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Ab initio study of the diffusion of Mn through GaN. Johann von Pezold Atomistic Simulation Group Department of Materials Science University of Cambridge. Dilute Magnetic Semiconductors (DMS). Host semiconductor + magnetic dopant Ferromagnetic coupling Spin and Charge D o F (Spintronics)
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Ab initio study of the diffusion of Mn through GaN Johann von Pezold Atomistic Simulation Group Department of Materials Science University 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
Mn d-states Mn d-states DOS (Mn0.0156Ga0.9844)As DOS (Mn0.0156Ga0.9844)N Mechanism of Ferromagnetism in DMS Mean field approach (Dietl et al.) • FM due to Zener p/d exchange interaction • Large carrier density essential (~ 1020 cm-3). 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 c along 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
0.137 eV 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) 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 a 0.81 eV
Diffusion of Mn0 along a – global maximum • Off Tetrahedral site, steric hindrance
Diffusion of Mn0 along a –local minimum I • Just below N plane, slightly off centre of hexagonal channel
Diffusion of Mn0 along a –local maximum ΔE global min – local max: 120 meV
Σ p dα s DOS arb units dβ Diffusion of Mn0 along a – Global minimum 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 c 1.94 eV
Diffusion of Mn0 along c – global minimum • Very similar to global min along a
Diffusion of Mn0 along c – global maximum • 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.