1. Liping Yu , Alex Zunger PHYSICAL REVIEW LETTERS 108, 068701 (2012)
Identification of Potential Photovoltaic Absorbers Based on First-Principles Spectroscopic Screening of Materials
Liping Yu , Alex Zunger
PHYSICAL REVIEW LETTERS 108, (2012)
Kishida Takuto

2. Contents Ⅰ.Introduction Ⅱ. Discussion & Result Ⅲ. Summary
Photovoltaic (PV) absorbers
Shockley and Queisser (SQ) limit
Ⅱ. Discussion & Result
Spectroscopic limited maximum efficiency (SLME)
Which materials are good potential PV absorbers.
Ⅲ. Summary
Ⅳ.Future plan

3. Photovoltaic (PV) absorbers
Ⅰ.Introduction
Photovoltaic (PV) absorbers
PV absorbers
PV absorbers have attracted attention as clean energy for the next generation.
Solar energy that reaches the earth in one hour is comparable to the energy humanity consumes in a year.(about 1kW/m2)
⭕ Energy source is the sun ⭕ CO2 is not emitted.
❌ Conversion efficiency is not high ❌ Price is high.
Classification
Silicon series
Si : 24.7 % ( Theoretical limitation 29 % )
Solar cell
Compound series
GaAs : 28.3 % , CIGS : 20.3 % , CdTe : 16.7 %
Organic series
Dye sensitization : 11.2% , Organic thin film : 7.9 %

4. Shockley and Queisser (SQ) limit
Ⅰ.Introduction
Shockley and Queisser (SQ) limit
In 1961,Shockley and Queisser
offered p-n junction PV absorbers
efficiency limit by numerical calculation.
Efficiency limit η is expressed
as a function of energy gap Eg.
SQ limit
Efficiency limit is calculated using the ideal value.
△Not taking account of direct or indirect gap.
△Radiative recombination is the only recombination process. ・

5. Spectroscopic limited maximum efficiency
Ⅰ.Introduction
Spectroscopic limited maximum efficiency
(SLME)
The SLME captures the leading physics of absorption, emission, and recombination characteristics, resolving a spread of different efficiencies for materials having the same gap.
(ⅰ) the existence of various energetic sequences of DA, DF and indirect band gaps
(ⅱ) the specific shape of the absorption near the threshold
(ⅲ) the dependence of radiative recombination losses on the energy separation between the minimum gap Eg and Egda

6. Ⅱ. Discussion & Result
SLME
Taking account of direct or indirect gap →Classifying materials into four ‘‘optical types’’(OT1~4)
OT1
OT2
OT3
OT4

7. Comparison of SQ efficiency and SLME
Ⅱ. Discussion & Result
Comparison of SQ efficiency and SLME
The power conversion efficiency of a thin film (L) solar cell depends on the fraction of the radiative electron-hole recombination current (fr) and the photon absorptivity [a(E)] .
SQ efficiency
Radiative recombination is the only recombination process
for all optical types of materials.
× nonradiative recombination dominates
SLME
where k is the Boltzmann constant, T is the temperature, and Δ= Egda – Eg

8. Comparison of SQ efficiency and SLME
Ⅱ. Discussion & Result
Comparison of SQ efficiency and SLME
For photon absorptivity a(E)
SQ efficiency
SLME
where L is the thickness of the thin film,
α(E) is the calculated absorption coefficient from first principles.
SLME improves upon the SQ efficiency formula in the description of both fr and a(E)

9. Calculation method GW approximation （G0W0+HSE06）
Ⅱ. Discussion & Result
Calculation method
GW approximation （G0W0+HSE06）
This method has been widely and successfully applied in firstprinciples quasiparticle electronic-structure calculations for many materials.
Predicted minimum band gaps for some I-III-VI compounds have an average error of less than 12% with respect to experiments.(L=0.5μm)
Ip-IIIq-VIr chalcopyrite group materials
I = Li , Na , K , Rb , Cs , Cu , Ag
III = B , Al , Ga , In , Tl , Sc , Y
VI = O , S , Se , Te

10. Chalcopyrite materials
Ⅱ. Discussion & Result
Chalcopyrite materials c a Cu In Se
CuInSe2(Ⅰ-Ⅲ-Ⅵ2)
Chalcopyrite semiconductor.
Experimental energy gap
=1.04[eV] (direct gap)
Lattice parameter
a=5.786[Å]
c/a=2.016

11. GW gaps of 215 compounds For example
Ⅱ. Discussion & Result
GW gaps of 215 compounds
(ⅰ)For OT1, within the same structure type,
the band gap of materials decreases with
increasing atomic number of one atom when
the other two atoms are held fixed.
For example
(ⅱ)The optical types can change if the
stoichiometry changes within the same element set.
Cu3TlSe2(OT3)→Cu5TlSe3(OT4)
→Cu7TlSe4(OT1)→CuTlSe2(OT2)

12. GW gaps of 215 compounds (OT2、space group #225) → Eg = 0.07 eV NaTlO2
Ⅱ. Discussion & Result
GW gaps of 215 compounds
(ⅲ)For the same compound, the minimum band gap (Eg) may vary by
more than 2 eV in different crystal structures,
whether or not the optical type changes
(OT2、space group #225) → Eg = 0.07 eV
(OT4、space group #166) → Eg = 2.27 eV
NaTlO2
(ⅳ) All reported I3III1VI3 materials
have small differences (less than 0.2 eV) between Egdf, Egda, and Eig .
(except Li3BO3 which has a 0.43 eV difference between Egda and Edfg. )

13. SLME for I-III-VI thin film materials
Ⅱ. Discussion & Result
SLME for I-III-VI thin film materials
The SQ efficiency limit depends only
on Eg for all optical types , predicting
that the best gap for a PV absorber is
1.34 eV, at which ηSQ = 33.7%
Around the same Eg, ηSQ depends on
the ‘‘optical types’’ and absorption spectra.
For example
AgInTe2 (OT1)
Cu7TlS4 (OT1)
CuYTe2(OT3)
Eg[eV]
1.17
SLME[%]
27.6
22.6
7.5

14. Which materials are good potential PV absorbers
Ⅱ. Discussion & Result
Which materials are good potential PV absorbers
There are about 25 materials with SLME higher than 20% .
These high-SLME materials
have the band gaps ranging
from 0.8 to 1.75 eV.
25 materials with high SLME
18 out of 25　→　OT1 , 7 out of 25　→　OT3
None of them have been found to be OT2 or OT4
→OT2 and OT4 materials are least favorable for PV absorbers.

15. Which materials are good potential PV absorbers
Ⅱ. Discussion & Result
Which materials are good potential PV absorbers
High-SLME materials ( Ip-IIIq-VIr )
CuInSe2 , CuGaSe2 , CuInS2
CuInTe2 , CuGaTe2 , AgInS2
AgInSe2 , AgInTe2 , AgGaSe2 , AgGaTe
that have been found experimentally to be
reasonable solar absorbers but are much less studied.
Most of these previously recognized absorber materials
within this group have (1:1:2) stoichiometry.
Materials with other stoichiometries also have high SLME.
(e.g., AgIn5Se8 , Cs3AlTe3 )

16. Ⅱ. Discussion & Result
Cu-Tl-Ⅵ materials
All six high-SLME Cu-Tl-VI materials
(four Cu7TlS4 , Cu3TlS2 , Cu3TlSe2)
Non-(1:1:2) stoichiometry
Contain only Tl of +1 oxidation state
Tl is highly toxic
→ These Tl-containing materials
might be disfavored.
Tl1+ → Other nontoxic elements in the 1+ oxidation state.
Cu-Tl-VI → Cup-IIIq-VIr → Cup-(ⅠⅡ)q-VIr
Cup-(ⅠⅡ)q-VIr materials that have SLME more than 20%, not involving Tl.
Cu7TlS4 → Cu7(ⅠⅡ) S4 Cup-IIIq-VIr → Cup-(ⅠⅡ)q-VIr Cup-(ⅠⅡ)q-VIr materials that have SLME more than 20%, not involving Tl.

17. Ⅲ. Summary
SLME improves upon the SQ efficiency formula for the initial material screening.
SLME considers different optical types and material-dependent nonradiative recombination loss.
Testing the idea on a couple of hundred generalized I- III-VI chalcopyrites using first-principles spectroscopy calculations and identifying potential PV absorber materials .
→ Cup-(ⅠⅡ)q-VIr materials that have SLME more than 20%,
not involving Tl that is highly toxic

18. Ⅳ.Future plan Cu-Tl-VI → Cup-(ⅠⅡ)q-VIr (Tl1+) 2+ 3+ 1+ Cu - Tl - VI
Cu ⅠⅡ - VI3
Cu -
- VI
For example
Ⅰ = Na , K
Ⅱ = Fe , Mg
Cu K Mg - S3