Defect physics of CuInSe2 chalcopyrite semiconductor

Yoshida-lab Hiroki Uede

S. B. Zhang, Su-Huai Wei, Alex Zunger, H. Katayama-Yoshida, Phys. Rev. B 57, 9642 (1998).

Defect( 欠陥 )Chalcopyrite semiconductor( カルコパイライト型半導体 )

Contents

I. IntroductionII. Calculation methodIII. Calculation resultsIV. SummaryV. My work

Application of CuInSe2 and motivation

山口真史他 著 『太陽電池の基礎と応用』 丸善株式会社　

visible light

p-type conductor at high doping ?

Photovoltaic solar cell• high absorption coefficient• high efficiency• self-healing • create p- and n-type CuInSe2 crystal

superconducting matter?

Photovoltaic solar cell( 太陽光発電 )Absorption coefficient ( 吸収係数 )Superconducting matter( 超伝導物質 )

cationanion

Chalcopyrite structure

cation1

cation2

anion

What is Chalcopyrite structure?

Diamond structure Zinc-blende structure ×2閃亜鉛鉱型構造

CuInSe2

• Chalcopyrite semiconductor

• Experimental energy gap =1.04[eV] (direct gap)

• Lattice parameter a=5.786[Å] η=c/a=2.016

c

a

Cu

In

SeCopper Indium Diselenide for Photovoltaic Applications, editedby T. J. Coutts, L. L. Kazmerski, and S. Wagner (Elsevier, Amsterdam,1986).

Details• In this study, calculate defect formation energy

for the defect α=VCu, VIn, InCu, CuIn and Cui.• Place defect α at the center of a 32-atom

supercell.

Cu

In

Se

InCu

VCuVIn

CuIn

Cui

Defect formation energy( 欠陥生成エネルギー )

Vacancy of atom( 原子空孔 ) Antisite( 逆サイト ) Interstitial ( 格子間 )

VCu ,VIn :vacancy of atom Cu, InInCu :antisite of atom In on site CuCuIn :antisite of atom Cu on site InCui :Cu type interstitial

Defect formation energyfor a neutral(q=0) defect

(1)

(2)

𝑛Cu 𝜇Cu

q

CuInSe2 crystal

𝜇CuInSe2𝜇¿𝑛¿

Fermi energy

𝜇Se

thermal equilibrium

defect

atom

electron

q :charge state:formation energy :total energy of supercell (with the defect α):total energy of supercell (without the defects), :numbers of Cu & In atoms , , :chemical potential of atom, :total energy of ground-state solid

thermal equilibrium( 熱平衡 )

Defect formation energyfor a charge(q≠0) defect

(4) (5)

(3)

𝑛Cu 𝜇Cu

q

CuInSe2 crystal

𝜇CuInSe2𝜇¿𝑛¿

Fermi energy

𝜇Se

thermal equilibrium

defect

atom

electron

q :charge state:Fermi energy:total energy of N-electrons(defect free) :total energy of the CuInSe2 with holes:total energy of the neutral defect with M-electrons:total energy of a defect with

Limits of Fermi energy and atomic chemical potential

• Fermi energy bound between the valence band maximum(VBM) and conduction band minimum(CBM)

CBM

VBMEnergy gap

Valence band

Conduction band

• Chemical potential

thermal equilibrium valence band( 価電子帯 )=HOMOconduction band( 伝導帯 )=LUMO

Defect transition energy level

𝜀𝛼 (𝑞 /𝑞′ )=[∆𝐸 (𝛼 ,𝑞)−∆𝐸 (𝛼 ,𝑞′ ) ]/(𝑞′−𝑞)

:defect transition energy levelα :kind of defectcharge state → q

Defect transition energy level( 欠陥遷移エネルギー準位 )

Computational details

• Density Functional theory(DFT)• Local Density Approximation(LDA) by the general potential

Linearized Augmented Plane-Wave(LAPW) method• Muffin-tin radius of 2.2 a.u. • the Ceperley-Alder exchange correlation potential as

parametrized by Perdew and Zunger • cut-off energy is 10 Ry• equivalent k points of the 10 special k points in the irreducible

zinc-blende Brillouin zone

Density Functional theory （密度汎関数法）Local Density Approximation （局所密度近似）Linearized Augmented Plane-wave 　 method （線形化補強平面波法）Exchange correlation potential （交換相関ポテンシャル）

Calculation results

Formation energy of VCu is low

VCu has a shallow acceptor level

Defect transition energy level

Formation energy of VCu & InCu are negative

Defect formation energy vs. Fermi energy

Formation energy of a defect pair

(6)

α,β :type of defect : A pair with noninteracting constituents

: A pair with interacting constituents

:the defect pair ordering

)()( ffneutral ΔHΔHΔH

)2(),(),( 2 CuCufford InVHmnΔHmnH

)(βΔH)(αΔH)β(αΔHδH ffqq

f00

int

defect pair( 欠陥対 )

Defect pair at B(Cu-poor, In-rich) is lower defect formation energy than other defect pair

Calculate results offormation energy of a defect pair

A(Cu-rich, In-rich)B(Cu-poor, In-rich)C(Cu-rich, In-poor)

Summary

• Defect formation energy of Cu vacancies is negative at Cu-poor, In-rich 　　　 → The self-doping ability of p-type• Defect pair is low formation energy at Cu-poor, In-rich 　　　→ self-compensation by and

Cu-poor, Se-rich is best for p-metal

My work

• Calculate chalcopyrite structure as a p-type doped superconductor material

• Calculate superconducting critical temperature TC

Calculate band structure of CuAlS2, chalcopyrite structure