Multitechnique Approach for Determining Energy Levels and Exciton

Article pubs.acs.org/JPCC

Multitechnique Approach for Determining Energy Levels and Exciton Binding Energies of Molecules for Organic Electronics Phillip S. Johnson, Idris Boukahil, and F. J. Himpsel* Department of Physics, University of WisconsinMadison, 1150 University Avenue, Madison, Wisconsin 53706, United States

Kenneth L. Kearns, Joo H. Kang, Jui-Ching Lin, Anne Leugers, and Greg Meyers Analytical Sciences, Core Research and Development, The Dow Chemical Company, 1897 Building, Midland, Michigan 48667 United States

Sukrit Mukhopadhyay Organic Polymers and Organometallics, Core Research and Development, The Dow Chemical Company, 1776 Building, Midland, Michigan 48674, United States

David H. K. Jackson and T. F. Kuech Department of Chemical and Biological Engineering, University of WisconsinMadison, Madison, Wisconsin 53706, United States ABSTRACT: The energies of the frontier orbitals and their electron−hole binding energy are key quantities in organic electronics, such as organic light-emitting diodes (OLEDs) and solar cells. A method is developed for obtaining these quantities from ultraviolet photoelectron spectroscopy (UPS) and optical absorption spectroscopy, combined with calculations of the ionization energy (IE) and the electron affinity (EA). This method provides a more efficient and accurate determination of the lowest unoccupied molecular orbital (LUMO) together with the exciton binding energy. The concept is extended to element-sensitive core-level spectroscopies, such as X-ray photoelectron spectroscopy (XPS) and X-ray absorption spectroscopy (XAS), in order to obtain core exciton binding energies. Two prototypical organic molecules for OLED applications are used as examples, i.e., N,N′-di(1-naphthyl)-N,N′-diphenyl-(1,1′biphenyl)-4,4′-diamine (NPD) and dipyrazino[2,3-f:2′,3′-h]quinoxaline-2,3,6,7,10,11hexacarbonitrile (HAT:CN). These methods have the potential to facilitate the systematic tailoring of molecules for applications in organic electronics. The method devised for determining the LUMO is consistent with previous reports using conventional techniques.

1. INTRODUCTION Organic electronics have expanded rapidly since the first designs of an OLED1 and a dye-sensitized solar cell.2 In the meantime, OLEDs and solar cells based on small organic molecules or polymers have become commercialized. For efficient OLED devices, it is critical to understand the energies of the frontier orbitals that form the charge transport and injection layers.3−5 In addition to the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), it is important to know the binding energy of the exciton that is formed by an electron in the LUMO and a hole in the HOMO. Since an exciton contains two charged particles rather than one, it represents a more complex object that requires more sophisticated theoretical approaches, such as solving the Bethe−Salpeter equation or using time-dependent density functional theory. Excitons are particularly important in solar cells using organic molecules. © 2016 American Chemical Society

The exciton binding energy reduces the HOMO−LUMO gap by the Coulomb attraction between electron and hole. Since the absorption of a solar photon creates an exciton, extra energy is needed to break it up into free carriers. To obtain the energies of the HOMO and LUMO experimentally, one can use photoemission and inverse photoemission spectroscopies.6−11 The exciton binding energy is then obtained as the difference between the HOMO−LUMO gap (= transport gap) and the optical gap for creating an exciton consisting of an electron in the LUMO and a hole in the HOMO. The latter is easily found by optical absorption spectroscopy. However, inverse photoemission has a very low cross section (typically 10−8 photons per electron) in the Received: October 6, 2015 Revised: December 30, 2015 Published: January 2, 2016 1366

DOI: 10.1021/acs.jpcc.5b09783 J. Phys. Chem. C 2016, 120, 1366−1374

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The Journal of Physical Chemistry C ultraviolet range, which requires long integration times and degrades the energy resolution to typically 0.6 eV. Furthermore, the long irradiation of organic molecules with electrons raises the possibility of radiation damage.8 Two-photon photoemission uses a pump−probe scheme to populate empty intermediate states and then probe them by photoemission.12−15 This technique provides high-energy resolution and lifetime information but preferentially selects long-lived intermediate states. As a result, there is a need for a method that determines the LUMO (and unoccupied energy levels in general) both efficiently and accurately. An energy resolution of about 0.1 eV or better is desirable for organic electronics. The complexity of the molecules used in OLEDs and organic solar cells calls for a technique that is element- and bondspecific. That is not the case for the techniques discussed so far. Spectroscopies based on core levels, such as X-ray absorption spectroscopy (XAS) and X-ray photoelectron spectroscopy (XPS), have this capability. A specific atom in a well-defined oxidation state can be selected by the choice of the core level binding energy via XPS, and a specific unoccupied orbital located at that atom can be identified via XAS. While XAS requires a tunable synchrotron light source, it is rather straightforward to implement by detecting the total yield of secondary electrons that are generated by the decay of a core hole. When using element-specific core-level spectroscopies, one also needs to know the core level binding energies (here C 1s and N 1s), together with the binding energies of the core excitons formed between an electron in the LUMO and a core hole in the C 1s or N 1s core levels. The core exciton binding energy is crucial for obtaining accurate results for unoccupied energy levels, since it is generally larger than that of valence excitons (3−4 eV vs 1−2 eV in organic solids). This can be rationalized by the fact that the charge is more concentrated for core electrons than for valence electrons. Consequently, the average distance between the charge densities of electron and hole is shorter for core excitons and generates a larger Coulomb energy. The exception is an interatomic electron− hole pair, such as an electron at a N site interacting with a hole at a C site. In that case the electron−hole interaction is weak, but the absorption cross section is also very small, making such transitions difficult to detect.

Figure 1. Schematic energy diagram involving all the levels discussed in this work. The colored arrows represent the techniques described in this work. For X-ray and optical absorption spectroscopy the simple one-electron energy level scheme is modified by the electron−hole (e−h+) interaction (black double arrows). The ionization energy (IE) and the electron affinity (EA) are obtained easily and accurately from density functional calculations.

calculated ground state energies of the positive and negative molecular ion. The binding energies of valence and core excitons follow from a difference between eq 1 with optical and X-ray absorption spectroscopy, respectively. For the valence exciton formed by a hole in the HOMO and an electron in the LUMO one obtains Ee − h = (IE − EA) − Eex

Eex is the “optical gap”, defined as the energy of the lowest excitation in the optical absorption spectrum. A similar formula holds for core excitons which combine a core hole with an electron in the LUMO. In that case, the HOMO−LUMO gap (IE−EA) is replaced by the core−LUMO gap. The optical excitation energy Eex becomes Eex(core), the lowest excitation in the X-ray absorption spectrum of a core level (core = C 1s, N 1s here). For the core exciton binding energy, Ee−h(core) one obtains

2. CONCEPT Figure 1 illustrates the energy levels that become involved when all these techniques are employed. There are three reference levels which are associated with different techniques. The vacuum level (EVac) is the reference for the calculations, the Fermi level (EF) forms the reference for UPS and XPS, and the HOMO serves as reference level for X-ray and optical absorption spectroscopy. Here we develop a methodology to obtain all the energy levels in Figure 1 by a combination of UPS, XPS, optical absorption spectroscopy, XAS, and density functional calculations. In particular, we address the difficulties in obtaining the LUMO energy ELUMO and the exciton binding energies (double arrows in the upper right corner of Figure 1). The key is a determination of the LUMO energy by a combination of UPS and ground state total energy calculations, using the relation E LUMO = E HOMO + (IE − EA)

(2)

Ee − h(core) = (E LUMO − Ecore) − Eex (core)

(3)

The core level energy Ecore is obtained from XPS. Like the HOMO energy EHOMO, it is referenced to EF (i.e., negative). The LUMO energy is obtained again from eq 1. This methodology is tested using NPD and HAT:CN as prototypes. Of particular interest are the results for the LUMO level, where our method provides a new avenue. For NPD, there exists a combined photoemission and inverse photoemission study to determine the HOMO and LUMO.8 The energies of the HOMO and LUMO were not given explicitly, but one can extract two occupied levels from the photoemission

(1)

The HOMO energy EHOMO is directly measured by UPS, while the ionization energy (IE) and the electron affinity (EA) are 1367


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The Journal of Physical Chemistry C spectrum (a shoulder at about −1.6 eV representing the HOMO and a peak at −2.0 eV), together with a shoulder at about +3.7 eV in inverse photoemission assigned to the LUMO. These correspond to our photoemission result of two similar occupied levels (a shoulder at −1.2 eV and a peak at −1.7 eV), together with a LUMO at +3.7 eV obtained from eq 1. A similar comparison for HAT:CN data gives a HOMO peak at −4.9 eV in photoemission and a LUMO peak at +1.9 eV in inverse photoemission.11 These correspond to our photoemission result of −4.8 eV for the HOMO peak and a LUMO peak at +1.5 eV from eq 1. Regarding the exciton binding energies, we find smaller values for valence excitons than for core excitons, as expected from the arguments given above. For example, in NPD we obtain a binding energy of 1.7 eV for the valence exciton from eq 2 versus a binding energy of 3.2 eV for the C 1s exciton from eq 3. A complete set of all relevant energies will be given after the spectroscopy results in Tables 1−3.

oxidized carbon while no spectral changes is noticed for HAT:CN. For both UPS and XPS it is important to realize that small amounts of dopants, impurities, and defects are able to change the pinning of the Fermi level EF within the gap. Since EF serves as reference level for UPS and XPS, the positions of the HOMO and the core levels are sensitive to the doping, the preparation of the samples, and radiation-induced gap states.16 These effects need to be considered when comparing data sets with different sample preparation. The movement of EF within the HOMO−LUMO gap does not affect optical and X-ray absorption spectroscopy, since their energy reference is the HOMO. Optical Absorption Spectroscopy. The optical spectroscopy measurements were performed using a PerkinElmer Lambda 950 scanning double monochromator. The spectra were acquired at 2 nm resolution with 1 nm/point from 200 to 600 nm. The instrument was calibrated and autozeroed with air in both sample and reference paths. The films, deposited on quartz discs, were measured at 90° relative to the beam, with air in the reference beam path. X-ray Absorption Spectroscopy (XAS). XAS spectra were obtained at the U2 VLS-PGM beamline at the Synchrotron Radiation Center (SRC) in Madison, WI. The photon energy was calibrated as described previously,17 resulting in an absolute accuracy of ±0.15 eV and a relative accuracy of ±0.05 eV (between different peaks in the same spectrum). All spectra were obtained with total electron yield detection and normalized to the electron yield of an upstream gold mesh. The effect of hydrocarbon contamination on the Au mesh was corrected via dividing the normalized sample spectrum by the normalized spectrum of a clean Au film. This “double division” eliminates any C signal from the mesh. Radiation damage was minimized by using the narrowest possible exit slits.16 Repeated scans on the same spot did not exhibit any spectral changes. All XAS spectra were acquired at normal incidence with total electron yield detection, which has a probing depth of about 5 nm. For the N 1s spectra a linear background originating from the tail of the C 1s edge was subtracted. It was matched to the energy region below the N 1s edge.

3. EXPERIMENTAL TECHNIQUES Thin Film Preparation. Physical vapor deposition (PVD) of NPD or HAT:CN was carried out in an Åmod deposition chamber from Angstrom Engineering. NPD and HAT:CN were purchased from Luminescence Technologies Corporation. NPD was sublimed prior to use, and HAT:CN was used as received. Each material was placed in an alumina crucible which was resistively heated using a tungsten boat. Crucibles and boats were purchased from the R.D. Mathis Company. ITOcoated glass substrates were used for XAS, XPS, and UPS experiments. Quartz slides were used for optical absorption measurements. Substrates were placed on a rotating substrate holder and held onto the holder using either metal clips or double-sided carbon black tape (SPI Supplies). The rate of rotation was approximately 60 rpm; the rotation maintained uniform film thickness for each substrate used during the deposition. A deposition rate of 2 Å/s was used as determined by a quartz crystal microbalance (QCM). The deposition rate was constant throughout the deposition to within ±10%. The total thickness of each film was nominally 50 nm and confirmed using variable angle spectroscopic ellipsometry. The temperature of the substrate was not controlled during deposition and is assumed to be near ambient. UPS and XPS. UPS spectra of the valence levels were acquired using the He I line (21.2 eV photon energy). The Fermi level was determined from the high-energy cutoff in the spectrum of a sputter-cleaned gold sample. The positions of the HOMO was determined with respect to the Fermi level EF by selecting the highest energy peak in the inverse second derivative of the UPS spectrum; the fairly weak HOMO features were brought out more clearly by determining peaks in the negative second derivative. This procedure eliminated constant and linear backgrounds. XPS spectra were collected on NPD and HATCN films deposited on ITO-coated glass substrates with a PHI VersaProbe II spectrometer at a takeoff angle of 45°. The excitation source was monochromatic Al Kα source (1486.6 eV). The Fermi level was calibrated via the Au 4f7/2 line at 84.0 eV. We also tested the effect of radiation damage by acquiring additional spectra after prolonged irradiation. Radiationinduced shifts are absent for HAT:CN, while about 0.1 eV shift to higher binding energy is observed for NPD (close to the accuracy of the absolute energy calibration). In addition, NPD shows further sign of degradation as evidenced by presence of

4. COMPUTATIONAL METHODOLOGY Hybrid density functional theory (DFT), at the B3LYP/6-31g* level,18,19 was used to compute the ground-state (S0) geometries of NPD and HAT:CN. These calculations were performed using the G09 suite of programs.20 Keeping the geometries of the molecules fixed, the following set of singlepoint calculations were performed at the DFT level, using the PBE functional21 and TZP basis set using the ADF package.22 These are (i) the ground-state energy, (ii) the core exciton energy Ecore‑ex required to excite an electron from a core level to an unoccupied level, (iii) the core ionization energy IEcore required to extract a core electron, and (iv) the electron affinity energy EA, which is the energy released when an electron is added to the molecule. For calculating (ii), the ΔSCF method23 was primarily used. In these calculations, the core orbitals of all the atoms are kept frozen, except for the atom where the core hole is located. This frozen core approximation ensures the localization of the core excitation onto a specific C or N site. It is important to note that the ΔSCF procedure allows the charge density to relax after excitation of the electron from the core to the unoccupied level. For each molecule, Ecore‑ex was 1368


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The Journal of Physical Chemistry C computed by exciting an electron from the core level to several low-lying unoccupied levels. For the sake of comparison, Ecore‑ex between a core level and the LUMO was also computed for NPD, using the transition state method (TS), following Slater’s rule.24 The core electron−hole interaction Ee‑h(c) was computed according to the formula Ee − h(c) = (IEcore − EA) − Ecore−ex

(4)

Equation 4 is the analogue of eq 3 for calculated energies instead of experimental energies. Likewise, Ee−h(c) in eq 4 is the theoretical analogue of Ee−h(core) in eq 3. Furthermore, Ecore−ex in eq 4 is the analogue of Eex(core) in eq 3. There are three carbons with different bonding environments in NPD, as shown in Figure 2: (1) an sp2 carbon atom Figure 3. UPS spectra of HAT:CN and NPD. Shoulders representing the HOMO are converted to peaks by taking the negative of the second derivative (top curves).

Figure 2. Molecular structures of NPD and HAT:CN. In NPD, the three different bonding environments of carbon are labeled.

neighboring two sp2 carbon atoms and a hydrogen (labeled 1 in Figure 2), (2) an sp2 carbon atom neighboring two sp2 carbon atoms and a nitrogen atom (labeled 2), and (3) an sp2 carbon atom neighboring three sp2 carbon atoms (labeled 3). Since the bonding environments of these carbon atoms are different, Ee−h(c) (core → LUMO excitation) was computed by localizing the core electron at one of the three inequivalent carbon atoms. The two nitrogen atoms of NPD are equivalent. For both NPD and HAT:CN, the ionization energy (IE) required to extract a valence electron was also computed at the PBE/TZP level. The transport gap (Eg) then corresponds to the expression Eg = IE − EA

Figure 4. XPS spectra of the C 1s and N 1s core levels in NPD and HAT:CN. The peak binding energies of the relevant features are given in eV relative to the Fermi level EF. The dominant peaks are used in Figure 6 to reference the energy scales of the XAS spectra to the Fermi level.

(5)

Core level XPS spectra of NPD and HAT:CN deposited on ITO-coated glass are shown in Figure 4. The C 1s spectrum of NPD in Figure 4a displays a strong peak at 284.6 eV arising from double-bonded carbon atoms in the phenyl rings. The contribution from C atoms bonded to N is not resolved due to their weak intensity (only 6 C atoms bonded to N versus 38 C atoms binding exclusively to C). It is contained in the asymmetric tail of the C 1s peak toward higher binding energy. A two-line fit gives a binding energy of 285.5 eV. Only a single N 1s peak is observed for NPD in Figure 4b, as the two N atoms in NPD are bonded the same way. For HAT:CN, the C 1s peak at 287.2 eV in Figure 4c is responsible for two types of carbon atoms, both π-bonded to N. These are located in 6-fold rings and in peripheral nitrile groups. The small C 1s peak at 285 eV is caused by C contamination of either the ITO substrate27 or a C layer on top

5. SPECTROSCOPIC RESULTS Figure 3 shows UPS spectra of NPD and HAT:CN (without background subtraction). The negative of the second derivative is also given (top curves). These curves were used to determine the position of the shoulders more accurately. NPD exhibits a shoulder at −1.2 eV representing the HOMO and a peak at −1.7 eV for the next occupied level. Two analogous features have been found previously for NPD.8 One can also define an onset at −0.8 eV by linear extrapolation from the inflection point to the background. Such onsets are often quoted in the literature.25−28 Peaks versus onsets will be discussed in more detail after Table 3. In HAT:CN the HOMO lies much lower, with a peak at −4.8 eV and an onset at −3.7 eV, similar to previous results.11,27,28 1369


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The Journal of Physical Chemistry C of the HAT:CN film. This peak is well-separated from the intrinsic HAT:CN peak. The N 1s spectrum of HAT:CN in Figure 4d shows a single peak at 400.2 eV which contains both types of nitrogen atoms in HAT:CN (double-bonded imine and triple-bonded nitrile), in agreement previous results.27,29 Based on previous theoretical work by others, the single XPS line was decomposed into two lines, split by 0.8 eV.29 We chose not to introduce such a decomposition. Figure 5 shows the optical absorption spectra of NPD and HAT:CN. As done for the UPS spectra in Figure 3, one can

Figure 5. Optical absorption spectra of NPD and HAT:CN. The optical gaps are taken from the position of the lowest energy peaks or shoulders as indicated by the arrows. The optical gaps along with onset values are listed in Table 7.

define the energies of peaks and onsets. NPD exhibits a shoulder at 3.2 eV and a peak at 3.7 eV which look like a mirror image of the peak and shoulder found in UPS. That points toward excitations from the two levels seen in UPS to the LUMO. The onset occurs at 3.0 eV. HAT:CN exhibits a peak at 3.8 eV for the LUMO with an onset at 3.3 eV. There is noticeable fine structure, which could be due to vibrational excitations or to quantum well states in the π*-manifold. Figure 6 shows XAS spectra of NPD and HAT:CN for the C 1s and N 1s absorption edges. The lowest excitations from the C 1s and N 1s levels into the LUMO are marked by the vertical dash. These form the core excitons. In order to use the Fermi level EF as energy reference, the photon energy scale of the XAS spectra has been reduced by the XPS binding energies of the core levels as indicated by the value in parentheses from Figure 4. The atom and orbital sensitivity of XAS shows up clearly in the NPD spectra of Figure 6. The LUMO corresponds to the lowest π* orbital of the CC double bonds. It generates the dominant peak in the C 1s spectrum. There is no detectable feature at that energy in the N 1s spectrum, indicating that the C 2p π-system has very little overlap with the N 1s core level. The leading peak of the N 1s spectrum occurs at much higher energy (nominally 2.5 eV above EF). It is assigned to the σ* orbital of the amine nitrogen. This orbital also serves as an example of how to apply eqs 1−3 to higher-lying unoccupied orbitals above the LUMO. To find the σ* transition in the C 1s XAS spectrum of NPD, one would have to subtract the binding energy of the C−N XPS peak at 285.5 eV, which is 0.9 eV larger than that of the C−C XPS peak at 284.6 eV. That places the amine σ* orbital at 1.6 eV above EF in the C 1s XAS spectrum. There is a weak feature at this energy, but it shows again that the C 1s and N 1s spectra

Figure 6. X-ray absorption spectra of NPD and HAT:CN, shifted down by the core level binding energies from XPS (given in parentheses). Thereby all energies are referenced to the Fermi level EF. The bottom part of each panel summarizes all the other experimental and theoretical results. These are listed in Tables 1−3.

are highly selective in projecting out orbitals localized at specific C and N sites. The XAS spectra of HAT:CN in Figure 6 contain two strong π* transitions. The lower peak is assigned to the doublebonded imine nitrogens at the core of the molecule and the higher peak to the triple-bonded nitriles at the periphery. This assignment is based on a previous study involving comparisons with a variety of reference molecules.30 For imines the lowest N 1s-to-π* transition was found at photon energies of 398.8 ± 0.3 eV and for nitriles at 400.0 ± 0.3 eV, depending slightly on the molecular environment. Here we find the corresponding transitions at 398.4 and 399.7 eV. Previous N 1s XAS spectra for HAT:CN on graphene29 show two dominant peaks at threshold and a weak peak at higher energy with spacings similar to those in Figure 6. But the photon energy scale is shifted, probably due to a different photon energy calibration. Based on calculations, the peaks at the N 1s edge were assigned to a combination of imine (pz) and nitrile (pz, px,y) π* orbitals, with the lowest peak having mainly imine (pz) character and the second peak mainly nitrile (px,y) character.29 This interpretation is consistent with our assignment. Figure 6 combines the XAS spectra with the other spectroscopic results, UPS (Figure 3), XPS (Figure 4), optical absorption (Figure 5), and density functional calculations of the HOMO−LUMO gap Eg = IE − EA . Together these results provide a complete energy level diagram analogous to Figure 1, but 1370


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The Journal of Physical Chemistry C turned on its side. All energies are referenced to the Fermi level EF. The HOMO energy EHOMO is obtained directly from Figure 3. The LUMO energy ELUMO is obtained by adding the difference between the calculated ionization energy IE and electron affinity EA to the UPS value of the HOMO energy EHOMO. A comparison of the calculated HOMO−LUMO gap (IE − EA) with the optical gap from Figure 5 yields the electron−hole binding energy of the valence exciton that is formed between HOMO and LUMO (horizontal double-arrow labeled Ee−h Opt in Figure 6). The analogous binding energies for core excitons are obtained in the same fashion (horizontal double-arrows labeled e−h+ C 1s and e−h+ N 1s). This procedure is applied to NPD and HAT:CN in the two panels of Figure 6. The energy levels appearing in Figures 1 and 6 are listed in Table 1. Table 2 lists the excitation energies from optical and Xray absorption spectroscopy, and Table 3 combines these results with the calculated HOMO−LUMO gap to obtain exciton binding energies via eqs 1−3.

significant for the device characteristics in organic electronics. A simple estimate of the extramolecular polarization energy is obtained8 by considering a spherical cavity in a homogeneous dielectric with dielectric constant ε: P+ = P− = P = (1 − ε−1)·e2/ d. This is an upper limit, since screening is reduced at the surface by up to a factor of 2. An approximation for the diameter d of the cavity is the nearest-neighbor distance in the molecular crystal. Using ε = 3.0 for NPD31 and ε = 3.2 for HAT:CN32 together with d = 9.6 Å for NPD33 and d = 6.9 Å for HAT:CN,34 we obtain P = 0.50 eV for NPD and P = 0.72 eV for HAT:CN. For establishing the energy diagram of Figure 1 via the method developed in eqs 1−5, one has to replace the calculated ionization energy IE by (IE − P+), the electron affinity EA by (EA + P−), and the HOMO−LUMO gap by [(IE − EA) − (P+ + P−)] . In well-ordered molecular crystals it is possible to observe dispersive bands with typical band widths of 0.3−0.5 eV. The corresponding valence band maximum lies about half a bandwidth above the LUMO of an isolated molecule. Likewise, the conduction band minimum lies half a bandwidth below the LUMO. Since the band dispersion is not resolved in our case, we take the observed peak position as the center of the band (compare a similar strategy for handling vibrational broadening in the next paragraph). For complex molecules the assignment of spectral features to energy levels is nontrivial due to vibrational sidebands which are often unresolved in molecular solids. In the gas phase,35 one can define vertical transitions (for the maximum of the Franck− Condon envelope) or adiabatic transitions (for the zerophonon peak). The equivalent definitions in molecular solids are the peak and the onset of a transition. We prefer to use the peak to define an energy level, since peaks are easier to define than onsets. The latter depend on the extrapolation procedure (linear, power law, exponential, etc.), on inhomogeneous broadening, and on the experimental resolution. For comparison with some of the literature we also list onsets in Tables 1 and 2 (given in parentheses). They are obtained by linear extrapolation from the inflection point to the background. If only a shoulder is observed instead of a peak, its position is determined accurately via the minimum in the second derivative of the spectrum (see the UPS spectra in Figure 3). In addition to these straightforward definitions of the peak position and onset one can include more sophisticated corrections, such as polarization energies (bulk and surface), finite bandwidth corrections, and vibrational losses.8

Table 1. Experimental Energy Levels Obtained from UPS and XPS (in eV Relative to the EF) level

NPD

HAT:CN

ELUMOa EHOMO EC 1s EN 1s

+3.7 −1.2 (−0.8) −284.6 −399.7

+1.5 −4.8 (−3.7) −287.2 −400.2

a

The LUMO energy ELUMO is obtained by adding the calculated HOMO−LUMO gap Eg = (IE − EA) to the HOMO energy EHOMO using eq 1. Eg is listed in Table 8. Results for the high-energy onset of the HOMO peak are listed in parentheses for a comparison with the literature.

Table 2. Lowest Excitation Energies Eex (in eV) excitation

NPD

HAT:CN

Eexa Eex(C 1s)a Eex(N 1s)a

3.2 (3.0) 285.1 402.2

3.8 (3.3) 285.7 398.5

a

These energies are obtained from optical and X-ray absorption spectroscopy. The low-energy onset of the optical absorption is listed in parentheses.

Table 3. Binding Energiesa Ee−h of the Valence and Core Excitons (in eV) e−h binding

NPD

HAT:CN

Ee‑h Ee−h(C 1s) Ee−h(N 1s)

1.7 3.2

2.5 3.0 3.2

6. COMPUTATIONAL RESULTS The calculated electronic properties IEcore, Ecore−ex, and Ee−h(c) defined in section 4 are listed in Table 4 for NPD and HAT:CN. These are relevant to core excitations. For both molecules, Ecore−ex was obtained by exciting a 1s core electron (located either on a carbon or nitrogen atom) to the LUMO. The computed values of Ee−h(c) depend on the choice of the method. Compared to ΔSCF, the TS method underestimates Ee−h(c) by 0.1−0.3 eV, depending on type of core electron and the nature of the molecule. Such variations are comparable to those reported in the literature.36 The electron−hole binding energy for NPD agrees well with that in Table 3, but it comes out too large for HAT:CN. As will be discussed in section 7, this is likely due to the fact that the theoretical electron−hole binding energies in Table 4 involve two-particle excitations, with an electron in the LUMO plus a core hole. Consequently, they are less precise than the results in

a

These binding energies are all with an electron in the LUMO. They are obtained via eqs 2 and 3, respectively, using the energy levels from Table 1 and the excitation energies from Table 2.

It should be noted that the experiments are for molecular films while the calculations are performed on isolated (gas phase) molecules. To match the experiments, the dielectric screening of a hole in the HOMO (or an electron in the LUMO) by the surrounding molecules needs to be taken into account. Thereby the HOMO is shifted upward in energy by the polarization energy P+ and the LUMO downward by P− (both taken positive). As a consequence, the HOMO−LUMO gap (= transport gap) is reduced by (P+ + P−). This can be 1371


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The Journal of Physical Chemistry C Table 4. IEcore, Ecore−ex, and Ee−h(c) in eV Calculated at the PBE/TZP Level for NPD and HAT:CNa NPD

HATCN

Ecore−ex ΔSCF

IEcore

a

Ee−h(c) ΔSCF (TS)

TS

295.4

291.2

291.5

411.8

408.1

408.3

Ecore−ex IEcore

core electron (C 1s) 3.3 (3.0) 299.3 core electron (N 1s) 2.8 (2.6) 413.5

Ee−h(c)

ΔSCF

TS

ΔSCF (TS)

291.3

291.5

4.2 (4.0)

405.2

405.3

4.6 (4.5)

Ecore−ex is calculated for excitations into the LUMO using ΔSCF and TS. For NPD, the core electron is located on carbon number 1 in Figure 2.

Table 3, which require only a calculation of (IE − EA). That does not involve any excited particles. Table 5 addresses the variation of the core level excitations between the three inequivalent C atoms of NPD in Figure 2.

Table 7. Calculated Values of IEcore, Ecore−ex, and Ee−h(c) in eV for HAT:CN (at the PBE/TZP Level)a core electron (C 1s)

Table 5. IEcore, Ecore−ex, and Ee−h(c), in eV, Computed at PBE/TZP Level for NPDa

core electron (N 1s)

level

IEcore

Ecore−ex

Ee−h(c)

IEcore

Ecore−ex

Ee−h(c)

LUMO* LUMO+3*

299.3

291.3 293.4

4.2 2.2

413.5

405.2 407.7

4.6 2.1

a

no.

IEcore

ΔSCF

TS

ΔSCF (TS)

The core 1s electrons, localized on either carbon or nitrogen atoms, are excited to a few low-lying unoccupied molecular orbitals. Asterisks indicate molecular orbitals with energies within the numerical accuracy.

1 2 3

295.4 296.5 296.0

291.2 292.2 291.7

291.5 292.4 291.9

3.3 (3.0) 3.4 (3.1) 3.4 (3.2)

Table 8 lists the ionization energy (IE), electron affinity (EA), and the transport gap Eg of NPD and HAT:CN.

core electron (C 1s) Ecore−ex

Ee−h(c)

a

The 1s core electron is localized at one of the three types of carbon atoms labeled in Figure 2 and excited to the LUMO. Ecore−ex was computed using both ΔSCF and TS.

Table 8. Calculated Values of IE, EA, and Eg = IE − EA in eV for NPD and HAT:CN

The spread of the Ee−h(c) values is 0.2 eV, which is smaller than the variation between different methods of calculation. Thus, the effect of the local environment on Ee−h(c) was neglected for high energy excitations of NPD and HAT:CN. From this point onward, the ΔSCF method was preferred over the TS method. Table 6 gives core level excitations into various low-lying unoccupied orbitals for NPD. The core hole is located either on

core electron (N 1s)

level

IEcore

Ecore−ex

Ee−h(c)

IEcore

Ecore−ex

Ee−h(c)

LUMO* LUMO+2 LUMO+3* LUMO+5

295.4

291.2 291.8 292.3 292.8

3.3 2.7 2.2 1.7

411.8

408.1 408.5 408.8 409.2

2.8 2.4 2.1 1.7

IE

EA

Eg

5.8 10.1

0.9 3.8

4.9 6.3

7. DISCUSSION The various techniques discussed in previous sections all served one purpose, i.e., finding an efficient and accurate way to establish a complete energy level scheme analogous to Figure 1. As explained in section 1, there are two major hurdles for composing such a level scheme for molecular solids: (1) determination of the LUMO level and (2) determination of the exciton binding energies. To get around problem 1, we combine the UPS result for the HOMO level with calculations of the HOMO−LUMO gap Eg = (IE − EA). The LUMO energy is then obtained simply by adding the calculated HOMO−LUMO gap to the experimental HOMO energy via eq 1. The calculation of the ionization energy (IE) and the electron affinity (EA) is rather straightforward. It involves the difference between two ground state energies (those of the positive and negative molecular ion), which can be handled easily and with sufficient accuracy by ground state density functional calculations. The quantities IE = EVac − HOMO and EA = EVac − LUMO both contain the vacuum level EVac, but it drops out when taking the difference (IE − EA). That eliminates the sensitivity of the vacuum level to surface dipole layers and surface contamination in actual devices. With the LUMO energy in hand, it is straightforward to obtain the binding energies of valence and core excitons via eqs 2 and 3, respectively. One simply subtracts the lowest excitation energies in optical or X-ray absorption spectroscopy from the HOMO−LUMO gap or the core−LUMO gap. No additional

Table 6. Calculated Values of IEcore, Ecore−ex, and Ee−h(c) in eV for NPD (at the PBE/TZP Level)a core electron (C 1s)

molecule NPD HAT:CN

a

A 1s core electron, localized on a carbon or nitrogen atom, is excited to a few low-lying unoccupied molecular orbitals. Asterisks indicate molecular orbitals with energies within the numerical accuracy.

carbon number 1 in Figure 2 or on a nitrogen. Compared to the LUMO, the electron−hole interaction Ee−h(c) is reduced for higher-lying unoccupied orbitals (by about 1 eV). C 1s core holes exhibit a larger electron−hole interaction than N 1s holes for excitations into the LUMO, but this difference is comparatively smaller for higher-lying orbitals. Table 7 is equivalent to Table 6, but for HAT:CN. Similar to NPD, Ee−h(c) is lower for higher-lying orbitals. Contrary to NPD, Ee−h(c) is smaller for C 1s than N 1s holes (for excitations to the LUMO). This difference is negligible for excitations into higher-lying orbitals. 1372


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The Journal of Physical Chemistry C

8. SUMMARY In summary, we have developed an efficient methodology to obtain the HOMO and LUMO valence levels, the C 1s and N 1s core levels, and the binding energies of valence and core excitons for materials used in OLED applications. This is accomplished by combining UPS, XPS, optical absorption spectroscopy, and X-ray absorption spectroscopy with firstprinciples calculations of the ionization potential and the electron affinity. The method is demonstrated using two molecules (NPD and HAT:CN) which are prototypical OLED materials. By combining straightforward experiments and calculations, we obtain a complete picture of the energy levels and exciton binding energies in organic conductors, without having to resort to difficult experiments or complicated calculations. This is particularly important for the determination of the LUMO, where an efficient and accurate combination of experiment and theory is used (UPS plus ground state total energy calculations). This method is extended to exciton binding energies. Valence excitons play an important role in organic photovoltaics, and the binding energies of core excitons are crucial for extracting energy levels for unoccupied states from element- and bond-specific XAS data. Exploring trends among all these energies during chemical functionalization can enable a systematic optimization of materials used for devices.

theoretical input is required beyond EA and IE. Theoretically, an exciton is difficult to handle properly, since it represents a two-particle problem (as discussed in section 1). That is more complex than a one-particle problem (such as an electron or a hole), which in turn is more complex than a zero-particle problem (such as the ground state without any excited electron or hole). A purely experimental determination of the exciton binding energy is also difficult for organic solids because most of them do not exhibit a well-defined series of hydrogenic exciton lines, as in crystalline semiconductors at low temperature. The effect of the electron−hole interaction on the energy level scheme can be appreciated by inspecting the position of the LUMO transitions in the X-ray and optical absorption spectra in Figure 6. Without electron−hole interaction these should all coincide with the position of the LUMO, but the Coulomb attraction between electron and hole shifts them toward lower energies (see the horizontal double-arrows labeled Ee−h(C 1s), Ee−h(N 1s), and Ee−h). It also becomes apparent that the binding energy of the core excitons in X-ray absorption spectroscopy is significantly larger than that of the valence exciton in optical absorption spectroscopy. This observation supports a qualitative explanation of the exciton binding energy in terms of the charge distributions of electron and hole. A more detailed analysis of various excitonic transitions can be extracted from the theoretical results in Tables 4−8, particularly for the core excitons. The calculated binding energy agrees with experiment for NPD, but it comes out about 1 eV higher than observed for HAT:CN (compare Table 4 with Table 3). The trends are captured correctly. In HAT:CN for example, the N 1s exciton binding energy is larger than the C 1s exciton binding energy. A similar comparison for NPD cannot be made, since the cross section is too small at the N 1s edge to observe the exciton. This indicates a missing piece in current calculations of the electron−hole interaction. In addition to the energy levels, one needs to include the transition probabilities for the excitations. After including a realistic broadening of the spectral features,37 one would obtain theoretical XAS spectra that can be compared directly to the data. This would also resolve the question whether the peak or the onset of the core-to-LUMO transition should be used for determining the exciton binding energy. In fact, the overestimate of the exciton binding energies by the calculations might be reduced when using onsets instead of peaks for extracting energy levels experimentally (compare Tables 1 and 2). The HOMO energies EHOMO in Figure 6 would move toward higher energy and with them the onsets of the LUMO energies ELUMO according to eq 1. As a result, the exciton binding energies would increase. On the other hand, using onsets instead of peaks in the absorption spectra would increase the exciton binding energies. Clearly, a realistic simulation of the XAS spectra is called for. For excitations into higher-lying orbitals the calculations predict reduced exciton binding energies (see Tables 6 and 7). This makes sense in view of the charge distributions of higher orbitals. Since they have to be orthogonal to all the lower-lying orbitals, their wave functions tend to be farther from the core holes. Consequently, the single-electron approximation becomes more accurate as one moves up toward higher-lying transitions in XAS.

■

AUTHOR INFORMATION

Corresponding Author

*Phone 608-263-5590; e-mail [email protected] (F.J.H.). Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This research was supported by the NSF through the University of Wisconsin Materials Research Science and Engineering Center (DMR-1121288).

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REFERENCES

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Multitechnique Approach for Determining Energy Levels and Exciton

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