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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