SUPPORTING INFORMATION
Role o Random Tex u e Sca e ing on he Abso p ance Enhancemen in
Halide Pe o ski e Laye s
Meng-Hsueh Kuo1,2 , B anisla Dzu ňák1, Neda Neyko a1,2, Lucie Lando á1,2, I ana
Beshajo á Pelikáno á1, Zdeněk Remeš2, S e aan De Wol 3 and Jakub Holo ský1,2
1 Cen e o Ad anced Pho o ol aics, Facul y o Elec ical Enginee ing, Czech Technical
Uni e si y in P ague, Technická 2, 16627 P ague, Czech Republic
2 Ins i u e o Physics, Czech Academy o Sciences, Cuk o a nická 10, 16200 P ague, Czech
Republic
3 King Abdullah Uni e si y o Science and Technology (KAUST), KAUST Sola Cen e
(KSC), Thuwal, 23955-6900, Saudi A abia
Calcula ions
Po uba’s model [1]:
Complex e ac i e index 𝑁 can be de ined om e ac i e index 𝑛 and abso p ion
coe icien 𝛼 as ollows ( i is imagina y uni and 𝜆 is wa eleng h):
𝑁=𝑛+i𝛼𝜆
4𝜋
F esnel in ensi y coe icien s o pe pendicula incidence o e lec ance 𝑅 and ansmi ance
𝑇 (𝑛1 is e ac i e index o medium on he i s , incoming side, 𝑛2 is e ac i e index o
medium on he second, ansmi ing side) a e de ined as ollows:
𝑡12 =2𝑛1
𝑛1+𝑛2 ,𝑇12=𝑛2
𝑛1|𝑡12|2
𝑟12 =𝑛1−𝑛2
𝑛1+𝑛2 ,𝑅12 =|𝑟12|2
The amoun o specula ly ansmi ed o e lec ed ligh is ob ained by mul iplying F esnel
in ensi y coe icien s by scala sca e ing heo y [2] sca e ing ac o s (𝜎 is RMS oughness,
𝑛𝑓is e ac i e index o ilm, 𝑛𝑎 is he e ac i e index o ambien , 𝜑 is he angle o
incidence ha o apped ligh can be app oxima ed by 𝜋/𝑛𝑓 ):
𝑆𝑇=exp[−(2𝜋(𝑛𝑓−𝑛𝑎)𝜎
𝜆)2]
𝑆𝑅,0 =exp[−(4𝜋𝑛𝑓𝜎
𝜆)2]
𝑆𝑅=exp[−(4𝜋𝑛𝑓𝜎cos𝜑
𝜆)2]≅exp[−(4𝜋𝑛𝑓𝜎cos(𝜋/𝑛𝑓)
𝜆)2]
The ligh abso bed di ec ly wi hou sca e ing e en is (𝑑 is he ilm hickness):
𝐴𝑑𝑖𝑟 =𝑆𝑇(1−𝑒−𝛼𝑑)
Rela i e po ion o pho ons sca e ed a he hi ing he i s su ace and a he hi ing he
su ace a e e lec ion om he back side o he ilm is (indices 𝑓and 𝑠 mean ilm and
subs a e, espec i ely):
𝑃0=(1−𝑆𝑇)+𝑆𝑇𝑅𝑓𝑠𝑒−2𝛼𝑑𝑅𝑓𝑎(1−𝑆𝑅0)
P obabili y o sca e ed ligh escaping h ough escape cone in o subs a e, o Lambe ian
case is:
𝑃𝑒𝑠𝑐 =(𝑛𝑠/𝑛𝑓)2
The mul iplica ion ac o o a e age op ical pa h inc ease o Lambe ian dis ibu ion.
Angles 𝛽and 𝛾 a e he in eg a ion limi s ha a e linked o escape cone:
𝑌𝛽𝛾= ∫𝑠𝑖𝑛
𝛾
𝛽𝜑 𝑑𝜑
∫𝑠𝑖𝑛
𝛾
𝛽𝜑cos𝜑𝑑𝜑
Figu e S1: Illus a ion o he di e en con ibu ions in o Po uba model.
The po ion o ligh (sca e ed and non-sca e ed) abso bed be ween i s and second
sca e ing e en (𝛾 is he angle o escape cone in o subs a e o which he condi ion is
sin(𝛾)=𝑛𝑠𝑛𝑓
⁄):
𝐴1=(1−𝑃𝑒𝑠𝑐)[1 − exp (−2𝑌𝛾𝜋/2𝛼𝑑)]+𝑃𝑒𝑠𝑐[1 − exp (−𝑌0𝛾𝛼𝑑)]
The ela i e in ensi y educ ion be ween he i s and second sca e ing e en is:
𝑃1=(1−𝑃𝑒𝑠𝑐) exp (−2𝑌𝛾𝜋/2𝛼𝑑)
The po ion o ligh (sca e ed and non-sca e ed, inside and ou side o escape cone) abso bed
be ween i s and second sca e ing e en (𝛾 is he angle o escape cone in o subs a e o
which he condi ion is sin(𝛾)=𝑛𝑠𝑛𝑓
⁄):
𝐴2=[(1−𝑃𝑒𝑠𝑐)(1−𝑆𝑟)+𝑆𝑟)][1 − exp (−2𝑌𝛾𝜋
2𝛼𝑑)]+𝑃𝑒𝑠𝑐(1−𝑆𝑟)[1
− exp (−𝑌0𝛾𝛼𝑑)][1+𝑅𝑓𝑠 exp (−𝑌0𝛾𝛼𝑑)]
The ela i e in ensi y educ ion be ween each wo consecu i e sca e ing e en s is (o non-
sca e ed ligh and ligh sca e ed ou side escape cone):
𝐴2=[(1−𝑃𝑒𝑠𝑐)(1−𝑆𝑟)+𝑆𝑟)]exp (−2𝑌𝛾𝜋
2𝛼𝑑)
Al oge he he in ensi y o abso bed ligh is he sum o an in ini e ow:
𝐴=𝐴𝑑𝑖𝑟+𝑃0𝐴1+ 𝑃0𝑃1𝑅𝑓𝑎𝐴2 1
1−𝑃2
T anspa en conduc i e oxide (TCO) laye s p epa a ion
The samples A, B, and C we e p epa ed on Co ning glass using RF magne on spu e ing
om 2 inch ZnO (99,99%) a ge wi h subs a e o a ge dis ance 35 mm a RF powe 75
W, 150 W and 175 W, espec i ely. A gon p essu e was 2×10-2 Pa. Wi hou any addi ional
in en ional hea ing he subs a e empe a u e was app oxima ely100 °C. Deposi ion ime was
10 minu es.
FA0.9Cs0.1PbI3 ma e ial p epa a ion
The 1M FA0.9Cs0.1PbI3 pe o ski e ilms we e deposi ed om a p ecu so solu ion p epa ed
by dissol ing 0.9 mmol o FAI, 0.1 mmol o CsI, and 1 mmol o PbI2 in 1 ml o a mixed
sol en consis ing o DMF and DMSO in a 4:1 a io. This p ecu so solu ion was
con inuously s i ed a 60 °C o 1 hou and hen le o s i o e nigh . The esul ing
pe o ski e solu ion was hen spin-coa ed on o he subs a e, i s a 1000 pm o 10 seconds,
ollowed by 5000 pm o 30 seconds. Du ing he second spin-coa ing s ep, 200 µL o e hyl
ace a e was d opped on o he spinning subs a e 5 seconds be o e he end. Finally, he
samples we e annealed a 100 °C o 15 minu es. All ab ica ion s eps we e pe o med in a
ni ogen- illed glo ebox.
CH3NH3PbI3 ma e ial p epa a ion
Samples MAPI A and MAPI B we e ab ica ed om p ecu so solu ions con aining 1mmol
o PbI2 and 1 mmol o CH3NH3I dissol ed, in 1 ml o DMF. Di e en amoun o MACl
(2.5 w % o MAPI A and 1.5 w % o MAPI B) we e added o hese solu ions. A e s i ing
o e nigh , he solu ions we e spin-coa ed on o glass subs a es a 4500 pm o 40 seconds.
The esul ing ilms we e hen annealed a 100 °C o 3 minu es o c ea e he CH3NH3PbI3
·MACl laye s. Once cooled o oom empe a u e, he ilms we e b ie ly exposed o CH3NH2
gas o abou 2 seconds. A e he gas was eleased om he ilms, he ilms we e subjec ed
o a inal annealing a 150 °C o 10 minu es o p oduce high-quali y CH3NH3PbI3 ilms. All
he s eps we e pe o med in a ni ogen- illed glo ebox. Mo e de ails can be ound in
publica ion [3]
Sample MAPI C was deposi ed on co ning glass subs a es om a p ecu so solu ion
pe o med by dissol ing 1.5 mmol PbI2 and 1.5 mmol MAI in 1.5 ml sol en mix u e o
GBL and DMSO in a a io o 3:2. This mix u e was con inuously s i ed a 60 °C. The
esul ing pe o ski e solu ion was hen spin-coa ed on o he subs a e, i s a 1000 pm o
10 seconds and hen a 5000 pm o 30 seconds. Du ing he second spin-coa ing s ep, 150
µL o chlo obenzene was d opped on o he spinning subs a e 5 seconds be o e he end.
Finally, he samples we e annealed a 100 °C o 10 minu es. All he s eps we e pe o med
in a ni ogen- illed glo ebox.
Pho o he mal De lec ion Spec oscopy measu emen s
The Pho o he mal De lec ion Spec oscopy measu emen s we e pe o med by a home-made
se up equipped wi h 150W Xe lamp and Ando Kyme a 328i. Sli s we e se o 1 mm.
Focusing op ics wi h magni ica ion 1:1 was used. Combina ion o g a ing numbe o g oo es
and sli wid hs ga e heo e ical esolu ion ∆𝐸/𝐸≈0.01, whe e E was pho on ene gy. Real
esolu ion, acco ding o spec al linewid h measu emen s, was ∆𝐸/𝐸≤0.02. As a he mal
sensi i e liquid, Flu ec PP1 was used. Re ac i e index was 1.25. Simul aneously,
ansmi ance and e lec ance we e measu ed by in eg a ion sphe es in on and behind he
cu e e (no di ec ly in on o behind he sample), cu e e in e nal dimensions we e 10 x10
mm. Abso p ance om PDS e ec was absolu ely scaled acco ding o 1−𝑅−𝑇 measu ed
by in eg a ing sphe es. Abso p ion coe icien was hen e alua ed om
abso p ance/ ansmi ance a io om a smoo h sample on glass acco ding o equa ions om
e . [4]. Fo o he pu poses o abso p ance compa ison he simple equa ion is assumed o be
𝐴≅1 − exp (−𝛼𝛿𝑑). Mo e accu a ely, he equa ion eads 𝐴𝑒𝑥𝑝 ≅(1−𝑅0) [ 1−
exp (−𝛼𝛿𝑑𝑒𝑥𝑝)] , whe e 𝑅0 is he e lec ance on he i s su ace, 𝑑𝑒𝑥𝑝 is ac ual hin- ilm
hickness. In high abso p ion egion, he 𝑅0 e lec ance equal o he expe imen ally
obse ed e lec ance o he eal s ack, bu o he pu poses o his s udy we assume 𝑅0≅𝑅
e e ywhe e. F om expe imen ally ob ained 𝐴𝑒𝑥𝑝 we calcula ed abso p ance 𝐴 ha is
co ec ed o e lec ance e ec s and co ec ed o hickness a ia ions as
𝐴≅1 − exp [𝑑/𝑑𝑒𝑥𝑝 ∗ ln(1−𝐴0/(1−𝑅))].
1.4 1.6 1.8 2.0 2.2 2.4 2.6
102
103
104
105
MAPbI3
abso p ion coe icien (1/cm)
pho on ene gy (eV)
1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8
2.3
2.4
2.5
2.6
2.7
e ac i e index (-)
pho on ene gy (eV)
MAPbI3
Figu e S2: Abso p ion coe icien and e ac i e index o MAPI pe o ski e laye ob ained
om PDS measu emen and nume ic i ing p ocedu e.
Fou ie T ans o m Pho ocu en Spec oscopy measu emen s
On he samples dedica ed o FTPS measu emen s, he plana elec odes we e p epa ed by
e apo a ion gold ough mechanical mask. The con ac dis ance is 0.5 mm. The elec ode
pa e n is in Figu e S2.
Figu e S3: elec ode pa e n
o FTPS measu emen s.
Figu e S4: Ske ch o he FTPS sample a angemen and
he e ec o he illumina ion di ec ion and he ole o
apped ligh . In he case o glass side he long a elling
pho ons con ibu e mo e o he measu emen .
FTPS was pe o med by FTIR The mo Nicole 8700 equipped wi h ex e nal ungs en ligh
sou ce and ex e nal ol age sou ce and p e-ampli ie Kei hley 428. Vol age bias 10 V was
applied, gi ing DC cu en in he ange o ~10 nA. P eampli ica ion 108 V/A was applied.
In a ed glass op ical il e RG 780 om Tho labs was used o supp ess isible pa o he
spec um and o collec sub-bandgap pa o he spec um. Scan speed eloci y was 0.16 cm/s
leading o modula ion equency a ound 4 kHz. F equency dependence was co ec ed based
on he measu emen s a wice and h ee imes highe modula ion equencies.
Scanning Elec on Mic oscopy measu emen s
The hicknesses o he pe o ski e hin ilms we e de e mined om sample c oss sec ions
using scanning elec on mic oscope MAIA 3, TESCAN a ol age o 5 kV.
S 160 (in . no. 2024 23a)
M 160 (in . no. 2025 I3)
L 160 (in . no. 2025 C3)
S 250 (in . no. 2025 G3)
M 250 (in . no. 2025 B3)
L 250 (in . no. 2025 A3)
S 500 (in . no. 2024 C2)
M 500 (in . no. 2025 D15)
L 500 (in . no. 2024 E1)
Figu e S5: SEM images o CH3NH3PbI3 samples.
A omic Fo ce Mic oscopy
Su ace oughness was measu ed by AFM using WiTec alpha300 SNOM sys em u ilizing
non-con ac AFM me hod wi h Si p obes. Measu ed sample a ea was 5 × 5 µm.
RMS=51 ± 8 nm
RMS=72 ± 17 nm
S 160 (in . no. 2024 23a)
M 160 (in . no. 2025 I3)
RMS=67 ± 13 nm
L 160 (in . no. 2025 C3)
RMS=125 ± 19 nm
RMS=105 ± 23 nm
S 250 (in . no. 2025 G3)
M 250 (in . no. 2025 B2)
RMS=210 ± 40 nm
L 250 (in . no. 2025 A2)
RMS=210 ± 70 nm
RMS=390 ± 60 nm
S 500 (in . no. 2024 C2)
M 500 (in . no. 2025 D15)
RMS=63 ± 14 nm
L 500 (in . no. 2024 E1)
Figu e S6: Mo phology o na i e oughness o MAPI samples.
ZnO A, RMS = 26 ± 6 nm
ZnO A wi h Au, RMS = 26 ± 6 nm
ZnO B, RMS= 34 ± 10 nm
ZnO B wi h Au, RMS= 32 ± 9 nm
ZnO C, RMS = 50 ± 17 nm
ZnO C wi h Au, RMS = 61 ± 17 nm
FTO, RMS = 173 ± 42 nm
FTO wi h Au, RMS = 150 ± 50 nm
Figu e S7: Mo phology o nano- ough TCO subs a es be o e (le image) and a e ( igh
image) he deposi ion o gold laye .
