First Principle Design of Diluted

Magnetic Semiconductor: Cu doped

GaN

S.-C. Lee*, K.-R. Lee, and K.-H. Lee

Computational Science CenterKorea Institute of Science and Technology,

KOREA

Diluted Magnetic Semiconductors

Diluted Magnetic Semiconductor (DMS)- A ferromagnetic material that can be made by doping of impurities, especially transition metal elements, into a semiconductor host.

- Conducting spin polarized carriers of DMS are used for spin injection.

- Compatible with current semiconductor industry.

Spin Field Effect Transistor

Mechanisms of Ferromagnetism in DMS

TM TM TM

Long-ranged interaction of transition metals via delocalized carrier can stabilize ferromagnetic phase.

All valence electrons of the anion atoms between TM should be spin polarized.

The spin polarized carrier can deliver information

Success and Failure of Mn doped GaAs

• Mn substitutes Ga in zincblende structure– Structure is compatible with

GaAs 2DEG

• Tc is correlated with carrier density

• Ferromagnetic semiconductor with ordering temperature ~ 160 K

• Finding a new DMS material having high Tc

Ku et al., APL 82 2302 (2003)

Mn

Beyond GaMnAs

T. Dietl, Semicond. Sci. Technol. 17 (2002) 377

What will happen if other transition elements are used as dopants?

Mn doped GaN: Can it be a DMS?

Positive

Negative

• Theoretically predicted by Dietl

• High Tc was observed above room T.

• Ferromagnetic behavior by SQUID exp

eriments

• Possibility of precipitates

• XMCD or anomalous Hall Effect has not been

observed.

• Ferromagnetism can be achieved by short

ranged double exchange mechanism

Material specific or chemical effect has not been considered!

Let’s Back to the DMS Basics

TMTM

Local Moments and Splitting Valence Bands Simultaneously

Transition Element(V, Cr, Mn, Fe, Co,

Ni and Cu)

1st NN Nitrogen 4th Nitrogen

2nd NN Nitrogen 3rd NN Nitrogen

5th Nitrogen

Design Rule: Finding a TM that induces spin polarization of valence band

Start from Scratch

Calculation Methods

Planewave Pseudopotential Method: VASP.4.6.21 XC functional: GGA(PW91) Cutoff energy of Planewave: 800 eV 4X4X4 k point mesh with MP Electronic Relaxation: Davidson followed by RMM-DIIS Structure Relaxation: Conjugate Gradient Force Convergence Criterion: 0.01 eV/A Gaussian Smearing with 0.1 eV for lm-DOS Treatment of Ga 3d state

Semicore treatment for GaN Core treatment for GaAs

TM dopant: V, Cr, Mn, Fe, Co, Ni, and Cu Ferromagnetism by clustering can be excluded

Localized Moment due to MnDelocalized Carrier

due to p-d Exchange Interaction

Electronic Structure of Mn doped GaAs

Magnetic Moments of TM in GaN Host

More-than Half filledLess-Than Half filled

Spin Density of TM doped GaN

Less-Than Half filled

More-than Half filled

GaN:Cr GaN:Mn

GaN:Co GaN:Cu

GaFeN: Magnetic Insulator GaCoN: Half Metal

GaNiN: Magnetic Insulator GaCuN: Half Metal

Partial DOSs having More-than Half Filled States

Valence Band Splitting

SCL et al. JMMM (2007)SCL et al. Solid State Phenomena (2007)

Strength of p-d Hybridization

p-d hybridization results in a spin dependent coupling between the holes and the Mn ions.

pdH N s S

TM in GaN ΔEvalence (eV) Noβ (eV) Local Moment(μB)

Fe 0.4203 -3.3624 4

Co 0.2902 -3.0955 3

Ni 0.3780 -6.0480 2

Cu 0.3961 -12.6752 1

GaAs:Mn 0.3231 -2.0678 5

7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.00

20

40

60

80

100

120

140

160

En

erg

y D

iffe

ren

ce (

me

V, E

AF

M-E

FM)

Distance between Cu atoms (Angstrom)

Magnetic Interaction in Larger Supercell

216-atom supercell

Co, CuCo, Cu

Cu is the most probable candidate in GaN host

Experimental Confirmation

Appl. Phys. Lett. 90, 032504 (2007). NanoLett, Accepted 2007

Ion Implantation Nanowire

Stability of Ferromagnetic Cu

Non-Magnetic Magnetic

Number of electrons in frontier level or unfilled statesPara: 0.98 for Cu, 3.2 for TotalFerro: 0.27 for Cu, 0.82 for TotalFerromagnetic alignment drastically decrease the number of electrons in frontier level

“Antibonding conjecture” Dronskowski (2006)

t2g

eg

sp3M 3d

EF

Mainly p

Mainly M d M-N Antibonding

M-N Bonding

4 antibonding d-character electrons in frontier level Energetically unfavored

Electron Configurations of Non-Magnetic Phase

Electron Configurations of Magnetic Phase

t2g

eg

Only 1 electron in frontier levelEnergetically favored

Spin polarized configuration can decrease the number of antibonding electrons

sp3

M 3d

EF

up down

Non-Magnetic Magnetic

Spin-downExpandedLarge HybridizationLong-ranged

Spin-upContracted

Small HybridizationShort-ranged

And More …

Magnetic Moments of TM in GaN Host

More-than Half filledLess-Than Half filled

Why Cu is good Mn is bad?

7.3 7.54 6.27

5.62 6.22

5.3 5.89

Absolute Electronegativity

Why Cu is Good and Mn is Bad in GaN?

2p3d

σg

σu*

TMN

Cu doped GaN Mn doped GaN

2p

3d

TMN

Cu Mn

Electronegativity difference Small Large

d-character in antibonding state

Weaker Stronger

Carrier in antibonding state Delocalized Localized

Summary

Cu Cu

Cu is a probable candidate. Electronegativity can help to design a novel DMS material

Quantitative analysis is also needed.

Formation Energies of Cu in GaN Host

Formation Energy of Cu

CuGa 0.00

CuN 2.56

CuI 5.42

Cu(in fcc metal)+Ga32N32 Ga(in orthorhombic)+ Ga31Cu1N32

Cu(in fcc metal)+Ga32N32 1/2N2(in N2 molecule)+Ga32N31Cu1

Cu(in fcc metal)+Ga32N32 Ga32N32Cu1

Local Moments of Cu

Cu Cu

• Total Magnetic Moment: 2.0 μB

• Cu Projected Moment: 0.65 μB

• Charge State: Cu+2

• Possible for Hole Doping: 3d9+h

Roles of Transition Metal Impurities

Local Magnetic Moment

TM TM

Split Valence Band

Spin Polarized Carrier!!