䝘䝜ᵓ㐀ᙧᡂ䞉᪂ᶵ⬟Ⓨ⌧䛻䛚䛡䜛㟁Ꮚㄽ䝎䜲䝘䝭䜽䝇௦⾲⪅䠖 ᢲᒣ῟(ᮾ኱ᕤ䠅ศᢸ⪅䠖 ᒾ⏣₶୍䠄⟃Ἴ኱ᩘ⌮≀㉁䠅
ᐇ✵㛫ᡭἲ䚸RSDFT䚸Si䝘䝜ᵓ㐀㔜⏣⫱↷䠄㜰኱ᇶ♏ᕤ䠅㔞Ꮚ໬Ꮫ䚸ᐇ✵㛫Car-ParrinelloMD䚸⏕࿨⛉Ꮫᐑᓮ๛䠄≀ᮦᶵᵓ䠅䜸䞊䝎䞊䠪ᡭἲ䚸CONQUEST䚸⏕య཯ᛂ䚸⏺㠃ᑿᓮὈຓ䠄໭㝣ඛ➃኱䠅኱つᶍィ⟬ᡭἲ䚸OpenMXᅵ⏣ⱥ஧䠄⏘⥲◊䠅᭷㝈せ⣲ᇶᗏ䚸FEMTECK䚸㟁ụ(䝥䝻䝖䞁⛣ື䠅㐃ᦠ◊✲⪅䠖 ෆ⏣࿴அ䠄ᮾ኱ᕤ䠅ᐇ✵㛫ἲ䚸ᖹ㠃Ἴἲ䚸䝘䝜⛉Ꮫᖹᒣ༤அ䠄ᮾᕤ኱⥲ྜ⌮ᕤ䠅⾲㠃䞉⏺㠃䝘䝜ᵓ㐀䛾㢧ᚤศගᐇ㦂◊✲༠ຊ⪅䠖 David Bowler (U College London) CONQUEST
Mauro Boero (U Strasbourg) CPMD᪂Ꮫ⾡䠖䝁䞁䝢䝳䞊䝔䜱䜽䝇㻙≀㉁䝕䝄䜲䞁 㻞㻜㻝㻜ᖺ㻥᭶㻝㻤᪥

1ᡭἲ䛾㛤Ⓨ䛸䛭䛾ᛂ⏝ ≀㉁䝕䝄䜲䞁䛻䛿ຊ䛾ィ⟬䛜㔜せ¾ Ᏻᐃᵓ㐀䚸‽Ᏻᐃᵓ㐀䚸཯ᛂ䛾㠡Ⅼ䛾᥈⣴ LDA/GGA䛾㝈⏺䜢㉸䛘䛶

¾ 䜶䝛䝹䜼䞊䜼䝱䝑䝥䚸ᙉ┦㛵⣔ၥ㢟ї䝝䜲䝤䝸䝑䝗䠄GGA+HFA䠅ỗ㛵ᩘ䛾ྍ⬟ᛶ䚸DMatrixFTї௚⌜䛸䛾䝁䝷䝪䝺䞊䝅䝵䞁䠖ከయၥ㢟 ኱つᶍィ⟬䛷10nmᵓ㐀䠄10୓ཎᏊ⣔䠅䛾DFTィ⟬¾ 㟁Ꮚ䝕䝞䜲䝇䚸㟁ụ䚸⏕య⣔䠖䝘䝜⏺㠃䛾Ᏻᐃᛶ䚸㟁Ꮚ≧ែїRSDFT, CONQUEST, OpenMX, FEMTECK䛾㧗ᗘ໬ї௚⌜䛸䛾䝁䝷䝪䝺䞊䝅䝵䞁䠖㟁Ꮚ䚸䝇䝢䞁䚸⇕㍺㏦
 ཯ᛂ䝎䜲䝘䝭䜽䝇¾ ⏕యෆ཯ᛂ䠄䜲䜸䞁㍺㏦䚸㓝⣲཯ᛂ䚸䚸䚸䠅䚸≀㉁⏕ᡂ཯ᛂ䠄䜶䝢䝍䜻䝅䝱䝹ᡂ㛗䚸ཎᏊᣑᩓ䚸䚸䚸䠅

їRS-CPMD, MetaDynamics᪂Ꮫ⾡䠖䝁䞁䝢䝳䞊䝔䜱䜽䝇㻙≀㉁䝕䝄䜲䞁 㻞㻜㻝㻜ᖺ㻥᭶㻝㻤᪥

2䝝䜲䝤䝸䝑䝗䠄DFA & HFA䠅ỗ㛵ᩘ

Matsushita, Nakamura & Oshiyama (2010)

a=b=1/4 (Perdew)

a=0, b=1(Hirao)

a=1/4, b=0(Sucseria)

E XC

aE XSR  HF  (1  a ) E XSR  DFA  bE XLR  HF  (1  b) E XLR  DFA  ECDFAa, b : Empirical or First-principle

Adiabatic Theorem for Osystem:

E XC³ E O dO
10XC,᪂Ꮫ⾡䠖䝁䞁䝢䝳䞊䝔䜱䜽䝇㻙≀㉁䝕䝄䜲䞁 㻞㻜㻝㻜ᖺ㻥᭶㻝㻤᪥

E XC,Oe2
U (r)U (r')<O V̂ee <O  ³ d 3 r ³ d 3 r'
2| r  r'|3䝞䞁䝗䜼䝱䝑䝥䛸⮬ᕫ┦஫స⏝(self interaction)
First Excitation Energy of N-electron System 'SCF(N) :' SCF ( N )I ( N )  A( N )Janak Theorem : H i ( f i )E ( N  1)  E ( N  1)  2 E ( N )wEwf f fi'SCF ( N ) H N 1 ( N  1)  H N ( N )H N 1 ( N )  H N ( N )  'XC
whereFractional charge state 䛸䛿mixed state :'XC
O

౛䛘䜀 total energy
LDA/GGA 䛷䛿䚸 H i ( f ) H i ( fG E XC
G E XCG n N 0
G n N 0
¦ pD <D O <DD
H(1  f ) E N  f EN 10)  cfi 䛜ᬑ㏻䚹E(N)䛿ୗ䛻ฝ concave⮬ᕫ┦஫స⏝䛷‽఩䛜ୖ᪼䛒䜛䛔䛿delocalization error: H2+HFA䛿䚸SIE free᪂Ꮫ⾡䠖䝁䞁䝢䝳䞊䝔䜱䜽䝇㻙≀㉁䝕䝄䜲䞁 㻞㻜㻝㻜ᖺ㻥᭶㻝㻤᪥4DFT Energy as a function of fractional charge- Si4006H1038 Dot ᒾ⏣䠖
LDA inRSDFTneutral(WRWEtot

Discontinuity mainly
from kinetic energy &Pseudopotential energy.

[A bit from exchange energy0-1

fractionalcharge
RFFXSDWLRQ1

EKIN

([EX(NLQexchange



kinetic
-1


0


RFFXSDWLRQ

fractional charge

0-1

1RFFXSDWLRQ(F0㻡㻛㻟㻢 RFFXSDWLRQ1

ionicpseudopotential-1(QOE䠪䠨䠬䠬EC

correlation



fractional charge
1-1

10RFFXSDWLRQ኱つᶍDFT䠄LDA/GGA䠅ィ⟬ḟୡ௦䝔䜽䝜䝻䝆䞊䜢ᨭ䛘䜛䝘䝜≀㉁䞉ᵓ㐀䛾≀ᛶண䝅䝸䝁䞁䞉䝘䝜䝗䝑䝖䝞䞁䝗䜼䝱䝑䝥䝗䝑䝖䜈䛾㟁Ⲵὀධ䜶䝛䝹䜼䞊䝯䝰䝸䞊䜈䛾ㄞ䜏᭩䛝㟁ᅽ┤ᚄ7nm䝅䝸䝁䞁䞉䝘䝜䝽䜲䝲䞊planer transistor

Surrounding gate transistorᮾᕤ኱ᒾ஭䜾䝹䞊䝥ᙧ≧䚸᪉఩䚸┤ᚄ䚸䚸䚸᭱㐺䛺䝘䝜ᵓ㐀䛿䠛᪂Ꮫ⾡䠖䝁䞁䝢䝳䞊䝔䜱䜽䝇㻙≀㉁䝕䝄䜲䞁 㻞㻜㻝㻜ᖺ㻥᭶㻝㻤᪥

6䜎䛪䛿<100> 䝽䜲䝲䞊䠖ᵝ䚻䛺᩿㠃
3 nm

6 nm

10 nm

circledumbell⌮᝿ⓗ䛺Ỉ⣲⤊➃squareelipse䠄㓟໬䛻䜘䜛䠅䝷䝣䝛䝇஧䛴䛾せ⣲9 䝞䝹䜽䝞䞁䝗ᵓ㐀䛾䝽䜲䝲䞊᪉ྥ䜈䛾ᑕᙳ
9 㔞Ꮚຠᯝ䛻䜘䜛䜻䝱䝸䝲䞊䛾㑅ᢥ

1.0

lightele

heavy lightele
holeheavyhole

-1.0

expt

0.190.920.15

0.5-2.00.00

calc

0.19

0.95

0.170.3᪂Ꮫ⾡䠖䝁䞁䝢䝳䞊䝔䜱䜽䝇㻙≀㉁䝕䝄䜲䞁 㻞㻜㻝㻜ᖺ㻥᭶㻝㻤᪥

CBM

0.0VBM
0.05

0.10

0.15

0.20

0.25

0.30

7circle 6 nm
1.12.0double
Quadruple

1.5Energy [eV]1.00.5m*=1.95

Eg=0.634 eV

0.0singleȴEshiftȴ
0.6ȳ
m*=0.311

m*=0.236kX

m*=1.13m*=0.972-0.5ȴEshift=0.0371 eV-1.0ȳXk᪂Ꮫ⾡䠖䝁䞁䝢䝳䞊䝔䜱䜽䝇㻙≀㉁䝕䝄䜲䞁 㻞㻜㻝㻜ᖺ㻥᭶㻝㻤᪥

8

Effective Mass Theory for the Circle
Envelop 㛵ᩘ uP䠖 \ nk P ( x, y, z ) | uP ( x, y )\ nk ( x, y, z )z

D = 6 nm, mt=0.236, ml=0.972

H1 = 0.10 eV

H2 = 0.25 eV

H3 = 0.47 eV᪂Ꮫ⾡䠖䝁䞁䝢䝳䞊䝔䜱䜽䝇㻙≀㉁䝕䝄䜲䞁 㻞㻜㻝㻜ᖺ㻥᭶㻝㻤᪥

H4 = 0.53 eV
90.5 eV

Conduction bands vs Cross section by RSDFT

Circle 3nm
ȳX

Square 3nm

Dumbbell 3:6nm

Circle 6nm
ȳX ȳX

Ellipse 3:6nm'Eshift and m* as well as degeneracy vary as functions ofshapes and sizes of the cross sections᪂Ꮫ⾡䠖䝁䞁䝢䝳䞊䝔䜱䜽䝇㻙≀㉁䝕䝄䜲䞁 㻞㻜㻝㻜ᖺ㻥᭶㻝㻤᪥10DOS ( states / eV atom )⌧ᐇ䝘䝜⣔䛾䝅䝭䝳䝺䞊䝅䝵䞁䠖⾲㠃䝷䝣䝛䝇䜢䜒䛴^ŝ(ϭϬϬ)Et䛾≧ែᐦᗘ1.0gap

0.8
0.6
0.4
0.2
0.0-12-10-8-6-4
Energy (eV)-202Energy㓟໬䛻䜘䛳䛶䝷䝣䛺⾲㠃䜢䜒䛴䚸┤ᚄ10nm䛾
Si(100)䝘䝜䝽䜲䝲䞊䛾᩿㠃ᙧ≧䠖14366-ཎᏊ⣔䛻ᑐ䛩䜛
RSDFTィ⟬Iwata, Takahashi, Oshiyama, Boku, Shiraishi: J. Comp. Phys. 2010

DOS ( States / eV atom )䝇䝟䜲䜽≧ᵓ㐀䠖э ⾲㠃㏆ഐ≧ែ䛾Ꮡᅾ
㍺㏦≉ᛶ䚸ගᏛ≉ᛶ
1.0

Cf. DOS of Si crystal

0.8
0.6
0.4
0.2
0.0-12᪂Ꮫ⾡䠖䝁䞁䝢䝳䞊䝔䜱䜽䝇㻙≀㉁䝕䝄䜲䞁 㻞㻜㻝㻜ᖺ㻥᭶㻝㻤᪥

-10-8-6-4(eV)-20211኱つᶍDFTィ⟬䠖䛔䛟䛴䛛䛾䜰䝥䝻䞊䝏
OpenMX ᑿᓮOpen source package for Material eXplorer䛃 is a package for nano-scale material simulations based on
density functional theories (DFT) [1], norm-conserving pseudopotentials [2,20,21], and pseudo-atomic
localized basis functions [23]. Since the code is designed for the realization of large-scale ab initio
calculations on parallel computers, it is anticipated that OpenMX can be a useful and powerful tool for
nano-scale material sciences in a wide variety of systems such as bio-materials, carbon nanotubes,
magnetic materials, and nanoscale conductors.

FEMTECH ᅵ⏣᭷㝈せ⣲ᇶᗏ䚸᭤⥺ᗙᶆ⣔䚸୪ิᛶ䛜㧗䛔䚸䜸䞊䝎䞊䠪ἲ䜒ᐇ⿦䛧䛶䛔䜛 ї ⇞ᩱ㟁ụ䜔䝸䝏䜴䝮㟁ụ䜢୰ᚰ䛸䛧䛯ᛂ⏝ィ⟬
CONQUEST ᐑᓮ䚸Bowler㟁Ꮚ㌶㐨䛾ỗ㛵ᩘ䛸䛧䛶䛾䜶䝛䝹䜼䞊䛾᭱ᑠ໬䛷䛿䛺䛟䚸ᐦᗘ⾜ิ䛾ỗ㛵ᩘ䛸䛧䛶䛾䜶䝛䝹䜼䞊䛾᭱ᑠ໬ї ᐦᗘ⾜ิ䛾ᐇ✵㛫䛷䛾ᒁᡤᛶ䜢฼⏝䛧䛶䚸 䜸䞊䝎䞊䠪ィ⟬Si(001)ୖ䛾Ge 䠏ḟඖᵓ㐀⣙䠎䠏䠌䠌䠌ཎᏊ⣔䛻ᑐ䛧䛶ィ⟬䛥䜜䛯㟁Ⲵᐦᗘ䛾➼್㠃䠄Ⰽ䛿㧗䛥䜢⾲䛩䠅᪂Ꮫ⾡䠖䝁䞁䝢䝳䞊䝔䜱䜽䝇㻙≀㉁䝕䝄䜲䞁 㻞㻜㻝㻜ᖺ㻥᭶㻝㻤᪥

12཯ᛂ䝎䜲䝘䝭䜽䝇≀㉁⏕ᡂ䛾㔞Ꮚㄽ䜶䝢䝍䜻䝅䝱䝹ᡂ㛗䚸䝸䝋䜾䝷䝣䜱䞊䚸㓟❅໬䚸䚸䚸ཎᏊᣑᩓ
CPMD for Siϭϵϵϲ-ϮϬϬϬᮍ᮶㛤ᣅ䜶䝢ᡂ㛗䛾㔞Ꮚㄽinterstitial
diffusion

Koizumi, Shigeta,Boero, Oshiyama(2010)

T=1000K䝍䞁䝟䜽㉁ෆ཯ᛂ䛾㔞Ꮚㄽ䝅䝖䜽䝻䞊䝮㓟໬㓝⣲䛷䛾䝥䝻䝖䞁㍺㏦

䛘䠛䟿Rare 䛺event 䛾䝅䝭䝳䝺䞊䝅䝵䞁䛿䚸䚸䚸᫬㛫㍈䛷䛾䝍䝇䜽 e.g. 䝯䝍䞉䝎䜲䝘䝭䜽䝇䛯䜣䜁䛟㉁䛿ᕧ኱ศᏊ䠖✵㛫㍈䛷䛾䝍䝇䜽᪂Ꮫ⾡䠖䝁䞁䝢䝳䞊䝔䜱䜽䝇㻙≀㉁䝕䝄䜲䞁 㻞㻜㻝㻜ᖺ㻥᭶㻝㻤᪥

RS-CPMD +MetaDynamics +Hybrid EXC13⏕య⣔䜒ᐦᗘỗ㛵ᩘ⌮ㄽ䛾䝍䞊䝀䝑䝖⏕యෆ䜶䝛䝹䜼䞊ኚ᥮䜢ᢸ䛖䝅䝖䜽䝻䞊䝮㓟໬㓝⣲䛷䛾䝥䝻䝖䞁㍺㏦䛾ᚤどⓗᶵᵓ䠖䝨䝥䝏䝗㙐䜢㉺䛘䜛⤒㊰䛾Ⓨぢ཯ᛂ⤒㊰䛷䛾⮬⏤䜶䝛䝹䜼䞊ኚ໬཯ᛂ⤒㊰䛾ྠᐃKamiya, Boero, Tateno, Shiraishi & Oshiyama: JACS (2007)

Something New?
䛯䛸䛘䜀䚸

Spin Polarization of Cation Vacancy in Nitride Semiconductors
Gohda & Oshiyama: PRB78, 161201 (R) (2008).JPSJ 79, 083705 (2010)

But that·s not all «.

- Hysteresis has been observed evenat Room temperature in Gd-, Cr-, Eudoped GaN 䛆ᮅ᪥䜾䝹䞊䝥䛇᪂Ꮫ⾡䠖䝁䞁䝢䝳䞊䝔䜱䜽䝇㻙≀㉁䝕䝄䜲䞁 㻞㻜㻝㻜ᖺ㻥᭶㻝㻤᪥- Gigantic magnetic moment of 4000 PBper Gd atom in epitaxially grown sample,
and more in implanted sample (cf. Gd atom8 PB) 䛆Ploog 䜾䝹䞊䝥䛇15

Spin-Polarized Cation Vacancy in Nitrides

Density of States

Neutral VGa in GaNElectronorbitals
responsible
for spin

upspindownspin

Density of States

Neutral VAl in AlN & VIn in In0.5Ga0.5N
gap

gap

Energy gain due to spin polarization:
0.58 eV (InGaN), 0.69 eV (GaN),
0.90 eV (AlN)

Nearly degenerate 3-folddefect levels near valenceband top split due toexchange interaction,
causing spin polarization
with P = 3PBsĂĐĂŶĐŝĞƐŝŶŽǀĂůĞŶƚ^ĞŵŝĐŽŶĚƵĐƚŽƌƐ͕ůŝŬĞ^ŝ
V2

V1

Symmetry-lowering (Jahn-Teller)
distortion makes it stable

Symmetry-lowering,pairing or resonant-bond distortion
makes it stable

t2
a1
Td

D2d

Quantitative agreement:

Sugino& Oshiyama, PRL (1992);
Saito & Oshiyama, PRL (1994),
Ogut & Chelikowski, PRL (1999)

actual wavefunction ofdeep state in V1

D3d

Ci

Rebonding that gains covalent energy,
though cost of distortion,
is a principal factor

Vacancy in group-III nitrides
Nitrogen is too small to rebond!
Covalent radii:
0.75 A (N) Symmetry keeping breathing
1.26 A (Ga) relaxation is a principal factor
1.44 A (In)1.18 A (Al)Then,
what has been overlooked is:
Exchange interaction among
gap states originated from N
dangling bondsэ
Possibility of spin polarization

Is GGA enough?
㟁Ꮚ┦㛵䛾ၥ㢟ᡭἲᨵⰋ䛾ᚲせᡭἲ䛾㛤Ⓨ䛸䛭䛾ᛂ⏝ ≀㉁䝕䝄䜲䞁䛻䛿ຊ䛾ィ⟬䛜㔜せ¾ Ᏻᐃᵓ㐀䚸‽Ᏻᐃᵓ㐀䚸཯ᛂ䛾㠡Ⅼ䛾᥈⣴ LDA/GGA䛾㝈⏺䜢㉸䛘䛶

¾ 䜶䝛䝹䜼䞊䜼䝱䝑䝥䚸ᙉ┦㛵⣔ၥ㢟ї䝝䜲䝤䝸䝑䝗䠄GGA+HF䠅ỗ㛵ᩘ䛾ྍ⬟ᛶ䚸DMatrixFTї௚⌜䛸䛾䝁䝷䝪䝺䞊䝅䝵䞁䠖ከయၥ㢟 ኱つᶍィ⟬䛷10nmᵓ㐀䠄10୓ཎᏊ⣔䠅䛾DFTィ⟬¾ 㟁Ꮚ䝕䝞䜲䝇䚸㟁ụ䚸⏕య⣔䠖䝘䝜⏺㠃䛾Ᏻᐃᛶ䚸㟁Ꮚ≧ែїRSDFT, CONQUEST, OpenMX, FEMTECK䛾㧗ᗘ໬ї௚⌜䛸䛾䝁䝷䝪䝺䞊䝅䝵䞁䠖㟁Ꮚ䚸䝇䝢䞁䚸⇕㍺㏦
 ཯ᛂ䝎䜲䝘䝭䜽䝇¾ ⏕యෆ཯ᛂ䠄䜲䜸䞁㍺㏦䚸㓝⣲཯ᛂ䚸䚸䚸䠅䚸≀㉁⏕ᡂ཯ᛂ䠄䜶䝢䝍䜻䝅䝱䝹ᡂ㛗䚸ཎᏊᣑᩓ䚸䚸䚸䠅

їRS-CPMD, MetaDynamics᪂Ꮫ⾡䠖䝁䞁䝢䝳䞊䝔䜱䜽䝇㻙≀㉁䝕䝄䜲䞁 㻞㻜㻝㻜ᖺ㻥᭶㻝㻤᪥

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