Organic semiconductor density of states controls the energy level alignment at electrode interfaces

Abstract

Minimizing charge carrier injection barriers and extraction losses at interfaces between organic semiconductors and metallic electrodes is critical for optimizing the performance of organic (opto-) electronic devices. Here, we implement a detailed electrostatic model, capable of reproducing the alignment between the electrode Fermi energy and the transport states in the organic semiconductor both qualitatively and quantitatively. Covering the full phenomenological range of interfacial energy level alignment regimes within a single, consistent framework and continuously connecting the limiting cases described by previously proposed models allows us to resolve conflicting views in the literature. Our results highlight the density of states in the organic semiconductor as a key factor. Its shape and, in particular, the energy distribution of electronic states tailing into the fundamental gap is found to determine both the minimum value of practically achievable injection barriers as well as their spatial profile, ranging from abrupt interface dipoles to extended band-bending regions.

ARTICLE

Received 9 Jan 2014 | Accepted 20 May 2014 | Published 18 Jun 2014

Minimizing charge carrier injection barriers and extraction losses at interfaces between organic semiconductors and metallic electrodes is critical for optimizing the performance of organic (opto-) electronic devices. Here, we implement a detailed electrostatic model, capable of reproducing the alignment between the electrode Fermi energy and the transport states in the organic semiconductor both qualitatively and quantitatively. Covering the full phenomenological range of interfacial energy level alignment regimes within a single, consistent framework and continuously connecting the limiting cases described by previously proposed models allows us to resolve conicting views in the literature. Our results highlight the density of states in the organic semiconductor as a key factor. Its shape and, in particular, the energy distribution of electronic states tailing into the fundamental gap is found to determine both the minimum value of practically achievable injection barriers as well as their spatial prole, ranging from abrupt interface dipoles to extended band-bending regions.

DOI: 10.1038/ncomms5174 OPEN

Organic semiconductor density of states controls the energy level alignment at electrode interfaces

Martin Oehzelt1,2, Norbert Koch1,2 & Georg Heimel2

1 Helmholtz-Zentrum Berlin fr Materialien und Energie GmbH, Bereich Solarenergieforschung, Albert-Einstein-Stra 15, 12489 Berlin, Germany. 2 Institut fr Physik, Humboldt-Universitat zu Berlin, Newtonstra 15, 12489 Berlin, Germany. Correspondence and requests for materials should be addressed to M.O. (email: mailto:[email protected]

Web End [email protected] ).

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Organic electronics has tremendous potential for extending and complementing the range of conventional semiconductor applications and has, to some extent, already

entered the market. This is especially true for organic light-emitting diodes (OLEDs)16 in displays of mobile devices and, very recently, in television panels. In the elds of solid state lighting, integrated circuits based on organic eld-effect transistors (OFETs)711 and organic photovoltaic cells (OPVCs)1216, commercial breakthrough is still ahead, with considerable effort in fundamental as well as applied research currently undertaken. All these devices have in common one or more organic semiconductor layer(s), possessing (as every semiconductor) a non-vanishing energy gap between occupied and empty electronic states. Electrical connection of the organic semiconductor(s) to peripheral circuitry, however, must inevitably be realized by metallic contacts, with a wide range of elemental metals and degenerately doped inorganic or organic semiconductors employed today3,16,17. These are characterized by a continuum of electronic states lled up to a common electron chemical potential, often referred to as the Fermi level, EF.

Depending on the intended function of the organic electronic device, charges must either be injected from the metallic electrode into the organic semiconductor (OLED/OFET) or they must be collected from the organic semiconductor by the metallic electrode (OPVC)18,19.

In Fig. 1a, a typical situation for the energetic alignment of all relevant electronic states is sketched schematically. We immediately realize that, in such a situation, charge carriers encounter energy barriers, De for electrons and Dh for holes, if they are to be injected and that, for their extraction, corresponding energy losses occur. This has led the community to acknowledge that minimizing these barriers/losses and, in a broader sense, controlling interfacial energy level alignment in general, is a key factor for improving device performance18,2029.

If, for a specic material pair, the situation sketched in Fig. 1a is found unsatisfactory, the obvious strategy is to reduce barriers/

losses by either moving EF towards the occupied or unoccupied molecular levels (for example, by modifying the electrode work function or by choosing a different electrode material) or to move one of the molecular levels closer to EF (typically by choosing a different organic semiconductor).

As the ultimate limit of such a strategy, one could assume that it was possible to eliminate barriers/losses altogether (Fig. 1b). In practice, however, this was only observed for monolayers of select molecules3034, but could never be achieved for multilayer organic semiconductor lms of device-relevant thickness. There, in contrast, non-vanishing energy barriers were found to remain (Fig. 1c). Several models have been developed in the past to explain this phenomenon2029,3541, each of which will be discussed to some detail in corresponding sections below. They differ not only in their intended range of applicability (from a single organic semiconductor layer26 to thick lms23,25,27,29) but also in the envisioned regimes of electronic coupling strength between organic and electrode (from weak coupling with a passivated electrode23,25,27,29 to intermediate coupling with an atomically clean metal26) as well as in the assumed energy distribution of the electronic states in the organic (from discrete23,25,29 to continuous26,27).

Here, we present results from a numerical electrostatic model, which allows treating all these various scenarios on equal footing. The full wealth of all encountered interfacial phenomena is described qualitatively and, provided required input data are available, even quantitatively24. With previous models naturally emerging as different limiting cases, we consolidate diverging views in literature regarding the physical origin of non-vanishing injection barriers (Fermi level pinning by metal-induced density of gap states26 versus nite-temperature occupation of discrete molecular levels23,25) as well as their spatial prole (interface dipole26,29 versus band bending25,27), and we provide a single, coherent framework for understanding the energy level alignment at interfaces between metallic electrodes and organic semiconductors.

Initial Final

VL

EA

IE

Wffilm

a b

Unoccupied

eV(z)

LUMO

EF

e

h

e

EF

h

HOMO

Occupied

BE

BE

1..............NLayer

BE

1..............NLayer

Metal Organic

Metal Organic

Metal Organic

Figure 1 | Sketch of the energy level alignment at organic/electrode interfaces. (a) Schematic showing the Fermi-Dirac occupation function with Fermi level EF for the metallic side of the interface. The difference in binding energy (BE) between EF and the onsets of occupied and unoccupied density of states (DOS) on the organic semiconductor side are the charge injection barriers, Dh for holes and De for electrons, respectively. (b) Example of a possible initial situation for the iterative electrostatic model described in the text. The energy differences between the onsets of the DOS derived from the highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) to the vacuum level (VL) dene the ionization energy (IE) and the electron afnity (EA) of the organic semiconductor, respectively. The energy difference between EF and VL is the work function of the organic lm (Wflm). (c) Final energy level alignment after convergence of the iterative scheme discussed in the text. With increasing distance zfrom the electrode, the DOS increasingly shifts to higher BE by the local electron potential energy eV(z), thus increasing Dh and decreasing De with

respect to the initial situation.

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ResultsIntroducing the model. Our model is inspired by the earlier work of Vasquez et al.26,39 and, more recently, of Blakesley et al.27,28, as well as of Greiner et al.23 and Ley et al.25 Going beyond refs 23,25, however, we take into account a continuous density of states (DOS) both for the occupied and the unoccupied levels in the organic semiconductor. For simplicity, we start with the common choice27,42,43 of one Gaussian peak, G(E EH,sH),

arising from the energy distribution of the highest occupied molecular orbitals (HOMOs) and one, G(E EL,sL), from the

distribution of the lowest unoccupied molecular orbitals (LUMOs) as indicated in Fig. 1b. To unambiguously dene these peaks, both the energies of their maxima, EH and EL, and their standard deviations, sH and sL, need to be specied. The latter can be approximated, for example, by the width of the HOMO-derived feature observed in ultraviolet photoelectron spectroscopy (UPS). Here, we adapt the constant value of sH

sL 0.25 eV, found for the archetypical organic

semiconductor pentacene44. From UPS and inverse photoelectron spectroscopy also the ionization energy (IE 4.8 eV)44 and the electron afnity (EA 2.6 eV)45 of

pentacene are known. These quantities are typically determined from the energy difference between the vacuum level (VL) and the low-binding energy onset of the UPS spectrum and the high-binding energy onset of the inverse photoelectron spectroscopy spectrum, respectively. Choosing the onset of a Gaussian peak to be the energy, where the tangent through the inection point crosses the base line, puts the peak centres 2s away from the so obtained onsets, that is, at EH 5.3 eV and EL 2.1 eV,

respectively. Also indicated in Fig. 1b is the work function, Wflm, given by the energy difference between the Fermi level and the VL outside the organic semiconductor lm. Note that, in the specic situation shown, Wflm is actually higher than the IE of the organic semiconductor, where electrons reside at energies above EF before charge equilibration. It is, therefore, clear that in the course of establishing a common electron chemical potential, charge will ow across the interface. To quantify the amount of transferred charge in the general case, we discretize the organic semiconductor lm into layers of thickness Dz and distance z from the electrode surface. We then calculate the charge density r(z) in each of these layers by integrating

r z

e n

Z 1

1

1gH e b E E

F

1

;

2

Here, gH and gL are the HOMO and LUMO (spin-) degeneracies, both 2 in the case of pentacene, and b 1/kBT with

kB the Boltzmann constant and T the temperature, set to 300 K throughout the paper. Finally, the energy distributions of HOMO- and LUMO-derived levels are DH[E eV(z)]

G[E EH eV(z), sH] and DL[E eV(z)] G[E EL eV(z),

sL] in our model case, unless otherwise noted. We stress, however, that (i) any peak shape can be used instead of a Gaussian, (ii) each discretization interval could have a different DOS to account, for example, for image-charge screening by the metal, (iii) more molecular states can easily be taken into account by adding the respective terms in the curly brackets and (iv) potential temperature effects can be included in the standard deviation s s(T); for the values used here, 2s 0.50 eV is about 20 times

bigger than kBT at T 300 K and, therefore, the temperature

dependence of fH/L(E) has only little impact on level alignment.

Finally, the electrostatic potential across the organic semiconductor lm, V(z), is rst set to zero for calculating an initial guess of the charge density via equation (1). Once known, this r(z) serves to nd the next V(z), which, going beyond refs 23,25, we obtain by numerically solving the generalized one-dimensional Poisson equation

r e z

rV z

rz

e0

1

fLE

1gL eb E E

F

1

:

3

with the discrete-difference method on a variable grid, using the second-order, central-difference scheme with mixed Dirichlet [V(0) 0] and von Neumann [V 0(d) 0] boundary conditions,

where d is the total thickness of the considered organic lm and e0 the vacuum permittivity. For our rst illustrative case of a homogenous pentacene lm, we assume a static dielectric constant e of B3.6, as recently determined by impedance measurements47; note, however, that each discretization interval could, in principle, also be given a different dielectric constant. The DOS of each discretization interval is then shifted in energy by the respective eV(z), as shown in Fig. 1c, and the next r(z)

is again generated by occupying all states in the organic up to EF.

This self-consistent process is iterated until the difference in charge density between cycles is less than one electron per layer and square meter and the nal injection barriers are obtained as De EF EA and Dh IE EF.

Some illustrative results. To illustrate the results delivered by the method just described, we rst consider 20 layers (B30 nm) of standing pentacene with EF set to lie right at the energy of the

HOMO peak maximum. The self-consistent solution of the Poisson equation for this situation is depicted in Fig. 2a,b, showing the charge density and the electron potential energy, respectively. The charge density rapidly vanishes with increasing distance from the electrode surface and reaches almost zero at 5 nm. The corresponding potential energy, which locally shifts HOMO, LUMO and VL by the same amount (IE and EA remain constant), is characteristic for band bendinga term somewhat liberally borrowed from inorganic semiconductor physics despite the fundamental difference that, instead of actual bands there, a distribution of localized states is assumed here. Although this phenomenon has often been attributed to (impurity or

8 <

:

dE fH E

DH E eV z

1

with e the (positive) elementary charge, n the number of molecules per unit area and per discretization interval Dz. As the IE and EA values reported above pertain to pentacene molecules standing on the electrode with their long molecular axes almost parallel to the surface normal44,45, we accordingly choose Dz 1.42 nm, the distance d001 between the

crystallographic (001) planes in the pentacene single crystal46; Dz then corresponds to the height of one molecular layer. For the sake of simplicity, we consider layer-by-layer growth of pentacene only, with n 4.1 1018 molecules/(m2 Dz). Note, however, that

fractional coverages and different growth modes could easily be incorporated by accordingly choosing layer-specic values for n.

The rst integral in the curly brackets of equation (1) yields the number of holes in the occupied DOS of the organic semiconductor and the second integral the number of electrons in the unoccupied DOS. While of noticeable consequence only for highly degenerate systems, we, nevertheless, follow refs 23,25 by

allowing, in contrast to refs 27,28, only single charging of each molecule, which slightly modies the Fermi function for each individual energy level under consideration to

fHE

1

Z 1

1

dE fL E

DL E eV z

)

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intentional) doping29,48,49 in the past, it has recently been argued to arise also in intrinsic organic semiconductors, both of the conjugated-polymer27 and the small-molecule variety24,25. In trying to relate our results to experimental observations, it is important to recall that the work function measured by, for example, UPS or Kelvin probe only reveals the electron potential energy eV(zZd) just outside the organic lm (highlighted in

Fig. 2b). As pointed out in refs 5053, however, the sequence of

eV(d) values obtained by increasing the total thickness d of an organic lm in a step-wise manner and probing the surface potential at each step does not, in fact, recover the electron potential energy prole eV(z) within the organic lm for any

thickness (Fig. 2c).

Fermi level pinning. With this in mind, we now plot in Fig. 3a the total potential energy change, eV(d), across pentacene lms

of increasing d, for a series of different Fermi level energies. Clearly, when EF lies around mid-gap of the organic semiconductor, only very little charge is transferred from/to the metal electrode and, consequently, the potential energy prole remains close to at. Upon EF approaching either the HOMO or the

LUMO levels, however, pronounced charge transfer and, accordingly, ever higher and steeper potential energy changes across the organic lm are obtained. Practically, the Fermi level is

shifted by choosing electrodes of different work function, Wfelec,

dened by the energy difference between EF and the VL just above the bare electrode surface with no organic material present. The energy barriers/losses for charge carriers, De and Dh, are then related to Wfelec and eV(d) through

De Wf

elec

ID eV d EA; 4

Dh IE Wfelec ID eV d

; 5 where ID is the interface dipole. Either because of contamination through atmospheric and/or solvent exposure or owing to deliberate passivation with inert buffer layers, the ID is often found to be (close to) zero for practically employed electrodes in organic electronics. However, microscopic charge rearrangements originating in a variety of physical and/or chemical phenomena occurring between the electrode surface and the rst organic layer can, in general, lead to appreciable IDs22,37,38,5456. If available, for example, through a fully atomistic and quantum-mechanical treatment on a particular system, then they can, of course, be readily incorporated into the present model through equations (4) and (5). To study the impact of Wfelec on De/h on

more general grounds, however, we refer to an effective electrode work function

Feff Wf

elec

ID; 6

a b c

0.010

0.008

0.006

0.004

0.002

0.000

0.0

(z) (C m2 nm1 )

eV(z) (eV)

0.2

0.4

0.6

0.8

1.0

Measurement

eV(z) (eV)

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0 10 20 30 0 10 20 30 0 5 10 20

15 25

z (nm) z (nm) z (nm)

Figure 2 | Exemplary results of the iterative electrostatic model. (a) Calculated charge density r(z), and (b) electron potential energy eV(z) within a

d 30 nm thick (E20 layer) pentacene lm. Surface sensitive experimental methods (for example, UPS or Kelvin probe) only determine the total

electron potential energy drop eV(d) across the entire organic-semiconductor lm. (c) eV(z) for a range of different lm thicknesses d up to 30 nm,

highlighting that the series of experimentally determined eV(d), shown as line connecting open circles, does not reproduce the band-bending eV(z) within the organic semiconductor for any thickness.

a b c

1.0

0.5

0.0

0.5

1.0

0

2

+

[afii9838]+

[afii9838]+

2

0

S=0

eV(d) (eV)

e(eV)

1

1

h(eV)

e(eV)

1

1

h(eV)

S=1

S=0

[afii9838]

2

0

[afii9838]

0 10 20 30 0 10 20 30

0

1 2 3 4 5 6

2

d (nm) d (nm)

eff (eV)

Figure 3 | Impact of effective substrate work function on band bending and barriers. (a) Total electron potential energy change eV(d) across

pentacene lms of varying thickness d for a series of Fermi level energies ranging from 0.15 eV below EL, the initial LUMO peak energy (top trace), to0.05 eV above EH, the initial HOMO peak energy (bottom trace). (b) Data from a converted to injection barriers De for electrons (left axis) and Dh for holes (right axis). Dashed horizontal lines indicate respective values of zero and the vertical line highlights the cut visualized in c. (c) Injection barriers

De (left axis) and Dh (right axis) as a function of effective substrate work function Feff for a d 10 nm thick pentacene lm with ( ) and without (J)

polaronic relaxation energies l (for holes) and l (for electrons) taken into account. The transitions between the regions with slope S 0 and S 1 mark

the so-called pinning work functions, F for LUMO pinning and F for HOMO pinning. The lowest achievable injection barriers are not related to l/ .

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in the following. Before charge equilibration, that is, with V(d) 0, the initial barriers are then simply given by

De Feff EA and Dh IE Feff, respectively.

This now allows us to make the transition from relative potential energy changes for different values of EF (Fig. 3a) to absolute values of De and Dh for a series of effective electrode work functions, both of which are now quantities readily accessible through experiment. Figure 3b illustrates that changing Feff indeed permits tuning the interfacial energy barriers/losses, but only within a certain range. For our model case of pentacene, the achievable minimum separation between EF and EA/IE rapidly converges to De Dh 0.4 eV with increasing lm

thickness, where decreasing Feff below B3.0 eV does not further reduce De and increasing Feff beyond B4.4 eV does not further reduce Dh. A more convenient way of visualizing these data is to directly plot the energy barriers as a function of Feff for a given

lm thickness, for example, d 10 nm as indicated by the vertical

line in Fig. 3b.

The obtained functional dependence (open symbols in Fig. 3c) is characterized by a slope of zero (S 0) for low Feff, a region

with S 1 for intermediate Feff, and again S 0 for high Feff. The

transitions between the different regions are marked by the so-called pinning work functions, F 3.0 eV for LUMO and F 4.4 eV for HOMO pinning with the latter matching the experimental value for a 10-nm lm of pentacene36. The term pinning refers to the observation that, for multilayer organic semiconductor lms of device-relevant thickness, EF cannot cross the HOMO or LUMO level onsets (marked as horizontal lines) and, thus, energy barriers/losses cannot be completely eliminated; regardless of the choice for Feff, the Fermi level appears to be stuck at specic energy separations (B0.4 eV for d 10 nm) well

above/below the respective peak onsets.

In the past, this observation has led to the postulation of material-specic, discrete, quantum-mechanical states at these energies, the so-called integer charge-transfer (ICT) states, with ICT shifted up in energy from the HOMO onset and ICT

shifted down in energy from the LUMO onset into the gap of the organic semiconductor29. As already pointed out in refs 25,27,28, however, the fact that the pinning energies of EF in the organic semiconductor gap emerge naturally (and quantitatively correct) from electrostatics alone: (i) lifts the necessity for invoking the existence of such states and (ii) invalidates the interpretation of their energy separation from the HOMO and LUMO onsets as the respective polaron-binding energies l and l . We explicitly illustrate this latter point in Fig. 3c for our Gaussian

DOS (cf. ref. 28). For our considered model case, pentacene, the polaron-binding energy, that is, the energy stabilization of an

excess charge in the organic semiconductor by geometric relaxation of the charged molecule itself (internal relaxation energy) and of the surrounding lattice (external relaxation energy), was found to be only l / 0.07 eV (refs 57,58) with

the latter being negligible compared with the former59. This value is taken into account in equation (1) by shifting the HOMO and LUMO levels symmetrically towards each other, thus effectively reducing the gap of the organic semiconductor. The magnitude of the resulting changes (closed symbols in Fig. 3c) is, not unexpectedly, comparable to the absolute value of l / and, thus, its contribution to the observed minimum barriers is smaller than the typical experimental accuracy of B0.1 eV; polaronic effects will, therefore, no longer be considered in the following.

Film thickness and Gaussian DOS. Briey returning to Fig. 3b, it is evident that the relationship between De/h and Feff changes

with the total thickness of the organic lm. In Fig. 4a, we show vertical cuts through the data presented in Fig. 3b not only for d 10 nm, as discussed in Fig. 3c, but for an entire series of

thicknesses. As a direct consequence of band bending within the organic lm, the substrate work functions where LUMO/HOMO pinning sets in successively decrease/increase with decreasing lm thickness down to F B2.4 eV and F B4.7 eV, respec

tively, for a monolayer of pentacene, which, again, compares favourably to experiment35. Evidently, the thinner the organic semiconductor lm, the lower De and Dh can be made by, respectively, decreasing or increasing Feff until, in the extreme case of a monolayer, they vanish for Feff 5.5 eV and

Feff 1.8 eV, respectively (cf. refs 3033).

The same could, arguably, be achieved also for thicker layers if the DOS tailing into the gap of the organic could be eliminated; it is the presence and the occupation of these gap states, after all, that prevents EF from further approaching the HOMO/LUMO onsets. The origin of the gap states is commonly attributed to structural imperfection/defects28,42,6062. Their density and energy distribution can experimentally be determined only on a case-by-case basis6062, as they depend on specics of sample preparation and environment, that is, exact lm structure and composition60. To elucidate their impact on energy level alignment on more general grounds, we vary the width of the HOMO- and LUMO-related DOS while keeping it Gaussian-shaped, which has been shown to phenomenologically emulate also the impact of exponential tails27. Leaving, at the same time, the energies of the peak maxima, EH and EL, unchanged, trivially leads to the HOMO and LUMO onsets moving into the gap and, consequently, to EF getting pinned ever farther in the gap as well

a b c

0

0

1

2

1.5 nm

30 nm

[afii9846]=0.1 eV

[afii9846]=0.4 eV

0.0

0.5

1.0

2.5

e(eV)

2

1

0

1 2 3 4 5 6

S=1

h(eV)

e(eV)

2

1

0

S=1

eV(z) (eV)

1.5

2.0

S=0

S=0

1

2

h (eV)

[afii9846]=0.1 eV

[afii9846]=0.4 eV

eff (eV)

1 2 3 4 5 6eff (eV)

0 2 4 6 8 10

z (nm)

Figure 4 | Impact of lm thickness and width of Gaussian DOS. (a) Injection barriers De for electrons (left axis) and Dh for hole (right axis) as a function of effective substrate work function Feff for pentacene lms of thicknesses from d 1.5 nm to 30 nm. (b) Injection barriers De (left axis) and Dh

(right axis) as a function of Feff for a d 10 nm thick pentacene lm with the standard deviations of the Gaussian HOMO and LUMO DOS varied

from sH/L 0.1 eV up to sH/L 0.4 eV while retaining a constant IE and EA. (c) Electron potential energy proles eV(z) at the highest effective substrate

work function Feff 6.5 eV for all sH/L treated in b.

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(not shown). A maybe less trivial result is presented in Fig. 4b. There, we keep the HOMO and LUMO onsets, which represent the physical material parameters IE and EA, respectively, at constant energy. Varying the width of the DOS then requires adjusting the energy separation between the peak maxima accordingly. Even under these conditions, however, reducing the Gaussian width of HOMO- and LUMO-related DOS leads to(i) the transition between the regimes of Fermi level pinning (S 0) and the SchottkyMott limit (S 1) to become more

abrupt, (ii) EF successively approaching the respective onsets in the pinning regimes and (iii) the spatial extent of the band-bending region to be reduced, as evidenced in Fig. 4c. The range of minimal energy barriers (B0.2 eV to B0.6 eV) emerging from our model spans the entire range of values observed in experiment44,55, highlighting the decisive role of disorder in the organic semiconductor in determining interfacial energy level alignment60. Note also that, for T40 K, nite barriers remain even in the limiting case sH/L-0 of discrete molecular states, which is, in fact, the only case treated in refs 23,25.

From band bending to interface dipole. Notably, the phenomenology described so far, the characteristic shape in Figs 3c and 4 in particular, is only ever observed for weakly interacting electrodeorganic interfaces. There, either through surface contamination or by design, the organic semiconductor is electronically decoupled from the metallic states by a thin, wide-gap buffer layer, which, in following refs 27,28, we did not explicitly take into account so far. As shown in the Supplementary Discussion, even doing so does not alter the fact that the inter-facial energy level alignment between organic semiconductor and metallic electrode always falls into one of three regimes, HOMO pinning, SchottkyMott limit and LUMO pinning, characterized by slope parameters S dDe/dFeff dDh/dFeff of (close to)

zero, one and again zero, respectively (cf. Supplementary Figure1). If, however, the buffer layer is eliminated completely in experiments, which can be achieved by, for example, depositing the organic semiconductor directly onto atomically clean metal surfaces in ultrahigh vacuum, also fractional slope parameters between 0 and 1 are frequently observed26,36,39,55,63. Despite having explored a good portion of the parameter space available in our model, we failed to generate non-integer values of S so far, whereas they are readily (and often quantitatively correct) predicted by the induced density of interface states model26,39.

This is surprising insofar, as this model is, in essence, quite similar to ours. Besides typically treating only molecular monolayers and assuming the organic DOS to be constant around EF for evaluating S, the main difference lies in the peak shape, which the authors take to be Lorentzian rather than Gaussian. This is entirely reasonable for the envisioned situation, where direct electronic coupling of the monolayer molecular levels to the metal leads to homogenous life-time broadening dominating over disorder-induced inhomogeneous (that is, Gaussian) broadening60. Having already elucidated the impact of the latter in Fig. 4b, we now choose a Voigt peak function with successively increasing Lorentzian weight to represent the DOS of the rst organic layer, while retaining pure Gaussians for all subsequent layers. The Feff-dependence of the resulting injection barriers into a d 10 nm lm of pentacene is shown in Fig. 5a,

containing also the limiting, pure-Gaussian case already reported in Fig. 3c for comparison.

Clearly, with increasing weight of the Lorentzian contribution, ever lower/higher substrate work functions are required to reach the same barriers for electrons/holes. More importantly, however, the Feff-region of non-vanishing slope parameter expands, where

S itself decreases from unity to a value of 0.42 for a Lorentz dominated (75%), down to 0.35 for an exclusively Lorentzian DOS, which brackets the experimental observed values of 0.37 and 0.40 for pentacene55,63.

This remarkable transition between phenomenologically distinct energy level alignment regimes is accompanied by profound changes in the electron potential energy prole eV(z) within

the organic semiconductor lm (Fig. 5b). On increasing the Lorentz weight in the rst-layer DOS, the spatially extended band-bending region in the organic is successively compressed towards the immediate interface with the electrode until, in the case of a pure Lorentzian, it collapses into a potential energy step across only the very rst molecular layer. The abruptness of this step, which is not a unique feature of the Lorentzian peak shape per se but simply a consequence of the (compared to the Gaussian) higher DOS around EF, has led to it being assimilated into the interface dipole (as dened above) in the past. This can be justied by considering that the combined action of all interfacial effects reduces the work function that subsequently deposited molecules see to, in our case, Feff eV(d) 6.5

eV 2.1 eV 4.4 eV, which is, again, the HOMO-pinning work

function F of pentacene. Therefore, no further charge transfer

a b c

0

0.0

2

1

0

[afii9846]=0.1 eV

[afii9846]=0.4 eV

e(eV)

2

1

0

Lorentz

eV(z) (eV)

Gauss

h(eV)

0.2

0.4

0.6

0.8

1.0

1.2

Gauss

1

Lorentz

e(eV)

0

1

2

h(eV)

2

1 2 3 4 5 6

0 2 4 6 8 10

S < 1

eff (eV)

1 2 3 4 5 6eff (eV)

z (nm)

Figure 5 | Fractional slope parameters and band bending versus interface dipole. (a) Injection barriers De for electrons (left axis) and Dh for hole (right axis) as a function of effective substrate work function Feff for a d 10 nm pentacene lm. The peak shape of the HOMO- and LUMO-derived DOS in

the rst layer is successively varied from pure Gaussian over Voigt to pure Lorentzian. (b) Electron potential energy eV(z) within a d 10 nm pentacene

lm and a Feff of 5.3 eV. Changing the peak shape of the HOMO- and LUMO-derived DOS in the rst layer from pure Gaussian over Voigt to pure Lorentzian leads to a collapse of the spatially extended band-bending region to an interface dipole across the rst molecular layer. (c) Injection barriers

De for electrons (left axis) and Dh for holes (right axis) as a function of effective substrate work function Feff for a d 10 nm pentacene lm. The DOS

of the rst layer is kept xed to a Lorentzian peak shape of width 0.25 eV, whereas the standard deviations sH/L of the Gaussian peak shapes in all subsequent layers increase from 0.1 eV up to 0.4 eV. Although the range of linearity decreases succeedingly, the value of the slope parameter So1 remains unchanged.

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between the monolayer-covered electrode and succeeding organic semiconductor layers occurs and, with Dh having reached its minimum value of 0.4 eV already, no additional shifts in electron potential energy arise. Deviation from a strictly linear evolution of Dh/e is not observed until the Gaussian DOS of subsequent bulk layers again tails across EF for extreme values of Feff, thereby causing residual band bending. The range of linearity is thus restricted by the amount of energetic disorder in the bulk (exemplied by sH/L-values ranging from 0.1 eV up to 0.4 eV in

Fig. 5c), but the absolute value of the slope parameter So1 is not affected. This noteworthy result rationalizes the success of the induced density of interface state model in correctly reproducing the interfacial energy level alignment in the limiting case of atomically clean metals with intermediate work functions, despite it considering only monolayer coverage.

DiscussionTo summarize, we present the results of a single, versatile electrostatic model, from which all observed regimes of energy level alignment at metal/(insulator/)organic semiconductor interfaces emerge naturally. Although designed to accommodate unprecedented detail and complexity, it contains prior work as limiting cases, notably, that of Ley et al.25, which is limited to producing either VL alignment (S 1) or Fermi level pinning

(S 0) as a consequence of considering only discrete molecular

states; that of Blakesley et al.27,28, which does not explicitly include insulating buffer layers and, thus, overestimates interfacial charge densities, as shown in the Supplementary Discussion; and that of Vazquez et al.26, which is limited to a single molecular layer with Lorentzian DOS and, thus, fails to predict band bending. In providing a unied picture of the underlying physical mechanisms, our model conrms that the DOS of the organic semiconductor is the central, decisive quantity, responsible for all experimentally encountered phenomena and that controlling it is, therefore, key to minimizing charge carrier injection barriers and/or extraction losses beyond what is possible by adjusting the electrode work function alone.

Using high (for holes) and low (for electrons) work-function electrodes is, of course, still a necessary prerequisite. Our results illustrate, however, that there are intrinsic limits to this strategy and that, to overcome these limits, the amount of electronic states in the energy gap of the organic semiconductor (as well as their energetic separation from its band edges) must be reduced. Besides eliminating defects within the organic semiconductor, our model suggests electronic decoupling from the metallic electrode to be a critical component in achieving this, thereby providing a theoretically well-founded justication for the wide-spread use of thin passivating buffer layers. As a further benecial consequence of cleaning out the gap, spatially extended band-bending regions are predicted to develop within the organic semiconductor, which, in contrast to sharply localized interface dipoles, further lower effective injection barriers in OLEDs under applied bias voltage and facilitate the efcient collection of photo-generated charge carriers in OPVCs by imposing a drift direction. Our results thus provide a solid theoretical basis for past and present efforts in optimizing the interfacial energy level alignment at organic semiconductor/electrode contacts and will, hopefully, inspire future work.

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Acknowledgements

We thank Philipp Herrmann for fruitful discussions. This work was supported by the DFG (SFB951) and the Helmholtz-Energy-Alliance Hybrid Photovoltaics.

Author contributions

M.O. and G.H. devised the model and co-wrote the paper. M.O. implemented the model and performed all calculations. N.K. contributed to content discussions and the writing of the paper.

Additional information

Supplementary Information accompanies this paper at http://www.nature.com/naturecommunications

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How to cite this article: Oehzelt, M. et al. Organic semiconductor density of states controls the energy level alignment at electrode interfaces. Nat. Commun. 5:4174 doi: 10.1038/ncomms5174 (2014).

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