Silicon Quantum Computer
Kohei M. Itoh
Keio University, Yokohama, Japan
Collaborators: Yoshi Yamamoto and Yoshi Matsumoto
Quantum Information in Group IV Semiconductors Workshop
March 28-29, 2003
Semiconductor Isotope Engineering
List of stable isotopes
28Si
92.2%
29Si
4.7% → 1/2
（nuclear spin）
30Si
3.1%
70Ge
72Ge
73Ge
74Ge
76Ge
20.5%
27.4%
7.8% → 9/2
（nuclear spin）
36.5%
7.8%
99.999%
69Ga
60.1% → 3/2
71Ga 39.9% → 3/2
（nuclear spin）
75As
100%
→ 3/2
Mass and nuclear spin
control through manipulation
of stable isotopes
28Si
possible with $10k/gram
1
Isotope effect on thermal conductivity
Thermal conductivity of 99.86% 28Si
300K 60% increase
400K 40-50% increase
with respect to natural Si
ISONICS, Golden, CO
•99.92% 28Si epi-layers of
1-100 microns on 4-6 inch Si
T. Ruf, et al. Solid State Commun. 2000
29Si
nuclear spin quantum computer
28
28
Qubit #1 ω1
28
28
Qubit #2 ω2
Qubit #4 ω4
28
28
28
29
28
1
large field
gradient
1.5 Tesla/µm
29
29
29
28
Copies
28
28
|ωn+1- ωn |~20kHz
29
29
29
28
28
28
28
29
29
29
28
Qubit #3 ω3
29
29
28
28
Position
28
2
28
3
B
2
29Si
•
•
•
•
wire fabrication
Form regular step arrays on
slightly miscut 28Si(111)7×7
surface (~ 1º from normal)
Steps are straight, with about
1 kink in 20000 sites.
29Si chains formed by “Step
Decoration” from 28Si steps
Angle of miscut controls
chain spacing
28Si
29Si
40×70nm2
340×390nm2
J.-L. Lin, et al., JAP
84, 255 (1998)
Row-by-row growth
The step-flow growth was
observed as the appearance of
new adatoms at the edge
Short rows are thermally
diffused to form a longer row
which is energetically stable
< 112 >
Tsub
350℃
Growth rate 0.8×10-2BL/min
U(5)
T. Hasegawa, et al., Phys. Rev.
B48, 1943 (1995).
3
Short-term goal
1 µm
Homogeneous and strong gradient
B=5 T
2 µm
magnet
28Si
29Si
シリコン基板
layers
substrate
Micro-magnet
磁性体
28Si
(I=0)
Qubit#1 ω1
29Si
(I=1/2)
28Si
Qubit#2 ω2
29Si
substrate
Magnetic field B
1
width
0.8
Distance (μm)
Magnetic field simulation
0.6
0.4
0.2
0
0
1
2
3
4
5
6
磁性体の幅[μm]
Width
of magnet (μm)
２µm
distance
and
gradient
Ｓｉ
gradient (T/μm)
4
3
2
1
0
0
1
2
3
4
5
6
Width磁性体の幅[μm]
of magnet (μm)
4
Enriched Si crystals
Natural abundance
28Si: 92.2 %
29Si: 4.7 %
30Si: 3.1 %
99.92%
28Si
single crystal
10 mm
99.3%
29Si
single crystal
10 mm
99.3%
30Si
single crystal
28Si
n/
30Si
n Isotope
Superlattices
n: # of monolayers
28Si
n = 8, 12, 24
~ 200 nm
30Si
1 monolayer = 1.36 Å
28Si
30Si
layer ≡
nat.Si
(92.2 %
layer ≡ 98.74 %
30Si
28Si)
Buffer layer (nat.Si)
Si [001] substrate
Characterization
Secondary Ion Mass Spectrometry (SIMS)
Raman Spectroscopy
5
MBE Equipment
Main Ch.
Growth conditions
RSH
EB gun
L. L. Ch.
Pressure
~ 5 × 10-9 Torr
Temperature
TSP
IP
GV
Si substrate
Substrate: 650ºC
K-cells: 1400ºC
TMP
Growth rate
28Si
0.1 ~ 0.5 Å/sec.
30Si
Ge isotopes
Knudsen-cells
SIMS of Superlattices
SIMS Intensity (a.u.)
6.5 nm
3.3 nm
2.2 nm
a) n = 24
b) n = 12
c) n = 8
30Si
28Si
0
10
20
30
40
Depth (nm)
50
60
6
Phonons of Superlattices
Ex)
nat.Si
30
4/ Si4
superlattice
X
ωΓ
<001>
TO
LO
LA
1 ML
(a/2)
TA
1 cycle of
28Si /30Si (4a)
4
4
0
Bulk’s a
π/4a
π/a
k [100]
Vibrational modes in 28Si12/30Si12
30Si
28Si
7
Raman Spectroscopy
Backscattering geometry
Laser
Buff.
Sub.
~ 523.5
(Si Sub.)
514.86
509.04
506.49
Raman Intensity [arb. unit]
Superlattice
520.32
(× 2)
(a) n = 24
513.72
507.54
(b) n = 12
Conditions
508.62
✓ Ar+ laser (514.5 nm)
518.44
✓ ~ 4 K (liq. He)
500
510
520
(c) n = 8
530
540
Raman Shift [cm-1]
Comparison with theory
30
LO7(28Si)
n = 24
Number of n
20
LO5(28Si)
LO3(30Si)
15
LO3(28Si)
n = 12
10
30
n=8
5 LO1( Si)
0
490
Si
substrate
Raman Intensity [arb. unit]
25
n = 24
n = 12
LO1(28Si)
500
510
520
530
-1
Raman peak position [cm ]
n=8
500
510
520
530
540
Raman Shift [cm-1]
8
Sputter growth growth and reactive ion etching of
NiFe
NiFe
2µm
Si substrate
Ti
buffer
80Å
After reactive ion etching
1µm
Conclusion
28Si/30Si
Isotope Superlattices
28Si
30Si
Self-Assembled
Ge/Si(100)Quantum Dots
A. V. Kolobov et al.,
APL 81, 3855 (2002)
70Ge
or
76Ge
Buffer layer (nat.Si)
Si [001] substrate
Si [001] substrate
9