Defect physics of CuInSe2
chalcopyrite semiconductor
S. B. Zhang, Su-Huai Wei, Alex Zunger, H. Katayama-Yoshida,
Phys. Rev. B 57, 9642 (1998).
Yoshida-lab
Hiroki Uede
Defect(欠陥)
Chalcopyrite semiconductor(カルコパイライト型半導体)
Contents
I.
II.
III.
IV.
V.
Introduction
Calculation method
Calculation results
Summary
My work
Application of CuInSe2 and motivation
visible light
Photovoltaic solar cell
•
•
•
•
high absorption coefficient
high efficiency
self-healing
create p- and n-type CuInSe2 crystal
p-type conductor at high doping ?
superconducting matter?
Photovoltaic solar cell(太陽光発電)
Absorption coefficient (吸収係数)
Superconducting matter(超伝導物質)
山口真史他 著 『太陽電池の基礎と応用』 丸善株式会社
What is Chalcopyrite structure?
cation1
anion
cation
cation2
anion
Diamond structure
Zinc-blende structure ×2
閃亜鉛鉱型構造
Chalcopyrite structure
CuInSe2
• Chalcopyrite
semiconductor
• Experimental energy gap
=1.04[eV] (direct gap)
• Lattice parameter
a=5.786[Å]
η=c/a=2.016
c
Cu
In
Se
Copper Indium Diselenide for Photovoltaic Applications, edited
by T. J. Coutts, L. L. Kazmerski, and S. Wagner (Elsevier, Amsterdam,1986).
a
Details
• In this study, calculate defect formation energy
∆𝐻𝑓 𝛼, 𝑞 for the defect α=VCu, VIn, InCu, CuIn and Cui.
• Place defect α at the center of a 32-atom supercell.
InCu
VIn VCu
VCu ,VIn :vacancy of atom Cu, In
InCu :antisite of atom In on site Cu
CuIn :antisite of atom Cu on site In
Cui :Cu type interstitial
CuIn
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)
Cui
Cu
In
Se
Defect formation energy
for a neutral(q=0) defect
∆𝐻𝑓 𝛼, 𝑞 = 0 = ∆𝐸 𝛼, 𝑞 = 0 + 𝑛Cu 𝜇Cu + 𝑛In 𝜇In (1)
solid
solid
∆𝐸 𝛼, 𝑞 = 0 = 𝐸 𝛼, 𝑞 = 0 − 𝐸 CuInSe2 + 𝑛Cu 𝜇Cu
+ 𝑛In 𝜇In
(2)
thermal equilibrium
𝜇Cu + 𝜇In + 2𝜇Se = 𝜇CuInSe2
q :charge state
∆𝐻𝑓 𝛼, 𝑞 :formation energy
𝐸 𝛼, 𝑞 = 0 :total energy of supercell
(with the defect α)
𝐸 CuInSe2 :total energy of supercell
(without the defects)
𝑛Cu , 𝑛In :numbers of Cu & In atoms
𝜇Cu , 𝜇In , 𝜇Se :chemical potential of atom
solid solid
𝜇Cu
, 𝜇In :total energy of ground-state solid
thermal equilibrium(熱平衡)
atom
𝑛Cu
𝑛In
𝜇Cu 𝜇In 𝜇Se
𝜇CuInSe2
Fermi energy 𝐸𝐹
electron
defect
q
CuInSe2 crystal
Defect formation energy
for a charge(q≠0) defect
∆𝐻𝑓 𝛼, 𝑞 = ∆𝐻𝑓 𝛼, 𝑞 = 0 + 𝛿𝐸 CuInSe2 , −𝑞 + 𝛿𝐸 𝛼, 𝑞 + 𝑞𝐸𝐹 (3)
𝛿𝐸 CuInSe2 , −𝑞 = 𝐸 𝑁+𝑞 CuInSe2 − 𝐸 𝑁 CuInSe2 (4)
𝛿𝐸 𝛼, 𝑞 = 𝐸 𝑀−𝑞 𝛼, 𝑞 − 𝐸 𝑀 (𝛼, 𝑞 = 0) (5)
thermal equilibrium
𝜇Cu + 𝜇In + 2𝜇Se = 𝜇CuInSe2
q :charge state
𝐸𝐹 :Fermi energy
𝐸 𝑁 CuInSe2 :total energy of N-electrons(defect free)
𝐸 𝑁+𝑞 CuInSe2 :total energy of the CuInSe2
with 𝑞 holes
𝐸 𝑀 (𝛼, 𝑞 = 0):total energy of the neutral defect
with M-electrons
𝐸 𝑀−𝑞 (𝛼, 𝑞):total energy of a defect with 𝑞
atom
𝑛Cu
𝑛In
𝜇Cu 𝜇In 𝜇Se
𝜇CuInSe2
Fermi energy 𝐸𝐹
electron
defect
q
CuInSe2 crystal
Limits of Fermi energy and
atomic chemical potential
• Fermi energy bound between the
valence band maximum(VBM) and
conduction band minimum(CBM)
• Chemical potential
Conduction band
CBM
Energy gap
VBM
Valence band
valence band(価電子帯)=HOMO
conduction band(伝導帯)=LUMO
thermal equilibrium
𝜇Cu + 𝜇In + 2𝜇Se = 𝜇CuInSe2
Defect transition energy level
𝜀𝛼 𝑞/𝑞′ = ∆𝐸 𝛼, 𝑞 − ∆𝐸 𝛼, 𝑞′ /(𝑞′ − 𝑞)
𝜀𝛼 𝑞/𝑞 ′ :defect transition energy level
α :kind of defect
charge state 𝑞 ′ → 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
Defect transition energy level
Defect formation energy vs. Fermi energy
VCu has a shallow acceptor level
Formation energy of VCu is low
Formation energy of VCu & InCu are negative
Formation energy of
a defect pair
∆𝐻𝑓 𝛼 + 𝛽 = ∆𝐻𝑛𝑒𝑢𝑡𝑟𝑎𝑙 + 𝛿𝐻𝑖𝑛𝑡 + 𝛿𝐻𝑜𝑟𝑑 (6)
α,β :type of defect
∆𝐻𝑛𝑒𝑢𝑡𝑟𝑎𝑙 : A pair with noninteracting constituents
ΔH neutral  ΔH f ( )  ΔH f ( )
𝛿𝐻𝑖𝑛𝑡 : A pair with interacting constituents
δHint  ΔH f (αq  β q )  ΔH f (α0 )  ΔH f (β 0 )
𝛿𝐻𝑜𝑟𝑑 :the defect pair ordering
2
H ord (n, m)  ΔH f (n, m)  H f (2VCu  InCu
)
defect pair(欠陥対)
Calculate results of
formation energy of a defect pair
A(Cu-rich, In-rich)
B(Cu-poor, In-rich)
C(Cu-rich, In-poor)
−
Defect pair 2VCu
+ In2+
Cu at B(Cu-poor, In-rich)
is lower defect formation energy than other defect pair
Summary
• Defect formation energy of Cu vacancies is negative
at Cu-poor, In-rich
→The self-doping ability of p-type
−
• Defect pair 2VCu
+ In2+
Cu is low formation energy
at Cu-poor, In-rich
→self-compensation by VCu and InCu
Cu-poor, Se-rich is best for p-metal
My work
Calculate band structure of CuAlS2, chalcopyrite structure
• Calculate chalcopyrite structure as a p-type doped
superconductor material
• Calculate superconducting critical temperature TC