introduction to vasp and more - gist · introduction to vasp and more july 5, 2012 ... -fast...

Introduction to VASP and more

July 5, 2012

Joo-Hyoung LeeSchool of Materials Science and Engineeging

Gwangju Institute of Science and Technology

VASP• This lecture is focused on theoretical background in VASP.

• Practical aspects for running VASP will be covered in the next sessions.

What is VASP?

• Computer program for electronic structure and quantum mechanical molecular dynamics, based on density functional theory which uses pseudopotential and plane wave basis

VASP• What can it do?

- Total energy

- Band structures

- Density of states

- Forces and geometry optimization : stress tensor

- Phonon dispersion

- Optical properties : dielectric function

- Molecular dynamics

- Magnetism

- and more ...

VASP and its friends

Implementation of density functional theory (DFT)

DFT

• A quantum mechanical modeling method used in physics and chemistry to investigate the electronic structure (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases.

(Wikipedia)

Birth of DFT

Schroedinger

Eq.

1926

Dirac Eq.

19281927

Thomas-Fermi

theory Hartree-Fock

method

1935 1964, 1965

Density functional

theory

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.

P. A. M. Dirac, Proc. Roy. Soc. 123, 714 (1929)

Figures: courtesy by Google

DFT• Theorem 1 - The total energy of the ground state is uniquely determined by the

electron density.

• Huge breakthrough!- Reformulating an N-electron system with 3N degrees of freedom in terms

of the electron density which has only 3 degrees of freedom

Hohenberg and Kohn, Phys. Rev. 136, B864 (1964)

E = E[n(r)]

Ψ(r1, r2, · · · , rN ) −→ n(r)

# of e- # of points for ! # of points for n(r)

1 8 8

10 810 8

100 8100 8

(N=2)

N N

N

(N: # of grid points)

DFT• Theorem 2- The correct ground state electron density minimizes the energy functional,

and the minimum is the correct ground state energy.

• It provides a variational principle by which ng(r) can be calculated.• Kohn-Sham equation (single particle)

Hohenberg and Kohn, Phys. Rev. 136, B864 (1964)Kohn and Sham, Phys. Rev. 140, A1133 (1965)

Eg = E[ng(r)]

− 2

2m∇2 + vext(r) + ve

coul(r) + vxc(r)

ψnk(r) = nkψnk(r)

n(r) =# of e

nk

|ψnk(r)|2

Solving Kohn-Sham equation

− 2


coul(r) + vxc(r)

ψnk(r) = nkψnk(r)

n(r) =# of e

nk

|ψnk(r)|2

More unknowns than equations

Many codes for DFT

FLAPW

Kohn-Sham equation

− 2


coul(r) + vxc(r)

ψnk(r) = nkψnk(r)

Relativistic

Non-relativistic

LDAGGA

Hybrid

Full-potential

pseudopotentialPlanewave :VASP, ABINITLAPW : FLAPW, WIEN2KNumerical : SIESTA, OPENMX

Basis function• Plane wave and its extension

- Plane wave

- Linearized Augmented Plane wave (LAPW)

|ψnk =

G

Cnk(G)|φk(G)

MT region

Int. region

r|φk(G) =

Ω−1/2ei(k+G)·r Int.lm[Alm(k + G)ul(El, r)+

Blm(k + G)ul(El, r)]Ylm(r) MT.

r|φk(G) =1√Ω

ei(k+G)·r

Basis function• Why Plane wave basis (as in VASP, ABINIT and QUANTUM-ESPRESSO)?

- Simple and analytic expression for the Hamiltonian matrix and total energy

- Easy to program

- Fast calculation using Fast Fourier Transform (FFT)

• Energy cutoff (ENCUT in INCAR, or ENMAX in POTCAR)

- Maximum kinetic energy of a plane wave

- It defines the number of plane waves to expand a wavefunction

φk(G)|− 2

2m∇2|φk(G) =

2(k + G)2

2m≤ Ecut

DFT

− 2


coul(r) + vxc(r)

ψnk(r) = nkψnk(r)

Relativistic

Non-relativistic

LDAGGA

Hybrid

Full-potential


Full-potential• No approximation to an external potential

- Explicit treatment of core electrons during self-consistent cycle

• Weinert (JMP 22, 2433 (1981))

- Pseudo-charge method to solve the Poisson’s equation for obtaining the Coulomb potential

- Combined with the LAPW basis to result in FLAPW method

Pseudopotential• Observation that the core electrons are not involved in chemical

bonding

• Attractive nuclear potential is largely canceled by the repulsion due to the core electrons

• First introduced by Hellmann (1934)

• Early development by Phillips and Kleinman (PR 116, 287, 880 (1959)) from the orthogonalized plane wave (OPW) method due to Herring (PR 57, 1169 (1940))

- OPW : plane wave which is made to be orthogonal to the core wavefunctions

- OPW is used to expand the valence wavefunctions

|PW,G =1√Ω

eiG·r

|OPW,G = |PW,G −

c

|ψcψc|PW,G

Pseudopotential• Underlying idea

Z/r

VPS

!PS

!AE

Rcut

r

Figure 3. Schematic illustration of an atomic all–electron wave function (solid line) and the corresponding atomicpseudo wave function (dashed line) together with the respective external Coulomb potential and pseudopotential.

removed from the calculation which makes the calculation of energy differences betweenatomic configurations numerically much more stable.

In principle one might just take the distribution of the core electrons and combine theirHartree potential with the Coulomb potential of the nucleus to an ionic core potential.However, this is not very useful since the valence wave functions still have to maintaintheir nodal structure in order to be orthogonal to the core states. Much more practical isto replace immediately the ionic core potential by a pseudopotential which will lead tonodeless valence wave functions, as we will show in the following.

3.2 Normconserving Pseudopotentials

Present day pseudopotentials are constructed from ab initio calculations for isolated atoms.Let us assume we have solved the Kohn–Sham equations for a single atom of the chemicalspecies for which we would like to generate a pseudopotential. This can be done easilysince due to the spherical symmetry of atoms the wave functions can be written as a prod-uct of a radial function and a spherical harmonic. The Schrodinger equation then reducesto one–dimensional differential equations for the radial functions which can be integratednumerically. A typical result for a radial function from such an “all–electron” atom cal-culation together with the corresponding external Coulomb potential is shown in Figure 3.Our aim is now to replace the effective all–electron potential within a given sphere withradius by a much weaker new potential with a nodeless ground state wave functionto the same energy eigenvalue as the original all–electron state which matches exactly theall–electron wave function outside (depicted with dashed lines in Figure 3).

Why should this be possible at all? This can be understood by the following line ofarguments. The radial Schrodinger equation for a fixed potential and fixed energy (not

9

(Meyer, 2006)

Pseudo wavefunction

Pseudo potential

All-electron wavefunction

All-electron potential

Cutoff radius

Pseudopotential• Norm-conserving pseudopotential- Hamann, Schlüter and Chiang, PRL 20, 1494 (1979)

- Bachelet, Hamann and Schlüter, PRB 26, 4199 (1982)

- Kleinman and Bylander, PRL 20, 1425 (1982)

- Rappe, Rabe, Kaxiras and Joannopoulos, PRB 41, 1227 (1990)

- Troullier and Martins, PRB 43, 1993 (1991)

Rc

0φ∗

PS(r)φPS(r)r2dr = Rc

0φ∗

AE(r)φAE(r)r2dr

For optimum transferability

Pseudopotential : Generation• Solve DFT problem for an reference atomic configuration

• Radial component

ψnlm(r) = φnl(r)Ylm(θ, φ)

− 2

2m

d2

dr2+

l(l + 1)2mr2

+ VAE(r)− nl

φAE

nl (r) = 0

− 2

2m

d2

dr2+

l(l + 1)2mr2

+ VPS(r)− nl

φPS

nl (r) = 0

Same

Pseudopotential• Ultrasoft pseudopotential (Vanderbilt, PRB 41, 7892 (1990))

- Motivation

NPW

Accuracy

RC ↑

RC ↓

Z/r

VPS

!PS

!AE

Rcut

r

Figure 3. Schematic illustration of an atomic all–electron wave function (solid line) and the corresponding atomicpseudo wave function (dashed line) together with the respective external Coulomb potential and pseudopotential.

removed from the calculation which makes the calculation of energy differences betweenatomic configurations numerically much more stable.

In principle one might just take the distribution of the core electrons and combine theirHartree potential with the Coulomb potential of the nucleus to an ionic core potential.However, this is not very useful since the valence wave functions still have to maintaintheir nodal structure in order to be orthogonal to the core states. Much more practical isto replace immediately the ionic core potential by a pseudopotential which will lead tonodeless valence wave functions, as we will show in the following.

3.2 Normconserving Pseudopotentials

Present day pseudopotentials are constructed from ab initio calculations for isolated atoms.Let us assume we have solved the Kohn–Sham equations for a single atom of the chemicalspecies for which we would like to generate a pseudopotential. This can be done easilysince due to the spherical symmetry of atoms the wave functions can be written as a prod-uct of a radial function and a spherical harmonic. The Schrodinger equation then reducesto one–dimensional differential equations for the radial functions which can be integratednumerically. A typical result for a radial function from such an “all–electron” atom cal-culation together with the corresponding external Coulomb potential is shown in Figure 3.Our aim is now to replace the effective all–electron potential within a given sphere withradius by a much weaker new potential with a nodeless ground state wave functionto the same energy eigenvalue as the original all–electron state which matches exactly theall–electron wave function outside (depicted with dashed lines in Figure 3).

Why should this be possible at all? This can be understood by the following line ofarguments. The radial Schrodinger equation for a fixed potential and fixed energy (not

9

Pseudopotential• Ultrasoft pseudopotential

O 2p wavefunction

ψAE(r)ψPS(r)

ψUS(r)

Pseudopotential• Projector Augmented Wave (PAW) method (Blöchl, PRB 50, 17953 (1994))

- Unified approach of augmented wave (accuracy) and pseudopotential (computational feasibility) for electronic structure

- Takes into account the region around atoms where wavefunctions strongly vary

- Has access to “true” wavefunction, not just pseudized wavefunction, through transformation

|Ψn = T |Ψn

True wavefunction Transformation operator

Auxiliary function

Pseudopotential• Projector Augmented Wave (PAW) method- Reformulate KS equation and others using the auxiliary functions

- The auxiliary functions are expanded with plane waves- Transformation operator???

T = 1 +

i

(|φi − |φi)pi|

All-electron partial waves from true atomic potential

Pseudo partial waves from pseudopotential

Projector function

Pseudopotential• Projector Augmented Wave (PAW) method

|Ψn = |Ψn +

i

(|φi − |φi)pi|Ψn

−= + -

True density : no transferability problemNumber of plane waves : as small as USPP

As accurate as all-electron method

Pseudopotential

• In VASP

- Ultrasoft pseudopotential

- PAW pseudopotential

DFT

− 2


coul(r) + vxc(r)

ψnk(r) = nkψnk(r)

Relativistic

Non-relativistic

LDAGGA

Hybrid

Full-potential


DFT• vxc[n(r)]

!

!

!

!!

!! !

!

!

Interacting Non-interacting

Interaction between electrons : vecoul[n(r)] + vxc[n(r)]

Exchange-correlation potential• LDA : local density approximation, fully local

• Exchange

• Correlation

- Parametrization by Perdew and Zunger (PRB 23, 5048 (1981)) from quantum Monte Carlo simulations (Ceperley and Alder, PRL 45, 566 (1980)) in VASP

Exc[n] =

n(r)xc(n(r))dr

vxc =δExc[n]δn(r)

: Exchange-correlation energy of a uniform electron gasxc(n(r))

Ex = −

σ

k

[nσ(r)]4/3dr

Exchange-correlation potential• GGA : generalized gradient approximation, semi-local

• VASP uses many GGA, especially by PW-91 (PRB 46, 6671 (1992)) and PBE (PRL 77, 3865 (1996)).

• Exchange

• Correlation

Exc[n↑, n↓] =

f(n↑(r), n↓(r),∇n↑(r),∇n↓(r))dr

vxc =∂Exc[n]∂n(r)

−∇ · ∂Exc[n]∂(∇n(r))

Ex[n] = −

3kF n

4π

1 + 0.1965s sinh−1(7.796s) + (0.274− 0.151e−100s2

)s2

1 + 0.1964s sinh−1(7.796s) + 0.004s4dr

Ec[n] =

(c(rs, ζ) + H(t, rs, ζ))dr

Exchange-correlation potential• Hybrid functional- Combination of exact exchange and exchange-correlation energy

- Better band gap

- Not fully first-principles (kind of “empirical”)

EPBE0xc =

14Exx +

34EPBE

x

+ EPBEc

EB3LYP = 0.7Exx + 0.8ELDAx

+ 0.72∆EB88x + 0.81ELYP

c

+ 0.19EVWMc

Becke, JCP 98, 5648 (1993) G. Kresse

k-point• We need to evaluate the following integral (considering a single band for

simplicity) e.g. density of states, charge density, matrix elements etc.

• Since an integration over continuous k-values is not possible in computations, it is necessary to use a summation over some discrete, special k-points.

Xk = ψk|X|ψk

X =1

ΩG

FBZXkf(k)dk

1ΩG

FBZdk −→

k

wk

k-point• How to generate special k-points?

- Monkhorst-Pack scheme (PRB 13, 5188 (1976))

- Equally spaced mesh in the first Brillouin zone

Shifted Monkhorst-Pack mesh

Centered on Γ

25 k-points

Centered around Γ

Shifted by (1/8, 1/8, 0)16 k-points

Yet the same k-point density.

7 / 19

Shifted Monkhorst-Pack mesh

Centered on Γ

25 k-points

Centered around Γ

Shifted by (1/8, 1/8, 0)16 k-points

Yet the same k-point density.

7 / 19

!-centered

! !=

Image by Kong

k-point• Symmetry consideration

Symmetry on k in the first Brillouin zone

Sψik(r) = ψik(Sr)

Sψik(r) = ψik(Sr)

= uik(Sr)eik·Sr

= uik(r)eikr

k = S−1k

n(r) =

k

ωk

occ.

i

ni ,k(r)

k ∈ irreducible Brillouin zone

ωk =# of sym. connected k

total # of k in FBZ9 / 19

Irreducible Brillouin zone

Example:

MP-mesh for 2D square lattice

4×4×1 MP mesh = 16 k-points in the FBZ.

4 equivalent k4,4 = (38 ,38) ⇒ w1 = 0.25

4 equivalent k3,3 = (18 ,38) ⇒ w2 = 0.25

8 equivalent k4,3 = (38 ,18) ⇒ w3 = 0.50

Brillouin zone integration

n(r) =1

4

occ.

i

ni ,k4,4+1

4

occ.

i

ni ,k3,3+1

2

occ.

i

ni ,k4,3

10 / 19Irreducible zone Irreducible k-points

wk =# of equiv. k-pt.total # of k-pt. X =

416

Xk3,3 +816

Xk4,3 +416

Xk4,4

Image by Kong

k-point• Smearing method- In metallic systems, we need to perform the BZ integration with a function

that is discontinuous at the Fermi level

- High Fourier components

- Dense k-grid

- Solution : Replace a step function with a smoother function

- Example : band energy

- ISMEAR in INCAR

- Fermi-Dirac smearing (-1), Gaussian smearing (0), Methfessel & Paxton method (N > 0)

k

wkkΘ(k − µ)

k

wkkf(k − µ

σ)

k-point• Tetrahedron method- Divide up the first Brillouin zone into tetrahedra

- Compute the matrix elements at each vertex

- Linear-interpolate the matrix elements to find an interpolation function

- Perform the Brillouin zone integration using the interpolation function

- Quadratic correction term by Blöchl (PRB 49, 16223 (1994))Linear tetrahedron method

Idea:

1. dividing up the Brillouin-zone into tetrahedra

2. Linear interpolation of the function to be integratedXn within these tetrahedra

3. integration of the interpolated function Xn

A. EICHLER, SAMPLING THE BRILLOUIN-ZONE Page 18

Linear tetrahedron method

Idea:

1. dividing up the Brillouin-zone into tetrahedra

2. Linear interpolation of the function to be integratedXn within these tetrahedra

3. integration of the interpolated function Xn

A. EICHLER, SAMPLING THE BRILLOUIN-ZONE Page 18

Running VASP• VASP site

- http://www.vasp.at

• Necessary files to run VASP

- INCAR : Controlling calculations

- POSCAR : Cell parameters and atomic positions

- POTCAR : Pseudopotential file

- KPOINTS : k-point meshes

• Convergence test

- With respect to ENCUT

- With respect to k-mesh

Thermoelectricity• Temperature gradient ⇔ Electricity: Solid-state conversion

V=S"TSeebeck effect

Waste heat recovery

"T

Q=!IPeltier effect

Cooling/heating

I

Thermoelectricity• Efficiency: thermoelectric figure of merit, ZT

ZT =S2σT

κl + κe

- S: Seebeck coeff.

- #: electrical conductivity

- $l: lattice thermal conductivity

- $e: electronic thermal conductivity

• Goal: Increase ZT

777

prostate, followed by epithelial neoplasia,and a similar process was observed in theforestomach. These findings suggest theexistence of a TGF-!–induced signalingpathway that is initiated in the stroma andterminates, either directly or indirectly, inepithelial cells. That TGF-! indirectly pro-motes tumors by stimulating stromal reac-tivity and fibrosis is well established (17),but the fascinating discovery of Bhowmicket al. is that TGF-! signaling can act as anindirect tumor suppressor. Moreover, thefact that loss of T!RII in stromal fibro-blasts leads so quickly and so inexorably to

epithelial carcinoma provides a clear coun-terexample to the assumption that muta-tions in epithelial cells are the required ini-tiating factors for carcinoma. Thus, farfrom being a mere “landscaper,” the tissuemicroenvironment is a powerful regulatorof tumor induction as well as tumor sup-pression—a role that clearly merits not on-ly further exploration, but also respect!

References1. M. J. Bissell, D. Radisky, Nature Rev. Cancer 1, 46

(2001).2. N. A. Bhowmick et al., Science 303, 848 (2004).3. P. A. Kenny, M. J. Bissell, Int. J. Cancer 107, 688 (2003).

4. B. Mintz, K. Illmensee, Proc. Natl. Acad. Sci. U.S.A. 72,3585 (1975).

5. D. S. Dolberg, M. J. Bissell, Nature 309, 552 (1984).6. M. S. O’Reilly et al., Cell 88, 277 (1997).7. Y. Maeshima et al., Science 295, 140 (2002).8. M. H. Sieweke et al., Science 248, 1656 (1990).9. M. H. Barcellos-Hoff, S.A. Ravani, Cancer Res. 60, 1254

(2000).10. M. D. Sternlicht et al., Cell 98, 137 (1999).11. R. M. Peek Jr., M. J. Blaser, Nature Rev. Cancer 2, 28

(2002).12. R. J. Farrell, M. A. Peppercorn, Lancet 359, 331 (2002).13. D. A. Wirtzfeld et al., Ann. Surg. Oncol. 8, 319 (2001).14. K. W. Kinzler, B. Vogelstein, Science 280, 1036 (1998).15. K. A. Waite, C. Eng, Nature Rev. Genet. 4, 763 (2003).16. G. C. Blobe et al., N. Engl. J. Med. 342, 1350 (2000).17. D. M. Bissell et al., Hepatology 34, 859 (2001).18. The authors are funded by the U.S. Department of

Energy (OBER).

W ith the widespread use of semi-conductors in microelectronicsand optoelectronics, it is hard to

imagine that the initial excitement was dueto their promise not in electronics, but inrefrigeration (1). The discovery in the1950s that semiconductors can act as effi-cient heat pumps led to premature expecta-

tions of environ-mentally benign sol-id-state home re-frigerators and pow-er generators con-

taining no moving parts. Except for spe-cialized applications, however, the visionof widespread use of thermoelectric ener-gy–conversion devices has remained elu-sive. At issue are some fundamental scien-tific challenges, which could be overcomeby deeper understanding of charge andheat transport in semiconductor nanostruc-tures. Lyeo et al. (2) report in this issue anexperimental technique that could improveour grasp of these phenomena, while Hsuet al. (3) report the synthesis of a new classof materials that could potentially be usedfor power generation.

Thermoelectric materials are ranked by afigure of merit, ZT, which is defined as ZT =S2"T/k, where S is the thermopower orSeebeck coefficient, " is the electrical con-ductivity, k is the thermal conductivity, and Tis the absolute temperature. To be competitivecompared with conventional refrigerators and

generators, one must develop materials withZT > 3. Yet in five decades the room-temper-ature ZT of bulk semiconductors has in-creased only marginally, from about 0.6 to 1(see figure). The challenge lies in the fact thatS, ", and k are interdependent—changing onealters the others, making optimization ex-tremely difficult. The only way to reduce kwithout affecting S and " in bulk materials isto use semiconductors of high atomic weightsuch as Bi2Te3 and its alloys with Sb, Sn, andPb. High atomic weight reduces the speed ofsound in the material, and thereby decreasesthe thermal conductivity. Although it is possi-ble in principle (4) to develop bulk semicon-ductors with ZT > 3, there are no candidatematerials on the horizon.

It is, therefore, encouraging to seeHsu et al. (3) report on page 818 that

AgPbmSbTe2+m has ZT # 2 at 800 K for m =18. Although the temperature may be toohigh for refrigeration, it is appropriate forpower generation. What is interesting,however, is the discovery that this materialcontains regions 2 to 4 nm in size that arerich in Ag-Sb and are epitaxially embeddedin a matrix that is depleted of Ag and Sb.Presumably, the electronic band structureand vibrational properties of these nano-regions are different from those of the sur-rounding material, suggesting quantumconfinement. However, several questionsremain: Are there quantum effects in thesenanostructures and, if so, do they play anyrole in raising the ZT of the material? Is theacoustic impedance of the nanodots verydifferent from that of the matrix and, if so,do they scatter acoustic phonons and there-by reduce thermal conductivity? How doesthe structure and size depend on m, and arethere ways to maximize ZT?

Over the past decade, these questionsabout quantum effects have received in-creasing attention, and their answers holdpromise (5, 6) in increasing ZT. In the past3 years, reports have suggested that nano-structured thin-film superlattices (7) of

Bi2Te3 and Sb2Te3 have ZT ~2.4 at room temperature,whereas PbSeTe/PbTe quan-tum dot superlattices (8) haveZT ~ 1.3 to 1.6. Seen histori-cally, this is a huge jump overan extremely short period (seefigure). What is the underly-ing science? In semiconduc-tors, electrons and holes carrycharge, whereas lattice vibra-tions or phonons dominateheat transport. Electrons (orholes) and phonons have twolength scales associated withtheir transport—wavelength,$, and mean free path, !. Bynanostructuring semiconduc-tors with sizes comparable to$, sharp edges and peaks intheir electronic density of

M AT E R I A L S S C I E N C E

Thermoelectricity inSemiconductor Nanostructures

Arun Majumdar

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

1950 1960 1970 1980Year

1990 2000 2010

(ZT)300K

Bi2Te3 and alloys with Sb, Se

Discovery of compoundswith ZT < 1

Thermoelectric improvements. History of thermoelectric fig-ure of merit, ZT, at 300 K. Since the discovery of the thermo-electric properties of Bi2Te3 and its alloys with Sb and Se in the1950s, no bulk material with (ZT)300K > 1 has been discovered.Recent studies in nanostructured thermoelectric materials haveled to a sudden increase in (ZT)300K > 1.

The author is in the Department of MechanicalEngineering, University of California, Berkeley, CA94720, USA, and Materials Sciences Division,Lawrence Berkeley National Laboratory, Berkeley, CA94720, USA. E-mail: [email protected]

Enhanced online atwww.sciencemag.org/cgi/content/full/303/5659/777

P E R S P E C T I V E S

www.sciencemag.org SCIENCE VOL 303 6 FEBRUARY 2004

(A. Majumdar, Science 303, 777 (2004))

!

!

!

!

!

!

!!!!

!

!

!

!

!

!

!

!

!

! ! ! ! ! ! !

!

!

! ! ! ! ! ! !

!

INSULATORS

SEMI-

CONDUCTORS

S

ZT

!

"

SEMIMETALS

Carrier concentration

METALS

(M. Dresselhaus)

ZnSe1-xOx

•Calculate S2" for ZnSe1-xOx

-DFT+BTE- 64 atoms/cell

- Ecutoff : 600 eV

-GGA

- one O atom/32 Se atoms (x=3.125%)Zn SeO

ZT =S2σT

κl + κe

Materials by design

ZnSe1-xOx: DOS and bands

-1 0 1 2 3E - EVBM (eV)

0

10

20

30DO

S (e

V/ce

ll)ZnSe

-1

0

1

2

3

E - E

F (e

V)

! X M ! R-1

0

1

2

3

E - E

F (e

V)

! X M ! R

ZnSe

-1 0 1 2 3E - EVBM (eV)

0

10

20

30

DOS

(eV/

cell)

ZnSe1-xOx

-1

0

1

2

3

E - E

F (e

V)

! X M ! R-1

0

1

2

3

E - E

F (e

V)

! X M ! R

ZnSe1-xOx

(Lee et al., Phys. Rev. Lett., 104, 016602 (2010))

• Projected DOS

-1 0 1 2 3E - EF (eV)

0

0.1

0.2

0.3

0.4

0.5DO

S (s

tate

s/eV

·cel

l)O sO pO dZn sZn pZn d

O-s and Zn-sp3

Peaks due to hybridization between O and Zn states

Why is there a peak?


• |S| is up to 30 times increased from that of pure ZnSe.

• S2# shows 180 times enhancement compared to that of ZnSe.

Seebeck coeff. Power factor

1020 1021

ne (cm-3)

0

100

200

S (µ

V/K)

ZnSeZnSe1-xOx

1020 1021

ne (cm-3)

10-4

10-3

10-2

S2 ! (W

/mK2 ) ZnSe

ZnSe1-xOx

Impact of the peak


Waiting for experimental verification

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