F
IGU
RE
1:
B
an
d d
iag
ram
o
f a
do
ub
le-
ba
rrie
r q
ua
ntu
m-w
ell
d
iod
e in
eq
uil
ibri
um
(t
op
) a
nd
un
der
a
pp
lied
bi
as
(bo
tto
m).
S
ha
ded
re
gio
ns
ind
ica
te
the
Fer
mi
sea
of
elec
tro
ns
in
the
deg
ener
ate
ly
do
ped
em
itte
r a
nd
coll
ecto
r la
yers
.
- 12
00
-112
5 -
- -1
20
0
FIG
UR
E
2:
Th
e 7
- V
ch
ara
cter
isti
cs
of
a sy
mm
etri
c D
BQ
W
dio
de
wh
ich
con
tain
a a
n u
nd
op
ed 5
0A
th
ick
Ga
As
QW
cl
ad
by
two
un
do
ped
25
A
thic
k A
lAs
ba
rrie
r la
yers
a
nd
two
n-d
op
ed
GaA
s la
yers
[7
1.
Dio
de
are
a is
=
2.8
10
"^
cmf
corr
esp
on
din
g to
a
peak
cu
rren
t d
ensi
ty
of
30
kA
/cm
^ at
300
K
.
140
curr
ent
as
wa
s th
e ca
se
wit
h th
e fi
rst
rep
ort
s.
Th
e m
ate
ria
l q
ua
lity
h
as
ste
ad
ily
imp
rove
d,
ma
kin
g it
p
oss
ible
to
o
bse
rve
the
ND
R
at
roo
m
tem
pe
ratu
re
[4-7
].
Rec
entl
y,
pea
k to
v
all
ey
(PT
V)
rati
os
in
cu
rre
nt
of
ne
arl
y 3
:1
we
re
ob
tain
ed
at
roo
m
tem
per
atu
re
[6,7
] a
nd
9:1
at
77
K
[7],
see
F
ig.
2.
As
wil
l be
re
vie
we
d in
th
e n
ex
t S
ecti
on
, th
e N
DR
in
D
BQ
W
dio
de
s is
a
con
seq
uen
ce
of
the
dim
en
sio
na
l c
on
fin
em
en
t o
f st
ate
s in
a
QW
, a
nd
the
con
serv
ati
on
of
en
erg
y a
nd
late
ral
mo
me
ntu
m
in
tun
ne
lin
g.
In
ad
dit
ion
to
tha
t,
the
op
era
tio
n o
f th
ese
st
ruc
ture
s h
as
oft
en
be
en
d
iscu
ssed
in
c
on
ne
cti
on
wit
h a
reso
na
nt
tun
ne
lin
g ef
fect
a
na
log
ou
s to
th
at
in
a F
ab
ry-P
ero
t re
son
ato
r.
Th
is
effe
ct
is
pre
sum
ed
to
occ
ur
wh
en
the
en
erg
ies
of
inc
ide
nt
ele
ctr
on
s in
th
e
emit
ter
ma
tch
tho
se
of
un
oc
cu
pie
d st
ate
s in
th
e Q
W.
Un
de
r su
ch
co
nd
itio
ns,
th
e
am
pli
tud
e o
f th
e re
son
an
t m
od
es
bu
ild
s u
p in
th
e Q
W
to
the
ex
ten
t th
at
the
elec
tro
n w
ave
s le
ak
ing
ou
t in
b
oth
d
ire
cti
on
s c
an
ce
l th
e re
fle
cte
d w
av
es
an
d
enh
an
ce
the
tra
nsm
itte
d o
ne
s.
Th
is
ph
ysi
ca
l p
ictu
re
has
le
d to
a
de
sig
n st
rate
gy
inte
nd
ed
to
op
tim
ize
the
Fa
bry
-Pe
rot
reso
na
tor
co
nd
itio
ns.
I
n p
art
icu
lar,
R
ICC
O
and
AZ
BE
L
[8]
po
inte
d o
ut
tha
t a
ch
iev
em
en
t o
f a
ne
ar-
un
ity
reso
na
nt
tra
nsm
issi
on
req
uir
es
eq
ua
l tr
an
smis
sio
n co
effi
cien
ts
for
bo
th
ba
rrie
rs
at
the
op
era
tin
g p
oin
t —
a
co
nd
itio
n n
ot
fulf
ille
d fo
r b
arr
iers
d
esi
gn
ed
to
be
sym
me
tric
in
the
ab
sen
ce
of
an
ap
pli
ed
fiel
d.
To
co
un
ter
tha
t,
a re
son
an
t-tu
nn
eli
ng
stru
ctu
re
wa
s p
rop
ose
d [9
] in
w
hic
h a
sym
me
tric
D
BQ
W
wa
s b
uil
t in
th
e b
ase
o
f
a b
ipo
lar
tra
nsi
sto
r,
an
d th
e F
ab
ry-P
ero
t c
on
dit
ion
s w
ere
m
ain
tain
ed
thr
ou
gh
the
use
of
min
ori
ty-c
arr
ier
inje
cti
on
.
Hig
h-f
req
ue
nc
y o
pe
rati
on
of
DB
QW
d
iod
es
wa
s re
ce
ntl
y c
on
sid
ere
d [8
,10
] o
n
the
ass
um
pti
on
tha
t th
e u
nd
erl
yin
g m
ec
ha
nis
m
of
ND
R
req
uir
es
the
Fa
bry
-Pe
rot
reso
nan
t e
nh
an
ce
me
nt
of
the
tun
ne
lin
g p
rob
ab
ilit
y.
It
wa
s fo
un
d th
at
the
do
min
an
t d
ela
y re
sult
s fr
om
th
e re
son
ato
r c
ha
rgin
g ti
me
, w
hic
h is
o
f th
e o
rde
r
of
the
reso
na
nt-
sta
te
life
tim
e.
Fo
r a
QW
b
ou
nd
ed
by
50
A-t
hic
k A
lGa
As
ba
rrie
rs,
sim
ple
es
tim
ate
s [1
0]
ga
ve
a fr
eq
ue
nc
y li
mit
in
th
e lo
w
gig
ah
ert
z ra
ng
e.
At
hig
her
fr
equ
enci
es,
the
am
pli
tud
e o
f a
n e
lec
tro
n w
av
efu
nc
tio
n in
th
e Q
W
can
no
t re
ad
just
it
self
in
re
spo
nse
to
a
n e
xte
rna
l fie
ld
va
ria
tio
n to
p
rov
ide
reso
nan
t e
nh
an
ce
me
nt
of
the
tra
nsm
issi
on
coef
fici
ent.
T
he
se
esti
ma
tes,
con
tra
sted
w
ith
the
ex
pe
rim
en
tal
resu
lts
[2]
in
wh
ich
a D
BQ
W
stru
ctu
re
wa
s
use
d as
a
det
ecto
r a
nd
mix
er
of
far-
infr
are
d ra
dia
tio
n at
2.
5 T
Hz
, h
av
e le
d o
ne
of
us (
SL
) to
th
e su
gg
est
ion
tha
t th
e F
ab
ry-P
ero
t re
son
an
t tr
an
smis
sio
n p
lay
s o
nly
a
min
or
role
(i
f a
ny
) in
th
e o
pe
rati
on
of
DB
QW
d
iod
es.
It
h
as
be
en
s
ho
wn
[10
,11
]
that
th
e N
DR
ca
n a
rise
so
lely
d
ue
to
ele
ctr
on
tun
ne
lin
g in
to
a sy
stem
o
f st
ate
s o
f
red
uce
d d
ime
nsi
on
ali
ty.
In
this
p
ictu
re,
elec
tro
ns
sub
seq
ue
ntl
y le
ave
th
e Q
W
by
tun
nel
ing
thro
ug
h th
e se
con
d (c
oll
ecto
r)
ba
rrie
r,
so
tha
t th
eir
tr
an
spo
rt
thr
ou
gh
the
enti
re
DB
QW
st
ruc
ture
is
d
escr
ibed
b
y se
quentia
l ra
the
r th
an
reso
na
nt
tun
nel
ing
.
1 2
Mech
anis
m
of
Opera
tion
of
Q
uant
um
We
ll D
iod
es
l et
us
re
vie
w
the
me
ch
an
ism
o
f N
DR
in
d
ou
ble
-ba
rrie
r Q
W
stru
ctu
res
—
wit
ho
ut
inv
ok
ing
a re
son
an
t F
ab
ry-P
ero
t ef
fect
. F
igu
re
3 il
lust
rate
s th
e F
erm
i
sea
of
elec
tro
ns
in
a d
eg
en
era
tely
d
op
ed
em
itte
r.
As
su
min
g th
at
the
AlG
aA
s
141
FIG
UR
E
3:
Illu
stra
tio
n o
f th
e N
DR
m
ech
an
ism
in
Q
W
dio
des
. T
he
shad
ed
disk
w
ith
in
the
Fer
mi
sph
ere
corr
esp
on
din
g to
a
deg
ener
ate
ly
do
ped
em
itte
r,
des
crib
es
all
th
e el
ectr
on
s w
hic
h ca
n tu
nn
el i
nto
th
e Q
W
wh
ile
con
serv
ing
thei
r la
tera
l m
om
enta
. In
a
n id
eal
dio
de
at
zero
te
mp
era
ture
th
e re
son
ant
tun
nel
ing
occ
urs
in
a
volt
ag
e ra
ng
e d
uri
ng
wh
ich
the
shad
ed
disk
m
oves
d
ow
n fr
om
th
e p
ole
to
th
e eq
ua
tori
al
pla
ne
of
the
emit
ter
Fer
mi
sph
ere.
A
t h
igh
er
bia
ses
reso
nan
t el
ectr
on
s n
o lo
ng
er
exis
t.
ba
rrie
r is
fr
ee
of
imp
uri
tie
s a
nd
inh
om
og
en
eit
ies,
th
e la
tera
l e
lec
tro
n m
om
en
tum
(k,,k
^)
is
con
serv
ed
in
tun
ne
lin
g.
Th
is
me
an
s th
at
for
< E
Q
< E
p (w
he
re
Ep;
is
the
bo
tto
m
of
the
co
nd
uc
tio
n b
an
d in
th
e e
mit
ter
an
d E
g is
th
e b
ott
om
o
f th
e
sub
ba
nd
in
the
QW
) tu
nn
eli
ng
is
po
ssib
le
on
ly
for
ele
ctr
on
s w
ho
se
mo
me
nta
li
e
in
a d
isk
co
rre
spo
nd
ing
to
k^
— E
g (s
ha
ded
d
isk
in
the
fig
ure
),
wh
ere
K^k
l/lm
-
Eg
- E
Q.
On
ly
tho
se
ele
ctr
on
s h
av
e is
oe
ne
rge
tic
sta
tes
in
the
QW
wit
h th
e sa
me
k^
an
d k^
. T
his
is
a
ge
ne
ral
fea
ture
o
f tu
nn
eli
ng
into
a
two
-
dim
en
sio
na
l sy
stem
o
f st
ate
s.
As
the
em
itte
r-b
ase
p
ote
nti
al
rise
s,
so
do
es
the
nu
mb
er
of
ele
ctr
on
s w
hic
h ca
n tu
nn
el:
th
e sh
ad
ed
dis
k m
ov
es
do
wn
wa
rd
to
the
eq
ua
tori
al
pla
ne
of
the
Fe
rmi
sph
ere
. F
or
Eg
— 0
th
e n
um
be
r o
f tu
nn
eli
ng
ele
ctr
on
s p
er
un
it
are
a e
qu
als
m
Ep/
xh^.
W
he
n E
Q
rise
s a
bo
ve
Eg,
th
en
at
T
- 0
the
re
are
n
o e
lec
tro
ns
in
the
em
itte
r w
hic
h ca
n tu
nn
el
into
th
e Q
W
wh
ile
co
nse
rvin
g th
eir
la
tera
l m
om
en
tum
. T
he
refo
re,
on
e ca
n e
xp
ec
t a
n a
bru
pt
dro
p
in
the
tun
ne
lin
g c
urr
en
t.
Ex
ten
sio
n o
f th
is
pic
ture
to
th
e c
ase
o
f se
vera
l
sub
ba
nd
s in
th
e Q
W
is s
tra
igh
tfo
rwa
rd.
Th
is
seq
ue
nti
al-
tun
ne
lin
g m
ec
ha
nis
m
of
ND
R
is
ex
pe
rim
en
tall
y
dis
tin
gu
ish
ab
le
fro
m
the
Fa
bry
-Per
ot
mo
de
l.
In
pa
rtic
ula
r,
it
do
es
no
t d
ep
en
d
on
the
sym
me
try
of
tra
nsm
issi
on
coef
fici
ents
o
f th
e tw
o b
arr
iers
, a
nd
sho
uld
n
ot
de
gra
de
, th
ere
fore
, if
th
e tr
an
spa
ren
cy
of
the
sec
on
d (c
oll
ecto
r)
ba
rrie
r is
en
ha
nc
ed
. W
ith
in
the
seq
ue
nti
al-
tun
ne
lin
g m
od
el,
th
e te
rah
ert
z re
sult
s [2
] ca
n
be
ex
pla
ine
d -
sin
ce
rec
tifi
ca
tio
n o
f a
n e
xte
rna
l si
gn
al
by
a D
BQ
W
dio
de
req
uir
es
the
rea
dju
stm
en
t o
f o
nly
th
e p
ha
se
of
ele
ctr
on
ic
wa
ve
fun
cti
on
s a
nd
no
t
the
ir
am
pli
tud
e,
so
tha
t th
e o
pe
rati
on
of
a d
etec
tor
is
no
t li
mit
ed
by
a
Fa
bry
-Per
ot
ch
arg
ing
tim
e [1
2].
T
he
effe
ct
is
co
nc
ep
tua
lly
sim
ila
r to
th
at
in
the
Esa
ki
dio
de
. It
sh
ou
ld
als
o b
e o
bse
rva
ble
in
v
ari
ou
s si
ng
le-b
arr
ier
stru
ctu
res
in
wh
ich
tun
ne
lin
g o
cc
urs
in
to a
tw
o-d
ime
nsi
on
al
syst
em
of
sta
tes.
Ind
ee
d,
ac
co
rdin
g to
th
e d
esc
rib
ed
mo
de
l,
in
DB
QW
st
ruct
ure
s th
e re
mo
va
l o
f
ele
ctr
on
s fr
om
th
e Q
W
oc
cu
rs
via
se
qu
enti
al
tun
ne
lin
g,
bu
t o
the
r m
ea
ns
of
ele
ctr
on
rem
ov
al
can
als
o b
e c
on
tem
pla
ted
, fo
r e
xa
mp
le,
reco
mbin
atio
n.
RE
ZE
K
et
al.
[13
] st
ud
ied
ele
ctr
on
tun
ne
lin
g th
ro
ug
h a
sin
gle
b
arr
ier
into
a
QW
lo
cate
d m
a p
-ty
pe
qu
ate
rna
ry
ma
teri
al.
I
n th
ese
e
xp
eri
me
nts
th
e d
iod
e c
urr
en
t re
sult
ed
142
fro
m
the
sub
seq
ue
nt
rec
om
bin
ati
on
of
tun
ne
lin
g e
lec
tro
ns
wit
h h
ole
s in
th
e
dir
ect-
ga
p Q
W.
Th
e o
bse
rved
st
ruc
ture
in
th
e d
ep
en
de
nc
es
of
the
cu
rre
nt
an
d
the
inte
nsi
ty
of
the
rec
om
bin
ati
on
rad
iati
on
on
the
ap
pli
ed
bia
s ca
n b
e
exp
lain
ed
in
term
s o
f th
e a
bo
ve
pic
ture
b
ase
d o
n th
e m
om
en
tum
c
on
serv
ati
on
.
FIG
UR
E
4:
Illu
stra
tio
n o
f a
sin
gle
-ba
rrie
r Q
W
stru
ctu
re
wh
ich
exh
ibit
s a
n N
DR
ef
fect
si
mil
ar
to
tha
t o
bse
rved
in
D
BQ
W
dio
des
. T
he
dra
in
con
tact
is
a
ssu
med
to
be
co
nce
ntr
ic
wit
h a
cyli
nd
rica
l em
itte
r el
ectr
ode.
T
he
"im
pen
etra
ble
" co
llec
tor
ba
rrie
r se
para
tin
g th
e Q
W
fro
m
the
con
du
ctin
g la
yer
un
der
nea
th
(th
e la
tter
is
sh
ort
ed
to
the
dra
in)
mu
st
be
thin
en
ou
gh
(<
10
00
A),
so
th
at
the
emit
ter-
to-Q
W
po
ten
tia
l co
uld
be
ef
fect
ivel
y co
ntr
oll
ed
by
the
emit
ter
bia
s.
In
the
exp
erim
ents
[7
] th
e tu
nn
el
ba
rrie
r a
nd
the
QW
th
ick
nes
ses
an
d co
mp
osi
tio
n w
ere
iden
tica
l to
th
ose
in
th
e co
ntr
ol
do
ub
le-b
arr
ier
stru
ctu
re
(Fig
. 2)
, w
her
eas
the
coll
ecto
r b
arr
ier
rep
rese
nte
d 5
00
A
thic
k A
LG
a,_
,As
laye
r w
ith
x—
0.3
.
Th
e N
DR
ef
fect
o
f a
sim
ila
r n
atu
re
can
als
o be
o
bse
rved
in
a
un
ipo
lar
sin
gle
-
ba
rrie
r st
ruct
ure
, as
w
as
firs
t p
rop
ose
d in
[1
1]
an
d d
em
on
stra
ted
in
[7].
L
et
the
emit
ter
be
sep
ara
ted
by
a th
in
tun
ne
lin
g b
arr
ier
fro
m
a Q
W
wh
ich
is
co
nfi
ne
d
on
the
oth
er
sid
e b
y a
thin
b
ut
imp
en
etr
ab
le
(fo
r tu
nn
eli
ng
) b
arr
ier.
F
ig.
4.
Th
e
dra
in
con
tact
to
th
e Q
W,
loca
ted
ou
tsid
e th
e e
mit
ter
are
a,
sho
uld
b
e el
ectr
ica
lly
con
nec
ted
to
a c
on
du
cti
ng
laye
r u
nd
ern
ea
th.
Ap
pli
ca
tio
n o
f a
ne
ga
tiv
e b
ias
to
the
emit
ter
wil
l re
sult
in
th
e tu
nn
eli
ng
of
ele
ctr
on
s in
to
the
QW
a
nd
the
ir
sub
seq
uen
t d
rift
la
tera
lly
tow
ard
th
e d
rain
co
nta
ct.
Th
ere
w
ill
be
no
ste
ad
y-s
tate
acc
um
ula
tio
n o
f e
lec
tro
ns
in
the
QW
u
nd
er
the
em
itte
r if
th
e d
rift
re
sist
an
ce
is
mad
e su
ffic
ien
tly
sma
ll.
Sin
ce
the
dra
in
co
nta
ct
is
sho
rte
d to
th
e c
on
du
cti
ng
laye
r u
nd
ern
ea
th
the
coll
ecto
r b
arr
ier
an
d it
s la
tera
l d
ista
nc
e fr
om
th
e e
dg
e o
f
the
emit
ter
mu
ch
ex
ce
ed
s th
e c
om
bin
ed
thic
kn
ess
es
of
the
two
ba
rrie
rs
an
d th
e
QW
, a
pp
lica
tio
n o
f a
dra
in-e
mit
ter
vo
lta
ge
resu
lts
in
a n
ea
rly
ve
rtic
al
elec
tric
fiel
d li
ne
un
de
r th
e e
mit
ter,
w
hic
h a
llo
ws
on
e to
c
on
tro
l b
y th
e a
pp
lie
d v
olt
ag
e
the
po
ten
tia
l d
iffe
ren
ce
be
twe
en
the
em
itte
r a
nd
the
QW
. O
f c
ou
rse
, th
is
co
ntr
ol
IS
mu
ch
less
ef
fect
ive
(by
the
leve
r ru
le)
tha
n it
w
ou
ld
be
if
the
sec
on
d b
arr
ier
wer
e as
th
in
as
the
tun
ne
l b
arr
ier.
E
xp
eri
me
nta
lly
, M
OR
KO
Q
et
al.
[7
] w
ere
a
ble
to
see
a p
ron
ou
nc
ed
ND
R
alr
ead
y at
ro
om
te
mp
era
ture
a
nd
at
77
K
the
ob
serv
ed
PT
V
rati
o in
c
urr
en
t w
as
mo
re
tha
n 2
:1.
As
exp
ecte
d,
the
ND
R
wa
s se
en
o
nly
tor
a n
ega
tive
p
ola
rity
o
f th
e e
mit
ter
bia
s -
wit
h a
pe
ak
cu
rre
nt
oc
cu
rin
g at
a
volt
age
wh
ich
is
hig
he
r th
an
tha
t o
bse
rved
in
a
co
ntr
ol
sym
me
tric
D
BQ
W
stru
ctu
re
by
a fa
cto
r g
ive
n b
y th
e ra
tio
of
the
ba
rrie
r th
ick
ne
sse
s (t
he
leve
r ru
le).
DR
AIN
C
ON
TAC
T
EM
ITT
ER
I
CO
NTA
CT
y/M
W/m
m.
MA
(n*
GoA
»)
TU
NN
EL B
AR
RIE
R
OW
IMP
EN
ET
RA
BL
E
BA
RR
IER
(AiG
oA
il (G
oA
il
lAiG
aA
ll
(n«
Go
Ail
143
J J
Tun
nelin
g in
S
uperlattic
es
We
ha
ve
est
ab
lish
ed
tha
t a
ll
tha
t is
re
qu
ire
d fo
r th
e N
DR
to
o
cc
ur
in
a re
son
an
t
tun
ne
lin
g st
ruc
ture
is
th
e re
du
ce
d d
ime
nsi
on
ali
ty
of
ele
ctr
on
ic
sta
tes
in
the
tun
ne
lin
g ra
ng
e.
On
e ca
n re
lax
this
re
qu
ire
me
nt
— b
y re
pla
cin
g th
e Q
W
by
a
sup
erl
att
ice
wit
h n
ar
ro
w
min
iba
nd
s (a
m
ult
iple
Q
W
stru
ctu
re,
for
wh
ich
the
tig
ht-
bin
din
g a
pp
ro
xim
ati
on
is
a g
oo
d d
esc
rip
tio
n).
C
lea
rly
, w
e ca
n e
xp
ec
t th
e
ND
R
effe
ct
in
tun
ne
lin
g fr
om
a
de
ge
ne
rate
ly
do
pe
d e
mit
ter
into
a
sup
erl
att
ice
.
Re
ce
ntl
y,
DA
VIE
S et
a
l.
[14
] re
po
rte
d si
mil
ar
effe
cts
in
tun
ne
lin
g b
etw
ee
n th
e
min
iba
nd
s o
f tw
o c
ou
ple
d su
per
latt
ices
.
Re
turn
ing
to
the
do
ub
le-b
arr
ier
QW
st
ruc
ture
o
f F
ig.
1,
we
wo
uld
li
ke
to
stre
ss
the
esse
nti
al
dif
fere
nc
e b
etw
ee
n th
e F
ab
ry-P
ero
t m
ec
ha
nis
m
of
the
ND
R
an
d th
e a
bo
ve
-de
scri
be
d m
ec
ha
nis
m,
wh
ich
inv
olv
es
sequentia
l ra
the
r th
an
reso
na
nt
tun
ne
lin
g th
ro
ug
h th
e tw
o b
arr
iers
. I
n th
e in
sta
nce
o
f a
sem
ico
nd
uc
tor
sup
erl
att
ice
, th
is
dif
fere
nc
e h
ad
be
en
c
lea
rly
ex
pla
ine
d b
y K
AZ
AR
IN
OV
a
nd
SU
RI
S
[15
].
In
an
ide
al
sup
erl
att
ice
co
nsi
stin
g o
f a
larg
e n
um
be
r o
f e
qu
all
y
spa
ce
d id
en
tic
al
qu
an
tum
w
ell
s,
on
e ca
n e
xp
ec
t a
reso
na
nt
(min
iba
nd
)
tra
nsm
issi
on
, a
na
log
ou
s to
th
e F
ab
ry-P
ero
t ef
fect
, a
nd
po
ssib
ly
an
ND
R
du
e to
the
Bra
gg
refl
ec
tio
ns,
if
th
e a
pp
lie
d fi
eld
is
such
th
at
the
po
ten
tia
l d
iffe
ren
ce
,
ac
qu
ire
d b
y a
n e
lec
tro
n o
ve
r m
an
y p
eri
od
s o
f th
e su
pe
rla
ttic
e,
is
less
th
an
the
wid
th
of
the
low
est
m
inib
an
d.
Th
ese
ef
fect
s,
pa
rtic
ula
rly
the
Bra
gg
refl
ec
tio
ns,
are
e
xtr
em
ely
d
iffi
cult
to
o
bse
rve
be
ca
use
o
f sc
att
eri
ng
an
d Z
en
er
tun
ne
lin
g
be
twe
en
ele
ctr
on
min
iba
nd
s [1
6].
FIG
UR
E
5:
Sch
ema
tic
illu
stra
tio
n o
f se
qu
enti
al
tun
ne
lin
g o
f el
ectr
on
s fo
r a
po
ten
tia
l en
erg
y d
rop
acr
oss
th
e su
per
latt
ice
per
iod
equ
al,
re
spec
tive
ly,
to
the
ener
gy
dif
fere
nce
b
etw
een
the
first
ex
cite
d st
ate
an
d th
e g
rou
nd
sta
te (
a)
an
d to
th
e en
erg
y d
iffe
ren
ce
bet
wee
n th
e se
con
d ex
cite
d st
ate
an
d th
e g
rou
nd
sta
te
of
the
wel
ls (
b).
In
the
op
po
site
li
mit
o
f a
stro
ng
elec
tric
fi
eld
an
en
ha
nc
ed
ele
ctr
on
cu
rre
nt
wil
l flo
w
at
sha
rply
d
efi
ne
d va
lues
o
f th
e e
xte
rna
l fie
ld,
wh
en
the
gr
ou
nd
sta
te
in
the
n-t
h w
ell
is
d
eg
en
era
te
wit
h th
e fi
rst
or
sec
on
d ex
cite
d st
ate
in
th
e
(n
+l)
-st
we
ll,
as
illu
stra
ted
in
Fig
. 5.
U
nd
er
suc
h c
on
dit
ion
s,
the
cu
rre
nt
is
du
e
to
ele
ctr
on
tun
ne
lin
g b
etw
ee
n th
e a
dja
cen
t w
ell
s w
ith
a su
bse
qu
en
t d
e-e
xc
ita
tio
n
in
the
(n +
l)
-st
we
ll.
In
oth
er
wo
rds,
e
lec
tro
n p
rop
ag
ati
on
thr
ou
gh
the
en
tire
sup
erl
att
ice
inv
olv
es
ag
ain
a
seq
ue
nti
al
rath
er
tha
n re
son
an
t tu
nn
eli
ng
.
14
4
FIG
UR
E
6:
Th
e p
ho
tocu
rren
t-vo
lta
ge
char
acte
rist
ics
at
X-0
.63
3/i
m
(pu
re
elec
tro
n in
ject
ion
) fo
r an
A
lg^
gln
osj
As/
G
ao47
lno5
3As
sup
erla
ttic
e w
ith
13
9A
th
ick
wel
ls
an
d b
arr
iers
a
nd
35
per
iod
s.
Th
e a
rro
ws
ind
ica
te
tha
t th
e p
eak
s co
rres
po
nd
to
reso
na
nce
s b
etw
een
the
gro
un
d st
ate
of
the
n th
wel
l a
nd
the
first
tw
o ex
cite
d st
ate
s o
f th
e (n
+.l
)st
wel
l.
"0
t 4
6 «
10
Kim
i H
AS.
|«l
Ex
pe
rim
en
tal
dif
fic
ult
ies
in
stu
dy
ing
this
p
he
no
me
no
n a
re
usu
all
y a
sso
cia
ted
wit
h th
e n
on
-un
ifo
rmit
y o
f th
e el
ectr
ic
fiel
d a
cro
ss
the
sup
erl
att
ice
an
d th
e
inst
ab
ilit
ies
ge
ne
rate
d b
y n
eg
ati
ve
dif
fere
nti
al
co
nd
uc
tiv
ity
. T
o e
nsu
re
a st
ric
tly
con
tro
lled
a
nd
spa
tia
lly
un
ifo
rm
elec
tric
fie
ld,
CA
PA
SS
O
et
al.
[1
7]
pla
ce
d th
e
sup
erla
ttic
e in
th
e i
reg
ion
of
a re
vers
e-b
iase
d p'
*'-i-n
'*'
jun
cti
on
. T
his
st
ruc
ture
all
ow
ed
for
the
firs
t ti
me
to
ob
serv
e th
e se
qu
en
tia
l tu
nn
eli
ng
reso
na
nc
e
pre
dic
ted
in
[15
].
Tw
o N
DR
p
ea
ks
ob
serv
ed
in
the
ph
oto
cu
rre
nt
cha
ract
eris
tics
.
Fig
. 6,
c
orr
esp
on
d to
th
e re
son
an
ce
s s
ho
wn
sch
em
ati
ca
lly
in
Fig
. 5.
F
or
the
seq
uen
tia
l tu
nn
eli
ng
reg
ime
, K
aza
rin
ov
an
d S
uri
s h
ad
pre
dic
ted
the
po
ssib
ilit
y
of
a la
ser
act
ion
at
the
inte
r-m
inib
an
d tr
an
siti
on
fre
qu
en
cy
—
an
effe
ct
no
t y
et
ob
serv
ed
ex
pe
rim
en
tall
y in
su
per
latt
ices
.
1.4
Negativ
e
Tra
nsc
on
du
cta
nce
T
rans
isto
r
Th
e p
rec
ed
ing
dis
cuss
ion
ha
s d
ealt
w
ith
the
bu
lk-c
arr
ier
tun
ne
lin
g in
to
a 2
-D
den
sity
o
f el
ectr
on
ic
sta
tes.
R
ecen
tly,
w
e p
rop
ose
d a
no
ve
l d
ev
ice
stru
ctu
re
[18
]
in
wh
ich
the
QW
is
li
ne
ar
rath
er
tha
n p
lan
ar
an
d th
e tu
nn
eli
ng
if
of
2-D
elec
tro
ns
into
a
1-D
d
en
sity
o
f st
ate
s.
Fig
ure
7
sho
ws
the
sch
ema
tic
cro
ss-s
ecti
on
FIG
UR
E
7:
Th
e n
ega
tive
d
iffe
ren
tia
l tr
an
sco
nd
uct
an
ce
dev
ice
[18]
. £q
is
th
e b
ott
om
o
f th
e 2
D s
ub
ba
nd
sepa
rate
d fr
om
th
e cl
ass
ica
l co
nd
uct
ion
ba
nd
min
imu
m
by
the
ener
gy
of
the
zero
-po
int
mo
tio
n in
y-
dir
ecti
on
; E
Q
is
the
bo
tto
m o
f th
e 1
-D
su
bb
an
d in
th
e q
ua
ntu
m
wir
e,
sepa
rate
d fr
om
E
g b
y th
e co
nfi
nem
ent
ener
gy
in
the
z-d
irec
tio
n.
In
the
op
era
tin
g re
gim
e th
e F
erm
i le
vel
Ep
lies
b
etw
een
Eg
an
d E
Q.
148
of
the
pro
po
sed
dev
ice.
It
c
on
sist
s o
f a
n e
pit
ax
iall
y g
ro
wn
un
do
pe
d p
lan
ar
QW
an
d a
do
ub
le
AlC
aA
s b
arr
ier
san
dw
ich
ed
be
twe
en
two
un
do
pe
d G
aA
s la
yers
a
nd
he
av
ily
do
pe
d G
aA
s c
on
tac
t la
yers
. T
he
wo
rk
ing
surf
ac
e d
efi
ne
d b
y a
V-g
roo
ve
etc
hin
g is
su
bse
qu
en
tly
ov
er
gr
ow
n e
pit
ax
iall
y w
ith
a th
in
AlG
aA
s la
yer
an
d
ga
ted
. A
pp
lic
ati
on
of
a p
osi
tiv
e g
ate
v
olt
ag
e V
Q
ind
uc
es
2-D
e
lec
tro
n g
ase
s at
the
two
inte
rfa
ce
s w
ith
the
ed
ge
s o
f u
nd
op
ed
Ga
As
laye
rs
ou
tsid
e th
e Q
W.
Th
es
e g
ase
s w
ill
act
as
the
sou
rce
(S)
an
d d
ra
in (
D)
ele
ctr
od
es.
A
t th
e sa
me
tim
e,
the
re
is
a ra
ng
e o
f V
Q
in
wh
ich
ele
ctr
on
s a
re
no
t y
et
ind
uc
ed
in
the
"q
ua
ntu
m
wir
e"
reg
ion
(wh
ich
is
the
ed
ge
of
the
QW
la
ye
r)
—
be
ca
use
o
f th
e a
dd
itio
na
l
dim
en
sio
na
l q
ua
nti
zati
on
. T
he
op
era
tin
g re
gim
e o
f o
ur
dev
ice
is
in
this
ra
ng
e.
De
vic
e c
ha
rac
teri
stic
s ca
n b
e u
nd
ers
too
d a
lon
g th
e li
nes
d
esc
rib
ed
ab
ov
e in
co
nn
ec
tio
n w
ith
Fig
. 3.
I
n th
e p
rese
nt
case
th
e d
ime
nsi
on
ali
ty
of
bo
th
the
em
itte
r a
nd
the
ba
se
is
red
uc
ed
by
1,
so
tha
t th
e e
mit
ter
Fe
rmi
sea
be
co
me
s a
dis
k a
nd
the
sha
ded
d
isk
of
Fig
. 3
is
rep
lace
d b
y a
reso
na
nt
seg
me
nt.
Ap
pli
ca
tio
n o
f a
f>o
siti
ve
dr
ain
v
olt
ag
e V
^,
bri
ng
s a
bo
ut
the
reso
na
nt
tun
ne
lin
g
co
nd
itio
n a
nd
on
e e
xp
ec
ts
an
ND
R
in
the
de
pe
nd
en
ce
/(V
^).
W
ha
t is
m
ore
inte
rest
ing
, is
th
at
this
c
on
dit
ion
is
als
o c
on
tro
lle
d b
y V
Q.
Th
e c
on
tro
l is
effe
cted
b
y fr
ing
ing
elec
tric
fi
elds
: in
th
e o
pe
rati
ng
reg
ime
an
incr
easi
ng
VQ
> 0
low
ers
th
e el
ectr
ost
ati
c p
ote
nti
al
en
erg
y in
th
e b
ase
w
ith
resp
ec
t to
th
e
em
itte
r —
n
ea
rly
as
eff
ec
tiv
ely
as
d
oe
s th
e in
cre
asi
ng
Vp
(th
is
ha
s b
ee
n
co
nfi
rme
d [1
8]
by
solv
ing
the
co
rre
spo
nd
ing
elec
tro
sta
tic
pro
ble
m
exa
ctly
w
ith
the
he
lp
of
suit
ab
le
co
nfo
rma
l m
ap
pin
gs)
. A
t a
fixe
d V
Q
ha
vin
g es
tab
lish
ed
the
pe
ak
of
!{V
p),
we
can
the
n q
ue
nc
h th
e tu
nn
eli
ng
cu
rre
nt
by
inc
rea
sin
g V
Q.
Th
is
imp
lie
s th
e p
oss
ibil
ity
of
ac
hie
vin
g th
e negativ
e
tra
nsc
on
du
cta
nce
—
a
n
en
tire
ly
no
ve
l fe
atu
re
in
a u
nip
ola
r d
evic
e.
A
ne
ga
tiv
e-t
ran
sco
nd
uc
tan
ce
tra
nsi
sto
r ca
n p
er
for
m
the
fun
cti
on
s o
f a
co
mp
lem
en
tary
d
evic
e a
na
log
ou
s to
a
p-c
ha
nn
el
tra
nsi
sto
r in
th
e si
lic
on
CM
OS
log
ic.
A
cir
cu
it
form
ed
by
a
co
nv
en
tio
na
l n
-ch
an
ne
l fi
eld-
effe
ct
tra
nsi
sto
r a
nd
ou
r d
evic
e ca
n ac
t li
ke
a lo
w-
po
we
r in
ve
rte
r in
w
hic
h a
sig
nif
ica
nt
cu
rre
nt
flo
ws
on
ly
du
rin
g sw
itc
hin
g.
Th
u.
fea
ture
ca
n fin
d a
pp
lic
ati
on
s in
lo
gic
ci
rcu
its.
2.
Infr
are
d
Plto
todete
ctors
on
a
Sili
con
Clii
p
2.1
Intr
oduc
tion
As
is
we
ll
kn
ow
n,
the
ce
leb
rate
d si
lic
on
tec
hn
olo
gy
ha
s n
ot
be
en
a
ble
to
pro
du
ce
an
on
-ch
ip
infr
are
d p
ho
tod
ete
cto
r fo
r lo
ng
-wa
ve
len
gth
fi
ber
-op
tics
co
mm
un
ica
tio
ns.
T
he
ob
vio
us
dif
ficu
lty
lies
in
th
e fa
ct
tha
t si
lic
on
ba
nd
ga
p LQ
is
wid
er
tha
n th
e p
ho
ton
en
erg
y in
th
e ra
ng
e o
f si
lica
-fib
er
tra
nsp
are
ncy
(X
1.3
— 1
.55
nm).
A
tte
mp
ts
ha
ve
be
en
m
ad
e to
o
ve
rco
me
this
d
iffi
cult
y b
y
usi
ng
Sc
ho
ttk
y-b
arr
ier
stru
ctu
res
wit
h p
ho
toe
xc
ita
tio
n o
f ca
rrie
rs
fro
m
the
met
al
(or
sili
cid
e)
into
si
lic
on
[19
].
Th
e th
resh
old
fo
r su
ch
a p
ho
toe
ffe
ct
is
de
term
ine
d
by
the
Sc
ho
ttk
y-b
arr
ier
he
igh
t a
nd
can
easi
ly
ma
tch
the
req
uir
ed
infr
are
d ra
ng
e;
ho
we
ve
r,
the
qu
an
tum
ef
fici
ency
o
f a
bso
rpti
on
in
such
st
ruct
ure
s is
u
sua
lly
low
.
So
far,
th
e o
nly
p
ract
ica
l w
ay
of
em
plo
yin
g si
lic
on
tec
hn
olo
gy
for
fib
er-o
pti
ck
co
mm
un
ica
tio
ns
ha
s b
ee
n
to
co
mb
ine
Si
inte
gra
ted
circ
uit
s w
ith
Ge
or
InG
aA
k-
146
zooo
l
— t
soo
l —
tso
ol
1 In
- )
Ge
n*
Ge
1 F
IGU
RE
8:
S
chem
ati
c il
lust
rati
on
of
the
com
po
siti
on
of
epit
ax
ial
laye
rs
in
Ge
/Si
infr
are
d p
ho
tod
etec
tors
: (a
) th
e o
rig
ina
l G
e pi
n st
ruct
ure
o
n a
sili
con
wa
fer
[20]
; a
nd
(b)
the
gli
tch
-gra
ded
st
ruct
ure
[2
1].
on
-ln
P
det
ecto
rs
on
a se
pa
rate
c
hip
. A
d
iffe
ren
t a
pp
roa
ch
to
this
p
rob
lem
is
base
d o
n g
ro
win
g si
ng
le-c
ryst
al
ge
rma
niu
m
pin
jun
cti
on
on
a si
lic
on
sub
stra
te,
I ig
. 8.
M
ole
cu
lar
be
am
e
pit
ax
y (M
BE
) g
ro
wn
dio
des
h
av
e b
ee
n
rep
ort
ed
[20
],
wh
ich
ha
d a
qu
an
tum
ef
fici
ency
p
= 40
%
at
X -
1
.3^
m.
Ho
we
ve
r,
the
de
vic
es
suff
ered
fr
om
a
rela
tiv
ely
h
igh
rev
ers
e-b
ias
pa
rasi
tic
lea
ka
ge
at
ro
om
tem
per
atu
re.
Th
is
lea
ka
ge
resu
lte
d fr
om
th
rea
din
g d
islo
cati
on
s o
rig
ina
tin
g at
the
Ge
/Si
inte
rfa
ce
du
e to
a
larg
e la
ttic
e m
ism
atc
h a
nd
pro
pa
ga
tin
g th
ro
ug
h th
e
ge
rma
niu
m
pin
jun
cti
on
. I
n th
e su
bse
qu
en
t w
or
k [2
1]
the
dis
loc
ati
on
de
nsi
ty
was
re
du
ced
by
a n
ov
el
MB
E
tric
k ca
lled
th
e "
gli
tch
gra
din
g"
, w
hic
h c
on
sist
s in
inse
rtin
g a
Si^
Ge
i_^
/Ge
sup
erla
ttic
e in
th
e e
pit
ax
iall
y g
ro
wn
ge
rm
an
ium
fil
m.
Fig
. 8b
. It
tu
rns
ou
t th
at
dis
loca
tio
ns
ten
d to
b
e tr
ap
pe
d in
th
e st
rain
ed
sup
erla
ttic
e re
gio
n a
nd
do
no
t p
rop
ag
ate
u
p in
to
the
wo
rkin
g d
iod
e re
gio
n (t
he
reg
ion
wh
ere
p
ho
tog
en
era
ted
carr
iers
a
re
sep
ara
ted
by
the
elec
tric
fie
ld).
Ult
ima
tely
, o
ne
sho
uld
be
a
ble
to
p
rod
uc
e o
n a
sili
co
n su
bst
rate
G
e o
r e
ve
n
InC
aA
s la
yers
co
mp
ara
ble
in
q
ua
lity
to
bu
lk
sam
ple
s.
In
this
a
pp
roa
ch
, n
o u
se
is
mad
e o
f th
e el
ectr
on
ic
pro
pe
rtie
s o
f th
e h
eter
oin
terf
ace
, n
or
of
the
Si
sub
stra
te
Itse
lf.
Th
e la
tter
m
ere
ly
serv
es
as
a ca
rrie
r v
eh
icle
fo
r a
n in
co
mm
en
sura
te
gro
wth
o
f a
use
ful
sin
gle
-cry
sta
l fo
reig
n se
mic
on
du
cto
r.
Ho
we
ve
r,
ther
e is
o
ne
pro
pe
rty
of
sili
co
n,
wh
ich
is
ve
ry
att
ract
ive
for
use
in
hb
er-o
pti
cs
co
mm
un
ica
tio
ns
an
d w
ho
se
uti
liza
tio
n re
qu
ires
co
mm
en
sura
te
ep
ita
xy
.
Sil
ico
n is
a
n id
eal
ma
teri
al
for
av
ala
nc
he
mu
ltip
lic
ati
on
of
ph
oto
ge
ne
rate
d
sign
als.
N
eit
he
r G
e n
or
InG
aA
s ar
e id
eal
av
ala
nc
he
ph
oto
de
tec
tor
(AP
D)
ma
teri
als
fr
om
th
e p
oin
t o
f v
iew
o
f th
e so
-ca
lled
e
xce
ss
nois
e
fact
or
F,
wh
ich
des
crib
es
the
sto
cha
stic
n
atu
re
of
av
ala
nc
he
mu
ltip
lic
ati
on
[22
].
Th
e F
fa
cto
r
gen
era
lly
dep
end
s o
n th
e a
va
lan
ch
e g
ain
M
a
nd
the
rati
o o
f th
e im
pa
ct
ion
iza
tio
n co
effi
cien
ts
K
- ot
„ la
.^
for
elec
tro
n a
nd
ho
les.
If
K
=
1 th
en
f =
M
an
d th
e to
tal
no
ise
po
we
r sc
ale
s <x
.
Su
ch
is
th
e si
tua
tio
n fo
r G
e w
ith
/«s
< 2
an
d In
Ga
As,
w
he
re
a„
la^,
<
2.
On
the
oth
er
ha
nd
, if
K
»
1 o
r
X
« 1
, th
en
F
= 2
even
fo
r A
4 »
1,
pro
vid
ed
av
ala
nc
he
is
init
iate
d b
y th
e
typ
e o
f ca
rrie
r w
ith
hig
he
r a.
It
is
we
ll
esta
bli
shed
[2
2]
tha
t in
Si
at
no
t to
o h
igh
elec
tric
fi
elds
(
< 3
x lO
^V
/cm
) th
e el
ectr
on
ion
iza
tio
n co
effi
cien
t is
su
bst
an
tia
lly
gre
ate
r th
an
the
ho
le
ion
iza
tio
n co
effi
cien
t.
Th
us,
p
rop
erl
y d
esi
gn
ed
Si
AP
D's
147
FIG
UR
E
9:
A
poss
ible
G
e/S
i h
i-lo
S
AM
A
PD
st
ruct
ure
[2
5]
wit
h se
pa
rate
a
bso
rpti
on
an
d m
ult
ipli
cati
on
reg
ion
s a
nd
hig
h-l
ow
el
ectr
ic
field
pr
ofil
e.
Its
imp
lem
enta
tio
n re
qu
ires
fu
rth
er
imp
rove
men
t in
th
e q
ua
lity
o
f th
e in
terf
acia
l g
erm
an
ium
la
yers
. L
arge
n
um
ber
o
f m
isfi
t de
fect
s,
resu
ltin
g in
a
hig
h pa
rasi
tic
da
rk
curr
ent,
ma
y be
ve
ry
diff
icu
lt
to
avoi
d.
can
ha
ve
the
no
ise
pe
rfo
rma
nc
e n
ear
the
theo
reti
cal
min
imu
m.
At
pre
sen
t,
the
re
are
c
om
me
rcia
lly
ava
ila
ble
si
lic
on
dev
ices
w
ith
K
~ 20
-
100
(of
cou
rse,
the
se
AP
D's
d
o n
ot
op
era
te
in
the
ran
ge
of
inte
rest
fo
r fi
be
r-o
pti
ca
l
co
mm
un
ica
tio
ns)
. It
w
ou
ld
be
ve
ry
att
ract
ive
to
imp
lem
en
t a
he
tero
stru
ctu
re
de
vic
e w
ith
separa
te
ab
sorp
tio
n a
nd
mu
ltip
lic
ati
on
reg
ion
s (S
AM
A
PD
),t
in
wh
ich
elec
tro
ns
ph
oto
ge
ne
rate
d in
a
Ge
or
InG
aA
s la
yer
wo
uld
su
bse
qu
entl
y
av
ala
nc
he
in
Si.
A
n e
xa
mp
le
of
such
a
stru
ctu
re
[25
] is
s
ho
wn
in
Fig
. 9.
It
co
mb
ine
s S
i m
ult
ipli
ca
tio
n w
ith
Ge
ab
sorp
tio
n la
yers
. It
als
o c
on
tain
s a
de
ple
ted
lay
er
of
acc
epto
rs
(ch
arg
e sh
ee
t)
bu
ilt
in
sili
co
n in
th
e v
icin
ity
of
the
Ge
inte
rfa
ce
, w
ho
se
pu
rpo
se
is
to
sep
ara
te
the
low
-fie
ld
reg
ion
in
the
op
tic
all
y
ac
tiv
e G
e la
yer
fro
m
a h
igh
-fie
ld
Si
laye
r w
he
re
ava
lan
che
mu
ltip
lic
ati
on
occ
urs
.
Sim
ila
r S
AM
A
PD
st
ruct
ure
s w
ith
hi-
lo
elec
tric
fi
eld
pro
file
s h
ave
b
een
succ
essf
ull
y fa
bri
cate
d in
II
I-V
co
mp
ou
nd
sem
ico
nd
uc
tors
[2
6],
h
ow
ev
er,
th
e
imp
lem
en
tati
on
wit
h G
e/S
i h
ete
roju
nc
tio
ns
req
uir
es
far
bet
ter
ma
teri
al
qu
ali
ty
in
the
inte
rfa
cia
l la
yers
th
an
tha
t p
rese
ntl
y a
vail
ab
le
wit
h a
ny
crys
tal
gro
wth
tec
hn
iqu
e.
2.2
Wa
veg
uid
e
Infr
ared
D
etec
tors
B
ase
d
on
Ge/
Si
Sup
erla
ttice
s
A
no
ve
l in
fra
red
ph
oto
de
tec
tor
stru
ctu
re
wa
s re
ce
ntl
y p
rop
ose
d [2
7],
w
hic
h
uti
lize
s th
e si
lic
on
ad
van
tag
e.
It
rep
rese
nts
a
wa
ve
gu
ide
in
wh
ich
the
core
is
a
stra
ine
d-l
ay
er
Ge
jSii
_^
/Si
sup
erla
ttic
e (S
LS
) sa
nd
wic
he
d b
etw
ee
n S
i la
yers
o
f a
low
er
refr
act
ive
ind
ex
. A
bso
rpti
on
of
infr
are
d ra
dia
tio
n o
ccu
rs
in
the
core
reg
ion
du
e to
in
terb
an
d e
lec
tro
n tr
an
siti
on
s,
an
d p
ho
tog
en
era
ted
carr
iers
a
re
co
lle
cte
d in
th
e S
i c
lad
din
g la
yers
. D
ue
to
the
rec
en
tly
dis
co
ve
red
effe
ct
of
ba
nd
ga
p n
arr
ow
ing
by
the
stra
in
in
Ge
,Si,
_^
a
llo
y la
yers
th
e fu
nd
am
en
tal
ab
sorp
tio
n th
resh
old
o
f th
e S
LS
is
shif
ted
to
lon
ge
r w
av
ele
ng
ths,
so
th
at
the
de
tec
tor
can
be
op
era
ted
in
the
ran
ge
of
sili
ca-f
iber
tr
an
spa
ren
cy.
If
the
all
oy
t C
onsi
dera
ble
rese
arch
ha
s l>
een
devo
ted
to t
he
use
of
IlI-
IV
com
pou
nd-
sem
icon
duct
or
SA
M
AP
D's
fo
r fi
ber-
optic
s co
mm
un
icat
ion
s (s
ee
[23]
an
d re
fere
nce
s th
erei
n).
E
xcel
len
t pe
rfor
man
ce h
as b
een
dem
onst
rate
d by
In
P/G
aocl
ngs
aAs
AP
D's
of
this
typ
e [2
4].
148
ab
sorp
tio
n th
resh
old
in
th
e G
e^
Si,
_j/
Si
SL
S as
a
fun
cti
on
of
the
Ge
co
nte
nt
in
the
all
oy
laye
rs
an
d fo
un
d a
go
od
ag
reem
ent
wit
h th
e th
eo
reti
ca
l p
red
icti
on
s.
At
X -
0.
6 th
e b
an
dg
ap
EQ
is
n
arr
ow
er
tha
n th
at
of
pu
re
un
stra
ine
d G
e,
an
d fo
r
X
> 0.
5 o
ne
has
E
Q
< 0
.8e
V.
Th
e a
bso
rpti
on
edg
e is
th
us
br
ou
gh
t d
ow
n b
y th
e
stra
in
to b
elo
w
the
ph
oto
n en
erg
y at
w
av
ele
ng
ths
of
sili
ca-f
iber
tr
an
spa
ren
cy.
2.1.
1 D
esig
n of
W
ave
gu
ide
D
etec
tors
an
d A
PD
's
Co
nsi
der
fi
rst
a w
av
eg
uid
e-d
ete
cto
r st
ruct
ure
in
w
hic
h th
e co
re
rep
rese
nts
a
sin
gle
a
llo
y la
yer.
F
ig.
10a.
W
e a
ssu
me
tha
t th
e G
e c
on
ten
t in
th
is
laye
r is
X
> 0.
5,
an
d th
at
the
ab
sorp
tio
n co
effi
cien
t at
w
av
ele
ng
ths
of
inte
rest
is
(I
= 1
0^
cm"
' (a
s in
dic
ate
d b
y th
e p
reli
min
ary
re
sult
s [2
8]
at
X —
l.S
/zm
).
To
be
in
the
ran
ge
of
co
mm
en
sura
te
gro
wth
, th
e a
llo
y th
ick
nes
s ti
mu
st
be
less
th
an
the
c ri
tica
l (0
.5)
— 1
00 A
. T
o a
go
od
ap
pro
xim
ati
on
, th
e fr
ac
tio
n F
o
f th
e
inte
gra
ted
inte
nsi
ty
of
the
lig
ht
wa
ve
wh
ich
fall
s w
ith
in
the
ab
sorb
ing
core
, is
giv
en
by:
r -
2ir^
—
(H
fore
-
"cla
d)
•
For
x
-0.5
, /i
-lO
OA
, a
nd
X-1
.3yu
m
on
e fi
nd
s r
-2
.3
xl
O-
^
Th
e ef
fect
ive
ab
sorp
tio
n co
effi
cien
t o
f su
ch
a w
av
eg
uid
e,
a^^f
=
aP
~
0.2
cm
-',
is
too
low
fo
r a
prac
tica
l u
se
(a
det
ecto
r w
ou
ld
ha
ve
to
be
seve
ral
cen
tim
eter
s lo
ng
an
d e
ve
n th
e
spee
d o
f li
gh
t is
no
t fa
st
en
ou
gh
ove
r su
ch
dis
tan
ces)
.
Th
e u
se
of
a su
per
latt
ice
is t
hu
s im
pe
rati
ve
. C
on
sid
er
the
stru
ctu
re i
llu
stra
ted
in
Fig
. 10
b.
Ign
ori
ng
in
firs
t a
pp
rox
ima
tio
n th
e in
flu
en
ce
of
stra
in
on
the
die
lect
ric
con
sta
nt,
th
e re
fra
ctiv
e in
de
x o
f a
n S
LS
can
be
esti
ma
ted
as
an
ave
rag
e
of
n^
(x)
an
d n
|i
ove
r o
ne
pe
rio
d a
nd
the
effe
ctiv
e a
bso
rpti
on
coef
fici
ent
of
an
p-s
i -L
IGH
T I
NT
EN
SIT
Y
DIS
TR
IBU
TIO
N
(k.S
l, S
TR
AIN
ED
A
LLO
Y L
AY
ER
n-S
l
P-S
I
s««
S'i-
.
._L h
n-S
i
FIG
UR
E
10:
Sch
ema
tic
illu
stra
tion
o
f st
rain
ed-l
aye
r G
e^S
ii.^
w
ave
gu
ide
dete
ctor
s [2
7]:
(a)
sin
gle
-la
yer
core
; (b
) SL
S co
re.
149
lay
ers
a
re
suff
icie
ntl
y th
in,
the
SL
S ca
n b
e g
ro
wn
by
MB
E
wit
ho
ut
nu
cle
ati
ng
dis
loc
ati
on
s.
Ex
pe
rim
en
tall
y,
suc
h st
ruc
ture
s w
er
e re
ce
ntl
y m
an
ufa
ctu
re
d a
nd
test
ed
. T
he
firs
t S
LS
wa
ve
gu
ide
pin
dio
de
s [2
8]
sh
ow
ed
an
inte
rn
al
qu
an
tum
eff
icie
nc
y o
f 4
0%
a
t X
—T
S/z
m
an
d a
fre
qu
en
cy
ba
nd
wid
th
of
clo
se
to
1 G
Hz
. T
he
firs
t A
PD
st
ruc
ture
[2
9]
sh
ow
ed
an
av
ala
nc
he
ga
in
as
hig
h as
M
-5
0 a
nd
a
qu
an
tum
e
ffic
ien
cy
of
10
0%
a
t M
-
10
. T
he
wa
ve
gu
ide
-de
tec
tor
ap
pro
ac
h is
en
tir
ely
c
om
pa
tib
le
wit
h th
e S
i in
teg
rate
d c
irc
uit
te
ch
no
log
y a
nd
off
ers
th
e
po
ssib
ilit
y o
f fa
bri
ca
tin
g a
co
mp
lete
re
ce
ive
r sy
ste
m
for
lon
g-w
av
ele
ng
th
fibe
r-
op
tic
s c
om
mu
nic
ati
on
s o
n a
sil
ico
n c
hip
. F
oll
ow
ing
[27
],
we
sha
ll
br
iefl
y d
isc
us*
be
low
th
e o
pti
mu
m
co
mp
os
itio
n o
f a
n S
LS
co
re,
as
de
ter
min
ed
by
the
tra
de
-off
be
twe
en
the
co
nfi
ne
me
nt
of
ra
dia
tio
n a
nd
the
sta
bil
ity
re
qu
ire
me
nts
fo
r a
Ce
,Si|
_,/
Si
SL
S,
as
we
ll
as
the
de
sig
n o
f a
SA
M
AP
D
wa
ve
gu
ide
stru
ctu
re,
in
wh
ich
low
-no
ise
av
ala
nc
he
mu
ltip
lic
ati
on
oc
cu
rs
in
on
e o
f th
e S
i c
lad
din
g
lay
ers
.
2.2.
1 M
ate
rial
Pro
pe
rtie
s of
S
train
ed-L
aye
r G
e^S
ij JS
i S
yste
ms
Le
t u
s fi
rst
dis
cu
ss
the
qu
est
ion
s o
f st
ab
ilit
y.
Th
e m
ax
imu
m
thic
kn
ess
/i
^ o
f a
sin
gle
st
rain
ed
GC
jSij
.^
all
oy
lay
er
wh
ich
can
be
gr
ow
n p
se
ud
om
or
ph
ica
lly
on
Si
dep
>en
ds
on
the
ge
rm
an
ium
c
on
ten
t,
de
cre
asi
ng
wit
h x.
P
EO
PL
E
an
d B
EA
N
[30
] h
av
e c
alc
ula
ted
/if(
x)
on
the
ass
um
pti
on
tha
t th
e fi
lm
gr
ow
s in
itia
lly
wit
ho
ut
dis
loc
ati
on
s,
wh
ich
are
th
en
ge
ne
rate
d a
t th
e in
terf
ac
e,
as
the
stra
in
en
er
gy
de
ns
ity
pe
r u
nit
a
rea
of
the
film
e
xc
ee
ds
the
are
al
en
erg
y d
en
sity
ass
oc
iate
d w
ith
an
iso
late
d d
islo
ca
tio
n.
Th
eir
re
sult
, w
hic
h im
pli
cit
ly
giv
es
l\)
in
[A]
by
the
eq
ua
tio
n
x^
/i,
- 1
3.3
ln
(E,/
4),
is
in
an
ex
ce
lle
nt
ag
ree
me
nt
wit
h th
e e
mp
iric
al
da
ta.
Ra
ma
n sc
att
eri
ng
stu
die
s [3
1]
ha
ve
sh
ow
n th
at
mo
st
of
the
stra
in
in
such
stru
ctu
res
resi
de
s in
th
e a
llo
y la
ye
r,
wit
h S
i c
lad
din
g la
ye
rs
be
ing
ne
arl
y
un
str
ain
ed
. A
s
ec
on
d G
e,S
ii_
j la
ye
r c
an
the
n b
e g
ro
wn
on
the
Si
cap
lay
er
(pr
ov
ide
d th
e la
tte
r is
2
-3
tim
es
thic
ke
r th
an
the
all
oy
lay
er)
, a
nd
the
seq
ue
nc
e
ca
n b
e re
f>ea
ted
ma
ny
tim
es
wit
ho
ut
a n
oti
ce
ab
le
inc
om
me
ns
ur
ate
g
ro
wth
(a
s
ma
ny
as
10
0 f)
eri
od
s h
av
e b
ee
n
rep
ort
ed
).
Th
e m
ax
imu
m
tota
l th
ick
ne
ss
of
suc
h
stra
ine
d la
ye
r su
fie
rla
ttic
es
(SL
S)
ca
n b
e e
stim
ate
d fr
om
th
e se
mi-
em
pir
ica
l ru
le
[32
] th
at
the
sta
bil
ity
of
the
SL
S a
ga
inst
th
e fo
rm
ati
on
of
dis
loc
ati
on
s is
eq
uiv
ale
nt
to
tha
t o
f a
sin
gle
a
llo
y la
ye
r o
f sa
me
thic
kn
ess
b
ut
av
era
ge
Gc
co
nte
nt.
T
his
ru
le
ca
n b
e re
pre
sen
ted
by
the
foll
ow
ing
ex
pre
ssio
n:
fifl
^(x,
r,T
) =
//
, (x
r),
wh
er
e r
=
X/T
is
th
e ra
tio
of
the
thic
kn
ess
o
f th
e a
llo
y la
ye
r to
th
e su
pe
rla
ttic
e
pe
rio
d (i
.e.
the
"d
uty
c
yc
le"
),
an
d /i
gts
th
e to
tal
thic
kn
ess
o
f th
e su
pe
rla
ttic
e.
Ne
xt,
w
e d
isc
uss
th
e e
ffe
cts
o
f st
rain
o
n th
e b
an
d
stru
ctur
e o
f a
n a
llo
y la
ye
r
An
imp
or
tan
t fin
ding
in
th
is
reg
ard
is
th
e th
eo
reti
ca
l c
alc
ula
tio
n o
f P
EO
PL
E
[33
]
wh
o c
on
sid
ere
d th
e b
an
dg
ap
na
rr
ow
ing
in
stra
ine
d G
e^
Sij
.^
all
oy
s g
ro
wn
on
Si
(10
0)
sub
stra
tes,
a
nd
fou
nd
tha
t th
e g
ap
is
sub
sta
nti
all
y re
du
ce
d in
c
om
pa
riso
n
wit
h th
e u
ns
tra
ine
d a
llo
y.
LA
NG
et
a
l.
[34
] h
av
e m
ea
sure
d th
e fu
nd
am
en
tal
180
SL
S co
re
is
giv
en
by
a^ff
—rP
a.
An
aly
sis
[27
] sh
ow
s th
at
a^ff
is
ma
xim
ize
d b
y
km
all
er
r,
wh
ich
for
'IS
LS
~''
SL
S*
imp
he
s m
ax
imiz
ing
the
sup
erl
att
ice
wid
th,
an
d
tha
i h
as
its
op
tim
um
v
alu
e fo
r th
ose
r
wh
ich
co
rre
spo
nd
to
r=
:l/
2.
rhy
sic
all
y,
as
the
sup
erl
att
ice
is
ma
de
thic
ke
r to
a
bso
rb
the
win
gs
of
the
lig
ht
iiil
eiis
ity
dis
trib
uti
on
, th
e S
LS
re
qu
ire
me
nt
of
de
cre
asi
ng
r le
ad
s to
le
ss
eff
icie
nt
ab
stir
pli
on
at
the
pea
k in
ten
sity
, th
us
mo
re
tha
n o
ffse
ttin
g th
e g
ain
. W
e c
an
r»|H
'ti
an
op
tim
um
v
alu
e a^
ff
<
0.2
a =
2
0c
m"
' in
a
n S
LS
co
nsi
stin
g o
f 12
fHT
ioU
s o
f 60
A
Ge
jSii
_;t
/14
0A
S
i.
Th
is
me
an
s th
at
the
wa
ve
gu
ide
len
gth
m
ust
be
of
ord
er
0.5
mm
fo
r h
igh
de
tec
tor
eff
icie
nc
y.
If
a pi
n d
ete
cto
r re
pre
sen
ts
a
rid
ge
wa
ve
du
ide
of
tha
t le
ng
th
an
d th
e w
idth
<
lO
^m
, th
en
its
ca
pa
cit
an
ce
is
less
th
an
ab
ou
t 0.
5 p
F,
ass
um
ing
a ty
pic
al
de
ple
tio
n w
idth
o
f l^
im.
Th
is
va
lue
of
the
mie
rna
l c
ap
ac
ita
nc
e is
a
cc
ep
tab
le
an
d c
om
pa
rab
le
to
tha
t o
f th
e c
on
ve
nti
on
al
pm
IK
det
ecto
rs.
No
te
tha
t th
e d
ete
cto
r q
ua
ntu
m
eff
icie
nc
y g
ro
ws
wit
h th
e
i.|>
iKal
p
ath
le
ng
th,
wit
ho
ut
de
gr
ad
ing
the
spe
ed
of
resp
on
se.
Th
e d
etec
tor
sen
siti
vit
y w
ill
be
fur
the
r im
pr
ov
ed
by
an
av
ala
nc
he
ga
in
in
Si
lUd
din
g la
yers
. T
o re
du
ce
an
ex
ce
ss
no
ise
, th
e A
PD
d
esi
gn
sh
ou
ld
be
gu
ide
d b
y
the
foll
ow
ing
pri
nc
iple
s;
i)
sin
ce
K
=
a^/a
^ »
1 in
S
i,
the
mu
ltip
lic
ati
on
sho
uld
b
e in
itia
ted
by
ele
ctr
on
s ra
the
r th
an
ho
les;
ii
) si
nc
e K
d
ec
rea
ses
sha
rply
wh
en
the
elec
tric
fi
eld
m
uc
h e
xc
ee
ds
the
ion
iza
tio
n th
re
sh
old
, £
,,
the
fiel
d in
the
ava
lan
che
lay
er
sh
ou
ld
be
ne
ar
the
thr
es
ho
ld,
£ >
£
, =
S
xlO
^V
/cm
, a
nd
the
thic
kn
ess
of
tha
t la
ye
r s
ho
uld
b
e w
ell
a
bo
ve
a~\E
,) =
C
S/z
m;
Hi)
the
fie
ld
in
the
SL
S la
yers
sh
ou
ld
no
t e
xc
ee
d ~
10
^V
/cm
, th
e io
niz
ati
on
thr
es
ho
ld
in
Ge.
A p
oss
ible
w
av
eg
uid
e A
PD
st
ruc
ture
is
il
lust
rate
d in
F
ig.
11
. I
n a
dd
itio
n to
an
un
do
pe
d G
e^
^S
ii-;
,/S
i S
LS
of
x>
0.6
, r
<
0.3
, a
nd
thic
kn
ess
/I
SL
S>
30
00
A,
it
lon
laii
is
an
un
do
pe
d S
i a
va
lan
ch
e la
ye
r o
f th
ick
ne
ss
d >
2u
m.
sep
ara
ted
fro
m
the
SL
S b
y a
thin
(
A<
10
"*
cm
) p
-ty
pe
Si
lay
er.
I
n th
e o
pe
ra
tin
g re
gim
e,
the
A
laye
r m
ust
b
e d
ep
lete
d b
y a
n a
pp
lie
d re
ve
rse
bia
s.
Th
e to
tal
surf
ac
e d
en
sity
o
f
iha
rge
in
this
la
ye
r s
ho
uld
, th
ere
fore
, b
e o
f o
rde
r K
E,
=2
X
lO'^
e/c
m^
T
his
w
ill
ait
iiev
e th
e d
esi
rab
le
hi-
lo
fie
ld
sep
ara
tio
n o
f th
e a
bso
rpti
on
an
d m
ult
ipli
ca
tio
n
laye
rs
an
d re
sult
in
a
low
-no
ise
SA
M
AP
D
stru
ctu
re.
EL
EC
TR
IC F
IEL
D (
V/c
ml
' '
1 1
1 I
2 3
X1
0=
Oe,
Si|.
,/S
i S
LS
a p
-Si
UN
OO
PE
D S
i 4
AV
ALA
NC
HE
L
AY
ER
FIG
UR
E
11
; A
w
av
eg
uid
e A
PD
st
ruct
ure
and
the
elec
tric
fi
eld
pro
file
[2
7].
Co
nce
ptu
all
y,
the
stru
ctu
re
is
an
alo
go
us
to
the
SA
M
AP
D o
f F
ig.
9.
p-S
i
n+
Sl
+ V
151
2.3
Con
clus
ion
De
ve
lop
me
nt
of
Si-
ba
sed
det
ecto
rs
for
op
tic
al
co
mm
un
ica
tio
ns
rep
rese
nts
o
ne
ol
the
mo
st
pra
cti
ca
l a
pp
lic
ati
on
s o
f si
lic
on
MB
E
rese
arc
h.
Th
e w
av
eg
uid
e-d
ete
cto
r
ap
pro
ac
h is
e
nti
rely
c
om
pa
tib
le
wit
h th
e S
i in
teg
rate
d c
irc
uit
te
ch
no
log
y a
nd
off
ers
th
e p
oss
ibil
ity
of
fab
ric
ati
ng
a c
om
ple
te
rec
eiv
er
syst
em
for
lon
g-
wa
ve
len
gth
fi
be
r-o
pti
cs
co
mm
un
ica
tio
ns
on
a si
lic
on
ch
ip.
RE
FE
RE
NC
ES
1.
R.
Tsu
a
nd
L.
Esa
ki,
Ap
pl.
P
hys
. L
ett.
2
2,
562
(19
73
);
L.
L.
Ch
an
g,
L.
Esa
ki
an
d R
. T
su,
ibid
. 24
, 59
3 (1
97
4).
2.
T
. C
. L
. C
. S
oll
ner
, W
. D
. G
oo
dh
ue,
P
. E
. T
an
ne
nw
ald
, C
. D
. P
ark
er
an
d D
. D
. P
eck
, A
pp
l.
Ph
ys.
Let
t.
43,
588,
(1
98
3).
3.
T
. C
. L
. G
. S
oll
ner
, P
. E
. T
an
ne
nw
ald
, D
. D
. P
eck
, a
nd
W.
D.
Go
od
hu
e,
Ap
pl.
P
hys
L
ett.
45
, 13
19,
(19
84
).
4 T
. S
hew
chu
k,
P.
C.
Ch
ap
in,
P.
D.
Co
lem
an
, W
. K
op
p,
R.
Fis
cher
a
nd
H.
Mo
rko
y,
Ap
pl.
P
hys
. L
ett.
46
, 50
8 (1
98
5).
5.
M.
Tsu
chiy
a,
H.
Sa
ka
ki
an
d J.
Y
ash
ino
, Ja
p.
J. A
pp
l.
Ph
ys.
24
, L
46
6 (1
98
5).
6.
T
. T
such
iya
an
d H
. S
ak
ak
i,
Tec
h.
Dig
est
of
IEE
E
Int.
Ele
ctro
n D
ev.
Mee
tin
g,
Dec
2-
4,
Wa
shin
gto
n,
DC
(1
98
5),
p.
662
7.
H
Mo
rk
oc
J.
Ch
en,
U.
K.
Red
dy,
T
H
end
erso
n,
P.
D.
Co
lem
an
, a
nd
S L
ury
i,
Ap
pl.
P
hys
. L
ett.
, to
be
pu
bli
shed
. 8.
B
. R
icco
an
d M
. Y
a. A
zbe
l, P
hys
. R
ev.
B 2
9,
1970
(1
98
4).
9.
F
. C
ap
ass
o a
nd
R.
A.
Kie
hl,
J.
Ap
pl.
P
hys
. 58
, 13
66
(19
85
).
10.
S.
Lu
ryi,
A
pp
l.
Ph
ys.
Let
t.
47,
490
(19
85
).
11.
S.
Lu
ryi,
T
ech
nic
al
Dig
est
of
the
IEE
E
Int.
E
lect
ron
Dev
. M
ee
tin
g,
Dec
. 2-
4,
Wa
shin
gto
n,
DC
(1
98
5),
p.
666.
12
G
. E
. D
erk
its,
to
be
pu
bli
shed
. 13
. E
. A
. R
ezek
, N
. H
olo
ny
ak
, Jr
., B
. A
. V
oja
k,
an
d H
. S
chic
hij
o,
Ap
pl.
P
hys
. L
ett.
70
.1
(19
77
).
14.
R.
A.
Dav
ies,
M
. J.
K
elly
, a
nd
T.
M.
Ker
r, P
hys
. R
ev.
Let
t. 5
5,
1114
(1
98
5).
15
. R
. F
. K
aza
rin
ov
an
d R
. A
. S
uri
s,
Sov
. P
hys
. -
Sem
ico
nd
. 5,
707
(1
97
1).
16
. L
. E
saki
a
nd
L.
L.
Ch
an
g,
Ph
ys.
Rev
. L
ett.
33
, 49
5 (1
97
4).
17
. F
. C
ap
ass
o,
K.
Mo
ha
mm
ed
, a
nd
A.
Y.
Ch
o,
Tec
h.
Dig
est
of
IEE
E I
nt.
Ele
ctro
n D
ev
Mee
tin
g,
Dec
. 2-
4,
Wa
shin
gto
n,
DC
(1
98
5),
p
. 76
4;
als
o A
pp
l.
Ph
ys.
Let
t.
48,
478
(19
86
).
18.
S.
Lu
ryi
an
d F
. C
ap
ass
o,
Ap
pl.
P
hys
. L
ett.
47,
13
47
(19
85
).
19.
T.
R.
Ha
rris
on
, A
. M
. J
oh
nso
n,
P.
K.
Tie
n,
an
d A
. H
. D
aye
m,
Ap
pl.
P
hys
. L
ett
41
, 73
4 (1
98
2).
20.
S.
Lu
ryi,
A
. K
asta
lsky
, a
nd
J.
C.
Bea
n,
IEE
E
Tra
ns.
E
lect
ron
Dev
ices
E
D-3
1,
1135
(1
98
4).
21
. A
. K
ast
als
ky,
S.
L
ury
i,
J.
C.
Bea
n,
an
d T
. T
. S
hen
g,
in
Pro
c.
1st
Int.
Sym
p.
Sili
con
MBE
, ed
. b
y J.
C.
Bea
n,
Ele
ctro
chem
. S
oc.
Pre
ss,
1985
, p
. 40
6.
22.
See
, fo
r ex
am
ple
, F
. C
ap
ass
o,
Ph
ysic
s o
f a
vala
nch
e p
ho
tod
iod
es,
in
Sem
iconducl
on
and
sem
imeta
ls,
vo
l. 2
2,
pa
rt D
, p
p.
1-1
72
, 19
85.
23.
G.
E.
Sti
llm
an
, L
. W
. C
oo
k,
G.
E.
Bu
lma
n,
N.
Ta
ba
tba
ie,
R.
Ch
in,
an
d P
D
. D
ap
ku
k,
IEE
E T
ran
s.
Ele
ctro
n D
evic
es
ED
-29,
13
55
(19
82
).
24.
J.
C.
Ca
mp
bel
l, A
. G
. D
enta
i, W
. S
Ho
lde
n,
an
d B
. L
. K
asp
er,
Ele
ctro
n L
ett.
19
, 81
8 (1
98
3).
25
. F
. C
ap
ass
o,
A.
Kas
tals
ky,
an
d S.
L
ury
i,
1983
(u
np
ub
lish
ed).
15
2
26
I- C
apas
so,
A.
Y.
Ch
o,
an
d P
. W
. F
oy,
Ele
ctro
n.
Let
t. 2
0, 6
35
(19
84
).
27
S L
ury
i, T
. P
. P
ears
all,
H
. T
em
kin
, a
nd
J. C
. B
ean
, IE
EE
Ele
ctro
n D
evic
e L
ett.
E
DL-
7, 1
04,
(19
86
)
28
H.
Tem
kin
, T
. P
. P
ears
all,
J.
C
. B
ean
, R
. A
. L
og
an
, a
nd
S.
Lu
ryi,
A
pp
l.
Ph
ys.
Let
t.,
lo
be p
ub
lish
ed.
2Y
T
P
Pea
rsal
l, H
. T
em
kin
, J.
C
. B
ean
, a
nd
S.
Lu
ryi,
to
be
pu
bli
shed
. JO
R
P
eop
le a
nd
J. C
. B
ean
, A
pp
l.
Ph
ys.
Let
t. 4
7,
322
(19
85
).
31
F.
Cer
deir
a, A
. P
incz
uk
, J.
C
. B
ean
, B
. B
atl
og
g,
an
d B
. A
. W
ilso
n,
Ap
pl.
P
hys
. L
ett.
45
, 11
38
(19
84
).
32
R
Hu
ll,
J.
C.
Bea
n,
F.
Cer
dei
ra,
A.
T.
Fio
ry,
an
d J.
M
. G
ibso
n,
Ap
pl.
P
hys
L
ett.
48
, 5
6(1
98
6).
33
R
. P
eopl
e,
Ph
ys.
Rev
. B
32,
1405
(1
98
5).
34
D
. V
. L
an
g,
R.
Peo
ple,
J.
C
. B
ean
, a
nd
A.
M.
Ser
gen
t,
Ap
pl.
P
hys
. L
ett.
47
, 13
33
(198
5).
15
3
