Hydrogen complexes in Mn x Ga 1 x As dilute magnetic - - PowerPoint PPT Presentation

Hydrogen complexes in MnxGa1−xAs dilute magnetic semiconductors: theoretical results

• P. Giannozzi

Scuola Normale Superiore di Pisa and Democritos National Simulation Center, Italy

• F. Filippone and A. Amore Bonapasta

Istituto di Struttura della Materia (ISM) del Consiglio Nazionale delle Ricerche, Italy April 5, 2005 Talk presented at 12th Brazilian Workshop on Semiconductor Physics, S˜ ao Jos´ e dos Campos

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Dilute Magnetic Semiconductors (DMS)

Semiconductors exhibiting magnetic properties (ideally, room-temperature ferromagnetism) hold promises as new materials for innovative devices based on spin electronics, or spintronics Most studied material: MnxGa1−xAs, with x up to ∼ 5 ÷ 6% Current picture of MnxGa1−xAs:

• Substitutional Mn provides both a localized moment from the half-filled d shell and a hole
• The hole is mostly delocalized on neighboring As atoms
• The hole is crucial for ferromagnetism
• Mn acts as a shallow acceptor, with an acceptor level at E ∼ 100 meV
• Magnetic moment per Mn atom: µ ≃ 4µB

Hydrogenation of semiconductors

H can easily diffuse into semiconductors General characteristics of hydrogenation:

• H can saturate dangling bonds and passivate defects (i.e. remove their electrical activity)
• H is an amphoteric impurity: it may passivate both donors and acceptors
• H passivation properties depend on the occupied site
• H is a structural local probe: it forms complexes with impurites, easily detected with IR

spectroscopy Exposure to H is a tool to modify magnetic properties and to achieve selective removal of ferromagnetism

Hydrogenation of DMS: Experiments

Brandt et al., APL 84, 2277 (2004); Goennenwein et al., PRL 92, 227202 (2004) formation of H-Mn complexes: H mode observed at 2140 cm−1 dramatic reduction of density

• f carriers

ferromagnetism disappears, replaced by paramagnetism

Hydrogenation of DMS: current picture

• H removes holes from the band structure
• No holes, no ferromagnetism (which needs

hole-mediated exchange)

• H-Mn complex expected to be similar to H-

Zn and H-Mg complexes in Mg- and Zn-doped GaAs: H backbonded at As neighbor of Mn Open questions:

• passivation (i.e. removal of the acceptor level)
• r compensation (i.e. filling of the level) ?
• geometry of Mn-H complexes?

is H really backbonded to As or does it prefer a different site?

As Mn bc H Ga (a) ab (b)

Theoretical framework: DFT-LSDA

Energy functional under an external potential V (r): EDF T[n+(r), n−(r)] = T0 +

• n(r)V (r)dr + EII + EH + Exc[n+(r), n−(r)]

(1) nσ(r) = charge density with spin polarization σ, n(r) = n+(r) + n−(r) total charge density T0 = kinetic energy, EII = nuclear interaction energy, EH = electrostatic (Hartree) energy Minimization of the above functional yields the Kohn-Sham equations:

• − 2

2m∇2 + V (r) + e2

• n(r′)

| r − r′ |dr′ + V σ

xc(r)

• ψσ

k,v(r) = ǫσ k,vψk,v(r)

(2) Exchange-correlation potential: V σ

xc(r) = δExc

δnσ(r) (3) Charge density: nσ(r) =

• k,v

f σ

k,v|ψσ k,v(r)|2

(4)

Theoretical framework: DFT-LSDA (2)

We use pseudopotentials and a plane-wave basis set in a supercell geometry

• exchange-correlation functional: spin-polarized, gradient-corrected PBE

(gradient corrections needed, simple LDA yields bad results for geometry of MnAs)

• Supercell geometry: consider a superset with enlarged period of the original zincblende lattice,

replace one Ga with Mn. With a 64-atom supercell, 1 Mn/supercell: x = 1/32 = 0.03125

• k-point grid: Monkhorst-Pack 444 grid
• ultrasoft (Vanderbilt) pseudopotentials – very useful for systems containing Mn!
• kinetic-energy cutoff (determines the dimension of the basis set): 25 Ry

All calculations performed using PWscf (http://www.pwscf.org)

LSDA results

“abMn”: E=0 eV

As As Ga As As Ga As As As As Ga As Ga As As Ga As Ga Ga Ga As Ga As Ga As Ga As Ga As As As As As Ga Ga As As Ga As Ga Ga As Ga As Ga Ga Ga Ga As Ga Ga As Ga Ga As As As Mn H Ga As Ga Ga Ga Ga

H bound to Mn in antibonding position: dH−Mn = 1.60˚ A, νH = 1761 cm−1, µ = 3µB “bcAs”: E=0.33 eV

Ga As Ga As Ga Ga As As Ga Ga As As Ga Ga Ga As As As Ga Ga Ga As Ga As Ga As Ga As Ga As As As Ga Ga Ga As Ga As As As Ga Ga H Mn As As As Ga Ga Ga As As Ga As Ga As As Ga Ga As As Ga As Ga As

H off-axis in the Mn-As bond: dH−Mn=1.62˚ A, dH−As=1.75˚ A νH = 1671 cm−1, µ = 5µB “abAs”: E=0.59 eV

As As Ga As As Ga As As As As As Ga Ga As As As Ga Ga Ga Ga Ga As As As As Ga Ga Ga As As As As As As As Ga Ga Ga Ga As As As Ga Ga Ga Ga Ga Ga Ga As As Ga Ga Ga As As As Ga Mn H As Ga Ga Ga Ga

H bound to As in antibonding position: dH−As=1.58˚ A, νH = 1926 cm−1, µ = 5µB Results are inconsistent with experiments: – The preferred configuration has H bound with Mn and Mn in a five-fold coordination – The value of µ indicates pairing of H with one d state from Mn – Passivation is not achieved: the acceptor level is still present at ∼ 120 meV – Vibrational frequency is much too low (exp: νH = 2143 cm−1)

LSDA results (2)

Other studied sites resulting in higher-energy configurations: “bcAsLin”: E=0.53 eV

As As Ga As Ga As As As As Ga As As As Ga Ga As Ga As Ga As Ga As Ga Ga As Ga As As Ga As As As Ga As Ga As As Ga Ga As Ga As Ga Ga As Ga Ga Ga As Ga Ga Ga As As Ga As Mn As Ga H Ga As Ga Ga Ga

H in the Mn-As bond (linear): dH−Mn = 1.82˚ A dH−As=1.56˚ A νH = 2119 cm−1, µ = 5µB “bcAsGa”: E=0.66 eV

As Ga As Ga As Ga As As Ga Ga As Ga As Ga As As Ga Ga As As Ga Ga As As Ga Ga As As Ga Ga As As Ga Ga As As Ga Ga As Ga As Ga As As Ga H Ga As As Ga Mn As Ga As Ga As As Ga Ga As Ga As Ga As Ga

H in Ga-As bond far from Mn: dH−Ga=1.83˚ A, dH−As=1.55˚ A νH = 2179 cm−1, µ = 5µB “abAsGa”: E=1.02 eV

As Ga As Ga As Ga As As Ga Ga As Ga As Ga As As Ga Ga As As Ga Ga As Ga As As Ga As Ga Ga As As Ga Ga As As Ga Ga As Ga As Ga H As As Ga Ga As As Mn Ga As As Ga Ga As As Ga Ga As Ga As Ga As Ga

H bound to As in antibonding position: dH−As=1.54˚ A, νH = 2162 cm−1, µ = 5µB Is there formation of di-hydrogen complexes?

LSDA results: H2 complexes

E=0.00 eV

As As Ga As As Ga As As As As As Ga Ga As As Ga As Ga Ga Ga Ga As As Ga As Ga Ga As As As As As As As Ga Ga As Ga Ga As As Ga Ga As Ga Ga Ga Ga Ga As Ga As Ga Ga As As As H Mn Ga H As Ga Ga Ga Ga

dH−Mn = 1.59˚ A, dH−As=1.55˚ A νH−Mn=1829cm−1, νH−As=2261cm−1 No passivation E=0.37 eV

As As Ga As Ga As As As As Ga As As Ga Ga As As Ga As Ga As Ga As Ga As Ga As Ga As Ga As As As Ga As Ga Ga As As Ga Ga As As Ga As Ga Ga Ga Ga Ga As Ga As Ga As Ga As H Mn As Ga Ga As H Ga Ga Ga

dH−Mn = 1.57˚ A, dH−As=1.54˚ A νH−Mn=1880cm−1, νH−As=2162cm−1

LSDA and highly correlated materials

Simple LSDA approaches can have serious trouble in dealing with highly correlated materials (i.e. atoms with localised, atomic-like electronic states) Fundamental problem: the inability of LSDA to find the correct occupancy of atomic-like electronic states may lead to qualitatively wrong results – but with the correct occupancy, results are quite good Deep reason: the lack of discontinuity in all current approximations to the exchange-correlation functional favors fractionary occupations of localised states

• M. Cococcioni and S. de Gironcoli, PRB

71, 035105 (2005) In MnxGa1−xAs, LSDA yields too shallow Mn 3d bands: ∼ 2.5eV below the top of the valence band, versus ∼ 4eV experimentally – corrected by LDA+U calculations (Shick et al, PRB 69, 125207 (2004))

DFT for highly correlated materials: the LDA+U approach

LDA+U: add a Hubbard-like correlation term to the energy (Anisimov et al, PRB 44, 943 (1991); PRB 48, 16929 (1993)). Simplified form: ELDA+U[n(r)] = EDF T[n(r)] + EU[n(r)], EU[n(r)] = U 2

• σ

Tr[nσ(1 − nσ)] (5) where nσ is the matrix of orbital occupancies for a set of atomic-like states φm: nσ

mm′ =

• σ
• k,v

f σ

k,vψσ k,v|Pmm′|ψσ k,v,

Pmm′ = |φmφm′| (6) Value of Hubbard U parameter?

• use as empirical, adjustable parameter
• estimate from experiments (i.e. difference between photemission and inverse photoemission)
• calculate from first principles

For Mn, typical value from experiments is U ≃ 4 eV.

LDA+U results

Relative energies of the various sites as a function of U:

−754.45 −754.4 −754.35 −754.3 −754.25 −754.2 1 2 3 4 5 6 Etot (Ry) U (eV) abMn abAs abAsGa bcAsGa bcAs

U ≃ 4 eV is also the value for which the Mn 3d shift towards their correct position!

LDA+U results (2)

Geometry of the ground state: H slightly off-axis in the Mn-As bond dH−Mn=1.88˚ A, dH−As=1.55˚ A νH = 2030 cm−1

Ga As Ga As Ga Ga As As Ga Ga As As Ga Ga Ga As As As Ga Ga As Ga As As Ga Ga As Ga Ga As As As Ga Ga Ga As As Ga As As Ga Ga As Mn H As As Ga Ga As Ga As As Ga Ga As As Ga As Ga As Ga As Ga As

Electronic structure: µ = 5µB, acceptor level completely removed (passivated)

(Tentative) Conclusions

• Simple LSDA does not account for the properties of H complexes in dilute magnetic

semiconductor MnxGa1−xAs: correlation effects are crucial

• Simple LDA+U seems to do the job
• H sits in the center of the bond between Mn and As, somewhat off axis
• H passivates the Mn impurity