1. Ciencia

Modelling the electronic properties
of phosphorus wires in silicon
Jackson Smith
J. H. Cole, D. W. Drumm, and S. P. Russo
!
Chemical and Quantum Physics, School of Applied Sciences,
RMIT University
! Single P donor
Si
±𝜓e
4.37 nm
! Single P donor
What is the
ideal
separation
distance for
two P wires
in Si?
Si
±𝜓e
4.37 nm
(a)
(b)
Si
P
[110]
5.46 nm
! P wire in Si
[001]
5.46 nm
[11̄0]
[110]
[11̄0]
Drumm et al. NRL 2013, Budi et al. PRB 2012, Drumm et al. PRL 2013
(a)
(b)
Si
P
[110]
5.46 nm
! P wire in Si
[001]
5.46 nm
[11̄0]
[110]
[11̄0]
Drumm et al. NRL 2013, Budi et al. PRB 2012, Drumm et al. PRL 2013
*
! P wire in Si
50 nm
*Weber et al. Science 2012
*
! P wire in Si
50 nm
Si
P
*Weber et al. Science 2012
(b)
(c)
(d)
(e)
(f)
[110]
(a)
1.54 nm
[11̄0]
(a)
(b)
(c)
(d)
(e)
(f)
[110]
! Probability density
1.54 nm
[11̄0]
(a)
(b)
(c)
(d)
(e)
(f)
[110]
! Probability density
1.54 nm
[11̄0]
! Band structure
1.00
Conduction band (CB)
Energy (eV)
0.50
0.00
-0.50
-1.00
Valence band
-1.50
Γ
XSC
! Band structure
1.00
kz
Conduction band (CB)
0.50
kx
Energy (eV)
ky
0.00
-0.50
-1.00
Valence band
-1.50
Γ
Drumm et al. PRL 2013
XSC
! Band structure
kz
ky
kx
Drumm et al. PRL 2013
45°$
! Band structure
-kx
Drumm et al. PRL 2013
+kx
! Band structure
0.05
-kx
+kx
Energy (eV)
0.00
-0.05
-0.10
-0.15
Bulk Si CB
-0.20
Γ
Drumm et al. PRL 2013
3
4X
! Band structure
0.05
-kx
+kx
Energy (eV)
0.00
-0.05
-0.10
-0.15
Bulk Si CB
-0.20
Γ
Drumm et al. PRL 2013
3
4X
! Band structure
0.05
Energy (eV)
[110]
0.00
-0.05
-0.10
-0.15
[11̄0]
Bulk Si CB
-0.20
Γ
3
4X
! Band structure
0.05
Energy (eV)
[110]
0.00
Γ2
-0.05
-0.10
Γ1
-0.15
[11̄0]
∆
-0.20
Γ
Bulk Si CB
3
4X
! Band structure
0.05
Energy (eV)
[110]
0.00
Γ2
-0.05
-0.10
Γ1
-0.15
[11̄0]
∆
-0.20
Γ
Bulk Si CB
3
4X
What do we expect the double wire band structures to look like?
Energy (eV)
0.00
-0.05
-0.10
-0.15
-0.20
-0.25
(a)
(b)
(c)
Energy (eV)
0.00
-0.05
-0.10
-0.15
-0.20
-0.25
(d)
(e)
(f )
3
X
4
Γ
3
X
4
Γ
Γ
0.05
Energy (eV)
0.00
Γ2
-0.05
∆
-0.10
Γ1
-0.15
-0.20
Γ
3
4X
3
X
4
(a)
(b)
d
(a)
(b)
Γ1 splitting
(a)
d
(b)
Valley splitting
(VS)
(a)
Γ1 splitting
d
(b)
200
Γ1 splitting
Double wire VS
Single wire VS
Energy (meV)
150
100
50
d
[110]
0
[11̄0]
0
1
2
3
4
Lateral separation of P wires, d (nm)
5
200
Γ1 splitting
Double wire VS
Single wire VS
Energy (meV)
150
100
50
d
[110]
0
[11̄0]
6 meV
0
1
2
3
4
Lateral separation of P wires, d (nm)
5
4.63 nm
Acknowledgements
Dr Daniel Drumm
Dr Akin Budi
Dr Manolo Per
Prof Lloyd Hollenberg
Dr Jared Cole
Prof Salvy Russo