Post on 12-Jan-2016
description
Ab initio study of the diffusion of Mn through GaN
Johann von PezoldAtomistic Simulation Group
Department of Materials ScienceUniversity of Cambridge
Dilute Magnetic Semiconductors (DMS)
Host semiconductor + magnetic dopant
Ferromagnetic coupling
Spin and Charge D o F (Spintronics)
Novel devices (e.g. spin FET, spin LED, magnetic recording ..)
GaN – based DMS
• III-Vs well established – (opto)-electronic devices
• (Ga,Mn)As, but TC ~ 110 K • Dietl et al.: RT ferromagnetism of (Ga,Mn)N
predicted [Science 287 (2000) 1019]
• huge research effort, both theoretical and experimental
• TC ≥ RT confirmed
• TC 10 – 940 K reported
Mechanism of Ferromagnetism in DMSMean field approach (Dietl et al.) • FM due to Zener p/d exchange interaction
• Large carrier density essential (~ 1020 cm-3).
Mn d-states
DOS (Mn0.0156Ga0.9844)As
Mn d-states
DOS (Mn0.0156Ga0.9844)N
Kulatov et al., Phys Rev B 66, 045203 (2002)
• Strong p-d hybridisation for (Mn,Ga)As, not for (Mn,Ga)N
FM coupling in (Mn,Ga)N (Sato et al.)
• localisation of d states strong, short- ranged (NN) exchange interaction (double exchange mechanism)
• Mn atoms need to form (nano) clusters for FM coupling
• Significant driving force for clustering observed by LDA/ASA calculations
[van Schilfgaarde et al. Phys. Rev. B 63, 233205 (2001)]
and by MC simulations [Sato et al. Jap J Appl Phys 44(30), L948 (2005)]
• Kinetics not considered so-far
Diffusion through GaN
2 obvious diffusion channels
along calong a/b
Method• 2x2x2 supercell of GaN (32 atoms)
• Mn constrained along c/a to sample PES, 32 configurations
• Four host atoms furthest away from Mn fully constrained – avoid relaxation to GS
• Full geometry optimisation for every configuration
• CASTEP, ultrasoft PSPs, nlcc for Ga
Charge State of Mni
• +4, +3, +2,+1, 0, -1 and -2 charge states were considered
• Only +1 charge state was found to be more stable than neutral Mni (under extremely electron deficient conditions)
Relative formation energy of interstitial Mn in different charge states vs EF
-0.2
0.3
0.8
1.3
1.8
0 0.5 1 1.5 2
EF [eV]
Fo
rmat
ion
en
erg
y [
eV]
1
0
0.137 eV
GaN tends to be intrinsically n-type and hence the +1 charge state is unlikely to be realised
Diffusion study for Mn0
Diffusion of Mn0 along aDiffussion barrier along a
-12653.80
-12653.70
-12653.60
-12653.50
-12653.40
-12653.30
-12653.20
-12653.10
-12653.00
-12652.90
-12652.80
0.33 0.38 0.43 0.48 0.53 0.58 0.63 0.68 0.73 0.78 0.83
position along a
tota
l en
ergy
-1.5
-1
-0.5
0
0.5
1
1.5
forc
e o
n M
n [
ev/A
]
Etot
force [Mn(a)]
relaxed
relaxed
relaxed
0.81 eV
Diffusion of Mn0 along a – global maximumDiffussion barrier along a
-12653.80
-12653.70
-12653.60
-12653.50
-12653.40
-12653.30
-12653.20
-12653.10
-12653.00
-12652.90
-12652.80
0.33 0.38 0.43 0.48 0.53 0.58 0.63 0.68 0.73 0.78 0.83
position along a
tota
l en
erg
y
-1.5
-1
-0.5
0
0.5
1
1.5
forc
e o
n M
n [
ev/A
]
Etot
force [Mn(a)]
• Off Tetrahedral site, steric hindrance
Diffusion of Mn0 along a –local minimum IDiffussion barrier along a
-12653.80
-12653.70
-12653.60
-12653.50
-12653.40
-12653.30
-12653.20
-12653.10
-12653.00
-12652.90
-12652.80
0.33 0.38 0.43 0.48 0.53 0.58 0.63 0.68 0.73 0.78 0.83
position along a
tota
l en
erg
y
-1.5
-1
-0.5
0
0.5
1
1.5
forc
e o
n M
n [
ev/A
]
Etot
force [Mn(a)]
• Just below N plane, slightly off centre of hexagonal channel
Diffusion of Mn0 along a –local maximumDiffussion barrier along a
-12653.80
-12653.70
-12653.60
-12653.50
-12653.40
-12653.30
-12653.20
-12653.10
-12653.00
-12652.90
-12652.80
0.33 0.38 0.43 0.48 0.53 0.58 0.63 0.68 0.73 0.78 0.83
position along a
tota
l en
erg
y
-1.5
-1
-0.5
0
0.5
1
1.5
forc
e o
n M
n [
ev/A
]
Etot
force [Mn(a)]
ΔE global min – local max: 120 meV
Diffusion of Mn0 along a – Global minimumDiffussion barrier along a
-12653.80
-12653.70
-12653.60
-12653.50
-12653.40
-12653.30
-12653.20
-12653.10
-12653.00
-12652.90
-12652.80
0.33 0.38 0.43 0.48 0.53 0.58 0.63 0.68 0.73 0.78 0.83
position along a
tota
l en
erg
y
-1.5
-1
-0.5
0
0.5
1
1.5
forc
e o
n M
n [
ev/A
]
Etot
force [Mn(a)]
-10
0
10
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3
Density of States (electrons/eV)
Energy (eV)
CASTEP Partial Density of States
s alpha s beta p alpha p beta d alpha d beta Sum alpha Sum beta
s
pdα
Σ
dβ
DO
S a
rb u
nits
strong N-Mn interaction; Mn off centre of hexagonal channel
DOS similar to that observed for subst Mn (impurity states in gap), broadening due to smaller supercell.
Diffusion of Mn0 along a – local minimum IIDiffussion barrier along a
-12653.80
-12653.70
-12653.60
-12653.50
-12653.40
-12653.30
-12653.20
-12653.10
-12653.00
-12652.90
-12652.80
0.33 0.38 0.43 0.48 0.53 0.58 0.63 0.68 0.73 0.78 0.83
position along a
tota
l en
erg
y
-1.5
-1
-0.5
0
0.5
1
1.5
forc
e o
n M
n [
ev/A
]
Etot
force [Mn(a)]
Diffusion of Mn0 along c
Diffusion barrier for Mn along c in GaN
-12654.0
-12653.8
-12653.6
-12653.4
-12653.2
-12653.0
-12652.8
-12652.6
-12652.4
-12652.2
-12652.0
-12651.8
-12651.6
-12651.4
-12651.2
-12651.0
0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50
position along c [2c]
tota
l en
erg
y [
eV]
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
forc
e o
n M
n [
eV/A
]
1.94 eV
Diffusion of Mn0 along c – global minimum
Diffusion barrier for Mn along c in GaN
-12654.0
-12653.8
-12653.6
-12653.4
-12653.2
-12653.0
-12652.8
-12652.6
-12652.4
-12652.2
-12652.0
-12651.8
-12651.6
-12651.4
-12651.2
-12651.0
0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50
position along c [2c]
tota
l ene
rgy
[eV
]
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
forc
e on
Mn
[eV
/A]
• Very similar to global min along a
Diffusion of Mn0 along c – global maximum
Diffusion barrier for Mn along c in GaN
-12654.0
-12653.8
-12653.6
-12653.4
-12653.2
-12653.0
-12652.8
-12652.6
-12652.4
-12652.2
-12652.0
-12651.8
-12651.6
-12651.4
-12651.2
-12651.0
0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50
position along c [2c]
tota
l ene
rgy
[eV
]
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
forc
e on
Mn
[eV
/A]
• Mn-Ga interaction clearly very unfavourable• very significant lattice relaxation• again Mn relaxes away from the centre of the hexagonal channel
Conclusion
• Anisotropic diffusion constants for the diffusion of Mn along a (0.81 eV) and c (1.94 eV) directions of GaN have been found.
• Diffusion driven by favourable Mn-N interaction and unfavourable Ga-Mn interaction
• The calculated diffusion barriers may explain the scatter in experimentally observed Tc’s
• The groundstate interstitial site of Mn in GaN has been identified. Under exptl. conditions only stable in neutral charge state. Exhibits spin polarisation.