Elementary steps in electrical doping of organic semiconductors
Item Type Article
Authors Tietze, Max Lutz;Benduhn, Johannes;Pahner, Paul;Nell, Bernhard;Schwarze, Martin;Kleemann, Hans;Krammer, Markus;Zojer, Karin;Vandewal, Koen;Leo, Karl
Citation Tietze ML, Benduhn J, Pahner P, Nell B, Schwarze M, et al. (2018) Elementary steps in electrical doping of organic semiconductors.
Nature Communications 9. Available: http://dx.doi.org/10.1038/
s41467-018-03302-z.
Eprint version Publisher's Version/PDF
DOI 10.1038/s41467-018-03302-z
Publisher Springer Nature
Journal Nature Communications
Rights This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/
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Link to Item http://hdl.handle.net/10754/627499
400 600 800 1000 1200 1400 1600 0.0
0.2 0.4 0.6 0.8 1.0 1.2
ZnPc:F6-TCNNQ (MR=0.4)
10 K 100 K 200 K 300 K
i-ZnPc
Norm. (1 - transmission) (a.u.)
Wavelength (nm) a
d
400 600 800 1000 1200 1400 1600
0.0 0.2 0.4 0.6 0.8 1.0 1.2
10 K 100 K 200 K 300 K
i-ZnPc
Norm. (1 - transmission) (a.u.)
Wavelength (nm)
ZnPc:F6-TCNNQ (MR=0.05)
c
400 600 800 1000 1200 1400 1600
0 10 20 30 40 50 60
100 - Transmission (%)
Wavelength (nm)
MeO-TPD:F6-TCNNQ (MR=0.1) 10 K 100 K 200 K 300 K
b
400 600 800 1000 1200 1400 1600 0
10 20 30 40 50 60 70 80 90
Absorption (%)
Wavelength (nm)
ZnPc (95 nm) ZnPc:F6-TCNNQ (MR=1, 148 nm) F6-TCNNQ (38 nm) glass
Supplementary Figure 1. Temperature-dependent transmission on p-doped films.
Transmission spectra of (a,b)ZnPc:F6-TCNNQ and(c)MeO-TPD:F6-TCNNQ thin films with di↵erent doping ratios measured under temperature variation in-betweenT= 10 K. . .300 K (solid lines). Reference spectra of undoped ZnPc film are shown as dash-dotted lines. (d)RT absorp- tion spectra of pure ZnPc and F6-TCNNQ films as well as of an highly doped ZnPc:F6-TCNNQ (MR= 1) sample.
600 800 1000 1200 1400 0.0
0.5 1.0 1.5
Norm. absorption (a.u.) MR=0.013
Wavelength (nm) 600 800 1000 1200 1400
0.0 0.5 1.0 1.5
Norm. absorption (a.u.)
Wavelength (nm) MR=0.40
600 800 1000 1200 1400 0.0
0.5 1.0
1.5 MR=0.26
Norm. absorption (a.u.)
Wavelength (nm)
600 800 1000 1200 1400 0.0
0.5 1.0
1.5 MR=0.19
Norm. absorption (a.u.)
Wavelength (nm)
600 800 1000 1200 1400 0.0
0.5 1.0
1.5 MR=0.094
Norm. absorption (a.u.)
Wavelength (nm)
600 800 1000 1200 1400 0.0
0.5 1.0
1.5 MR=0.047
Norm. absorption (a.u.)
Wavelength (nm)
600 800 1000 1200 1400 0.0
0.5 1.0 1.5
Norm. absorption (a.u.) MR=0.024
Wavelength (nm)
0.01 0.1 1
100 200 300 400 500
F6-TCNNQ- / MR (a.u.)
Molar Doping Ratio
a
b c
0.01 0.1 1
0 1 2
F6-TCNNQ- /(peak sum*mol%)
Molar Doping Ratio
Supplementary Figure 2. Fitting absorption spectra of p-doped films. (a)Gaussians peak fits of the normalized RT absorption spectra of ZnPc:F6-TCNNQ thin films of varying doping ratio. Red peaks at 995 and 1160 nm are sub-gap features attributed to ionized F6-TCNNQ molecules. (b)Integrated fitted intensity of the red F6-TCNNQ peaks weighted by the molar doping ratio MR =NA/NV.(c)Determined ratioAbs(F6-TCNNQ )/(Abs(peak sum)⇥c[mol%]) using the doping concentrationc[mol%] =NA/(NA+NV).
a
c
150 200 250 300 5
6
7 MR=0.01 (0.6 wt%)
T (K) NA,d- (1018 cm-3 )
0.3 0.4
NA,d- / NA
-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 2
3 4 5
ZnPc:F6-TCNNQ
5 kHz
150 K
200 K
1 / C2 (1015 F-2 )
Voltage (V) 290 K
T = 10K
b
d
200 250 300 6
7 8
NA,d- / NA
NA,d- (1018 cm-3 )
T (K)
NA-
0.5 0.6 MR=0.0085 (0.5 wt%)
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 3
4 5 6 7
1 / C2 (1015 F-2 )
Voltage (V)
218 K 233 K 253 K 273 K 293 K 303 K MeO-TPD:F6-TCNNQ
1 kHz
-2.0 -1.5 -1.0 -0.5 0.0
4 5 6 7
1 / C2 (1015 F-2 )
Voltage (V)
Ir(piq)3:F6-TCNNQ
500 Hz
210 K 230 K 240 K 250 K 260 K 270 K 280 K 286 K
e f
3.5 4.0 4.5 44.0
44.1 44.2 44.3
ln (p)
1000 / T (K-1) Ir(piq)3:F6-TCNNQ (0.5 wt%)
Eact = 9.5 meV
~ 110.0 K
Supplementary Figure 3. Mott-Schottky analysis. 1/C2(V) spectra of ITO/host:F6- TCNNQ(50 nm)/Al Schottky diodes determined by Impedance spectroscopy under varying tem- perature employing either (a) ZnPc or (c) MeO-TPD as host material. Red lines indicate linear fits for determining the density of ionized acceptors NA,d(T), forming the space charge layer at the metal/organic contacts due to depletion of free carriers p. Molecule densities N0 = 1.62⇥1021cm 3 (1.45⇥1021cm 3) for ZnPc (MeO-TPD) are used in the molar dop- ing ratio MR = NA/N0. Respective determined doping efficiencies NA,d/NA are shown in (b,d). Furthermore, Mott-Schottky plots determined on an ITO/Ir(piq)3:F6-TCNNQ(50 nm, 0.5 wt%)/Ir(piq)3(8 nm)/Al device and the respective thermal activation are shown in(e,f ). The ionization energy of the amorphous Ir(piq)3 measured by UPS is 5.03 eV [1], i.e., slightly lower than that of MeO-TPD (IE= 5.07 eV).
The uncertainty of the Arrhenius-type activation energyEactdetermined by fitting Mott-Schottky plots is estimated to 5 meV by statistics on 3 ZnPc:F6-TCNNQ diodes.
3 4 5 41.5
42.0 42.5 43.0
(0.25wt% ; 10 kHz) ZnPc: F6-TCNNQ
ln (p)
1000 / T (K-1)
~ 285.6 K
Eact = 24.6 meV
-0.6 -0.4 -0.2 0.0 0.2 0.4
4 6 8 10
12 ZnPc:F6-TCNNQ
10 kHz 1 / C2 (1015 F-2 )
Voltage (V)
218 K 233 K 253 K 273 K 293 K 313 K
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 4
6 8 10
12 ZnPc:F6-TCNNQ
5 kHz 1 / C2 (1015 F-2 )
Voltage (V)
218 K 233 K 253 K 273 K 293 K 313 K
3 4 5
41.5 42.0 42.5 43.0
ln (p)
1000 / T (K-1) Eact = 25.2 meV
~ 293.1 K (0.25wt% ; 5 kHz) ZnPc: F6-TCNNQ
101 102 103 104 105 106
0 5 10 15 20
ITO/MeO-TPD:F6-TCNNQ (MR=0.0085, 50 nm)/Al
Capacitance Cd (nF)
Frequency (Hz)
303 K 293 K 273 K 253 K 233 K 218 K
3 4 5
43.1 43.2 43.3 43.4 43.5 43.6 43.7
(MR=0.0085)
5 kHz Eact = 11.1 meV
ln (p)
1000 / T (K-1) MeO-TPD:
F6-TCNNQ
~ 129.2 K
-0.5 0.0 0.5
10-8 10-7 10-6 10-5 10-4 10-3
l (A)
V (V)
101 102 103 104 105 106
0 10 20
ITO/ZnPc:F6-TCNNQ (MR=0.0040, 200 nm)/Al
Capacitance Cd (nF)
Frequency (Hz)
313 K 293 K 273 K 253 K 233 K 218 K
a b
c
e
Dev#1
Dev#2
Dev#2
d
f
g h
Supplementary Figure 4. Impedance spectroscopy. 1/C2(V) spectra(a,c)and Arrhenius- type doping activation (b,d) of ITO/ZnPc:F6-TCNNQ(200 nm, 0.5 wt%)/Al Schottky diodes.
RespectiveC(f) spectra at zero bias andI(V) curves are shown in(e)and(f ), respectively. (g) C(f) spectra of an MeO-TPD:F6-TCNNQ Schottky diode at zero bias and varying sample tem- perature for comparison.(h)Mott-Schottky analysis at 5 kHz yields an Arrhenius-type activation of 11.1 meV.
Supplementary Note 1. Two- & Three-level System: Fermi level & Doping Efficiency For given dopant (acceptor) densityNAand temperatureT, the generalized neutrality condition
(1) p(T) +NCT+ (T) =NA(NA, T)
is presumed, in whichNCT+ denotes the number of holes bound in [D+A ] ground-state integer- charge transfer complexes (ICTCs) with binding energyEbCTand densityNA:
(2) NCT+ (T) =NA(NA, T) 0 BB
@1 1
1 + exp
✓EbCT EF kBT
◆ 1 CC A Thus, we get
(3)
p(T) =NA(NA, T) NA(NA, T) 0 BB
@1 1
1 + exp
✓EbCT EF kBT
◆ 1 CC A
= NA(NA, T) 1 + exp
✓ECTb EF kBT
◆ ⌘NCT(NA, T).
The expression on the right hand side corresponds to an ”occupation” of [D+A ] ICTCs with electrons, i.e., to the density of those being actually separated or isolated ionized dopant molecules.
Therefore, it is denoted asNCT, and for all ionized dopants the density condition
(4) NCT+NCT+ =NA
follows.
Ideally, all dopants are ionized: NA =NA. Exemplary solutions are shown in Supplementary Figure 6 and 8. For the case of weak dopants, however, incomplete dopant ionization is considered by applying
(5) NA(NA, T) = NA
1 + exp⇣E
A EF kBT
⌘
in Supplementary Equation (1)-(4). Respective solutions are shown in Supplementary Figure 9 for varyingEA= 0.1. . .0.5 eV and fixed binding energyEbCT= 0.64 eV of holes in ICTCs.
10-810-7 10-6 10-5 10-4 10-3 10-2 10-1 100 0.0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Fermi level (eV)
NA/NV
300 K 200 K 150 K
EV=
EA
10-8 10-7 10-6 10-5 10-410-3 10-2 10-1 100 10-10
10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
300k 200K 150K
Fraction
NA/NV
p/NA NA
-/NA
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 0.0
0.2 0.4 0.6 0.8
1.0 300k 200K 100K
p/NA NA-/NA
Fraction
NA/NV
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 0.0
0.2 0.4 0.6 0.8 1.0
p/NA NA-/NA 300k 200K 100K
Fraction
NA/NV
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 10-10
10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
300k 200K 100K
p/NA NA
-/NA
Fraction
NA/NV
a b
10-810-7 10-6 10-5 10-4 10-3 10-2 10-1 100 0.0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Fermi level (eV)
EV=
NA/NV
300 K 200 K 100 K
EA
10-810-7 10-6 10-5 10-4 10-3 10-2 10-1 100 0.0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Fermi level (eV)
EV=
EA
NA/NV
300 K 200 K 100 K
10-810-7 10-6 10-5 10-4 10-3 10-2 10-1 100 0.0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Fermi level (eV)
NA/NV
300 K 200 K 100 K
EV=
EA sA=sV=1 meV
sA=sV=1 meV
sA=sV=50 meV sA=sV=50 meV
sA=sV=100 meV
sA=sV=150 meV
sA=sV=100 meV
sA=sV=150 meV
s
A, s
VSupplementary Figure 5. Doping model with activation from acceptor statesEA. (a) Fermi level and(b) doping efficiency vs. the acceptor densityNA for a two level system consisting of two broadened Gaussians separated byEA EV = 0.64 eV. The neutrality condition p=NA is solved. The e↵ective valence density isNV = 2.4⇥1019cm 3. TemperatureT and the widths A= V = 1. . .150 meV are varied.
10-810-7 10-6 10-5 10-4 10-3 10-2 10-1 100 0.0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Fermi level (eV)
NA/NV
300 K 200 K 150 K
EV=
ECT
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 10-10
10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
300k 200K 150K
p/NA
NCT+/NA NA-/NA
Fraction
NA/NV
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 10-10
10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100
300k 200K 100K
p/NA NCT+/NA NA-/NA
Fraction
NA/NV
10-810-7 10-6 10-5 10-4 10-3 10-2 10-1 100 0.0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
300 K 200 K 100 K
Fermi level (eV)
NA/NV EV=
ECT
10-810-7 10-6 10-5 10-4 10-3 10-2 10-1 100 0.0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Fermi level (eV)
NA/NV
300 K 200 K 100 K
EV=
ECT
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 0.0
0.2 0.4 0.6 0.8
1.0 300k 200K 100K
p/NA NCT
+/NA
NA-/NA
Fraction
NA/NV
10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 0.0
0.2 0.4 0.6 0.8
1.0 300k 200K 100K
p/NA NCT
+/NA
NA-/NA
Fraction
NA/NV 10-810-7 10-6 10-5 10-4 10-3 10-2 10-1 100
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Fermi level (eV)
NA/NV
300 K 200 K 100 K
EV=
ECT
a b
sCT=sV=1 meV
sCT=sV=1 meV
sCT=sV=50 meV sCT=sV=50 meV
sCT=sV=100 meV
sCT=sV=100 meV
sCT=sV=150 meV sCT=sV=150 meV
s
CT, s
VSupplementary Figure 6. Doping model with activation from ICTCs withEbCT. (a) Fermi level and(b) doping efficiency vs. the acceptor densityNA for a two level system consisting of two broadened Gaussians separated byECTb EV = 0.64 eV. The neutrality con- dition p+NCT+ =NA =NA is solved. The e↵ective valence density isNV = 2.4⇥1019cm 3. TemperatureT and the widths CT= V = 1. . .150 meV are varied.
100 150 200 250 300 350 400 450 0.0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
T (K)
A=V= 200 meV 150 meV 100 meV 50 meV 25 meV 1 meV
EA
Fermi level (eV)
EV=
0.002 0.004 0.006 0.008 0.010 0
5 10 15 20 25 30 35 40
A=V= 200 meV 150 meV 100 meV 50 meV 25 meV 1 meV
~ kB*223.80 K= 19.3 meV
~ kB*3752.8 K= 0.323 eV
ln(p)
1/T 100 150 200 250 300 350 400 450
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Fermi level (eV)
T (K)
A=V= 200 meV 150 meV 100 meV 50 meV 25 meV 1 meV
EA
EV=
a
NA=1014cm-30.002 0.004 0.006 0.008 0.010 0
5 10 15 20 25 30 35 40
~ kB*3752.5 K= 0.323 eV
A=V= 200 meV 150 meV 100 meV 50 meV 25 meV 1 meV
~ kB*215.06 K= 18.5 meV
ln(p)
1/T
b
NA=2x1017cm-3100 150 200 250 300 350 400 0.0
0.2 0.4 0.6 0.8 1.0
p/NA NA-/NA
Fraction
T (K) 0.0 100 150 200 250 300 350 400
0.2 0.4 0.6 0.8 1.0
p/NA NA-/NA
Fraction
T (K)
A= V=1 meV A=V=100 meV
Supplementary Figure 7. Doping model with activation from acceptor states EA: Thermal activation behavior. Fermi level, free carrier density p and doping efficiency vs.
temperatureT for a two level system consisting of two broadened Gaussians separated byEA
EV = 0.64 eV. The neutrality condition p = NA is solved. The e↵ective valence density is NV = 2.4⇥1019cm 3. The widths A= V = 1. . .150 meV are varied. The acceptor density is fixed to(a)NA= 1014cm 3and(b)NA= 2⇥1017cm 3.
100 150 200 250 300 350 400 450 0.0
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
ECT
Fermi level (eV)
T (K)
CT= V= 200 meV 150 meV 100 meV 50 meV 25 meV 1 meV
EV=
0.002 0.004 0.006 0.008 0.010 0
5 10 15 20 25 30 35 40
CT=V= 200 meV 150 meV 100 meV 50 meV 25 meV 1 meV
~ kB*223.78 K= 19.3 meV
~ kB*3766.3 K= 0.324 eV
ln(p)
1/T
a
b
NA=1014cm-3
NA=2x1017cm-3 100 150 200 250 300 350 400 450
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2
Fermi level (eV)
T (K)
CT=V= 200 meV 150 meV 100 meV 50 meV 25 meV 1 meV
ECT
EV=
0.002 0.004 0.006 0.008 0.010 0
5 10 15 20 25 30 35 40
CT=V= 200 meV 150 meV 100 meV 50 meV 25 meV 1 meV
ln(p)
1/T
~ kB*215.06 K= 18.5 meV
~ kB*3752.5 K= 0.323 eV
100 150 200 250 300 350 400 0.0
0.2 0.4 0.6 0.8 1.0
p/NA NCT+/NA NA-/NA
Fraction
T (K) 0.0 100 150 200 250 300 350 400
0.2 0.4 0.6 0.8 1.0
p/NA NCT+/NA NA-/NA
Fraction
T (K)
CT=V=1 meV CT=V=100 meV
Supplementary Figure 8. Doping model with activation from ICTCs with ECTb : Thermal activation behavior. Fermi level, free carrier density p and doping efficiency vs.
temperature T for a two level system consisting of two broadened Gaussians separated by EbCT EV = 0.64 eV. The neutrality conditionp+NCT+ = NA = NA is solved. The e↵ec- tive valence density isNV = 2.4⇥1019cm 3. The widths A = V = 1. . .150 meV are varied.
The acceptor density is fixed to(a)NA= 1014cm 3 and(b)NA= 2⇥1017cm 3.
10-810-710-610-510-410-310-210-1100 0.00.2
0.40.6 0.81.0 1.21.4 1.61.8 2.02.2
EA=0.7 eV EA=0.5 eV EA=0.4 eV EA=0.2 eV EA=0.1 eV
Ferm i level (e V)
N
A/N
V ECTa b
E
A=0 .1…0. 5 eV
c d
10-810-710-610-510-410-310-210-1100 0.0
0.2 0.4 0.6 0.8 1.0
NA-/NA NCT+/NA p/NA
Fraction
N
A/N
V10-810-710-610-510-410-310-210-1100 0.0
0.2 0.4 0.6 0.8 1.0
NA-/NA NCT+/NA p/NA
Fraction
N
A/N
V10-810-710-610-510-410-310-210-1100 0.0
0.2 0.4 0.6 0.8
1.0 N
A -/NA NCT+/NA p/NA
Fraction
N
A/N
V10-810-710-610-510-410-310-210-1100 0.0
0.2 0.4 0.6 0.8
1.0 N
A -/NA NCT+/NA p/NA
Fraction
N
A/N
V100 150 200 250 300 350 400 0.0
0.2 0.4 0.6 0.8 1.0
NA-/NA NCT+/NA p/NA
Fraction
T (K)
100 150 200 250 300 350 400 0.0
0.2 0.4 0.6 0.8 1.0
NA-/NA NCT+/NA p/NA
Fraction
T (K)
100 150 200 250 300 350 400 0.0
0.2 0.4 0.6 0.8 1.0
NA-/NA NCT+/NA p/NA
Fraction
T (K)
100 150 200 250 300 350 400 0.0
0.2 0.4 0.6 0.8
1.0 NA-/NA NCT+/NA p/NA
Fraction
T (K)
EA=0.1 eV
EA=0.1 eV
EA=0.2 eV
EA=0.2 eV
EA=0.4 eV
EA=0.4 eV
EA=0.5 eV EA=0.5 eV
T=300 K
100 150 200 250 300 350 400 0.00.2
0.40.6 0.81.0 1.21.4 1.61.8 2.02.2
ECT
Ferm i level (e V)
T (K)
EA=0.7 eV EA=0.5 eV EA=0.4 eV EA=0.2 eV EA=0.1 eV
Supplementary Figure 9. Three-level doping model with thermal activation from ICTCs with ECTb and (deep) acceptor statesEA. Calculated doping efficiencyp/NA and fractions of ionized acceptors NA/NA as well as occupied ICTCs NCT+ /NA vs.(a)the doping concentration or(b)temperatureTfor a three-level system consisting of broadened Gaussians and following the neutrality conditionp+NCT+ =NA. Acceptor ionization is given by Supplementary Equation (5). The e↵ective valence density is set toNV = 2.4⇥1019cm 3, the ICTC binding energy EbCT = 0.64 eV, and the widths A = CT = V = 100 meV. T = 300 K in(a)and NA= 1014cm 3in(b). The acceptor level positions are varied betweenEA= 0.1. . .0.5 eV to emulate the transition from strong to weak doping. Respective Fermi level positions are plotted in(c,d).
Supplementary Note 2. UPS on ZnPc:F6-TCNNQ: Depletion layer widths w and doping efficiency at RT
The doping efficiencyp/NAis determined by UPS on incrementally deposited Ag/MeO-TPD(0.7 nm)/ZnPc(d= 4.5 nm)/ZnPc:F6-TCNNQ(x) samples and applying
(6) p=NA,d= 2"0"r V
e(w2+ 2wd).
Measured spectra of 4 samples are shown in Supplementary Figure 10 and the estimated depletion layer widthswas well as further parameters are summarized in Supplementary Table 1. The 0.7 nm thin MeO-TPD is applied to de-couple the film growth of ZnPc from the metal substrate and the 4.5 nm ZnPc bu↵er layer is used to avoid dopant agglomeration at the metal/organic interface, ensuring a homogenous doping profile through the sample.
18 17 16
Intensity (a.u.)
Binding energy (eV)2 1 0
i-ZnPc(4.5nm)
p-ZnPc 0/0.4/0.7/1.2/2.5/3.7/7.7 nm
MR=0.1773 18 17 16
Intensity (a.u.)
Binding energy (eV)2 1 0
p-ZnPc 0/3.5/7/12/18/26/34 nm
MR=0.0014
i-ZnPc(4.5nm)
18 17 16
Intensity (a.u.)
Binding energy (eV)2 1 0 MR=0.0023
0/2.0/5.0/9.5/14.5/19.5/26.0 nm
p-ZnPc
i-ZnPc(4.5nm)
18 17 16
Intensity (a.u.)
Binding energy (eV)2 1 0
p-ZnPc 0/1.0/2.5/4.5/6.5/8.5/11/14.5 nm
MR=0.0104
i-ZnPc(4.5nm)
Supplementary Figure 10. UPS on p-doped films at RT.UPS spectra of incrementally de- posited Ag/MeO-TPD(0.7 nm)/ZnPc(4.5 nm)/ZnPc:F6-TCNNQ(x,MR) samples of varying dop- ing ratio.
MR d w EF e V p/NA
(nm) (nm) (eV) (eV)
0.0014 4.5 23±2.0 0.71 0.62 0.164 0.0023 4.5 17.5±1.2 0.56 1.77 0.197 0.0042 4.5 12.5±1.7 0.46 0.87 0.211 0.0104 4.5 12.0±1.0 0.35 0.89 0.103 0.0279 4.5 9.0±1.5 0.27 1.06 0.064 0.1776 4.5 3.5±0.7 0.20 1.13 0.039
Supplementary Table 1. Depletion layer widths and doping efficiencies in ZnPc:F6- TCNNQ.Doping efficiency⌘dop=p/NA calculated by Supplementary Equation (6) from the depletion layer thickness w in Ag/MeO-TPD(0.7 nm)/ZnPc(4.5 nm)/ZnPc:F6-TCNNQ(x) sam- ples determined by incremental UPS (cf. Supplementary Figure 10). EF indicates the Fermi level in the doped layer for x w,dthe thickness of the intrinsic bu↵er layer, ande V the built-in potential. As dielectric constant"r= 4.0 is used.[2]
0 5 10 15 20 25 30 35 0.0
0.2 0.4 0.6 0.8 1.0 1.2 1.4
w
MR=0.010 MR=0.0014
MR=0.0023
Fermi level (eV)
x (nm)
MR=0.18 MR=0.028
MR=0.0042 undoped
0 10 20 30 40 50
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
100 K 150 K 200 K 250 K 300 K
MR=0.002
Fermi level (eV)
x (nm)
T=100K undoped
MR=0.01 MR=0.22
trapping
a b
Supplementary Figure 11. Depletion layer widths at metal/organic contacts in UPS. (a) Depletion layer widths w resolved by incremental UPS on Ag/MeO- TPD(0.7 nm)/ZnPc(4.5 nm)/ZnPc:F6-TCNNQ(x,MR) samples at RT.(b)Calculated level bend- ing and depletion widths at Schottky contacts of varying doping ratio and temperature (solid lines, vertical ticks mark the depletion widths w(T)) in comparison to UPS on Ag/ZnPc:F6- TCNNQ(xm) samples under liquid N2-cooling (symbols).
Supplementary Note 3. UPS on ZnPc:F6-TCNNQ: Temperature-dependent deple- tion widthw(T)and level bending
Ag/ZnPc:F6-TCNNQ(xm) samples of varying doping ratio are investigated by UPS under tem- perature variation (93 K< T <300 K). The evaporated organic layer thicknessesxmare larger than the expected depletion widths at RT. UPS spectra and determined Fermi level positions are given in Supplementary Figure 12. For samples withMR0.01 a shift ofEF by up to several 100 meV towards mid-gap is found when cooling to 100 K, which is understood to occur due to an increase in the depletion width w(T) beyond the organic layer thicknessxmas illustrated in Supplementary Figure 11 (b). For three doping ratios, the EF(T) UPS values (symbols) are compared to calculated level bendings (lines). The energy level bending within the depletion zone at Ag/ZnPc:F6-TCNNQ(x) interfaces is given by[3]
(7) EV(x, T) = 0
eNCT
"0"r
✓
w(T)x x2 2
◆
for xw ,
in which the temperature-dependent depletion width
(8) w(T) =
s2"0"rVbi(T) eNCT
is defined by the amount of isolated ionized dopants, thus free carrier density,NCT(T) =p(T), and respective built-in potentialVbi(T) = 0 EF(T). The carrier density at diminished tempera- turesp(T) is estimated from the doping efficiency measured by UPS at RT and the Arrhenius-type deactivation applying Eact= 20.7 meV. The built-in potentialVbi(T) is determined by the in- terface potential 0= 1.33 eV and the (unknown) bulk Fermi levelEF(T) beyond the depletion zone edge. Solutions of the generalized neutrality condition (Supplementary Equation (1)) yield EF(T) shifts towards the valence statesEV upon cooling. Respective dEF/dT correlations get weakened with increasing energetic disorder, however, do not exceed 100 meV when cooling from RT to 100 K (cf. Supplementary Figure 8). This circumstance is hence expected to only weakly superimpose the depletion layer enlargement e↵ect in the UPS experiments, and therefore, the approximationVbi(T) =Vbi(RT) is applied in Supplementary Equation (8).
ForMR= 0.22, the calculated depletion widthw(T = 100 K) = 13.8 nm is yet smaller then the organic layer thickness (xm = 14 nm), which is consistent with a practically negligible mea- sured EF(T) shift. For the lower doped samples, however, the depletion widths clearly in- crease beyond the organic layer thicknesses. In case of MR = 0.01, the measured Fermi level well matches the calculated level bending at 100 K. Furthermore, the calculated depletion width w(T = 100K) = 33.2 nm fits well to the value determined byC(f) spectroscopy at 100 K (cf.
Fig. 3, main article). The MR= 0.002 sample marks the transition to the trap filling regime already at RT, therefore, a much strongerEF(T) variation is found in UPS than calculated.
100 200 300 0.3
0.4 0.5 0.6 0.7
MR=0.01
T (K)
100 200 300
0.5 0.6 0.7 0.8 0.9 1.0 1.1
MR=0.002
T (K) 17 16
Intensity (a.u.)
Binding energy (eV)2 1 0
xm=35 nm
T/K=108/153/205/243/276/300 MR=0.0008
17 16
Intensity (a.u.)
Binding energy (eV)2 1 0
xm=26 nm
T/K=128/154/185/212/244/270/303 MR=0.002
17 16
Intensity (a.u.)
Binding energy (eV)2 1 0
xm=16 nm
T/K=108/128/153/205/243/276/300 MR=0.01
17 16
Intensity (a.u.)
Binding Energy (eV)2 1 0
xm=14 nm
T/K=100/165/223/273/RT MR=0.22 17 16
Intensity (a.u.)
Binding energy (eV)2 1 0
xm=20 nm
T/K=93/155/213/273/RT MR=0.00086
100 200 300
0.8 0.9 1.0 1.1 1.2 1.3 1.4
MR=0.0008 undoped
MR=0.00086
T (K)
Fermi level (eV)
17 16
Intensity (a.u.)
Binding energy (eV)2 1 0
xm=17 nm
T/K=103/127/155/184/215/243/270/303 MR=0.125
100 200 300
0.0 0.1 0.2 0.3 0.4
MR=0.22 MR=0.125
T (K) a
b
Supplementary Figure 12. UPS on p-doped films under liquid N2 cooling. (a)UPS spectra and(b)determined Fermi level positions w.r.t. the ZnPc HOMO onsets of Ag/ZnPc:F6- TCNNQ(xm,MR) samples measured under varying temperatureT= 93. . .300 K.
Supplementary Note 4. Monte Carlo simulations
Kinetic Monte Carlo simulations, similar to Ref.[4] including randomly chosen dopant sites[5], are performed for a Gaussian disordered energy landscape
(9) g(E) = 1
p2⇡ 2exp
✓ E E0
2 2
◆ ,
using nearest neighbor hopping on a simple cubic lattice with periodic boundary conditions. Boxes with 21⇥21⇥21 sites are simulated for dopant concentrations within 2⇥10 4. . .1⇥10 1. To check for finite size e↵ects, systems with 51⇥51⇥51 were investigated for concentrations below 1⇥10 2. Dopant cell energies are randomly distributed following the same standard deviation as for the matrix, with however, a mean value shifted up by 0.05 eV. The on-site interaction energy between dopant cells and charge carriers is limited to the nearest neighbor Coulomb binding energy.
This accounts for the high ionization probability that was found in the absorption measurements (cf. main article).[6] Deep traps are included, with a concentrationcT= 7⇥10 4, broadening of 25 meV, and mean depth ofET = 1.6 eV.[7] Hopping rates are calculated using Miller-Abrahams rates
(10) ⌫ij=⌫0
(exp⇣ E
j Ei kBT
⌘
, Ei< Ej
1 , Ei Ej
,
performing at least 107 hopping events. Results of 20 di↵erent energy landscapes are averaged.
Coulomb interactions of ionized dopants and charge carriers are calculated using Ewald-Summation,[8]
with a lattice constanta= 0.85 nm and dielectric constant"r= 4.0. After each hopping event, the hopping rates of all charge carriers within a radius of 8 cells of the target site are re-calculated.[9]
To extract the electrical mobility and to minimize field induced e↵ects, a low external electric field Eext= 5⇥106V/m is applied.
The electrical conductivity elis calculated by multiplying the determined e↵ective mobilityµe↵
(as described in Ref.[4]) with unit chargeeand thetotal number of charge carriers in the simu- lation, which is equal to the number of dopantsNA'NA:
(11) el=e⇥µe↵⇥NA
Eext ⌫0 a " host E0,host dopant E0,dopant T ET cT T
(V/m) (s 1) (nm) (eV) (eV) (eV) (eV) (eV) (eV) (K)
5e6 1.2e12 0.85 4.0 0.08 0 0.08 0.05 0.025 -1.6 7e-4 300
Supplementary Table 2. Monte Carlo simulation parameters for ZnPc:F6-TCNNQ.
Compilation of the parameters used for simulating the conductivity of ZnPc:F6-TCNNQ by Monte Carlo. The trap values{cT, ET, T}are taken from Ref.[7].
10-4 10-3 10-2 10-1 100 10-7
10-6 10-5 10-4 10-3
Mobility µeff (cm2 /Vs)
Molar doping ratio
w/o traps w/ traps
a b
10-4 10-3 10-2 10-1 100 0.0
0.2 0.4 0.6 0.8 1.0
Site Occupation Probability
Molar doping ratio
nn w/o traps nn w/ traps nn+1 w/o traps nn+1 w traps
c
Supplementary Figure 13. Monte Carlo transport simulations on ZnPc:F6-TCNNQ.
(a)E↵ective mobilityµe↵determined by Monte Carlo simulations on boxes with 213sites. Filling of deep traps with a relative concentration ofcT = 7⇥10 4, which corresponds to an absolute density ofNT= 7.2⇥1017cm 3 for p-ZnPc,[7] causes a strong rise inµe↵forMR<0.01. (b) Corresponding site occupations: Shown is the probability that sites, for which a nearest-neighbor (nn) or next nearest-neighbor (nn+1) site is a dopant, are occupied by a charge carrier (hole).
The (nn) probability is much higher than that of (nn+1) sites due to Coulomb attraction of the carriers to ionized dopants. Due to presence of deep traps, the occupation probabilities strongly drop forMR<0.005 each. This is illustrated in(c)where the spatial site occupation for holes is shown atMR= 10 3. For each site, the plotted dot sizes scales with the respective occupation probability. A large fraction of the holes is found in deep traps states. A respective site occupation plot w/o traps is given in Figure 5 of the main article.
Simulations with 513sites yield same occupation probabilities and mobility trends.
Supplementary References
[1] J. Huang, T. Watanabe, K. Ueno, and Y. Yang. Highly Efficient Red-Emission Polymer Phosphorescent Light-Emitting Diodes Based on Two Novel Tris (1-phenylisoquinolinato-C2, N) iridium (III) Derivatives.Adv.
Mater.19, 739-743 (2007).
[2] M. L. Tietze, W. Tress, S. Pf¨utzner, C. Sch¨unemann, L. Burtone, M. Riede, K. Leo, K. Vandewal, S. Olthof, P. Schulz, and A. Kahn. Correlation of open-circuit voltage and energy levels in zinc-phthalocyanine:C60bulk heterojunction solar cells with varied mixing ratio.Phys. Rev. B88, 085119 (2013).
[3] S. M. Sze, Physics of Semiconductor Devices.John Wiley and Sons, New York, 2. edition(1981).
[4] J. Zhou, Y. C. Zhou, J. M. Zhao, C. Q. Wu, X. M. Ding, and X. Y. Hou. Carrier density dependence of mobility in organic solids: A Monte Carlo simulation.Phys. Rev. B75, 153201 (2007).
[5] S. Olthof, S. Mehraeen, S. K. Mohapatra, S. Barlow, V. Coropceanu, J.-L. Brdas, S. R. Marder, and A. Kahn.
Ultralow Doping in Organic Semiconductors: Evidence of Trap Filling.Phys. Rev. Lett.109, 176601 (2012).
[6] J. Zhou, Y. C. Zhou, X. D. Gao, C. Q. Wu, X. M. Ding, and X. Y. Hou. Monte Carlo simulation of charge transport in electrically doped organic solids.J. Phys. D: Appl. Phys.42, 035103 (2009).
[7] M. L. Tietze, P. Pahner, K. Schmidt, B. L¨ussem, and K. Leo. Doped Organic Semiconductors: Trap-filling, Impurity Saturation, and Reserve Regimes.Adv. Funct. Mater.25, 2701 (2015).
[8] S. W. de Leeuw, J. W. Perram, and E. R. Smith, Simulation of electrostatic systems in periodic boundary conditions. I. Lattice sums and dielectric constants.Proc. R. Soc. Lond. A373, 27-56 (1980).
[9] M. C. Heiber and A. Dhinojwala. Dynamic Monte Carlo modeling of exciton dissociation in organic donor- acceptor solar cells.J. Chem. Phys.137, 014903 (2012).
