The 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 Kuo,*B anisla Dzu nák, Neda Neyko a, Lucie Lando á, I ana Beshajo áPelikáno á,
Zdenek Remes, Chih-Yu Chang, S e aan De Wol , and Jakub Holo sky*
Ci e This: ACS Appl. Ma e . In e aces 2025, 17, 49986−49992
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ACCESS Me ics & Mo e A icle Recommenda ions *
sı Suppo ing In o ma ion
ABSTRACT: Hyb id pe o ski es a e a class o hin- ilm semiconduc o s wi h
ema kably s eep abso p ion edges and high abso p ion coe icien . In he case o
sola cells, a ilm hickness o less han a mic ome e is usually su icien o abso b
mos o he ligh when combined wi h a back e lec o . O he wise, an e icien ligh
apping s a egy may be desi ed, e.g., in he case o andem o semi anspa en cells.
T adi ionally, ligh apping is accomplished by employing andomly nano ex u ed
subs a es. In his con ibu ion, abso p ion enhancemen s due o no only nano ough
bu also mic o ough subs a es and wi h o wi hou addi ional gold coa ing a e
e alua ed om he poin o gains in pho ocu en and om he poin o iew o alid
op ical models. We ind ha ligh apping om nano ex u ed subs a es ollows
mainly he Yablono i ch model, leading o an appa en shi o abso p ion edge. This
con as s wi h mic o ough subs a es and also he ema kable e icien ligh apping
capabili ies o ba e laye s due o hei na i e su ace oughness, whe e he pa h
enhancemen in his case is almos uni o m, making he laye op ically hicke by ac o wo o mo e. Ligh apping op ical models
as well as analy ical echniques a e e iewed, and new insigh s a e p esen ed.
KEYWORDS: halide pe o ski e, Yablono i ch model, Po uba model, nano ex u e, subs a e oughness, ligh apping, ligh sca e ing,
ligh abso p ance
■INTRODUCTION
Hyb id o ganic−ino ganic lead halide pe o ski es a e a class o
semiconduc o hin- ilm ma e ial wi h ema kable op oelec-
onic p ope ies, being cu en ly he only wide bandgap op
cell candida es o andem de ices wo king wi h c ys alline
silicon bo om cells exceeding 30% e iciency, as i s
demons a ed by esea che s a EPFL/CSEM Neucha el,
1
hen u he imp o ed by o he academic g oups,
2
un il he
eco d was inally aken o e by indus y company Longi
cu en ly wi h 34.85% e icien de ice.
3
Especially in andem
cells, whe e i is no possible o apply a back e lec o behind
he pe o ski e laye , incomple e abso p ance leads o ans-
mi ance o pho ons h ough he op cell, leading o
o e lapping componen s o he ex e nal quan um e iciencies
o he op and bo om cells in he ange o 600 nm −800
nm.
4,5
The on mic ome e scale- ex u ed su ace consid-
e ably educes his e ec due o geome ic ligh pa h
enhancemen as can be seen om compa ison o andems
wi h la and ex u ed on su ace om he same labo a o y.
1,6
A simila geome ical op ical pa h enhancemen concep was
success ully demons a ed by glass ex u ing.
7
The use o
pe iodic nanos uc u ing o ligh apping was s udied
ex ensi ely heo e ically, e.g., based on py amidal su ace
8,9
in e ed cones
10
o ZnO pho onic c ys als.
11
Expe imen ally,
his was demons a ed, e.g., by di ac ion g a ings, making use
o CD and DVD discs.
12
Con e sely, andom ex u ing o
anspa en conduc i e oxide (TCO) subs a es was expe -
imen ally demons a ed only wi h mode a e success,
13,14
mainly due o e y low con as o e ac i e indices
15
be ween
he TCO and pe o ski e laye s. Mo e success ul was he e o e
concep o andom nano ex u ing o he back e lec o
16
whe e
he con as was gua an eed by an in e ace wi h me al. Me al
in e aces p o ide plasmonic e ec s ha do inc ease use ul
abso p ance
17−19
bu p incipally also he pa asi ic abso p ance
can be inc eased.
20
The in e ace be ween he pe o ski e and
ai also p o ides su icien e ac i e index con as . In ea ly
days o pe o ski e sola cell echnology, idealized Yablono i ch
limi pa h enhancemen
21
o such a case was e alua ed
analy ically. The Yablono i ch limi ep esen s a heo e ical
model
22
gi ing maximum pa h enhancemen o 2n2(4n2 o
back e lec o ) whe e n ep esen s he laye e ac i e index.
(Fo CH3NH3PbI3laye we use alue n= 2.5 he e.) This ac o
comes om in ensi y enhancemen in medium wi h highe
Recei ed: May 17, 2025
Re ised: Augus 1, 2025
Accep ed: Augus 8, 2025
Published: Augus 20, 2025
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e ac i e index ncompa ed o acuum acco ding o Iin =
n2Iex .
22
As we deal wi h local enhancemen , whe e he
e e ence in ensi y is ha o he nea ambien ha may no
be ai bu glass o a liquid, we ob iously ha e o accoun o i s
e ac i e index namb oo. The limi can be w i en as ollows
23
Ä
Ç
Å
Å
Å
Å
Å
Å
Å
Å
Å
Å
É
Ö
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
Ñ
A
n n d
11
2 ( / )
Yablono i ch
amb
2
1
+
(1)
whe e he e ac i e index is educed by he e ac i e index o
ambien namb,αis he abso p ion coe icien , and dis he laye
hickness. eq 1 was de i ed only o he case whe e αd≪1,
howe e , o he pu poses o app oxima e de e mina ion o
sola cell e iciency limi s, i is some imes used in he whole
ange. Ano he model, based on scala sca e ing heo y
24
and
ay acing analysis was de eloped o bulk and su ace
sca e ing in he case o mic oc ys alline silicon by Po uba.
25
The model was o iginally de eloped o a laye on a smoo h
su ace wi h oughness on only one side. Fo he pu poses o
his wo k, we ecalcula ed he model o double-side
oughness, and we ea ed mo e accu a ely some o i s de ails.
The ecalcula ed e sion is labeled as *Po uba model (wi h
s a ). Equa ions o di e en e sions o he Po uba model a e
gi en in he Suppo ing In o ma ion. The main pa ame e o
he model is he oo -mean-squa e oughness (RMS). Finally,
he simples ma hema ical model o abso p ance enhancemen
due o ligh apping is he model o uni o m ex ension o he
pa h leng h by a cons an δ. Then, abso p ance ollowing he
Lambe −Bee law akes a simple o m o eq 2
A1 e d
(2)
No e ha in his model we do no accoun o any in e nal
e lec ions o ligh . The goal is o e alua e he po en ial o
andom oughness sca e ing and di e en sca e ing models
om he poin o insu icien abso p ance in lead halide
pe o ski e s uc u es in he ange om 500 o 800 nm.
■THEORY
Fo illus a ion, he abo e-men ioned models a e heo e ically
compa ed in Figu e 1. As he model pe o ski e ma e ial, we
chose he mos basic me hylammonium lead iodide
CH3NH3PbI3(MAPI). Op ical cons an s o his ma e ial
we e de e mined om op ical measu emen o a laye p epa ed
on a glass subs a e. Fo he de ails o ma e ial p epa a ion and
op ical p ope ies de e mina ion e e o he Suppo ing
In o ma ion. The simula ed hickness was 500 nm. This
ep esen s he baseline case (single pass). In all cases, he loss
om e lec ance was neglec ed. Fo di e en models, we
ocused on he abso p ance om 1.5 o 2.2 eV. Below he
bandgap, we obse ed (x-axis is s e ched he e) an appa en
abso p ion edge shi , and abo e he bandgap, we obse ed
how he cu e app oached comple e abso p ion. I can be seen
ha di e en models beha e di e en ly. Ve y e icien in
app oaching ull abso p ion was ex ending (e.g., doubling) he
pho on pa h leng h (double pass, δ= 2), which was equi alen
o implemen ing some s ong geome ical ligh apping/
managemen (e.g., back e lec o ). On he o he hand, he
Yablono i ch limi does no each ull abso p ion abo e
bandgap. The Yablono i ch limi was implemen ed he e by
g adually “swi ching on” om 5% o 100% by making a
weigh ed a e age be ween he single pass and Yablono i ch
limi . This ep esen ed he assump ion ha only pa o he
pho ons a e sca e ed. The Yablono i ch limi had he
s onges e ec on he appa en abso p ion edge shi . The
Po uba model was scaling wi h he alue o RMS and was a bi
simila o uni o m pho on pa h enhancemen , bu such
enhancemen would be limi ed o δ≤2. O iginally, he
Po uba model was de i ed o single-side oughness, whe e he
enhancemen was a bi highe o highe oughness. As in ou
case, we mainly deal wi h laye s deposi ed on he ough
subs a e, leading o oughness on bo h sides, we pe o med a
new, mo e de ailed de i a ion labeled by a s a (*Po uba) o
his case. Howe e , he compa ison showed ha he o iginal
model can also be adap ed o double-side oughness wi h good
accu acy. Fo de ails abou di e en e sions and hei
compa ison e e o he Suppo ing In o ma ion. To e alua e
he e ec on sola cell pe o mance, he abso p ance mul iplied
by sola adia ion AM1.5G spec um was in eg a ed and
ela i e pho ogene a ion enhancemen ac o s we e e alua ed;
see g aphical in e p e a ion in Figu e 2. I we y o
app oxima ely ela e he pa h enhancemen δ o RMS
oughness in he *Po uba model, we ob ain di e en ends
o di e en laye hicknesses, see inse o Figu e 2.
We see ha doubling he ligh pa h in a 500 nm hick laye
o CH3NH3PbI3 esul s in mo e han 16% ela i e e iciency
inc ease; ipling leads o 22% inc ease, which is almos as
good as he maximum o he Yablono i ch limi wi h 23%
Figu e 1. Abso p ance cu es ( he e lec ance is assumed o be ze o)
o CH3NH3PbI3laye s simula ed by di e en analy ical models o
di e en in ensi ies o he ligh apping e ec .
Figu e 2. G aphical ep esen a ion o ela i e pho ogene a ion
inc eases o di e en ypes o ligh apping models o he
CH3NH3PbI3laye on glass wi h 500 nm hickness. The inse
shows app oxima e ela ion be ween he Po uba model and uni o m
pa h enhancemen .
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49987
inc ease, while he Po uba model can inc ease he pho o-
cu en by only 16% ela i ely o double-side oughness.
In e es ingly, o single-side oughness he inc ease p edic ed
by he Po uba model is up o 19%.
■EXPERIMENTAL METHODS
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 in. ZnO (99,99%) a ge wi h a subs a e
o a ge dis ance o 35 mm a RF powe o 75, 150, and 175 W,
espec i ely. A gon p essu e was 2 ×10−2Pa. Wi hou any addi ional
in en ional hea ing, he subs a e empe a u e was app oxima ely 100
°C. Deposi ion ime was 10 min.
FA0.9Cs0.1PbI3Ma e ial P epa a ion. The 1 M 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 PbI2in 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 h 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 s, ollowed by
5000 pm o 30 s. 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 s be o e he
end. Finally, he samples we e annealed a 100 °C o 15 min. All
ab ica ion s eps we e pe o med in a ni ogen- illed glo ebox.
CH3NH3PbI3Ma 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 1 mmol o PbI2
and 1 mmol o CH3NH3I dissol ed in 1 mL o DMF. Di e en
amoun s 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 s. The
esul ing ilms we e hen annealed a 100 °C o 3 min 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 CH3NH2gas o abou 2 s. A e he gas
was eleased om he ilms, he ilms we e subjec ed o a inal
annealing a 150 °C o 10 min 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.
26
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 o PbI2and 1.5
mmol o MAI in 1.5 mL o 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 s and hen a 5000 pm o 30 s. 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 s be o e he end. Finally, he samples we e
annealed a 100 °C o 10 min. All he s eps we e pe o med in a
ni ogen- illed glo ebox.
■CHARACTERIZATIONS
Pho o he mal de lec ion spec oscopy (PDS) measu emen s
we e pe o med by using a cus om-buil se up equipped wi h a
150 W Xe lamp and an Ando Kyme a 328i spec og aph. The
sli wid h was se o 1 mm, and 1:1 magni ica ion ocusing
op ics we e employed. Fou ie ans o m pho ocu en spec-
oscopy (FTPS) measu emen s we e conduc ed by using a
The mo Nicole 8700 FTIR spec ome e equipped wi h an
ex e nal ungs en ligh sou ce, an ex e nal ol age sou ce, and a
Kei hley 428 p eampli ie . Scanning elec on mic oscopy
(SEM) was ca ied ou using a TESCAN MAIA 3 ope a ed
a an accele a ing ol age o 5 kV. A omic o ce mic oscopy
(AFM) was pe o med wi h a WiTec alpha300 SNOM sys em,
u ilizing he noncon ac mode wi h Si p obes. The angula
dis ibu ion unc ion (ADF) was ob ained by using a cus om-
buil op ical se up. Full de ails o he measu emen se ups and
calcula ion p ocedu es a e p o ided in he Suppo ing
In o ma ion.
■RESULTS
Na i e Pe o ski e Su ace Roughness. I we wan o
e alua e he abso p ance enhancemen , we ha e o know he
abso p ion coe icien and e ac i e index o a single laye on
glass (Figu e S5 in Suppo ing In o ma ion). We he e o e
s a wi h laye s on glass. We p epa ed a se o 9 di e en laye s
o CH3NH3PbI3on glass wi h a ying hicknesses and a ying
c ys allini y, in o de o con ol su ace oughness. The
hickness ca ego ies we e 160, 250, and 500 nm, and he
g ain size ca ego ies we e S, M, and L as small/medium/la ge.
Fo a ying c ys allini y, he p e iously de eloped ecipe was
used.
26
Abso p ance was hen e alua ed by measu emen o
Pho o he mal De lec ion Spec oscopy (PDS). This measu e-
men was pe o med in a liquid wi h a e ac i e index nliquid =
1.25, which was close o 1, and does no conside ably educe
he su ace sca e ing compa ed o he case o ai . In he
models, howe e , his de ail was conside ed. Fo accu a e
compa ison be ween he models and he samples ha
exhibi ed a sligh a ia ion in he hicknesses, he in e e ence
inges we e i s emo ed by di iding he measu ed
abso p ance by (1R)
27
and he hickness a ia ion was
co ec ed by unning he Lambe −Bee law back and o h
o ma ch he hickness o he espec i e ca ego y. The
hicknesses we e measu ed by c oss-sec ional SEM. Fo mo e
de ails, e e o he Suppo ing In o ma ion. We ied o
ep oduce he beha io by simples models, and we saw ha
al eady he model o uni o m pa h leng h enhancemen (δ> 1)
ep oduced all he expe imen al cu es su icien ly well, see
Figu e 3. Rema kably, he alues o uni o m pa h leng h
enhancemen s up o δ= 2.7 we e obse ed. Re e ing o Figu e
2, such a high alue may be achie ed only o samples wi h
only one sca e ing su ace in he Po uba model. Ob iously,
he ques ion is how he ue alue o he abso p ion coe icien
can be de e mined. We simply ook he lowes alue ha we
could obse e, in he case o sample L500, he only one
a ibu ed o he pa h leng h enhancemen o δ= 1.
Fo p o ing he abso p ance enhancemen independen ly
om any simula ions, we also measu ed he pho ocu en
spec um be ween he wo elec odes by Fou ie -T ans o m
Figu e 3. Abso p ance o CH3NH3PbI3laye s on glass measu ed by
PDS and ecalcula ed o he same hicknesses (labeled d e ), i ed by
he model (dashed line) wi h uni o m pa h leng h enhancemen
( alues o pa h leng h δa e gi en in b acke s oge he wi h RMS
oughness in nm).
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49988
Pho ocu en Spec oscopy (FTPS), om he laye side and
om he glass side. Fo mo e de ails, e e o he Suppo ing
In o ma ion. I is well-known om he pho ocu en me hod-
ology ha he size o he ac ual illumina ion and de ec ion a ea
has o be conside ed. The sca e ed ligh in he spec al egion
a ound 1.5 eV, whe e he abso p ion coe icien was a ound
100 cm−1had a pene a ion leng h o a ound 0.1 mm and
could he e o e a el pa allel o he subs a e. Like his, he
illumina ion o he laye h ough he gap be ween he
elec odes ga e di e en esul s compa ed o he si ua ion
when a much la ge a ea was illumina ed om he glass side.
The e ec is schema ically ske ched in Figu e S7. These e ec s
o illumina ion and elec ode geome y on he signal
enhancemen in low abso p ance egion we e desc ibed
ex ensi ely in ela ion o ligh apping in hin ilms o
mic oc ys alline silicon.
25,28
In Figu e 4, we compa ed FTPS
spec a measu ed by illumina ion om he laye side ( h ough
he elec ode gap) and by illumina ion om he glass side. In
he g aph, he a io o he wo cu es is also shown, indica ing
enhancemen s o a ound 30%. The alue was only app oxima e
as he wo spec a we e no malized o each o he a 1.7 eV.
The pu pose o his es was jus o p o e he exis ence o any
abso p ion enhancemen due o ligh apping.
The e ec o ligh apping equi es sca e ing ei he om
some bulk ea u es o om he su ace. The ligh apping
enhancemen δcan be compa ed o RMS alues ob ained om
a omic o ce mic oscopy (AFM), see Figu e S9 in he
Suppo ing In o ma ion. RMS alues and δ alues a e gi en
in he legend o Figu e 3. We see, howe e , ha he co ela ion
was no e y good in his case. This means ha he RMS as a
single numbe was no a su icien pa ame e o desc ibing he
ligh sca e ing e ec . To ind a be e co ela ion, he angula
dis ibu ion unc ion (ADF) o he sca e ed ligh in he
e lec ion mode om he laye side was measu ed wi h a ed
lase , see Figu e 5. Al hough sca e ing in eali y happens on
he in e nal su ace, while we can expe imen ally assess his
only on he ex e nal su ace, ADF can s ill se e o a ela i e
compa ison. In p inciple, he ela ion o in e nal and ex e nal
ADF is possible using exis ing sca e ing models.
15
The ADF
unc ions we e no malized o he lase in ensi y. Re e o he
Suppo ing In o ma ion o u he measu emen de ails. The
ligh sca e ing om he su ace was inc easing om sample
L160 (lowes ) o M500 (highes ). Compa ing wi h pa h leng h
enhancemen , we see ha M160 had he highes δ alue, which
had he highes ADF cu e among samples in 160 nm
hickness ca ego y. On he o he hand, he lowes δwas ound
o L500 ha had he lowes ADF in he 500 nm hickness
ca ego y. This means ha no only ADF alues bu also he
hickness has an e ec on ligh apping enhancemen .
Nano ough and Mic o ough Subs a es. While he
na i e pe o ski e su ace oughness in con ac wi h ai may
exhibi ema kable abso p ance enhancemen , he e ec o he
in e ace wi h he subs a e migh be mo e impo an
p ac ically. The e o e, we es ed he pe o ski e laye s p epa ed
on nano ough TCO subs a es and on mic o ough glass
subs a es. Mo i a ed by hin- ilm silicon echnology,
29,30
we
i s deposi ed a ious laye s o ZnO by adio equency
spu e ing wi h a ying powe densi y leading o a ying
su ace oughnesses (samples ZnO A, ZnO B, and ZnO C).
The hi d sample (FTO) was a comme cial SnO2:F U- ype
laye om Asahi Glass Company.
19,31
A omic o ce mic os-
copy (AFM) images a e p o ided in he Suppo ing
In o ma ion. To inc ease he e ac i e index con as , he
laye o gold (100 nm) was coa ed on he op o he su aces,
mimicking he su ace ex u ing o he back e lec o .
16
Pe o ski e laye s we e hen deposi ed by spin coa ing on
TCO and on glass o e e ence. De ails abou he laye
p epa a ion a e p o ided in he Suppo ing In o ma ion. To
a oid ins abili y issues linked o me hylammonium o mixed
halide pe o ski es, he ma e ial o choice o expe imen s wi h
di e en oughnesses was FA0.9Cs0.1PbI3. These laye s we e
s able when deposi ed on TCO subs a es. F om he c oss-
sec ional SEM images (inse o Figu e S9), we can see ha he
oughness o he subs a e had a negligible e ec on he su ace
oughness o he pe o ski e laye . We measu ed he
abso p ance by PDS. The measu emen was pe o med in a
ange whe e he abso p ance in pe o ski e domina ed o e he
abso p ance in TCO o gold. The la e one can be e ealed
due o i s almos cons an abso p ance con as ing wi h sha p
abso p ion edge o pe o ski e. Spec a we e co ec ed again by
di iding by (1R). We ied o in e p e he simula ed cu es in
he amewo k o simple models and we ound ha a
combina ion o he Yablono i ch model wi h a small
con ibu ion o uni o m pa h enhancemen (δ≤1.3) was
ep oducing he esul s wi h good app oxima ion, see Figu e 6.
No e ha o a laye on a ( hick) glass measu ed by PDS, he
e m
n( )
amb
2
was se o nglassnliquid o accoun o he e ac i e
index o he glass and he liquid. In he case o he gold laye ,
Figu e 4. Simple p oo o he ligh apping by he obse ed di e ence
be ween FTPS spec a measu ed by illumina ion om he glass side
and a laye side ( h ough he gap in he elec odes) o andomly
chosen samples.
Figu e 5. Angula Dis ibu ion Func ion o sca e ed ligh om
CH3NH3PbI3laye s on glass measu ed in e lec ance mode by a ed
lase .
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he ac o 2 in he Yablono i ch limi was eplaced by 4 and
n( )
amb
2
was se o
n( )
liquid
2
. In e es ingly, unlike he na i e
su ace oughness, o hese nano ough TCOs he Yablono-
i ch model is always necessa y, and in he case o ba e ZnO
samples and FTO wi h gold coa ing, he uni o m pa h
enhancemen does no apply a all. Fo he la e sample,
e en he comple e Yablono i ch limi was achie ed. The
pa ame e s a e summa ized in Table 1. The ligh apping
enhancemen also co ela ed wi h he ADF unc ions shown in
Figu e 7.
In pa allel wi h he nano oughness ob ained by ex u ed
TCO, we also in es iga ed a mic o ough su aces o glass
p epa ed by e y simple mechanical me hods. Co ning
mic oscopic slides CLS294775 ×50 we e used in di e en
ea men s, named glass 0, A, B, and F. Glass 0 was wi hou any
ea men , glass A and glass B we e g inded by sandpape wi h
densi y 2000 and 1200, espec i ely, and glass F was he
blas ed ( os ed) a ea o he mic oscope slide. Resul ing PDS
spec a a e shown in Figu e 8. F om he SEM images (inse o
Figu e 8), we see ha he pe o ski e laye canno con o mally
coa he glass F subs a e, and he hickness he e o e does no
ha e a physical meaning. Fo he calcula ions, howe e , we
assumed a alue o 500 nm. We again ep oduced he esul s
by he combina ion o uni o m pa h enhancemen (δ> 1) wi h
he Yablono i ch model. Fo glasses wi hou a gold coa ing,
excep glass F, a small (δ≤1.2) pa h enhancemen alone
desc ibed he ligh apping e ec . Fo glass F and he use o
gold coa ing, he Yablono i ch model mus be included bu
ne e ully as in he case o nano ough su aces. The
pa ame e s a e summa ized in Table 1. The ligh apping
enhancemen also co ela ed wi h he ADF unc ions as shown
in Figu e 9.
■CONCLUSIONS
In conclusion, his wo k s udies he ole o andom ex u e
sca e ing in enhancing abso p ance pa icula ly be ween 500
and 800 nm in hyb id halide pe o ski e laye s. Ou indings
Figu e 6. Abso p ance o FA0.9Cs0.1PbI3laye s on op o TCO
measu ed by PDS (wi hou co ec ion o a ying hicknesses o he
pe o ski e laye ). Inse shows he c oss-sec ional SEM images (whi e
scale ba ep esen s 1 μm).
Table 1. Model Fi Pa ame e s
ba e wi h gold coa ing
sample RMS (nm) enhancemen δYabl. con ib. (%) RMS (nm) enhancemen δYabl. con ib. (%)
ZnO A 26 ±6 1 10 26 ±6 1.3 50
ZnO B 34 ±10 1 15 32 ±9 1.2 75
ZnO C 50 ±17 1 25 61 ±17 1.2 65
FTO 173 ±42 1.15 35 150 ±50 100
glass 0 8 ±2 1 10 ±2 1.4 50
glass A 112 ±21 1.05 266 ±53 1.3 70
glass B 80 ±21 1.2 57 ±13 1.4 60
glass F 220 ±110 1.6 45 500 ±100 1.4 75
Figu e 7. Angula Dis ibu ion Func ion o sca e ed ligh om
nano ough TCO laye s wi h and wi hou gold coa ing, measu ed by a
ed lase .
Figu e 8. Abso p ance o FA0.9Cs0.1PbI3laye s on op o glass
subs a es wi h di e en oughnesses, measu ed by PDS and co ec ed
o he hickness a ia ions. The inse shows he c oss-sec ional SEM
images (whi e scale ba ep esen s 1 μm, in he case o glass F he
pe o ski e laye is highligh ed by yellow colo ).
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h ps://doi.o g/10.1021/acsami.5c09757
ACS Appl. Ma e . In e aces 2025, 17, 49986−49992
49990
e eal ha nano ough ex u ed subs a es o e limi ed gains
due o low e ac i e index con as . This can be emphasized
by in oducing a me al (Au) coa ing ha conside ably
imp o es he ligh apping, ending o ollow he Yablono i ch
limi , enhancing mainly medium abso bing pho ons. Mic o-
ough subs a es, p oduced by mechanical ea men o glass,
led o enhancemen ha is mo e ending o uni o m op ical
hickness enhancemen . In con as wi h ha is he na i e
su ace oughness o pe o ski e laye s in ai , which beha io
ollows uni o m op ical hickness comple ely, e ec i ely
ex ending he op ical pa h leng h se e al imes. Expe imen ally,
his can be e ealed by compa ing pho ocu en spec oscopy
be ween coplana con ac s, measu ed om he ilm and
subs a e side. The uni o m op ical hickness enhancemen is a
good i s app oxima ion o a much-sophis ica ed Po uba
model ha is based on scala sca e ing heo y, and in
ag eemen wi h his model, he op ical pa h enhancemen is
s onge in hinne laye s and laye s wi h only one sca e ing
su ace. Scala sca e ing heo y, aking RMS oughness as a
pa ame e , ep esen s a good base o modeling ligh apping
in sola cells as well as o e alua ion o op ical cons an s;
howe e , he RMS pa ame e does no co ela e o he one
ob ained om AFM measu emen s. This wo k highligh s he
impo ance o ligh apping enhancemen om he
pe spec i e o po en ial in imp o ing pe o ski e pho o ol aic
de ices.
■ASSOCIATED CONTENT
*
sı Suppo ing In o ma ion
The Suppo ing In o ma ion is a ailable ee o cha ge a
h ps://pubs.acs.o g/doi/10.1021/acsami.5c09757.
De ails o Po uba’s model calcula ions o su ace
oughness, conside ing one side and bo h sides’
sca e ing cases; se ups o PDS, FTPS, and ADF
measu emen s; SEM images o cha ac e ize he hick-
ness and su ace mo phology o CH3NH3PbI3pe o ski e
laye s; and AFM images o e alua e he su ace
oughness o CH3NH3PbI3pe o ski e laye s, nano ough
TCO subs a es, and mic o ough glass subs a es (PDF)
■AUTHOR INFORMATION
Co esponding Au ho s
Meng-Hsueh Kuo −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, 16627 P ague, Czech Republic; Ins i u e o
Physics, Czech Academy o Sciences, 16200 P ague, Czech
Republic; o cid.o g/0000-0001-8100-7439;
Email: [email p o ec ed]
Jakub Holo sky−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, 16627 P ague, Czech Republic; Ins i u e o Physics,
Czech Academy o Sciences, 16200 P ague, Czech Republic;
o cid.o g/0000-0002-4222-6070;
Email: [email p o ec ed]
Au ho s
B anisla Dzu nák −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, 16627 P ague, Czech Republic
Neda Neyko a −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, 16627 P ague, Czech Republic; Ins i u e o Physics,
Czech Academy o Sciences, 16200 P ague, Czech Republic;
o cid.o g/0000-0002-9992-4988
Lucie Lando á −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, 16627 P ague, Czech Republic; Ins i u e o Physics,
Czech Academy o Sciences, 16200 P ague, Czech Republic
I ana Beshajo á Pelikáno á −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, 16627 P ague, Czech
Republic
Zdene
k Remes−Ins i u e o Physics, Czech Academy o
Sciences, 16200 P ague, Czech Republic; o cid.o g/0000-
0002-3512-9256
Chih-Yu Chang −Depa men o Ma e ials Science and
Enginee ing, Na ional Taiwan Uni e si y o Science and
Technology, 10607 Taipei, Taiwan
S e aan De Wol −KAUST Sola Cen e (KSC), King
Abdullah Uni e si y o Science and Technology (KAUST),
23955-6900 Thuwal, Saudi A abia; o cid.o g/0000-
0003-1619-9061
Comple e con ac in o ma ion is a ailable a :
h ps://pubs.acs.o g/10.1021/acsami.5c09757
No es
The au ho s decla e no compe ing inancial in e es .
■ACKNOWLEDGMENTS
We acknowledge he suppo o Czech Science Founda ion
h ough he p ojec no. 23-06285S, Czech Technical
Uni e si y in P ague s uden g an SGS24/135/OHK3/3T/
13, Czech Technical Uni e si y in P ague-Na ional Taiwan
Uni e si y o Science and Technology Join Resea ch P og am
(g an no.: CTU-NTUST-2024-03), and he p ojec “The
Ene gy Con e sion and S o age”, unded as p ojec No.
CZ.02.01.01/00/22_008/0004617 by P og amme Johannes
Amos Comenius, call Excellen Resea ch.
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