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.