RESEARCH ARTICLE
www.ad ancedscience.com
Swi ching Response in O ganic Elec ochemical T ansis o s
by Ionic Diffusion and Elec onic T anspo
Juan Bisque ,* Bau zhan Ilyasso ,* and Ni Tessle *
The swi ching esponse in o ganic elec ochemical ansis o s (OECT) is a
basic effec in which a ansien cu en occu s in esponse o a ol age
pe u ba ion. This phenomenon has an impo an impac on diffe en aspec s
o he applica ion o OECT, such as he equilib a ion imes, he hys e esis
dependence on scan a es, and he synap ic p ope ies o neu omo phic
applica ions. He e we es ablish a model ha uni es e ical ion diffusion and
ho izon al elec onic anspo o he analysis o he ime-dependen cu en
esponse o OECTs. We use a combina ion o ools consis ing o a physical
analy ical model; ad anced 2D d i -diffusion simula ion; and he
expe imen al measu emen o a poly(3-hexyl hiophene) (P3HT) OECT. We
show he educ ion o he gene al model o simple ime-dependen equa ions
o he a e age ionic/hole concen a ion inside he o ganic film, which
p oduces a Be na ds-Mallia as conse a ion equa ion coupled wi h a diffusion
equa ion. We p o ide a basic classifica ion o he ansien esponse o a
ol age pulse, and he co esponden hys e esis effec s o he ans e cu es.
The shape o ansien s is basically ela ed o he main con ol phenomenon,
ei he he e ical diffusion o ions du ing doping and dedoping, o he
equilib a ion o elec onic cu en along he channel leng h.
J. Bisque
Ins i u o de Tecnología Química (Uni e si a Poli ècnica de
València-Agencia Es a al Consejo Supe io de In es igaciones Cien íficas)
A . dels Ta onge s, València 46022, Spain
E-mail: [email p o ec ed].es
J. Bisque
Ins i u e o Ad anced Ma e ials (INAM)
Uni e si a Jaume I
Cas elló 12006, Spain
B. Ilyasso
As ana IT Uni e si y
Mangilik El 55/11, EXPO C1, As ana 010000, Kazakhs an
E-mail: [email p o ec ed]
N. Tessle
And ew & E na Vi e bi Depa men o Elec ical and Compu e Enginee ing
Technion-Is ael Ins i u e o Technology
Hai a 32000, Is ael
E-mail: [email p o ec ed]
The ORCID iden ifica ion numbe (s) o he au ho (s) o his a icle
can be ound unde h ps://doi.o g/10.1002/ad s.202404182
© 2024 The Au ho (s). Ad anced Science published by Wiley-VCH
GmbH. This is an open access a icle unde he e ms o he C ea i e
Commons A ibu ion License, which pe mi s use, dis ibu ion and
ep oduc ion in any medium, p o ided he o iginal wo k is p ope ly ci ed.
DOI: 10.1002/ad s.202404182
1. In oduc ion
The ealiza ion o he poin con ac an-
sis o in 1947 ma ked he beginning o
he ansis o e a and he de elopmen
o a ious ansis o s uc u es aiming
o eplace he acuum- ube echnology.[1]
The demons a ion o he fi s mic op o-
cesso in 1971 by In el u ned he me al
oxide semiconduc o field effec ansis o
(MOSFET) in o he dominan ansis o
echnology. In e es ingly, be o e ounding
In el, Go don Moo e ex apola ed 4 yea s
o da a poin s o p edic ha he numbe
o ansis o s pe chip would double e e y
2 yea s.[2]This soon became he indus-
y’s a ge and wha is known oday as
Moo e’s law. Fo many yea s, he law was
ollowed by “simply” sh inking he size o
he ansis o . Howe e , as he challenges
accumula ed, new ansis o a chi ec u es
we e de eloped, and 3D in eg a ion became
necessa y. In pa allel, a end o imp o ing
pe o mance no jus by packing mo e
ansis o s bu also by pe o ming he
unc ions diffe en ly s a ed e ol ing.[3]
The appea ance o a ificial in elligence and he no ion o
mul i-le el logic has accele a ed he de elopmen o mul i-le el
swi ches, he mos amous o which is he mem is o amily.[4]
Recen de elopmen s show ha he good-old MOSFET ansis-
o and i s o ganic analog[5]can also be u ned in o a mul i-le el
swi ch by emb acing elec ochemis y as pa o he ansis o ’s
oolbox.[6–8]Specifically, he elec ochemical RAM (ECRAM) and
he o ganic elec ochemical ansis o (OECT) use ionic and elec-
onic conduc ion o es ablish new ope a ion mechanisms, wi h
he OECT also p o iding an in e ace o he biological wo ld.[9]
Recen ly, h ee- e minal de ices ha e been in es iga ed as p o-
g ammable esis o s o b ain-like compu a ion. I he ion ese -
oi is le elec ically open, he ions emain in he channel a he
se conduc i i y, wi h a non ola ile p ope y. This de ice class in-
cludes ENODe (Elec ochemical Neu omo phic De ice), and EIS
(Elec ochemical Ionic Synapse) configu a ions.[10–15]
I has been widely ecognized ha he dynamics o cha ge
and ion anspo exe a dominan influence on he ope a ion
o OECT.[16–18]In pa icula slow ionic mo ion o en c ea es a ki-
ne ic limi ing effec .[19,20]These cha ac e is ic dynamics ha e an
impo an influence on he swi ching ime o he OECT, and on
he memo y effec s o neu omo phic applica ions. An impo an
ea u e ha has been obse ed in OECTs is he hys e esis in he
ans e cu es.[16,21,22]
Ad . Sci. 2024,11, 2404182 2404182 (1 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
www.ad ancedsciencenews.com www.ad ancedscience.com
Figu e 1. a) Scheme o he model o he anspo inside he channel and ion exchange wi h he elec oly e. b) Scheme o he measu emen o he
ansien esponse o he OECT. c,d) The blue cu en is he s a iona y elec onic cu en Idc
d=Idc
s. The g een a ows a e he ansien cha ging elec onic
cu en s. In a ansien si ua ion, he diffe ence o g een cu en s a D and S elec odes, Ih(L)−Ih(0), equals he o al ion cu en en e ing he channel
film ( ed cu en s). The ol age dis ibu ion in quasi-equilib ium condi ions is indica ed o wo si ua ions: c) 𝜃=−1, uds <0, and (d) 𝜃=+1,
uds >0.
The analysis o he ansien beha io o o ganic ansis-
o s has been de eloped by a s anda d dis ibu ed ansmis-
sion line app oach o bo h he injec ion o elec onic cu en s
om he d ain and sou ce and he injec ed ionic cu en om
he elec oly e.[23–28]A pa icula ealiza ion is he Be na d and
Mallia as model[29]which has been widely used o he cha ac e -
iza ion o he ansien esponse o he OECTs.[24,29–31]Recen ly
we ha e de eloped a model o hys e esis in OECT[32] ha consis s
o an ex ension o he Be na ds and Mallia as model by coupling
he diffusion o in e cala ed ions explici ly. The analy ical model
p o ides some use ul dis inc ions o hys e esis effec s p o ided
ha he densi y o ions can be conside ed nea ly homogeneous
in he film. He e we es ablish a igo ous gene al o mula ion o
he model and he sui able app oxima ions ha can be used o
o mula e he cu en esponse o diffe en ypes o kine ic mea-
su emen s, such as ol age scan a a cons an a e, and sudden
connec ion. Ou me hod is o inco po a e he diffusion o ions in
he e ical di ec ion in a ansmission line o malism so ha we
can de e mine diffe en kine ic imes cons an s ha go e n he
cha ging and discha ging o he channel owa d he s eady-s a e
si ua ion, and he co esponden hys e esis phenomena.
Below we apply he model in es iga ion o he main hys e esis
effec s in bo h accumula ion and deple ion semiconduc o s.[27]
We also explo e he ealis ic ansien cu en and hys e esis e -
ec s using a 2D d i -diffusion simula ion model, ha akes in o
accoun he ionic dis ibu ion and diffusion bo h in he o ganic
film and he elec oly e.[33–37]Fu he mo e we show some cha ac-
e is ic expe imen al esul s o a poly(3-hexyl hiophene) (P3HT)
OECT, wo king in an accumula ion mode. These esul s p o ide
a consis en pic u e o he in e ac ion o ionic and elec onic e -
ec s ha go e n he majo hys e esis effec s obse ed in OECTs.
The simula ion allows one o explo e diffe en condi ions o inho-
mogenei y, and a new mechanism is iden ified whe e he chan-
nel cu en ollows he build-up o he anion densi y a he solu-
ion/semiconduc o in e ace.
2. Model
2.1. Geome y o he Model and Ca ie Dis ibu ion
The model shown in Figu e 1aconside s a ho izon al channel in
di ec ion x ha spans om 0 o x=L, wi h ho izon al cu en
Ad . Sci. 2024,11, 2404182 2404182 (2 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
Ihand local ol age uh. The e ical di ec ion in he channel is y.
No e ha cu en exi ing he d ain a x=Lis conside ed posi i e.
I zis he effec i e ca ion densi y, hen by local elec oneu al-
i y, he local hole densi y is
p=p0−z(1)
whe e p0in an in insic densi y due o doping. The densi y zde-
pends on he concen a ions o in e cala ed ca ions mand anions
a
z=m−a(2)
Ina olumeelemen o leng hdx he in e ace wi h he elec-
oly e is a y=d. We define an a e age concen a ion pe uni
ho izon al dis ance by he e ical in eg a ion o Equa ions (1)
and (2)
Z=w
d
∫
0
zdy=w
d
∫
0
mdy−w
d
∫
0
ady (3)
Hence
Z=M−A(4)
and he hole densi y is
P=w
d
∫
0
pdy=P0−Z(5)
An equilib ium concen a ion o ions
Zeq =Z(ug)(6)
is ob ained when he film is cha ged homogeneously a he ga e
po en ial ug. This unc ion can be ob ained by elec ochemical
me hods o a gi en ype o film[38–42]as commen ed in Sec-
ion 2.4.
Two diffe en OECTs ope a ion modes a e called deple ion and
accumula ion.[27]In accumula ion, he de ice is no mally OFF in
he absence o a ga e bias (i.e., he semiconduc ing polyme is
ini ially in i s neu al s age). In deple ion, he ac i e ma e ial in
he channel is ini ially doped and he OECT is na u ally in i s ON
s a e and is u ned OFF upon applica ion o a ga e ol age (dedop-
ing o he channel). Below we conside wo ypes o si ua ions:
i. In accumula ion (undoped semiconduc o ) P0=0, Z=−
A,P=A.
ii. In deple ion (doped semiconduc o ) A=0, Z=M,P=
P0−M.
2.2. Defini ion o Cu en s
The a ge measu emen we wish o desc ibe is he ansien
d ain cu en wi h espec o a s ep o ga e ol age indica ed in
Figu e 1b. We conside he p ope ies o cu en s in he channel
film.
The ho izon al flux o hole ca ie s is gi en by he d i ans-
po in he elec ical field
Jh(x, y)=−p(x, y)𝜇p
duh
dx (7)
He e μpis he mobili y. Mo e gene al anspo condi ions ha e
been in es iga ed,[43]bu he e we use he s anda d app oach. The
ho izon al cu en is
Ih(x)=qw
d
∫
0
Jh(x, y)dy (8)
whe e qis he elemen a y cha ge. The e o e
Ih(x)=−qP (x)𝜇p
duh
dx (9)
In Equa ion (9) he model is es ic ed o si ua ions in which
he e ical g adien o uhis no la ge.
The cu en ac oss he op in e ace o he olume elemen is
exclusi ely ionic. An ou wa d flux o posi i e ions Jm
and nega i e
ions Ja
p oduces a e ical cu en dI due o he a ea wdx,o
alue
dI (x)=qw(Jm
(x, d)−Ja
(x, d))dx (10)
The cu en conse a ion in he olume elemen o Figu e 1a
is
Ih(x+dx)−Ih(x)+dI (x)=0 (11)
The e o e
𝜕Ih
𝜕xdx =−qw [Jm
(x, d)−Ja
(x, d)]dx (12)
The simple applica ion o Ki chhoff’s ules p oduces he wo
classical equa ions o a ansmission line model, (10)and(12).[44]
This app oach has been de eloped in field-effec ansis o s[23]
and in OECT.[24–27]
The model equi es a comple ion by s a ing he e ical flux,
J . The flux depends on he ol age in he elec oly e jus ou side
he in e ace, ha is he ga e ol age ug, and on he ol age inside
he film, uh. This is de eloped in Sec ion 2.5.
2.3. Capaci i e Coupling
In he p e ious heo ies o OECTs he ion concen a ion inside
he film zis coupled capaci i ely o he ol age diffe ence ac oss
he in e ace. The o al ionic cha ge is qwddxz. Conside ing he
double-laye capaci ance pe uni a ea in he op su ace, cd,we
ha e[26,29,31]
qdz(x)wdx=cd(ug−uh(x))wdx (13)
In s eady s a e, he ho izon al cu en is cons an , Ih(x)=Ids.
The d ain-sou ce ol age is
uds =uh(L)−uh(0)(14)
Ad . Sci. 2024,11, 2404182 2404182 (3 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
and he in eg a ion o Equa ion (9)gi es
Ids =−
qdw𝜇
L[p0−cd
qd (ug−1
2uds)]uds (15)
This is a s anda d esul .[29,30]La e , i was disco e ed[19,30,45]
ha in OECT he capaci ance cdshows a co ela ion wi h leng h.
Then he olume capaci ance
c∗=cd
d(16)
is he cons an quan i y, since he ions fill he whole elemen in
Figu e 1a. This obse a ion leads one o conside he ela ed ideas
o ion in e cala ion in ba e y and elec och omic ma e ials[46–48]
and in conduc ing polyme s,[39,40] ha ha e been b oadly in es-
iga ed. Bu hen, a diffe en o malism han Equa ion (13)is e-
qui ed o accoun o he in e cala ion o ions om he elec oly e,
based on he ion diffusion concep .[49]Diffusion i sel gene a es
a chemical capaci ance due o he in e cala ion p ocess,[50–53]so
ha he capaci i e effec a ises na u ally.
2.4. The Chemical Capaci ance and he The modynamic
Equilib ium Func ions
As a p elimina y s ep o he gene aliza ion o he channel dynam-
ics including ionic diffusion, i is impo an o ema k on he
idea o he chemical capaci ance, ha appea s in he diffusion
anspo .[54]The chemical capaci ance o a species[50,51,53]is ob-
ained by he de i a i e o he he modynamical unc ion o he
densi y wi h espec o he elec ochemical po en ial. Fo he ions
in he o ganic film
c𝜇=qdZeq
dug
(17)
This equa ion exp esses he olume capaci ance c* men ioned
in (16) in he mo e gene al denomina ion o he chemical ca-
paci ance cμ ha is measu ed in he elec ochemis y o o ganic
conduc o s.[55–57]The bulk o igin o he ionic capaci ance is well
es ablished in o ganic films.[58]Fu he mo e, i is ob ained a
ela ion o he chemical capaci ance and he densi y o s a es
(DOS) g,[56,57]as ollows
c𝜇=qg(qug)(18)
The e o e, he chemical capaci ance gi es a di ec measu e o
he DOS. I also p o ides a figu e o me i o OECT.[45]
Fo an anion densi y ha dec eases a inc easing ug he chem-
ical capaci ance is
c𝜇=−qdAeq
dug
(19)
The sign in Equa ion (19) is due o he ac ha when he po-
en ial ugbecomes mo e nega i e, he concen a ion o anions
inc eases, so ha cμis posi i e.
Many o ms o Zeq(ug) a e possible acco ding o he p ope ies
o he o ganic film.[41,42,46,47,55,59,60]In cohe ence wi h he d i -
diffusion simula ions desc ibed la e , he e we use he densi y o
s a es (DOS) o inse ed anions
ga(qug)=− dAeq
d(qug)=A0
kBT[q(u −ug)
kBT]1∕2
(20)
The kBis he Bol zmann’s cons an , T he absolu e empe a-
u e, u he alence edge po en ial, A0a densi y pe leng h, om
he olume densi y a0=A0/wd. This is he DOS used o holes in
he simula ions below, which by elec oneu ali y applies o ions
as well. Acco dingly, he he modynamic unc ion is
Aeq (ug)=−
u
∫
ug
ga(x)dx =2
3A0[q(u −ug)
kBT]3∕2
(21)
Fo inse ion o ca ions
gm(qug)=− dMeq
d(qug)=M0
kBT[q(ug−uc)
kBT]1∕2
(22)
M0is a densi y pe leng h, om he olume densi y m0=
M0/wd. Fo a ca ion densi y ha inc eases a inc easing ug he
chemical capaci ance
c𝜇=qdMeq
dug
(23)
is posi i e.
The he modynamic unc ion is
Meq (ug)=−
ug
∫
uc
gm(x)dx =2
3M0[q(ug−uc)
kBT]3∕2
(24)
The gene al conclusions on ime ansien and hys e esis
de i ed below a e no dependen on he specific exp essions
Aeq,Meq, p o ided ha hese unc ions a e such ha he chem-
ical capaci ances emain posi i e.
2.5. Diffusion o In e cala ed Ions
He e we aim o in oduce he diffusion dynamics ha ha e ap-
plica ions o solid-s a e o elec ochemical ionic diffusion in o -
ganic and ino ganic ma e ials.[11,12]This analysis depa s om
he p e ious ea men s in he li e a u e based on Equa ion (13),
The diffusion o ions in he film is desc ibed by he conse a-
ion equa ion
𝜕z
𝜕 =−
𝜕J
𝜕y(25)
Ad . Sci. 2024,11, 2404182 2404182 (4 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
and he Fick’s law ha s a es ha he ion flux is p opo ional o
he ion diffusion coefficien Dion and he g adien o he concen-
a ion
J =−Dion
𝜕z
𝜕y(26)
Conside ing ha he bo om laye in Figu e 1a is blocking ions,
J (y=0) =0, he in eg al o (25)gi es
w
d
∫
0
𝜕z
𝜕 dy =−wJ (x, d)(27)
𝜕Z
𝜕 =−wJ (x)(28)
This las equa ion inco po a es he assump ion ha he ionic
cha ge e ically injec ed is compensa ed by he elec onic cha ge
o he opposi e sign om he immedia e su oundings. This is
he uni e sal assump ion used in in e cala ion sys ems such as
Li-ion ba e ies, ha a e desc ibed by he ion diffusion a e a he
bounda y wi h he elec oly e.[61]Howe e , his assump ion e-
qui es ha he dielec ic elaxa ion ime is sho , which occu s
when sufficien elec onic conduc i i y is a ailable. In mo e de-
ailed ea men s one should conside he coupling o ionic and
elec onic local cu en s[62,63]as u he discussed in Sec ion 3.3
and 6.3.
The conse a ion equa ion o ca ions and anions gi es he e-
sul s
wJm
(x)=−
𝜕M
𝜕 (29)
wJa
(x)=−
𝜕A
𝜕 (30)
F om Equa ions (9)and(12) he equa ions o he ansmission
linemodelcanbes a ed
Ih(x)=−q(P0−M+A)𝜇p
duh
dx (31)
𝜕Ih
𝜕x=q(𝜕M
𝜕 −𝜕A
𝜕 )(32)
2.6. Cu en and Elec onic T ansi Time
Fo a small uds ha p oduces a uni o m elec ical field, he cu en
(30) can be w i en
Ih(x)=−q𝜇p
uds
L(P0−M(x)+A(x))(33)
By in eg a ion o Equa ion (32) we ob ain
Ih(L)−Ih(0)=q
L
∫
0(𝜕M
𝜕 −𝜕A
𝜕 )dx (34)
We define d ain and sou ce cu en as
Is=Ih(0)(35)
Id=Ih(L)(36)
D ain and sou ce cu en s a e no equal in he ansien condi-
ion, due o he cha ging by he e ical cu en o in e cala ion,
as shown in Figu e 1c,d.
To confi m he in e p e a ion o signs o Equa ion (34)con-
side an elec onically blocking sou ce con ac , Ih(0) =0. We in-
jec a pulse o anions and Equa ion (34)gi es
Ih(L)=−q
L
∫
0(𝜕A
𝜕 )dx (blocking sou ce)(37)
I we inc ease he concen a ion o anions, by mo e nega i e
ug, hen ∂A/∂ >0, hence he cu en (37) is nega i e, as holes
en e he film om he igh side in Figu e 1c.
Le us define he sign o he ol age d op as
𝜃=uds
||uds||
(38)
The wo cases 𝜃±1 ha we desc ibe in he ollowing a e indi-
ca ed in Figu e 1c,d. The s anda d ope a ion o a p- ype ansis o
co esponds o uds <0o 𝜃=−1, as he hole ca ie s a e in-
jec ed om he sou ce o he channel (Idis posi i e). S udying
bo h signs o 𝜃, wi hin he scope o his model, is equi alen o
s udying bo h he d ain (𝜃=−1) and sou ce (𝜃=+1) cu -
en s, which is mos impo an o ansien s udies, as hey can
be sepa a ely measu ed and ha e dis inc beha io s.[23,64]
We in oduce he elec onic ansi ime along he channel
leng h[29]
𝜏e=L2
𝜇p||uds||
(39)
The cu en (33) is exp essed
Ih(x)=−𝜃qL
𝜏e(P0−M(x)+A(x))(40)
2.7. A Simple Solu ion: Be na d–Mallia as Model o he
Undoped Si ua ion
Assume an undoped sample in which he hole densi y is due o
in e cala ed anions A. To ob ain a unc ional model o he an-
sien cu en s, a solu ion o Equa ions (32)and(40)mus beob-
ained. We can combine hese equa ions as
𝜕A
𝜕x=𝜃𝜏e
L
𝜕A
𝜕 (41)
and we ob ain he in eg al
A(L)−A(0)=𝜃𝜏e
L
L
∫
0
𝜕A
𝜕 dx (42)
We allow o holes o be injec ed om bo h con ac s
(Figu e 1c). To ob ain he sou ce and d ain cu en s by Equa-
ions (35), (36)and(40), he sepa a e A(L), A(0) a e needed.
Ad . Sci. 2024,11, 2404182 2404182 (5 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
Following Be na d and Mallia as[29]we spli he le -hand side
o (42) in o wo diffe en pa s, by he ac ional cons an 0 <
<1
A(L)=Aa +𝜃 𝜏e
L
L
∫
0
𝜕A
𝜕 dx =Aa +𝜃 𝜏e
𝜕Aa
𝜕 (43)
A(0)=Aa +𝜃(1− )𝜏e
L
L
∫
0
𝜕A
𝜕 dx =Aa +𝜃(1− )𝜏e
𝜕Aa
𝜕 (44)
The Aa is an a e age concen a ion aken by a sui able p oce-
du e. Diffe en in eg a ion schemes[24,65,66] o jus i y he alue o
a e summa ized in e . [19] Remo ing he subsc ip a , he d ain
cu en in (36)is
Ih(L)=−𝜃qL
𝜏e
A−q LdA
d (45)
We no e ha he Be na ds-Mallia as Equa ion (45) is a s a e-
men o he cu en conse a ion in he film, by di iding Equa-
ion (34) in o wo sepa a e pa s.
2.8. Doped Semiconduc o
We ake he case A=0, Z=M,P=P0−M. By simila calcu-
la ions as be o e
Ih=−𝜃qL
𝜏e(P0−M)(46)
𝜕M
𝜕x=𝜃𝜏e
L
𝜕M
𝜕 (47)
Ih(L)=−𝜃qL
𝜏e(P0−M)+q LdM
d (48)
I a pulse ∂M/∂ >0 is injec ed a posi i e hole cu en Id=
q L∂M/∂ >0 has o lea e he channel.
2.9. Local Diffusion Effec
In addi ion o he cu en conse a ion, i mus be s a ed how he
Ae ol es wi h ime, which is no gi en by Equa ion (45). The p e-
ious models p oposed in he li e a u e, based on Equa ion (45),
ha e no conside ed explici ly he ion diffusion p ocess. Fo a
igo ous solu ion, one can sol e Equa ion (12) coupled o Equa-
ion (25). This is a complex p oblem ha will gene a e ano he
( e ical) ansmission line a each poin x.[67]
To ob ain a physically meaning ul bu app oxima ed solu ion,
we ha e sugges ed[32] ha he bounda y flux is gi en by a g a-
dien o concen a ion associa ed wi h diffe en elec ochemical
po en ials o he olume elemen o Figu e 1a, om he bo om
uh o he op ug.Then
Ja
(x, d)=−Dion
𝜕a
𝜕y≈DX
d[a(uh)−a(ug)] (49)
The e o e
𝜕A
𝜕 =Dion
d2[A(ug)−A(uh)] (50)
We define he ansi ime o diffusion
𝜏d=d2
Dion
(51)
Using he no ion ha he chemical capaci ance is cha ged by
a diffusion cu en , we can exp ess Equa ion (29)as
𝜕A
𝜕 =1
𝜏d(Aeq (ug)−A(uh)) (52)
Equa ions (45)and(52) a e he model in oduced in e . [32]
ha he e has been igo ously jus ified.
Simila ly o he inse ion o ca ions
𝜕M
𝜕 =1
𝜏d(Meq (ug)−M(uh)) (53)
No e ha he diffusion o ions in Equa ion (49) equi esaflow
o compensa ing holes. I he ime associa ed wi h hole compen-
sa ion is 𝜏 hen i is equi ed ha 𝜏 ≪𝜏d, as commen ed ea lie ,
o sa is y he elec oneu ali y condi ion. I only a e ical flow is
needed o he cha ge compensa ion hen
𝜏 =d2
𝜇p(ug−uh)(54)
Based on he gene al ansmission line app oach o Equa-
ions (9)and(12) one can add diffe en effec s ha influence
he ansien beha io , o example, a dis ibu ed in e acial ca-
paci ance as Equa ion (13)[24,68]and a se ies esis ance in he
elec oly e.[25]These imp o emen s a e commen ed on in Sec-
ion 3.3. The ealis ic 2D flows o cha ge will be discussed in he
simula ions in Sec ion 6.
3. T ansien Swi ching Dynamics
We s a he s udy o ansien beha io based on he model
o Equa ions (45, 52).[32]Le us summa ize he s uc u e o he
model. We conside an accumula ion semiconduc o , P0=M=
0, o a uds small ol age, in which A(x, ) is nea ly homogeneous,
wi h equilib ium unc ion Aeq gi eninEqua ion(20). In he s a-
iona y dc cu en he ca ion densi y ob ains he alue o equilib-
ium acco ding o he ga e ol age Aeq(ug). As men ioned be o e
he ol age applied o he ga e is ug. The ol age in he channel is
uh. The model o any ime-dependen si ua ion consis s on wo
equa ions o he h ee a iables Id,ug,A.
Id=−𝜃qL
𝜏e
A−qL dA
d (55)
𝜏d
dA
d =Aeq (ug)−A(56)
He e he concen a ion Acan be ega ded as A(uh), a unique
unc ion o he inne po en ial.
Ad . Sci. 2024,11, 2404182 2404182 (6 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
3.1. The Linea Equa ions o a Small Pe u ba ion
The p ope ies o swi ching will be in es iga ed by a small s ep
o he ex e nal ol age ΔVa =0 ha changes he ga e ol age
om an ini ial alue ug0
ug=ug0+ΔV(57)
The in e nal ol age in he film changes as
uh( )=ug0+Δ ( )(58)
whe e Δ ( =0) =0andΔ ( =∞)=ΔV. Conside ing he
chemical capaci ance o Equa ion (18), he change o he ion den-
si ies in Equa ions (55)and(56)is
A(ug0+Δ , )=Aeq (ug0)−c𝜇
qΔ ( )(59)
Aeq (ug0+ΔV)=Aeq (ug0)−c𝜇
qΔV(60)
Thus Equa ion (56) akes he o m
𝜏d
dΔ
d =ΔV−Δ (61)
The o al s ep o he cu en is
Ifin =Iin +𝜃c𝜇L
𝜏e
ΔV(62)
Iin =−𝜃qL
𝜏e
Aeq (ug0)(63)
wi h Ifin and Iin being he final and ini ial cu en s. The o al quan-
i y o elec onic cha ge
ΔQ=𝜃Lc𝜇ΔV(64)
en e s he channel o he new equilib ium si ua ion.
Now he ime-dependen cu en o Equa ion (55) can be ex-
p essed
Id=−𝜃qL
𝜏e
Aeq (ug0)+𝜃Lc𝜇
1
𝜏e
Δ +Lc𝜇 d(Δ )
d (65)
And using Equa ion (61)weha e
Id=−𝜃qL
𝜏e
Aeq (ug0)+𝜃Lc𝜇
1
𝜏e
Δ +Lc𝜇 1
𝜏d
(ΔV−Δ )(66)
The ansien cu en is composed o wo pa s. The second
e m co esponds o he ho izon al anspo o he injec ed
cha ge. The hi d e m is he compensa ion o he e ical injec-
ion o he cha ge. Bo h e ms, when combined, injec he o al
cha ge (64).
Le us w i e he Equa ion (66)in he o m
Id=−𝜃qL
𝜏e
Aeq (ug0)+Lc𝜇 1
𝜏d
ΔV+Lc𝜇(𝜃
𝜏e
−
𝜏d)Δ (67)
We ema k ha he cu en s ep a he fi s ins an is
ΔId( =0)=+Lc𝜇 1
𝜏d
ΔV(68)
We can analyze hese effec s by using he explici dependence
on ime. Equa ion (61)gi es
Δ =ΔV(1−e− ∕𝜏d)(69)
The e o e
Id( )=−𝜃qL
𝜏e
Aeq (ug0)+Lc𝜇 1
𝜏d
ΔV
+Lc𝜇(𝜃
𝜏e
−
𝜏d)ΔV(1−e− ∕𝜏d)(70)
In Figu e 2we show he ansien esponse o he pa ame e s
ou lined in Table 1. The e a e ou diffe en cases, dis inguished
by 𝜏e<𝜏
do ice e sa, and also by he sign o he cu en
𝜃, ha makes he s ep ei he inc ease o dec ease he cu en
in he final s a e. The ini ial alue o he ansien cu en is
only dependen on ΔV/𝜏d,byEqua ion(68). The cha ac e is ic
ime o he ansien is he e ical ion diffusion ime 𝜏d.This
is shown in se e al cases in Figu e 3. The final alue o he
cu en only depends on 𝜏e,Equa ion(62). The a ea o he cu e
co esponds o (64), so ha in Figu e 3 he spike is highe o
sho e cha ging ime 𝜏d.I 𝜏e<𝜏
d, Figu e 2g, he ini ial spike
is smalle han he equilib ium cu en , hence he cu en does
no make a spike bu inc eases since he fi s ins an .[29]In
he ansi ion be ween Figu es 2e and 2g, he ansien almos
anishes, as ema ked in e . [24].
3.2. Doped Semiconduc o
He e A=0, Z=M,P=P0−M. The equa ions o he gene al
ansien beha io a e
Ih(L)=−𝜃qL
𝜏e(P0−M)+q LdM
d (71)
𝜏d
dM
d =Meq (ug)−M(72)
Fo a small ol age s ep, ΔV he in e nal ol age in he film
changes as
uh( )=ug0+Δ ( )(73)
The o al s ep o he cu en is
Ifin =Iin +𝜃c𝜇L
𝜏e
ΔV(74)
He e Iin is he ini ial cu en ,
Iin =−𝜃qL
𝜏e(P0−Meq)(75)
Ad . Sci. 2024,11, 2404182 2404182 (7 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
Figu e 2. Undoped semiconduc o . a) Equilib ium anion densi y in he film. The s a iona y cu en b,c) acco ding o he sign 𝜃=uds /|uds| and (d-g) he
possible ou diffe en ypes o ansien esponse wi h espec o ime, o a s ep ol age a V0=−0.5 Vand ΔV=0.1 Va 0=0.5 ms. The b own
line is an immedia e cu en esponse. We ake he pa ame e s o Table 1,𝜏e=0.5 ms, a0=6.2 ×1018 cm−3,A0=6.2 ×1012 m−1,u =0, =0.5
and 𝜏das indica ed.
Ad . Sci. 2024,11, 2404182 2404182 (8 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
Table 1. Pa ame e s used in he simula ions.
Channel leng h L50 μm
hickness d100 nm
wid h w10 μm
Hole mobili y μp0.02 cm2Vs−1
Sou ce-d ain ol age |uds| 0.1 V
The mal ene gy kBT0.026 V
The ime-dependen cu en is
Id=−𝜃qL
𝜏e(P0−M(ug0))+𝜃Lc𝜇
1
𝜏e
Δ + Lc𝜇
d(Δ )
d (76)
This can be w i en
Id=−𝜃qL
𝜏e(P0−M(ug0))+ Lc𝜇
1
𝜏d
ΔV+Lc𝜇(𝜃
𝜏e
−
𝜏d)Δ
(77)
The e o e
Id( )=−𝜃qL
𝜏e(P0−M(ug0))+ Lc𝜇
1
𝜏d
ΔV
+Lc𝜇(𝜃
𝜏e
−
𝜏d)ΔV(1−e− ∕𝜏d)(78)
The ini ial s ep is again gi en by Equa ion (68)
The ou possible ypes o decays a e shown in Figu e 4.Fo a
be e compa ison o doped and undoped cases, we se he DOS
pa ame e uc=−1 V so ha Id=0 a he o igin. The deple ion
case is ob ained by shi ing he cu es o he igh by uc=0V.
3.3. In e p e a ion o T ansien s
Figu e 1b summa izes he model ha we ha e de eloped. The
measu emen consis s o applying a ol age pulse o he ga e
Figu e 3. Swi ching ansien s o an undoped semiconduc o , same as in
Figu e 2 o se e al alues o 𝜏d.
and eco ding he cu en ex ac ed a he d ain con ac , while
bo h ga e ol age and d ain cu en a e measu ed wi h espec o
he sou ce elec ode.[66,69]O cou se, he physical si ua ion can
be complica ed in se e al espec s, compa ed o he simplified
analy ical model, which has o be cla ified expe imen ally. This
is ou lined in Figu e 5a. The en ance o ions ins iga ed by he
change o ga e ol age induces he up ake o holes om S and D
elec odes. A complex pa e n o cu en s is o med, in which
1) The cu en o each ca ie can be domina ed by ei he d i
o diffusion.
2) The ca ie s a e coupled by local elec oneu ali y, wi h he
cha ge diffe ence esul ing in elec ical fields acco ding o he
Poisson equa ion.
3) Which species is mo ing p edominan ly, is de e mined by he
local conduc i i ies. I can be ei he elec ons o holes, caus-
ing diagonal cu en s as in Figu e 5a.
These ques ions ha e been amply s udied in he elec ochem-
is y o conduc ing polyme s,[70]and applying mul iple ca ie
ansmission lines.[70,71]In he OECTs he e could be a limi ing
ho izon al anspo o ions, o e ical anspo o holes, as men-
ioned in Equa ion (54).[18,43,72,73]The implica ions o b eaking
quasineu ali y a e discussed in Sec ion 6.3.
Despi e he complexi y o hese anspo p ocesses, we ha e
p o ided a solu ion o he p oblem o he ansien as ou lined
in Figu e 1c,d. This app oach is based on he combina ion o
Be na ds-Mallia as simplifica ion o he ansien conse a ion
equa ion, and he analysis o ion diffusion. The model hus con-
side s explici ly he in e io o he channel. We summa ize he
p ope ies o he model in he ollowing, and in Sec ion 6 he
mo e gene al ealis ic anspo will be conside ed, based on d i -
diffusion simula ions.
Fi s , we adop a sepa a ion o wo o hogonal cu en s, acco d-
ing o he p incipal na u e o he elec odes: D and S a e selec i e
o elec ons, while he op su ace o he channel is selec i e o
ions. The e o e, he e ical cu en is an ionic cu en assuming
ha he e ical elec onic cu en s can be neglec ed. While he
ho izon al cu en along he channel is elec onic.
When he ΔVgpulse is applied, i induces a a ia ion o he in-
e nal ol age uh, as indica ed in Equa ion (61). Consequen ly, we
ob ain a solu ion uh( ) ha kine ically depends only on he e ical
cu en , which in he model is defined by he ion diffusion effec .
This is gi en in Equa ion (69). The ansien du a ion depends
only on 𝜏d. This condi ion needs o be ex ended i he e a e addi-
ional elemen s in he e ical pa hway, as in Figu e 5b.Weshow
a se ies elemen o impedance Zs ha will ha e a capaci i e and
esis i e componen , e.g., a dis ibu ed in e acial capaci ance as
Equa ion (13),[24,68]and a se ies o cha ge ans e esis ance.[25]
The[24]su ace ol age is usand he cu en in he elec oly e is de-
e mined by he o e all impedance Zsand he po en ial diffe ence
(ug−us). These ex e nal elemen s can ul ima ely influence he
elaxa ion ime. This issue equi es a de ailed s udy ha will be
p esen ed elsewhe e. We ha e al eady ema ked ha a special so-
lu ion exis s in which he las e m o Equa ion (78) anishes,
[24]
which is an excep ion o he ansien being gene ally con olled
by he diffusion cha ac e is ic ime 𝜏d.
In esponse o ΔVgpulse, he Idcu en unde goes a a ia ion,
as i is ully modula ed by uh,Equa ion(55). We hus ob ain he
Ad . Sci. 2024,11, 2404182 2404182 (9 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
Figu e 13. The simula ed de ice s uc u e con aining he pa ame e s o a P-doped (1020cm−3) de ice. a) Ca ion densi y b) Hole densi y. Vgs =0V,
Vds =0.1 V, W =L=50 μm.
As seen in Figu e 11, a ela i ely low and low Vds, he hys e e-
sis exhibi s a capaci i e pa e n. A a fixed Vds, he capaci i e hys-
e esis swi ches o induc i e hys e esis a highe .WhenV
ds is
main ained a 50 mV, he swi ch be ween ypes o hys e esis was
obse ed a =62 mV s−1,anda
=120 mV s−1, he hys e esis
was p edominan ly induc i e.
Fo 𝜃=−1, he inc ease in scan a e does no lead o a change
in he hys e esis ype (see Figu e 12). An inc ease was only ob-
se ed in he hys e esis s eng h and a dec ease in he o e all
cu en le el by inc easing , which was consis en wi h he he-
o e ical model (Figu e 6d).
In addi ion, he ans e cu es o P3HT OECT we e mea-
su ed using an o ganic-based elec oly e. The elec oly e used
was po assium hexafluo ophospha e (F6KP) in ace oni ile.
Ace oni ile was chosen because i swells P3HT mo e effec i ely
han wa e , acili a ing he injec ion o anions. Addi ionally,
hexafluo ophospha e anions [PF6]−efficien ly pene a e he
P3HT bulk.[81]
As he case wi h KCl aqueous solu ion, he hys e esis ype o
he ans e cu e in OECT wi h he F6KP ace oni ile elec oly e
depends on he sign o 𝜃and he alue o he d ain bias. A
posi i e 𝜃and ela i ely low Vds o +50 mV, he hys e esis
Ad . Sci. 2024,11, 2404182 2404182 (16 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
Figu e 14. Cu en (blue), hole (g een), and ion (o ange) densi y as a unc ion o he ga e ol age. a) doped semiconduc o . b) undoped semiconduc o .
The dashed-do ed and he dashed black lines ma k he ol age a which he low ion-densi y and high ion-densi y ime-dependen esponses a e e alua ed.
o he ans e cu e was induc i e (Figu e S2a, Suppo ing
In o ma ion). When Vds inc eases, he hys e esis ype swi ches
o he capaci i e pa e n (Figu e S2b, Suppo ing In o ma ion).
Con e sely, a nega i e 𝜃and ela i ely low Vds o −50 mV,
he hys e esis was capaci i e. E en a a mo e nega i e Vds o
−200 mV, he hys e esis emains p edominan ly capaci i e.
5.3. Discussion o Expe imen al Resul s
The analysis o he ans e cu es e ealed hys e esis phenom-
ena consis en wi h he model o he p eceding sec ions. How-
e e , as al eady discussed, he model was based on he assump-
ion o limi a ion by ion diffusion kine ics, while in gene al o he
possibili ies exis , as commen ed in Figu e 5b. To ob ain he phys-
ical o igin o he obse ed hys e esis effec s, a mo e ex ensi e in-
es iga ion was needed, ha add esses he ansien cu en s in
combina ion wi h hys e esis. This s udy was beyond he scope o
he p esen pape . Such a mo e gene al s udy can also p o ide
insigh in o he de e mina ion o he ac o . In Equa ion (70)
influences some e ms o he ansien cu en , hus a de ailed ki-
ne ic analysis o he diffe en cha ac e is ic imes in he sys emis
needed.
Figu e 15. T ansien esponse o he d ain cu en (Vds =0.1 V) o a small s ep in he ga e ol age a e being s abilized a he bias ma ked wi h dashed-
do ed lines in Figu e 14. a–c) P-doped (1020 cm−3) semiconduc o . d– ) Undoped semiconduc o . a,d) d ain cu en . b,e) sou ce cu en . c, ) d ain
cu en and sou ce cu en imes −1.
Ad . Sci. 2024,11, 2404182 2404182 (17 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
Figu e 16. T ansien esponse o he d ain cu en (Vds =0.025 V) o a small s ep in he ga e ol age a e being s abilized a he bias ma ked wi h
dashed-do ed lines in Figu e 14. a–c) P-doped (1020 cm−3) semiconduc o . d– ) Undoped semiconduc o . a,d) d ain cu en . b,e) sou ce cu en . c, )
d ain cu en and sou ce cu en imes −1.
6. Simula ion o T ansien s and he Rela ed
Hys e esis
The pu pose o his Sec ion is o b idge be ween he elec o-
chemical model and expe imen al da a using a de ice simula ion
ha can include many de ails o he de ice s uc u e. We s a
wi h a simula ion ha aligns wi h he chemical physics pic u e
used by he elec ochemical model. In e ms o he 2D de ice
simula ions,[35] hese ansla e o he ollowing:
1) The elec oly e ac s as an infini e supply o ions. We se i s
hickness o 200 μm.
2) The elec oly e p esen s no se ial esis ance. We se he ions’
diffusion coefficien in he solu ion a leas six o de s o mag-
ni udes abo e ha o he diffusion in he 100 nm hick semi-
conduc o .
3) The e is no ol age d op a he ga e elec ode in e ace. The
ga e is ohmic o anions, and he anions densi y a he ga e
in e ace is se o i s alue in he solu ion. The con ac ac s as
a eflec ing mi o (non eac ing) o he ca ions.
4) The ionic double-laye capaci ance (Cdl) a he sou ce and
d ain elec odes is negligible. We se he effec i e double-laye
hickness a 0.2 nm (i.e., a eal capaci ance is ≈10−5Fcm
−2),
and he con ac o e lap wi h he semiconduc o (Lc)iskep
well below 1 μm.
5) To a oid con ac -limi ed injec ion, he sou ce and d ain con-
ac ba ie s a e se low enough such ha he hole’s cu en
is no educed due o he sho o e lap (100 nm).[82]
6) When he ions en e he semiconduc o , hey do no c ea e a
space cha ge ha would impede hei diffusion in o he film.
To ensu e a as supply esponse o he compensa ing holes,
we se hei mobili y a 5 cm2V−1s−1(Fo L =50 μmand
Vds =0.1 V i esul s in e=0.05 ms).
7) The mu ual a ac ion, h ough he Poisson equa ion, does
no affec he dynamics. The dynamic esponse is e alua ed
a low ion densi ies (<1018 cm−3) whe e he a ac ion is low.
Figu e 13 shows he simula ed de ice s uc u e
(w =L=50 μm), on op o which a e esul s om a simu-
la ion o a p-doped semiconduc o (1020 cm−3) and an elec oly e
ion concen a ion o 1018 cm−3(≈2 millimola ). No e ha he
choice o coo dina es in Figu e 13 implies ha o ud<us, he
cu en is posi i e. Figu e 13a,b show he ca ion a) and hole
b) densi y dis ibu ion unde bias condi ions o Vgs =0and
Vds =0.1 V. The hole and ca ion dis ibu ion shown in Figu e 13
ag ee wi h p e iously epo ed simula ion esul s. To ollow he
no a ion o he elec ochemical model, he Ids a e posi i e he e.
Figu e 14 shows he s eady-s a e cu en – ol age (blue line) e-
sponse o de ices based on doped a) and undoped b) semiconduc-
o s. The a e age densi y o he hole (g een line) and ions (o ange
line) in he semiconduc o a e plo ed on he igh axis. Fo he P-
doped (1020 cm−3) de ice, we no e ha he hole densi y is a mi o
image o he anion densi y ollowing holes =doping–anions. Fo
he undoped semiconduc o (Figu e 14b), he holes, ca ions, and
he cu en ha e a pe ec ly o e lapping shape. Hence, we ook
he oppo uni y and plo ed he cha ge densi ies on a log scale.
Ad . Sci. 2024,11, 2404182 2404182 (18 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
Figu e 17. The d ain (le ) and sou ce ( igh ) cu en s’ hys e esis esponse o a ol age sweep in he ga e ol age a e being s abilized a he ini ial
bias (Vgs =0.5 V) and o se e al d ain-sou ce ol ages (see Figu e). a,b) The semiconduc o is undoped, and he sweep speed is 0.05/ d. c,d) The
semiconduc o is undoped bu wi h esidual P doping o 1016 cm−3, and he sweep speed is 0.02/ d.
In he ollowing sec ions, we will p esen ansien esponses
in wo egimes. The fi s is he egime whe e he ion densi y
wi hin he semiconduc o is low (<1018 cm−3), and we ma k he
ele an wo king poin s wi h dashed-do ed lines in Figu e 14.
The second egime is o high ion densi y (>1019 cm−3) wi h
he ele an wo king poin ma ked by a dashed line. Figu e 14b
shows ha he cu en ises o ga e-sou ce bias below −0.2 V
while he a e age hole densi y seems fixed. As epo ed in e .
[36] his is he signa u e o he hin hole channel gene a ed by
anions accumula ion a he semiconduc o in e ace.
6.1. T ansien Response a Low Ion Densi y
To es o ag eemen be ween he semiconduc o de ice simula-
ions and he elec ochemical model, we pe o med a ansien
esponse analysis a bias le els whe e he ion’s densi y is low
(dashed-do ed lines in Figu e 14). To ensu e ha he densi ies
s ay low h oughou he esponse, we pe o med a small signal
analysis using a +30 mV s ep ol age a =0. Figu e 15 shows he
ansien esponse o de ices based on P-doped ( op aw) and
undoped (bo om aw) semiconduc o s. The le column shows
he d ain cu en (𝜃=1) and he middle one shows he sou ce
cu en (𝜃=−1). We used hole mobili y o μh=5cm2V−1s−1
(𝜏e=0.05ms) and ion diffusion cons an o D =10−6cm2s−1
(𝜏d=0.1ms). Since 𝜏e<𝜏
d he simula ions o he doped de ice,
Figu e 15a,b co espond o Figu e 4 ,g, espec i ely. We no e ha
he change in he shape o he esponses be ween Figu e 15a,b
ag ees wi h he elec ochemical model. Also, he s abiliza ion
ime co esponds nicely o he ion’s diffusion ime (𝜏d). The di -
e ence be ween he sou ce and d ain cu en s du ing ansien s
is bes isualized in Figu e 15c. The ac ha he sou ce d i es less
cu en han he one ex ac ed a he d ain is he signa u e o he
semiconduc o being discha ged ollowing he posi i e bias s ep.
The poin whe e he sou ce and d ain cu en con e ge ma ks
he end o he ansien .[23,64]
Mo ing o he undoped de ice, Figu e 15d,e co espond o
Figu e 2 ,g, espec i ely. We find ha Figu e 15d does no ag ee
wi h Figu e 2 , and when we place he sou ce and d ain cu en s
nex o each o he (Figu e 15 ), i seems as i no discha ge akes
place. This disc epancy sugges s ha he cu en o he undoped
de ice is no jus he hole cu en and ha he e is a significan
con ibu ion o displacemen cu en (𝜖dE/d ). Wi h he aid o
he simula ion, we isola ed he hole cu en s and plo ed hem as
dashed lines in Figu e 15 . As hey should, he hole cu en s a e
diffe en enough o indica e a discha ge ollowing he s ep in he
Ad . Sci. 2024,11, 2404182 2404182 (19 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
Figu e 18. The ansien esponse o he d ain cu en o a small s ep in he ga e ol age a e being s abilized a he ini ial bias o Vds =0.1 V and Vgs
was se acco ding o Figu e 14. a,b) Doped semiconduc o . c,d) undoped semiconduc o . a,c) Low ion densi y (Vgs was s abilized a he bias ma ked
wi h dashed-do ed lines in Figu e 14). b,d) High ion densi y (VGS was s abilized a he bias ma ked wi h dashed lines in Figu e 14). Fo he low ion
densi y, he s abiliza ion ime is simila o he ion diffusion ime ( d) and o he high ion densi y, i is much as e .
ga e ol age. The elec ic field ha is a ying is he one be ween
he sou ce and d ain e en hough Vds is cons an . The nonuni-
o mi y o he ion’s influx c ea es a ia ions in he elec ic field
while keeping he in eg al (i.e., Vds)cons an .
Ou nex goal is o e i y i making 𝜏ela ge such ha 𝜏e>𝜏
d
in e s he slope o he sou ce cu en (𝜃=+1), which would indi-
ca e ha he hys e esis loop e e sed di ec ion. As wi h Figu e 15,
we find in Figu e 16 ha he doped de ice ( op aw) ag ees wi h
he elec ochemical model while he undoped one (bo om aw)
does no . No e ha in Figu e 16b, he cu en flipped di ec ion,
and dec eases owa d he s eady s a e alue. The nonuni o mi y
o he undoped de ice mani es s i sel wi h he sou ce cu en
(𝜃=+1, Figu e 16e) s ill ising owa d he s eady s a e. This
poses a po en ial p oblem since he expe imen al da a o he
undoped P3HT de ice shows in e ed hys e esis a low Vds bias.
To add ess his issue, we simula e, in he ollowing sec ion, a
de ice wi h a non eac ing ga e elec ode, as in he expe imen s.
6.2. Hys e esis Response and Compa ison o Expe imen s
This subsec ion add esses he ansien esponse issue o p edic -
ing ha he hys e esis loop o 𝜃=+1 (sou ce cu en ) should
no change di ec ion o he undoped de ice a low Vds bias. This
is impo an since he expe imen al da a o he P3HT semicon-
duc o (Figu e 10) show he hys e esis changing di ec ion and
low Vds bias (𝜃=+1, Vds >0). Figu e 17a,b show he co e-
sponding simula ed hys e esis loops a se e al Vds alues o he
d ain and sou ce cu en s, espec i ely. We chose hole mobil-
i y (5 cm2V−1s−1) and ion diffusion (10−6cm2s−1)so ha a
Vds =50 mV, 𝜏e=𝜏d=0.1 ms. The scan a e was such ha when
mul iplied by he ion diffusion ime ( d) i equals 0.05 V. As ex-
pec ed om he simula ed ansien esponse, he hys e esis loop
o he sou ce cu en (𝜃=+1) does no change i s di ec ion a low
d ain-sou ce bias.
Examining he expe imen al da a (Figu e 10), we no e ha
he e is a sizable esidual cu en a posi i e ga e-sou ce bias.
This is he signa u e o esidual doping, which is common
o P3HT films, wi h some o he epo ed alues exceeding
1016 cm−3. To es i he esidual doping could educe he nonuni-
o mi y effec s and eco e he change in he hys e esis di ec-
ion, we epea ed he simula ions wi h an added P-doping o
1016 cm−3. The esul s a e p esen ed in Figu e 17c,d o he d ain
and sou ce cu en s, espec i ely. We no e ha , in ag eemen
wi h he expe imen al da a, he sou ce (𝜃=+1) cu en s’ hys-
e esis loop di ec ion changes a low Vds alues (Figu e 17d). As
Ad . Sci. 2024,11, 2404182 2404182 (20 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
s a ed in he expe imen al pa , such a change in di ec ion is no
obse ed o he d ain (𝜃=−1) cu en (Figu e 17c).
6.3. T ansien Response a High Ion Densi y
Ha ing b idged be ween he elec ochemical model and he ex-
pe imen al esul s, we use he 2D semiconduc o de ice simula-
ions o explo e an effec ha is no pa o he Be na ds–Mallia as
model. A he e y hea o any elec ochemical model, one can
find he cha ge neu ali y concep . Since (space) cha ge accumu-
la ion c ea es a epulsi e elec ic field o added cha ge, i is im-
possible o accumula e significan cha ge in a gi en olume. Fo
he s eady-s a e solu ion, cha ge neu ali y allows us o s a e ha
he densi y o holes equals ( o an excellen app oxima ion) he ion
densi y. This simplifies he equa ions, as we only need o ollow
he ions.
Howe e , such a conclusion is no necessa ily co ec o he
ansien . Du ing he ansien , he cha ge neu ali y p inciple
dic a es ha ions (holes) canno pene a e he film unless holes
(ions) a i e o compensa e o he ions’ (holes’) cha ge. Namely,
in he gene al case, he dynamics depend upon bo h eand d.
Na u ally, he c oss dependence, which is d i en by he Poisson
equa ion, is a unc ion o he cha ge (ion) densi y. In he p e i-
ous sec ions, we minimized his c oss-dependence by limi ing
he ga e-sou ce bias o a ange whe e he ion densi y is below
1018 cm−3. In he ollowing figu e, we will show esul s o he
ange in which he ion densi y is abo e 1019 cm−3.
In Figu e 18 we look a he effec o he hole ansi ime being
much sho e han he ion’s diffusion ime (𝜏e≪𝜏d). We exam-
ine only he d ain cu en (𝜃=−1), wi h he le column o he
low-densi y case and he igh one o he high-densi y. As no ed
in Figu e 14a, o he doped semiconduc o , he ga e bias ha
esul s in low ca ion densi y is nega i e, and he one esul ing in
high ca ion densi y is posi i e. Fo he undoped case, he high an-
ion densi y co esponds o mo e nega i e ga e bias (Figu e 14b).
Fo compa ison, we added esul s om longe diffusion imes.
Bo h Figu e 18a (doped) and Figu e 18c (undoped) show ha he
s abiliza ion ime cons an is close o he ion diffusion ime and
he use o exp(− /𝜏d), is jus ified. The high-densi y esul s, which
appea in he igh column, a e e y diffe en . The s abiliza ion
ime cons an s ill depends on he diffusion ime, bu i is now
much sho e . No ably, he o ange line ep esen ing he diffusion
ime o 10 ms exhibi s a s abiliza ion ime o ≈2 ms. Appa en ly,
he as holes expedi e he anspo o he ions.[18]
While Figu e 18 showed ha holes en e ing as would expe-
di e he ions, we use Figu e 19 o demons a e ha slow holes de-
lay he ions’ esponse. In Figu e 19 he hole mobili y is educed o
10−3cm2V−1s−1 esul ing in 𝜏e=250 ms. All he lines, s a ing
om 𝜏d=0.1 ms (blue line) and mo ing all he way o 𝜏d=25 ms
( ed line), con e ge oge he owa d he s eady s a e a longe han
30 ms. Again, i shows ha a high ion densi y, he esponse ime
depends on bo h he hole ansi ime (𝜏e) and he ion’s diffusion
ime (𝜏d).
7. Conclusion
We de eloped a gene al o mula ion o a 2D ansmission line
desc ip ion o an OECT. The gene al model conside s he ho -
izon al anspo o elec onic ca ie s and e ical diffusion o
Figu e 19. The d ain cu en ’s ansien esponse o a small s ep in
he ga e ol age a e being s abilized a he ini ial bias (Vds =0.1 V).
The hole ansi ime is much longe han he ion diffusion ime
(mh=10−3cm2V−1s−1,
d=250 ms). The semiconduc o is undoped,
and he esponse is a high ion densi y (dashed line in Figu e 13).
compensa ing ions, wi hou space cha ge effec s. Then we p o-
ided an analy ical ime-dependen model unde assump ions o
homogeneous cha ge dis ibu ion. This model is equi alen o
Be na ds–Mallia as conse a ion equa ion, ex ended by includ-
ing he diffusion effec so ha wo diffe en ime cons an s ha e
been iden ified, he ho izon al hole anspo 𝜏eand he e ical
ion diffusion 𝜏d, depending on anspo coefficien s, mo phol-
ogy, and ho izon al field.
The model enables a basic classifica ion o he ansien e-
sponse o a s ep ol age in e ms o he sign o he cu en and he
sign o he s ep. Based on hese elemen a y esponses we ound
he possible ypes o hys e esis beha io in ans e cu es. The
expe imen al esul s alida e he heo e ical model, demons a -
ing he influence o a ious pa ame e s such as d ain bias, scan
a e, and pola i y on he hys e esis beha io obse ed in OECT
ans e cu es. The analysis o ealis ic simula ion esul s shows
e y good ag eemen wi h he simple model, hence he model
p oduces a obus elemen a y classifica ion o he dynamic e-
sponses o OECT ha a e mainly go e ned by ion diffusion and
hole anspo issues. Howe e , addi ional effec s occu in ealis-
ic simula ion, since he ca ie densi y affec s he effec i e ans-
po pa ame e s and changes he esul s expec ed in single ca ie
pa ame e pic u es.
These findings con ibu e o a deepe unde s anding o he un-
de lying mechanisms go e ning he ope a ion o o ganic elec o-
chemical ansis o s.
Suppo ing In o ma ion
Suppo ing In o ma ion is a ailable om he Wiley Online Lib a y o om
he au ho .
Ad . Sci. 2024,11, 2404182 2404182 (21 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
Acknowledgemen s
The wo k o Juan Bisque was unded by he Eu opean Resea ch Coun-
cil (ERC) ia Ho izon Eu ope Ad anced G an , g an ag eemen no
101097688 (“Pe oSpike ”). Bau zhan Ilyasso hanks he Science Com-
mi ee o he Minis y o Science and Highe Educa ion o he Republic o
Kazakhs an o financial suppo unde he p ojec G an No. AP13067629.
Ni Tessle acknowledges he suppo by he Minis y o Inno a ion, Sci-
ence and Technology Is ael, he M-ERANET g an PHANTASTIC Call 2021.
Conflic o In e es
The au ho s decla e no conflic o in e es
Da a A ailabili y S a emen
The da a ha suppo he findings o his s udy a e openly a ailable in
Zenodo a [DOI], e e ence numbe 10925192.
Keywo ds
o ganic ansis o , hys e esis, ansien , swi ching, ionic diffusion
Recei ed: Ap il 19, 2024
Re ised: June 24, 2024
Published online: July 25, 2024
[1] R. G. A ns, Eng. Sci. Educ. J. 1998,7, 233.
[2] G. E. Moo e, IEEE Solid-S a e Ci c. Soc. Newsle . 2006,11, 33.
[3] S. K a insky, D. Belouso , S. Liman, G. Sa a , N. Wald, E. G.
F iedman, A. Kolodny, U. C. Weise , IEEE T ans. Ci cui s Sys . II: Ex-
p ess B ie s 2014,61, 895.
[4] L. Chua, IEEE T ans. Ci cui Theo y 1971,18, 507.
[5] J. H. Bu oughes, C. A. Jones, R. H. F iend, Na u e 1988,335, 137.
[6] M. Huang, M. Schwacke, M. Onen, J. Del Alamo, J. Li, B. Yildiz, Ad .
Ma e . 2022,35, 2205169.
[7] P. Thakka , J. Gosai, H. J. Gogoi, A. Solanki, J. Ma e . Chem. C 2024,
12, 1583.
[8] A. A. Talin, Y. Li, D. A. Robinson, E. J. Fulle , S. Kuma , Ad . Ma e .
2023,35, 2204771.
[9] J. Ri nay, S. Inal, A. Salleo, R. M. Owens, M. Be gg en, G. G. Mallia as,
Na . Re . Ma e . 2018,3, 17086.
[10] M.-K. Song, J.-H. Kang, X. Zhang, W. Ji, A. Ascoli, I. Messa is, A. S.
Demi kol, B. Dong, S. Agga wal, W. Wan, S.-M. Hong, S. G. Ca dwell,
I. Boyba , J. Seo, J.-S. Lee, M. Lanza, H. Yeon, M. Onen, J. Li, B. Yildiz,
J. A. del Alamo, S. Kim, S. Choi, G. Milano, C. Riccia di, L. Alff, Y. Chai,
Z.Wang,H.Bhaska an,M.C.He sam,e al.,ACS Nano 2023,17,
11994.
[11] M. Huang, M. Schwacke, M. Onen, J. del Alamo, J. Li, B. Yildiz, Ad .
Ma e . 2023,35, 2205169.
[12] X. Yao, K. Klyukin, W. Lu, M. Onen, S. Ryu, D. Kim, N. Emond, I.
Waluyo, A. Hun , J. A. del Alamo, J. Li, B. Yildiz, Na . Commun. 2020,
11, 3134.
[13] E. J. Fulle , F. E. Gabaly, F. Léona d, S. Aga wal, S. J. Plimp on, R. B.
Jacobs-Ged im, C. D. James, M. J. Ma inella, A. A. Talin, Ad . Ma e .
2017,29, 1604310.
[14] R. D. Nikam, M. Kwak, J. Lee, K. G. Rajpu , W. Bane jee, H. Hwang,
Sci. Rep. 2019,9, 18883.
[15] M. Onen, N. Emond, B. Wang, D. Zhang, F. M. Ross, J. Li, B. Yildiz,
J. A. del Alamo, Science 2022,377, 539.
[16] M. Koch, H. Tseng, A. Weissbach, B. Iniguez, K. Leo, A. Kloes, H.
Kleemann, G. Da bandy, IEEE J. Elec . De ices Soc. 2023,11, 665.
[17] B. D. Paulsen, K. Tyb and , E. S a inidou, J. Ri nay, Na . Ma e . 2020,
19, 13.
[18] S. T. Keene, J. E. M. Laulainen, R. Pandya, M. Mose , C.
Schnede mann, P. A. Midgley, I. McCulloch, A. Rao, G. G. Mallia as,
Na . Ma e . 2023,22, 1121.
[19] J. T. F iedlein, R. R. McLeod, J. Ri nay, O g. Elec on. 2018,63, 398.
[20] V. Kaphle, S. Liu, C.-M. Keum, B. Lüssem, Phys. S a us Sol. 2018,215,
1800631.
[21] D. Ohayon, V. D ue , S. Inal, Chem.Soc.Re .2023,52, 1001.
[22] A. Weissbach, L. M. Bonga z, M. Cucchi, H. Tseng, K. Leo, H.
Kleemann, J. Ma . Chem. C 2022,10, 2656.
[23] Y. Roichman, N. Tessle , MRS Online P oc. Lib . 2005,871, 47.
[24] J. T. F iedlein, M. J. Donahue, S. E. Shaheen, G. G. Mallia as, R. R.
McLeod, Ad . Ma e . 2016,28, 8398.
[25] V. A hanasiou, S. Pecqueu , D. Vuillaume, Z. Konkoli, O g. Elec on.
2019,72, 39.
[26] V. Kaphle, P. R. Paudel, D. Dahal, R. K. Radha K ishnan, B. Lüssem,
Na . Commun. 2020,11, 2515.
[27] R. Colucci, H. F. P. Ba bosa, F. Gün he , P. Ca assin, G. C. Fa ia, Flex.
P in . Elec . 2020,5, 013001.
[28] L. Bü gi, R. H. F iend, H. Si inghaus, App. Phys. Le . 2003,82, 1482.
[29] D. A. Be na ds, G. G. Mallia as, Ad . Func. Ma e . 2007,17, 3538.
[30] J. Ri nay, P. Leleux, M. Fe o, M. Sessolo, A. Williamson, D. A.
Kou sou as, D. Khodagholy, M. Ramuz, X. S akosas, R. M. Owens,
C. Bena , J.-M. Badie , C. Be na d, G. G. Mallia as, Sci. Ad . 2015,1,
e1400251.
[31] J. T. F iedlein, S. E. Shaheen, G. G. Mallia as, R. R. McLeod, Ad . Elec-
on. Ma e . 2015,1, 1500189.
[32] J. Bisque , J. Phys. Chem. Le . 2023,14, 10951.
[33] P. R. Paudel, J. T opp, V. Kaphle, J. D. Azoulay, B. Lüssem, J. Ma e .
Chem. C 2021,9, 9761.
[34] M. Skow ons, P. Paudel, B. Lüssem, p esen ed a 2023 IEEE In . Con .
on Flexible and P in able Senso s and Sys ems (FLEPS), Bos on, MA,
July 2023.
[35] S. Bi on, N. Tessle , Ene gy En i on. Sci. 2023,16, 2621.
[36] S. Bi on, N. Tessle , Ad . Elec . Ma e . 2024,10, 2300766.
[37] D. Shamalia, N. Tessle , J. Appl. Phys. 2024,135, 065501.
[38] M. D. Le i, G. Sali a, B. Ma ko ski, H. Telle , D. Au bach, J. Elec-
ochem. Soc. 1999,146, 1279.
[39] J. Bisque , G. Ga cia-Belmon e, J. Ga cía-Cañadas, J. Chem. Phys.
2004,120, 6726.
[40] Z. Pome an z, A. Zaban, S. Ghosh, J.-P. Lellouche, G. Ga cia-
Belmon e, J. C. Bisque , J. Elec oanal. Chem. 2008,614, 49.
[41] M. Cucchi, A. Weissbach, L. M. Bonga z, R. Kan elbe g, H. Tseng, H.
Kleemann, K. Leo, Na . Commun. 2022,13, 4514.
[42] I. N. Hulea, H. B. B om, A. J. Hou epen, D. Vanmaekelbe gh, J. J.
Kelly, E. A. Meulenkamp, Phys.Re .Le .2004,93, 166601.
[43] S. T. Keene, A. Rao, G. G. Mallia as, Sci. Ad . 2023,9, eadi3536.
[44] J. Bisque , Phys. Chem. Chem. Phys. 2000,2, 4185.
[45] S. Inal, G. G. Mallia as, J. Ri nay, Na . Commun. 2017,8, 1767.
[46] M. D. Le i, D. Au bach, Elec ochim. Ac a 1999,45, 167.
[47] J. Bisque , V. S. Vikh enko, Elec ochim. Ac a 2002,47, 3977.
[48] M. S ömme, Solid S a e Ionics 2000,131, 261.
[49] W. Weppne , R. A. Huggins, J. Elec ochem. Soc. 1977,124, 1569.
[50] L. G acia, J. Ga cía-Cañadas, G. Ga cia-Belmon e, A. Bel án, J.
And és, J. Bisque , Elec ochem. Solid S a e Le . 2005,8, J21.
[51] J. Bisque , Phys. Chem. Chem. Phys. 2008,10, 49.
[52] J. Bisque , Phys. Chem. Chem. Phys. 2003,5, 5360.
[53] J. Jamnik, J. Maie , Phys. Chem. Chem. Phys. 2001,3, 1668.
[54] M. Janssen, J. Bisque , J. Phys. Chem. C 2021,28, 15737.
[55] D. Vanmaekelbe gh, A. J. Hou epen, J. J. Kelly, Elec ochim. Ac a 2007,
53, 1140.
Ad . Sci. 2024,11, 2404182 2404182 (22 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
www.ad ancedsciencenews.com www.ad ancedscience.com
[56] J. Bisque , The Physics o Sola Ene gy Con e sion, CRC P ess, Boca
Ra on, 2020.
[57] J. Ga cía-Cañadas, F. Fab ega -San iago, H. Bolink, E. Paloma es, G.
Ga cia-Belmon e, J. Bisque , Syn h. Me . 2006,156, 944.
[58] G. Ga cia-Belmon e, J. Bisque , Elec ochim. Ac a 2002,47,
4263.
[59] A. M. Yao, V. Viswana han, J. Phys. Chem. Le . 2024, 1143.
[60] B. D. Paulsen, C. D. F isbie, J. Phys. Chem. C 2012,116, 3132.
[61] I. D. Rais ick, A. J. Ma k, R. A. Huggins, Solid S a e Ionics 1981,5,
351.
[62] M. Ga cía-Ba lle, J. Mayén Guillén, M. Chap an, O. Baussens, J.
Zacca o, J.-M. Ve ilhac, E. G os-Daillon, A. Gue e o, O. Almo a, G.
Ga cia-Belmon e, ACS Ene gy Le . 2022,7, 946.
[63] G. Ga cia-Belmon e, J. Bisque , E. C. Pe ei a, F. Fab ega -San iago, J.
Elec oanal. Chem. 2001,508, 48.
[64] M. G eenman, A. J. Ben-Sasson, Z. Chen, A. Facche i, N. Tessle ,
Appl. Phys. Le . 2013,103, 073502.
[65] T. Deyu, K. Loïg, C. Xa ie , B. Magnus, F. Robe , P oc. SPIE 8478,
O ganic Field-Effec T ansis o s XI, 84780L,Oc obe 112012.
[66] G. C. Fa ia, D. T. Duong, A. Salleo, O g. Elec on. 2017,45, 215.
[67] J. Bisque , J. Phys. Chem. B 2002,106, 325.
[68] D. E. Wa d, R. W. Du on, IEEE J. Solid-S a e Ci c. 1978,13, 703.
[69] P. R. Paudel, M. Skow ons, D. Dahal, R. K. Radha K ishnan, B.
Lüssem, Ad . Theo y Simula . 2022,5, 2100563.
[70] T. R. B umle e, R. P. Buck, J. Elec oanal. Chem. 1981,126, 73.
[71] J. Bisque , M. G ä zel, Q. Wang, F. Fab ega -San iago, J. Phys. Chem.
B2006,110, 11284.
[72] J. Guo, S. E. Chen, R. Gi idha agopal, C. G. Bischak, J. W. Ono a o,
K. Yan, Z. Shen, C.-Z. Li, C. K. Luscombe, D. S. Ginge , Na . Ma e .
2024,23, 656.
[73] C. Zhao, B. Lüssem, S. Zhang, S. Wang, W. Ma, Gian 2024,19,
100306.
[74] J. Bisque , PRX Ene gy 2023,3, 011001.
[75] A. K. Aimukhano , X. S. Rozhko a, B. R. Ilyasso , A. K. Zeinideno ,
N. Nu aje, Polym. Ad . Technol. 2021,32, 497.
[76] S. Holliday, R. S. Ash a , A. Wadswo h, D. Ba an, S. A. Yousa ,
C. B. Nielsen, C.-H. Tan, S. D. Dimi o , Z. Shang, N. Gaspa ini,
M. Alamoudi, F. Laquai, C. J. B abec, A. Salleo, J. R. Du an , I.
McCulloch, Na . Commun. 2016,7, 11585.
[77] C. Seoul, N.-H. Kim, Fibe s Polym. 2000,1, 25.
[78] L. Q. Flagg, R. Gi idha agopal, J. Guo, D. S. Ginge , Chem. Ma e .
2018,30, 5380.
[79] R. Gi idha agopal, L. Q. Flagg, J. S. Ha ison, M. E. Ziffe , J. Ono a o,
C. K. Luscombe, D. S. Ginge , Na . Ma e . 2017,16, 737.
[80] H.-S. Tseng, T. Puangniyom, C.-Y. Chang, J. A. Jana dhanan, H. Yu, W.-
C. Chen, C.-C. Chueh, Y.-S. Hsiao, Chem. Eng. J. 2024,486, 150371.
[81] D. T. Duong, Y. Tuchman, P. Chak h anon , P. Ca assin, R. Colucci,
T. F. Ja amillo, A. Salleo, G. C. Fa ia, Ad . Elec on. Ma e . 2018,4,
1800090.
[82] N. Tessle , Y. Roichman, App. Phys. Le . 2001,79, 2987.
Ad . Sci. 2024,11, 2404182 2404182 (23 o 23) © 2024 The Au ho (s). Ad anced Science published by Wiley-VCH GmbH
21983844, 2024, 36, Downloaded om h ps://ad anced.onlinelib a y.wiley.com/doi/10.1002/ad s.202404182 by Readcube (Lab i a Inc.), Wiley Online Lib a y on [30/01/2025]. See he Te ms and Condi ions (h ps://onlinelib a y.wiley.com/ e ms-and-condi ions) on Wiley Online Lib a y o ules o use; OA a icles a e go e ned by he applicable C ea i e Commons License
