KATILARIN ELEKTRON Yo ğ un Madde Fizi İŞİ M İ ğ inde Kullanılan Yazılımlardan ab-initio Tekni İ K YAPISININ BENZET ğ i-3

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KATILARIN ELEKTRONİK YAPISININ

BENZETİŞİMİ

Yoğun Madde Fiziğinde Kullanılan

Yazılımlardan ab-initio Tekniği-3

Doç.Dr. Yeşim Moğulkoç

E-posta: mogulkoc@eng.ankara.edu.tr Tel: 0312 2033550

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Ha#a

DERS İÇERİĞİ

1. Malzeme Bilimi: Temel Kavramlar

2. Yoğun Madde Fiziğinde Kullanılan Yazılımlardan ab-ini@o

Tekniği

3. Kristal Fiziği: Temel Kavramlar-1

4. Kristal Fiziği: Temel Kavramlar-2

5. KaEların Bant Teorisi

6. Elektronik Bant Yapıları: İletkenlik durumları

7. VİZE SINAVI

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Ha#a

DERS İÇERİĞİ

8. Durum Yoğunlukları ve Fermi Yüzeyleri

9. KaEların ElasVk Özellikleri:

ElasVk sabitleri, Young, Shear Modülleri..

10. KaEların OpVk Özellikleri:

Dielektrik sabitleri, Yansıma, soğurma, sönüm katsayıları, kırılma indisi

11. KaEların Titreşimsel Özellikleri:

Fononlar

12. Kristal yapının programlama yardımıyla kurulması

13. KaEnın elektronik bant yapısının programlama yardımıyla çizdirilmesi

14. FİNAL SINAVI

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Once the relaxation is complete with high kpoints and high cutoff, then do only single point calculations as follows:

a) Fix encut to 800 eV (in incar). Gradually vary kpoints (in kpoints) from 25x25x1 to 5x5x1. Plot E0 (in OSZICAR) vs kpoints.

b) Fix kpoints to 25x25x1. Vary encut from 300 eV to 800 eV in steps of 50. Plot E0 vs encut. Identify optimum kpoints and encut for this material.

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Graphene

K-points

5X5 11X11 15X15 21X21 25X25 29X29 31X31 35X35

E0 -.18434067E+02 -.18441804E+02 -.18455182E+02 -.18457623E+02 -.18459275E+02 -.18459119E+02 -.18459158E+02 -.18459101E+02

5 10 15 20 25 30 35 18.46 18.45 18.44 18.43 18.42 K Points

E0

22 24 26 28 30 32 34 36 18.4592 18.4591 18.459 K Points

E0

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Graphene

Encut E0 900 -.18460503E+02 850 -.18459275E+02 800 -.18459275E+02 750 -.18457712E+02 700 -.18455141E+02 650 -.18450863E+02 600 -.18445870E+02 550 -.18441799E+02 500 -.18441325E+02 450 -.18445504E+02 400 -.18445504E+02 350 -.18484323E+02 300 -.18529555E+02 250 -.18409306E+02 200 300 400 500 600 700 800 900 18.55 18.5 18.45 18.4 ENCUT

E0

800 810 820 830 840 850 860 870 880 890 900 18.5 18.45 18.4 ENCUT

E0

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K-points

5X5 11X11 15X15 21X21 25X25 29X29 35X35

E0 -.10370682E+02 -.10412261E+02 -.10410677E+02 -.10411698E+02 -.10412393E+02 -.10412326E+02 -.10412314E+02

Silicene

5 10 15 20 25 30 35 10.45 10.4 10.35 K Points

E0

20 22 24 26 28 30 32 34 36 10.4124 10.4123 10.4122 K Points E0

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encut E0 800 -.10412393E+02 750 -.10412391E+02 700 -.10412404E+02 650 -.10412390E+02 600 -.10412324E+02 550 -.10412211E+02 500 -.10412138E+02 450 -.10412120E+02 400 -.10411837E+02 350 -.10410181E+02 300 -.10405066E+02 250 -.10390390E+02

Silicene

200 300 400 500 600 700 800 10.42 10.41 10.4 10.39 ENCUT

E0

400 450 500 550 600 650 700 750 800 850 900 10.414 10.413 10.412 10.411 10.41 ENCUT

E0

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Charge Density

For the relaxed structure and with optimum kpoints and encut, do a single point calculation.

Plot charge density using VESTA (charge density is written in CHGCAR.2, use this file along with OUTCAR.2 in VESTA). Plot the charge density such that I can clearly see sigma (inplane C-C) orbitals and pi orbitals (out-of-plane). Increase the density of kpoints mesh and replot charge density.

Integrate charge density on each atom using bader analysis. How many electrons does each atom have?

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Graphene

Charge Density with optimum kpoints and encut K-Points : 25X25X1

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Graphene

_{Bader Analysis}

# X Y Z CHARGE MIN DIST ATOMIC VOL --- 1 1.2335 0.7122 7.0000 3.8211 0.5087 37.0103 2 0.0000 0.0000 7.0000 4.1789 0.6168 36.7844 --- VACUUM CHARGE: 0.0000 VACUUM VOLUME: 0.0000 NUMBER OF ELECTRONS: 8.0000

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Density of States

Where is the Fermi level? Plot density of states from DOSCAR.2.

Split DOSCAR.2 for density of states integrated on each atom.

Plot total DOS for spin up and spin down channels.

Plot integrated DOS for two channel.

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Graphene

Total DOS −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 −25 −20 −15 −10 −5 0 5 10 15 20 25 E −Ef(eV) −20 −15 −10 −5 0 5 10 15 20 −25 −20 −15 −10 −5 0 5 10 15 20 25 E −Ef(eV) DOS for Spin Up & Down Integrated DOS for Spin Up & Down K Points : 45X45X1 , ENCUT : 600 eV

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Total DOS −0.08 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 −25 −20 −15 −10 −5 0 5 10 15 20 25 E −Ef(eV) −0.25 −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 −25 −20 −15 −10 −5 0 5 10 15 20 25 E −Ef(eV) S- orbital P - orbital K Points : 45X45X1 ; ENCUT : 600 eV

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Total DOS

Silicene

−3 −2 −1 0 1 2 3 −15 −10 −5 0 5 10 15 E −Ef(eV) −20 −15 −10 −5 0 5 10 15 20 −15 −10 −5 0 5 10 15 E −Ef(eV) DOS for Spin Up & Down Integrated DOS for Spin Up & Down K Points : 45X45X1 , ENCUT : 600 eV

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Graphene

First Brillouin Zone

#kpoints for bandstructure of graphene 10 Line-modereciprocal 0.0 0.0 0.0 ! \Gamma 0.6667 0.3333 0.0 ! K 0.6667 0.3333 0.0 ! K 0.50 0.0 0.0 ! M 0.50 0.0 0.0 ! M 0.0 0.0 0.0 ! \Gamma

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Graphene

Band Structure Plot Blochl-tetrahedron smearing 0 10 20 30 40 50 60 −20 −15 −10 −5 0 5 10 15 20 K−Points E −Ef (eV)

K

M

Nikhil’s bandstructure •  Energy Set to Fermi Level Spin Up

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Band Structure Plot Blochl-tetrahedron smearing •  Energy Set to Fermi Level Spin Up 0 10 20 30 40 50 60 70 80 90 −20 −15 −10 −5 0 5 10 15 20 K−Points E −Ef (eV)

K

M

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Band Structure Plot Blochl-tetrahedron smearing

Silicene

0 10 20 30 40 50 60 70 80 90 −15 −10 −5 0 5 10 15 K−Points E −Ef (eV) Spin Up •  Energy Set to Fermi Level

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Input ﬁles for SCF calculaVons for graphene

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