Organic Hybrids: Phenoxy-allyl-PTCDI

ARTICLE pubs.acs.org/JPCC

Toward Functional Inorganic/Organic Hybrids: Phenoxy-allyl-PTCDI Synthesis, Experimentally and Theoretically Determined Properties of the Isolated Molecule, Layer Characteristics, and the Interface Formation of Phenoxy-allyl-PTCDI on Si(111):H Determined by SXPS and DFT Andreas Decker,*,† Sabin-Lucian Suraru,‡ Oscar Rubio-Pons,§,|| Eric Mankel,† Michel Bockstedte,§ Michael Thoss,§ Frank W€urthner,‡ Thomas Mayer,† and Wolfram Jaegermann†,^ †

Institut f€ur Materialwissenschaft, Technische Universit€at Darmstadt, Petersenstrasse 32, 64287 Darmstadt, Germany Institut f€ur Organische Chemie and R€ontgen Research Center for Complex Material Systems, Universit€at W€urzburg, Am Hubland, 97074 W€urzburg, Germany § Institut f€ur Theoretische Physik und Interdiziplin€ares Zentrum f€ur Molekulare Materialien (ICMM), Universit€at Erlangen-N€urnberg, Staudtstrasse 7/B2, 91058 Erlangen, Germany Lehrstuhl f€ur Theoretische Chemie, Technische Universit€at M€unchen, Lichtenbergstrasse 4, 85747 Garching, Germany ^ Center of Smart Interfaces, Technische Universit€at Darmstadt, Petersenstrasse 32, 64287 Darmstadt, Germany

)

‡

ABSTRACT: A new perylene diimide derivative, namely N,N0 diallyl-1,6,7,12-tetraphenoxyperylene-3,4:9,10-tetracarboxylic acid diimide (phenoxy-allyl-PTCDI, abbreviated PA-PTCDI), is introduced. The investigations presented in this paper aim at finding a molecule for use as a sensitzer in thin film silicon solar cells in order to enhance efficiency. The synthesis is described along with optical and electrochemical measurements of PAPTCDI in solution. A good agreement is found between the measured data and theoretical calculations. The molecule is characterized further by optical and photoemission data on thin films, which also show that the dye can be sublimed in vacuum. The interface between the dye and silicon is investigated on the model system Si(111):H with synchrotron-induced photoemission spectroscopy. The result is an electronic lineup with the gap centers of silicon and PA-PTCDI almost at identical positions and thus very similar band discontinuities from the lowest unoccupied molecular orbital (LUMO) to the conduction band as well as from the highest occupied molecular orbital (HOMO) to the valence band. This clearly permits a transfer of photogenerated electrons and holes from PA-PTCDI to silicon. The experimental valence band discontinuity matches very well the value calculated for a very similar PTCDI molecule.

’ INTRODUCTION In an attempt to increase the efficiency of thin film silicon solar cells, it was proposed to incorporate small organic molecules into a microcrystalline silicon (μc-Si:H) matrix.1 The aim of this approach is to combine the high optical absorption of organic molecules with the good electronic properties of inorganic semiconductors. Even though the concept of sensitization of inorganic materials with organic dyes dates back to the late 19th century,2 research on this topic accelerated only during the past decade. Additional possible applications for hybrid structures and interfaces of organic
inorganic semiconductors arise in the fields of light emitting diodes, field effect transistors, and sensors. The concept followed by our group has been described earlier.1,3 One challenge so far is to find a molecular absorber whose properties allow for the molecule to be inserted into a μc-Si:H matrix produced by hot-wire chemical vapor deposition (HWCVD). This process requires many properties of the r 2011 American Chemical Society

molecule to be within certain limits. First of all the molecule itself must be stable during sublimation in the vacuum. Second it has to have a relatively high sublimation temperature. This is due to the fact that in the HWCVD process microcrystalline silicon of high quality can only be achieved above a certain substrate temperature, in our case 150
250 C. Below this temperature amorphous silicon will prevail, leading to very different film properties including an increased energy gap of around 1.7 eV instead of 1.1 eV, the formation of a significant amount of gap states, and a reduced electrical conductivity. Consequently the probability of deposited molecules in a composite material to desorb again will be minimized with higher sublimation temperatures. An additional important requirement is that the molecule is not destroyed Received: June 6, 2011 Revised: September 20, 2011 Published: September 22, 2011 21139

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Figure 1. Structural formula of PA-PTCDI, C54H34N2O8.

during the harsh silicon HWCVD process, which involves hot silane and hydrogen radicals and comparatively high pressures, approximately 6
7 orders of magnitude above the vacuum chamber base pressure, which in our case is just below 10
8 mbar. Last but not least, the electronic lineup of the organic semiconductor with respect to silicon has to allow a transfer of photogenerated charges from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) states of the molecules to the surrounding silicon matrix. It is assumed that a favorable configuration existed if the HOMO and LUMO states were equally far away from the silicon valence band maximum and conduction band minimum, respectively, so that not only a F€orster transfer but also a Dexter transfer of the excited charge carriers is rendered possible. Also the band bending at the interface should be small enough in order not to hinder one charge carrier species to be injected from larger dye clusters to the silicon. Additional challenges arise in producing pinholefree layers of composites with high silicon crystallinity, as the presence of the molecules disturbs the formation of microcrystalline silicon, leading to higher amorphous fractions. In earlier publications, interfaces of different organic materials deposited onto silicon have been studied, both for fundamental research4 and for the bulk sensitization of devices.5 In this paper, we will show that some of the required properties are met by a novel dye. The dye is a perylene diimide derivative, namely N,N0 diallyl-1,6,7,12-tetraphenoxyperylene-3,4:9,10-tetracarboxylic acid diimide (phenoxy-allyl-PTCDI, abbreviated PA-PTCDI). Its structural formula can be seen in Figure 1. Perylene tetracarboxylic acid diimides (PTCDIs) are a prominent class of dyes with high absorption coefficients initially used as industrial pigments.6 Chemical modifications of the PTCDIscaffold can either be made at the imide-nitrogen or at the aromatic perylene core. While the former has only small influences on the absorption spectra and frontier orbitals, core-substitution opens up the possibility of tuning both and thus the color and redox states of the dyes. Aryloxy-substituents employed in this work lead to a bathochromic shift of the absorption maximum and more easy oxidation and reduction processes. Furthermore, core-substitution leads to a twist of the two naphthalene units and thus improves the solubility and minimizes aggregation in solution.7 The latter effect was considered to be important for the

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incorporation of the dye into bulk silicon without forming larger aggregates of the organic molecules. We expect Si-H bonds to be the neighboring environment for dyes incorporated into μc-Si:H. In order to eliminate the variability introduced by the HWCVD process, we use hydrogen terminated silicon wafers as a model system, acting as a substrate onto which organic molecules are deposited. Hydrogen-terminated silicon wafers have already been investigated for quite a while8,9 and are therefore relatively well understood. The advantages of using hydrogen-terminated silicon wafers are manifold: Hydrogen termination of the silicon surface prevents reconstruction of the dangling bonds and thus leads to a surface free of Fermi level pinning,10 which is very important when looking at charge transfer processes at interfaces. A flat, passivated surface also enhances the growth of ordered organic films.11 In addition, a similar chemical environment for the dyes can be provided with hydrogen-terminated silicon as with μc-Si:H. The band gap of μc-Si:H is very similar to that of crystalline silicon, which is important when determining the electronic lineup.12 In a UV photoelectron spectroscopy (UPS) experiment not shown here, it could also be verified that the ionization potential and thus the position of the valence band maximum below the vacuum level for the μc-Si:H prepared in our HWCVD process is at 5.08 eV. This correlates very well with the measured value of 5.23 eV for Si(111):H and the literature value of 5.17 eV given for c-Si,13 resulting in a very similar band diagram for both materials.

’ EXPERIMENTAL SECTION The development of the PA-PTCDI was carried out in the W€urzburg group. First characterizations of the molecules in solution with optical spectroscopy and cyclovoltammetry were conducted there. Supporting density functional theory (DFT) calculations were done by the Erlangen group. In the Darmstadt group, thin layers of the dye were produced by physical vapor deposition in an ultrahigh vacuum (UHV) evaporation chamber in the integrated system DAISY-MAT14 with subsequent in situ X-ray photoelectron spectroscopy (XPS) measurements with a monochromated Al Kα source and a hemispherical analyzer PHI 5700 (Physical Electronics). The interface experiment was performed in the integrated solid/liquid analysis system SoLiAS15 located at BESSY II using the dipole beamline TGM-7. For additional experiments, the SoLiAS was moved to the undulator beamline U49/2-PGM2. TGM-7 provides photons in the energy range between hν = 20
130 eV and is thus especially suited for the investigation of valence states with very high surface sensitivity. U49/2-PGM2 provides photons in the energy range between hν = 80
1500 eV and thus enables a wide range of core level spectroscopy. The photoemission spectra in the SoLiAS are recorded with a hemispherical analyzer Phoibos 150 (Specs). The base pressure in the analyzing chamber was at 3  10
10 mbar, whereas the deposition chamber had a base pressure of 1  10
8 mbar. Preparation of Si(111):H. The samples were cut from n-doped silicon wafers (IXYS) grown in the [111] direction, with a 4 μm thick epitaxial overlayer and a phosphorus concentration of 7.7  1015 cm
3. The wafers were covered with a native oxide of about 1.8 nm thickness as calculated from synchrotron-induced XPS (SXPS) data.16 The native oxide on Si(111) can be removed with ammonium fluoride: The cleaning procedure of the substrates follows largely the one proposed by Lublow and Lewerenz:17 The samples were 21140

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The Journal of Physical Chemistry C mounted vertically into a homemade Teflon sample holder. In order to remove surface contaminations, the samples were slewed in ethanol (p.a.) for 1 min, rinsed with Millipore water (18.2 MΩ cm) for 10 s, and blown dry with nitrogen. This was repeated once. To remove the native oxide, the samples were then etched in 40% aqueous ammonium fluoride solution (Sigma Aldrich, VLSI) for 100 s, rinsed in Millipore water for 30 s, and again blown dry. In a second etch step for 10 min in fresh NH4F, the sample surface was passivated with hydrogen. After a 10 s rinse with Millipore water, the samples were blown dry and mounted to a UHV sample holder. The samples were then put in a transport bag filled with nitrogen and taken to the UHV load lock, which had been flooded with nitrogen and was evacuated immediately after sample insertion. During the etching process the light in the fume hood was turned off in order to minimize photoinduced oxidation of the samples. The samples had contact with ambient air for less than 3 min between the last etching step and the start of the vacuum pumps. The first measurement technique used for determining the surface quality of the Si(111):H substrates was atomic force microscopy (AFM; MFP-3D, Asylum Research) in contact mode with n-doped silicon tips under ambient conditions. The pictures were evaluated using WSxM.18 In a second step to investigate the surface passivation quality, samples were measured with SXPS at beamline U49/2-PGM2 at BESSY II, revealing important information such as possible Fermi level pinning at surface states and the nominal coverage with contaminations. For all photoemission spectra presented in this paper, the procedures used for evaluation were the same: First a background removal of the Shirley type19 was applied. The determination of the position of the Si2p emissions was done with a doublet fit using a Voigt profile with a fixed spin
orbit splitting of 0.608 eV and an intensity ratio of 0.5.20 The valence band maximum of silicon returns only a very weak photoemission response, which is furthermore damped with increasing adsorbed film thickness. In addition, the valence band maximum exhibits a large dispersion.21 Therefore its energetic position was determined from the Si2p3/2 position, assuming a fixed distance of 98.74 eV between the two.20 Synthesis of PA-PTCDI. Reagents and solvents were obtained from commercial suppliers and purified and dried according to standard procedures.22 Column chromatography was performed on silica gel (Merck Silica 60, particle size 0.040
0.063 mm). Elemental analysis was performed on a CHNS 932 analyzer (Leco Instruments GmbH). 1H NMR data was recorded in CDCl3/CF3COOD and CD2Cl2 on a Bruker Avance 400 spectrometer. Residual undeuterated solvent was used as internal standard (7.26 ppm for CDCl3 and 5.32 ppm for CD2Cl2). Highresolution ESI-TOF mass spectrometry was carried out on a microTOF focus instrument (Bruker Daltronik GmbH). Solvents for spectroscopic studies were of spectroscopic grade and used as received. Synthesis of N,N0 -Diallyl-1,6,7,12-tetrachloroperylene-3,4:9,10tetracarboxylic Acid Diimide. A suspension of 1,6,7,12-tetrachloroperylene-3,4:9,10-tetracarboxylic acid dianhydride (500 mg, 0.943 mmol), allylamine (285 mg, 4.99 mmol), and propionic acid (7 mL) was heated to reflux for 16 h. The hot suspension was filtered. The precipitate was collected, dried, and purified by column chromatography (chloroform/hexane 4:1). An orange solid was obtained. (184 mg, 32%) 1 H NMR: (400 MHz, CDCl3, CF3COOD): 8.78 (s, 4H), 5.97 (ddt, 3J(Z) = 17.2 Hz, 3J(E) = 10.2 Hz, 3J = 5.8 Hz, 2H), 5.36 (ddt, 3J(Z) = 17.2 Hz, 2H), 5.15 (ddt, 3J(E) = 10.3 Hz, 2H), 4.89

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(ddd, 3J = 5.8 Hz, 4H). HRMS (ESI, pos-mode): calc. for C30H14Cl4N2O4 605.9713, found 605.9712. Elemental analysis: calc. for C30H14Cl4N2O4 C 59.24, H 2.32, Cl 23.31, N 4.61, found C 59.54, H 2.65, N 4.49. UV
vis: absorption: λmax = 518 nm (38300); fluorescence: λem = 547 nm. CV: (CH2Cl2, red
2
0.1 M TBAHFP, vs Fc/Fc+): Ered 1/2 (X /X ) =
1.04 V, E1/2
(X/X ) =
0.84 V. Synthesis of N,N0 -Diallyl-1,6,7,12-tetraphenoxyperylene3,4:9,10-tetracarboxylic Acid Diimide. N,N0 -Diallyl-1,6,7,12-tetrachloroperylene-3,4:9,10-tetracarboxylic acid diimide (2.58 g, 4.24 mmol), phenol (2.40 g, 25.4 mmol), and potassium carbonate (3.52 g, 25.5 mmol) were stirred in NMP at 140 C for 24 h. The mixture was poured into 1N hydrochloric acid (150 mL), and the precipitate was filtered off and dried. After column chromatography (pentane/dichloromethane 4: 6) a red solid was obtained (1.01 g, 1.20 mmol, 28%). 1 H NMR: (400 MHz, CD2Cl2): 8.14 (s, 4H), 7.34
7.26 (m, 8H), 7.16
7.11 (m, 4H), 7.01
6.94 (m, 8H), 5.92 (ddt,3J(Z) = 17.2 Hz, 3J(E) = 10.3 Hz, 3J = 5.5 Hz, 2H), 5.21 (ddt, 3J(Z) = 17.2 Hz, 2H), 5.15 (ddt, 3J(E) = 10.3 Hz, 2H), 4.69 (ddd, 3J = 5.5 Hz, 4H). HRMS (ESI, pos-mode): calc. for C54H35N2O8 839.2388, found 839.2389 for [M+H]+. Elemental analysis: calc. C 77.32, H 4.09, N 3.34, found C 77.11, H 4.26, N 3.33. UV
vis: absorption: λmax = 573 nm (45800); fluorescence: λem = 600 nm.
2
CV: (CH2Cl2, 0.1 M TBAHFP, vs Fc/Fc+): Ered 1/2 (X /X ) =
+ red ox
1.32 V, E1/2 (X/X ) =
1.18 V, E1/2 (X/X ) = 0.87 V. Optical Spectroscopy and Cyclovoltammetry on PAPTCDI in Solution. UV
vis measurements were performed in CH2Cl2 (10
5 M) in a conventional quartz cell (light pass 10 mm) on a Perkin-Elmer Lambda 950 spectrometer. Emission spectra were measured in a conventional rectangular quartz cell (10  10  40 mm) on a PTI QM4
2003 fluorescence spectrometer and are corrected against photomultiplier and lamp intensity. A long wavelength range emission-corrected photomultiplier R928 was used. For cyclic voltammetry (CV), a standard commercial electrochemical analyzer (EC epsilon; BAS Instruments, UK) with a three electrode single-compartment cell was used. Dichloromethane (HPLC grade) was dried over calcium hydride under argon and degassed before using. The supporting electrolyte tetrabutylammonium hexafluorophosphate (TBAHFP) was prepared according to the literature23 and recrystallized from ethanol/water. The measurements were carried out in dichloromethane at a concentration of about 10
4 M with ferrocene (Fc) as an internal standard for the calibration of the potential. Ag/AgCl reference electrode was used. A Pt disk and a Pt wire were used as working and auxiliary electrodes, respectively. Preparation of PA-PTCDI Layers. For film deposition, homemade evaporation cells of the Knudsen type were used. The cell temperature is measured with a thermocouple attached to the outside of the crucible. Prior to use, the evaporation cell was degassed in UHV at around 750 C for several hours. Because no literature was available on PA-PTCDI, the evaporation temperature had to be determined experimentally first. For this, a Si(111):H sample was repeatedly placed above the heated evaporation cell, 15 cm away from the top of the crucible, for 1 min. From in situ XPS measurements in the DAISY-MAT, the deposition rate was then determined for cell temperatures in the range between 170
300 C. At around 250 C the first indication toward the PA-PTCDI was visible in the spectra. The dye stoichiometry was verified by XPS from the integrated areas of the core level emissions and taking into account the respective atomic sensitivity factors.24 21141

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The Journal of Physical Chemistry C A layer of PA-PTCDI with a nominal thickness of about 31 nm was deposited on a Si(111):H substrate in the DAISY-MAT and then measured with XPS in order to further investigate the core levels of the dye. The spectra were recorded with a pass energy of 5.85 eV and a 45 emission angle of the photoelectrons relative to the sample normal. Binding energies were corrected with respect to the Fermi edge and the Ag 3d5/2 emission of a clean silver sample.25 The evaluation of the detail spectra consisted again of background removal of the Shirley type.19 Afterward, the lines were fitted using multiple Voigt functions for the different chemical species and additional Gaussian functions for shake-up and shake-off satellites. The stoichiometry of the molecule was taken into account by keeping the area of each chemical species (main line plus satellites) relative to the total area of the emission line constant according to the molecular formula. In order to determine the optical gap of PA-PTCDI in the solid state phase an additional film was deposited onto a quartz substrate. The direct optical transmittance was then measured with a Perkin-Elmer Lambda 900 spectrometer. Interface Experiment: PA-PTCDI on Si(111):H. For the interface experiment, a deposition rate of 0.6 nm/min was chosen, corresponding to a temperature of the evaporation cell of 280 C. The spectra were recorded at the TGM-7 using a pass energy of 5 eV and an 18 emission angle of the photoelectrons relative to the sample normal. The work function was determined from the cutoff of the secondary electron edge, which was recorded in normal emission with a pass energy of 0.5 eV and an additional bias of 6.00 V in order to separate the secondary electron edges of the sample and the analyzer. Binding energies were corrected with respect to the Fermi edge of a clean silver sample. The experimental resolution excluding the natural line width, as determined with the full width at half-maximum (fwhm) of the silver sample Fermi edge, was 150
580 meV, depending on the photon energy. After the measurement of the Si(111):H substrate, PA-PTCDI was deposited stepwise onto the sample and measured with synchrotron radiation in the range of 40
120 eV in order to ensure high surface sensitivity. The Si2p emission was measured with a photon energy of 120 eV, resulting in high surface sensitivity according to the universal inelastic mean free path curve for electrons in organic compounds.26 Because the beamline resolution is better at lower photon energies, the Si2p emission was also recorded with the second order of 61 eV photons, i.e., 122 eV. This resulted in a better discrimination of the two lines in the Si2p doublet. The PA-PTCDI HOMO was recorded with a photon energy of 40 eV and fitted using a Gaussian to determine its maximum position. For the determination of the electronic lineup, the maximum position of the HOMO was chosen rather than its onset because we assume a weak intermolecular interaction as well as weak polarization of the molecules. Other reasons for using the maximum position instead of the onset are that experimental broadening of the spectra also influences the first but not the latter, and that a comparison of theoretically and experimentally determined values is simplified. Computational Methods. PA-PTCDI. To characterize the structural, electronic, and photophysical properties of the isolated dye molecule, calculations have been performed at the DFT level of theory27 employing the quantum-chemistry package Gaussian 09.28 Geometries were optimized at the B3LYP/ 6-31G* level. Single-point calculations have been performed with time-dependent density functional theory (TD-DFT) at

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the B3LYP and HSE06 with the 6-311G* basis set.29,30 All calculations were performed without spatial symmetry restrictions. Si(111):H/PA-PTCDI. To characterize the structural and electronic properties of PA-PTCDI adsorbed at the Si(111):H surface, calculations have been performed with the Vienna ab initio simulation package (VASP),31,32 which incorporates the PAW method33 and the generalized-gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE)34 for the exchange-correlation energy. The simulations of the H-terminated Si(111) surface employ a periodically repeated slab to describe the extended surface. The slab contains six layers of silicon in addition to the H-termination and a vacuum larger than 15 Å. The PA-PTCDI molecules are absorbed on a 3  3 surface unit cell. During geometry optimization, the bottom layer was kept frozen at a bulk-like structure. In addition, single point calculations have been performed employing the hybrid functional HSE06,30 which allows an accurate description of band gaps of semiconductors. This is also true for the Si(111):H surface studied here. Geometry relaxation was performed without restrictions until the remaining force acting on each ion is less than 3.0  10
3 eV/Å. A 415 eV cutoff energy for the plane wave basis was used based on extensive convergence tests. The H-terminated Si(111) surface was simulated using a 3  3 in-plane periodic supercell and a 3  3  1 k-point mesh for the Brillouin zone (SBZ) sampling. Convergence of the k-point sampling has been tested by increasing the k-point mesh up to 8  8  1 centered at the Γ point.

’ RESULTS The Si(111):H Substrate. While the AFM pictures of the as is silicon wafer show a very smooth surface without any distinct features, a well-etched sample exhibits flat plateaus (cf. Figure 2). The maximum plateau width observed was 150 nm, whereas the maximum step height was 2 nm (approximately seven monolayers). From these numbers an approximate value for the wafer miscut was calculated with simple trigonometry, resulting in a medium wafer miscut of around 0.8. SXPS measurements of an etched substrate are shown in Figure 3. The survey (Figure 3a) was recorded with hν = 600 eV and exhibits clearly the Si2p and the Si2s emission lines. Additional surface contaminations due to hydrocarbons and suboxides are visible. These adsorbates dampen the substrate signal according to the Beer
Lambert law. The intensities of the C1s and O1s emission lines with respect to the Si2p emission line contain the information needed to calculate a nominal adsorbate thickness: First it is assumed that the adsorbates form segregated islands that each have exactly the thickness d of one monolayer, so that the substrate S is covered by a fraction α with adsorbate A and by a fraction β with adsorbate B. The measured signal intensity Ii, i = A,B,S is proportional to the atom density ni, the photoemission cross section σi, and the electron inelastic mean free path λi:35

I ¼ C3n3σ3λ

ð1Þ

with C a machine constant. Combining this with the Beer
Lambert law IðzÞ ¼ I 0 3 e
z=λ

ð2Þ

in order to obtain information on the signal origin depth z, the coverage of the substrate with adsorbates can be calculated 21142

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Figure 2. AFM pictures of an untreated silicon sample (left) and an etched silicon sample (right). The change toward flat terraces can be clearly seen.

Figure 3. SXPS spectra of an etched silicon wafer. (a) The survey shows the expected fingerprint of silicon. In addition, the surface is contaminated by hydrocarbons and suboxides indicated by the small emission intensities of carbon and oxygen. (b) The detailed spectrum of the Si2p emission clearly resolves the spin
orbit doublet. (c) In the valence band spectrum the peak at around 5
6 eV is attributed to the Si
H bond. The valence band maximum cannot easily be measured so that its position is calculated based on the position of the Si2p line.

Table 1. Parameters Used for Calculating the Adsorbate Coverage of the Silicon Substrate

to be IA 1 n A σ A λA α¼ IS IA IB 3 1
e
dA =λA þ þ n S σ S λS nA σA λA nB σB λB IB 1 n B σ B λB β¼ IS IA IB 3 1
e
dB =λB þ þ nS σ S λS n A σ A λA n B σ B λB

emission line

ð3Þ

modification

ð4Þ

Values for the parameters ni, σi, and λi were taken from the literature13,16,35
44 or calculated therefrom. They are summarized in Table 1. Using these numbers in the previous formulas returns a coverage with silicon oxide of 0.14 monolayers and with carbon of 0.13
0.60 monolayers, depending on the set of parameters used. Parameters for graphite return the lower value, numbers for methane result in a higher calculated coverage. Of course neither pure graphite nor pure methane will be present on the surface; their parameters merely show the extremes within which the coverage is assumed to be. The Si2p line was recorded with hν = 150 eV for achieving highest surface sensitivity. The Si2p doublet is clearly resolved and reveals minor suboxide components in the range of 101
102 eV. The formation of suboxides after hydrogen termination is due to the ex-situ preparation and takes place within very short

Si2p (111)

C1s graphite

methane

O1s SiO2

I/normalized to Si2p

1.000

n/1022 cm
3

5.0016

σ/Mb35

0.201

λ/nm36,37

1.454

1.159

1.19943,44

0.748

0.31413

0.33538

0.33239

0.440

d/nm

0.069 11.34

2.2941,42 0.196

0.079 4.5616 0.480

times depending on ambient temperature and humidity.45 The theoretical position of the Fermi energy within the silicon band gap can be calculated from the doping concentration.13 In our case, the doping concentration of 7.7  1015 cm
3 returns the Fermi level position 0.87 eV above the valence band maximum. Using the experimentally determined Si2p3/2 emission line position of 99.66 eV and its published distance to the VBM of 98.74 eV,20 the Fermi level is found 0.92 eV above the valence band maximum, in very good agreement with the value determined by the doping concentration. The fit with a single doublet shows a relatively large error due to the suboxide components not included into the fit. An additional deviation is induced by keeping the binding energy difference and the intensity ratio fixed according to literature values. 21143

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Table 2. Electronic Excitation Energies for the PA-PTCDI Molecule at the TD-DFT/B3LYP/6-311G* Levela state

ΔE [eV]

λ [nm]

f

char [%]

1

2.126

583

0.523

H
L/71

1

2.714 2.808

457 442

0.224 0.001

H-1
L/70 H-2
L/70

S1(ππ*)

S2 (ππ*) 1 S3 (ππ*) a

Figure 4. Absorption (red) and fluorescence (green) spectra of PAPTCDI recorded in dichloromethane at room temperature.

Shown are the excitation energy (ΔE) and the corresponding wavelength (λ), the oscillator strength (f) and the character of the excitation with respect to the frontier orbitals (HOMO-2 (H-2), HOMO-1 (H-1), HOMO (H), and LUMO (L)).

Table 3. Electronic Excitation Energies for the PA-PTCDI Molecule at the TD-DFT/HSE06/6-311G* Levela state

ΔE [eV]

λ [nm]

f

char [%]

1

2.150

577

0.529

H
L/70

1

2.731 2.825

454 439

0.223 0.017

H-1
L/69 H-2
L/69

S1(ππ*)

S2 (ππ*) 1 S3 (ππ*)

a Shown are the excitation energy (ΔE) and the corresponding wavelength (λ), the oscillator strength (f), and the character of the excitation with respect to the frontier orbitals (HOMO-2 (H-2), HOMO-1 (H-1), HOMO (H), and LUMO (L)).

Figure 5. Cyclic voltammogram of PA-PTCDI in dichloromethane (referenced against ferrocene/ferrocenium).

The valence band spectrum was measured with hν = 90 eV, again for achieving highest surface sensitivity, and clearly shows a visible peak between 5 and 6 eV that is attributed to the Si
H bond,21,46 indicating the H-termination of the surface. Care has to be taken when assigning Si:H peaks because their appearance and position strongly depends on the emission angle and on the crystal orientation according to the band structure.21 The valence band maximum cannot easily be measured due to the weakness of the signal on one hand and the dispersion of the valence band states on the other hand, so that its position is calculated based on the position of the Si2p3/2 line as described above. Optical Spectroscopy & Cyclovoltammetry on PA-PTCDI in Solution. The optical properties in solution were investigated by UV
vis absorption and fluorescence spectroscopy revealing an absorption maximum at 573 nm and an emission maximum at 600 nm, respectively, as can be seen in Figure 4. The absorption maximum corresponds to an optical gap of 2.16 eV. CV with ferrocene as the internal standard was performed in dichloromethane, in order to study the redox behavior of the PAPTCDI dye. The CV measurement is shown in Figure 5, and shows two reversible reduction waves at
1.32 V and
1.18 V, as well as one reversible oxidation at 0.87 V. This leads to HOMO and LUMO energy levels of
5.67 eV and
3.62 eV if the most commonly used ionization potential of ferrocene (4.8 eV) is applied.47 Hence an electrochemical gap of 2.05 eV is obtained, being in good agreement with the value obtained from the optical data. Optical Spectroscopy: Theoretical Results. The optical properties of PA-PTCDI have been characterized employing calculations at the TD-DFT level of theory. The results for the excitation energies and the character of the excited states are depicted in Tables 2 and 3. The corresponding frontier orbitals are shown in Figure 6. The energies of the HOMO and LUMO orbitals,
5.56 eV and
3.23 eV at the B3LYP level and
5.40

and
3.49 eV at the HSE06 level, are in good agreement with the electrochemical measurements. According to the theoretical results, the main absorption band of PA-PTCDI (cf. Figure 4) can be assigned to a ππ* excited state, localized on the central perylene core. The theoretical result for the excitation energy, 2.13 eV (B3LYP) and 2.15 eV (HSE06), agrees well with the experimentally measured maximum of the absorption band at 2.16 eV (573 nm). The very good agreement of the experimental result, which was obtained in solution, with the gas phase theoretical results also shows that the sensitivity of the absorption energy of the first excited state (1S1) of the PA-PTCDI molecule to solvent effects is rather small.48 The next higher-lying electronically excited states S2 and S3, which can also be assigned to ππ* transitions, are almost degenerate and located 0.6
0.7 eV above S1. The S2 state is also observed in the experimental absorption spectrum at 440 nm (cf. Figure 4), which is in good agreement with the calculated values of 457 nm (B3LYP) and 454 nm (HSE06). The S3 state, on the other hand, carries negligible oscillator strength. Due to their higher excitation energy and smaller absorption strength, the states S2 and S3 are of minor relevance in the present context. The comparison of the results obtained by the B3LYP and HSE06 hybrid functionals shows that the excitation energies and oscillator strengths are indeed very similar. The excitation energy calculated with HSE06 is slightly closer to the experimental absorption energy. The best agreement with experimental results is thus found for the screened hybrid functional. Properties of PA-PTCDI Layers. The photoemission spectra taken of the thick PA-PTCDI layer are displayed in Figure 7. The survey (cf. Figure 7a) shows only carbon, oxygen, and nitrogen as is expected from the molecular formula. The stoichiometry as calculated from the peak areas is within 1% of the expected values and thus of the same size as the measurement error generally accepted for photoemission spectroscopy. All detail spectra were treated as described above. The Gaussian widths wG returned by the peak fit analyses were in the range of 0.64
0.97 eV for the main lines, 1.43
1.83 eV for shake-up 21144

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Figure 6. Molecular (Kohn
Sham) orbitals of PA-PTCDI at the B3LYP/6-31G* level of theory. The green and red shaded surfaces represent different signs of the molecular orbitals in the ground electronic state. The HOMO orbital (a) and the LUMO orbital (b) are localized on the central bisimide perylene core of the PA-PTCDI.

Figure 7. Photoemission spectra of a PA-PTCDI film on Si(111):H. (a) The survey shows that only the atoms that are expected from the structural formula of the molecule are present. (b) The O1s emission splits up in two species. The higher binding energy species contains a shake-up satellite of the lower binding energy species. (c) Only two atoms in the molecule account for this emission line, resulting in a high noise level. (d) The C1s spectrum gives a very complex structure containing many satellites in addition to the three well-distinguishable peaks.

satellites, and up to 2.0 eV for shake-off satellites. The width of the Lorentzian wL included in the Voigt profile was 0.09
0.10 eV. Shake-up satellites were shifted from the main lines by 1.13
1.72 eV. These values are well below the optical gap of the molecule but can nonetheless be attributed to shake-up satellites as reported for fused aromatic rings.49 The two O1s emission lines (cf. Figure 7b) can be attributed to the different bonds of the oxygen atoms in the molecule: The carbonyl oxygen atoms are bound to one carbon atom only, whereas the oxygen atoms at the perylene bay positions have two

neighboring carbon atoms. The first species can be ascribed to the lower binding energy, and the latter to the higher binding energy, similar to the attribution in PTCDA.50,51 The intensity of the two emission lines should be identical according to the molecule stoichiometry, but in the spectrum an apparent ratio of around 3:2 is found. The deviation from the 1:1 stoichiometry is attributed to a strong shake-up satellite of the carbonyl oxygen atoms as found for PTCDA50
52 and also explicitly observed in other PTCDI derivatives.52
54 The fit parameters can be found in Table 4. 21145

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The N1s spectrum (cf. Figure 7c) consists of only one species and a small satellite as would be expected from the structural formula. The high noise is due to the fact that there are only two nitrogen atoms out of a total of 98 atoms in each molecule. The fit parameters can again be found in Table 4. In the C1s spectrum in Figure 7d, three major emission lines can be distinguished. These can be attributed in increasing binding energy to carbon atoms bound in C
C, C
O, and CdO, respectively. The asymmetry in the emission line originating from C
C can be explained by discriminating the carbon atoms in the PTCDI core, in the phenol groups, and in the allyl groups. The shift between these three emissions can be clarified when one is aware of the fact that the binding energy of a conjugated π-system generally decreases with increasing size of the π-system.49 Because the PTCDI core, the phenol groups and the allyl groups are separated by oxygen or nitrogen atoms differently large conjugated electron systems are assumed for each of these groups. This is supported by the calculations which show that the HOMO and LUMO are located on the PTCDI core only (cf. Figure 6). The intensities of the shake-up satellites are again quite strong for the C1s lines relative to their main lines. No shake-up satellites exist for the C
Cphenol and C
Callyl species because HOMO and LUMO are not located on these atoms as shown by the calculation above. No noticeable shake-up satellite for the C
O species was found. The shake-off satellites are shifted by around 7.0 eV with respect to their main lines and thus well above the ionization potential (see following chapter). Their total intensity accounts for 6.3% of the total peak area. The fit parameters for the C1s emissions can be found in Table 5. The optical transmittance of the PA-PTCDI layer on the quartz glas substrate is depicted in Figure 8. Here, 1-transmittance is shown in order to simplify a comparison with the absorption spectrum of PA-PTCDI in solution (cf. Figure 4), which shows that the optical properties of PA-PTCDI are preserved in the thin film. The position of the transmittance minimum, which in first approximation should equal the position of the absorption maximum, is located at 592 nm. This value translates into an optical gap of 2.09 eV and is thus red-shifted by 0.07 eV compared to the molecules dissolved in dichloromethane.

Interface Experiment: PA-PTCDI on Si(111):H. The spectra recorded for the interface experiment are shown in Figure 9 using vertical offsets for clarity. With increasing film thickness, all spectral features exhibit a shift to higher binding energies. The film thicknesses provided in the graphs were calculated according to the damping of the Si2p emission. Because no data is available on the inelastic mean free path λ of electrons in PA-PTCDI, we took an estimate of λ = 1 nm for the measured Ekin = 20 eV. The bottom spectrum in Figure 9 shows the as-prepared Si(111):H surface with the clearly visible peak in the valence band in the Figure 9c region between 5 and 6 eV attributed to the Si
H bond. After a few deposition steps, the PA-PTCDI HOMO becomes clearly visible at around 2.1 eV. Additional characteristic features of PA-PTCDI emerge at higher binding energies. The position of the Si2p3/2 line was independent of the photon energy so that only the spectra recorded with a photon energy of 61 eV are shown in Figure 9(b). No silicon oxide component was visible, indicating that the substrate was clean. With increasing film thickness, the secondary electron background increases. The Fermi level position with respect to the valence band maximum was calculated from the Si2p3/2 line. The resulting distance of 0.88 eV again indicates a surface free of Fermi level pinning. With increasing film thickness, the Si2p line shifts to higher binding energies by 0.11 eV. No chemically shifted component is induced in the Si2p emission as would be expected in the case of a chemical bond between the molecule and the silicon surface.55 As indicated in Figure 9c, the PA-PTCDI HOMO shifts an additional 0.17 eV to higher binding energies. The work function shown in Figure 9a is lowered by 0.19 eV only with increasing film thickness, suggesting an interface dipole of 0.09 eV. The discontinuity at the valence band/HOMO is 1.07 eV. The resulting band diagram derived from the experiment is shown in Figure 10. The size given for the optical gap is based on the optical spectroscopy data on a thick layer as presented above. It is smaller than the photoemission HOMO
LUMO gap because of the exciton binding energy as well as polarizational and vibrational effects.5,57 Due to lack of inverse photoemission (IPES) data, the size given for the photoemission HOMO
LUMO

Table 4. Results of the Peak Fit Analysis of the PA-PTCDI O1s and N1s O1s

binding energy [eV]

N1s

CdO

O
C
O

ππ*CdO

C
N

ππ*C
N

531.77

533.85

533.49

400.73

402.11

wG [eV]

0.97

0.92

1.83

0.87

1.70

wL [eV]

0.09

0.09

rel. area/%

38.3

50.0

0.09 11.6

91.4

Figure 8. Transmittance spectrum of a PA-PTCDI film on quartz glas.

8.6

Table 5. Results of the Peak Fit Analysis of the PA-PTCDI C1s

binding energy [eV] wG [eV]

C
CPTCDI

C
Cphenol

C
Callyl

C
O

CdO

ππ*C
C,PTCDI

ππ*CdO

284.91 0.65

285.29 0.71

285.69 0.64

286.78 0.72

288.40 0.65

286.44 1.56

289.53 1.43

5.4

3.1

wL [eV]

0.09

0.10

0.09

0.10

0.09

rel. area/%

19.7

37.0

11.1

13.2

4.1

21146

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Figure 9. Photoemission spectra of the interface experiment with PA-PTCDI deposited stepwise onto Si(111):H. The vertical gray and black lines are included as a guide to the eye. (a) The work function shifts continuously to lower values with increasing film thickness. (b) The Si2p emission clearly resolves both lines of the doublet. Its intensity is damped, whereas its position is shifted to higher binding energy with increasing film thickness. (c) The valence band clearly shows the Si
H bond at around 5
6 eV in the bottom spectrum. With increasing film thickness, the HOMO as well as additional states of the PA-PTCDI appear.

gap is based on an estimate, based on an empirical formula that, for many organic molecules, relates the UPS/IPES gap and the optical gap.56 Thus a discontinuity at the conduction band/ LUMO of 1.22 eV is calculated. This resembles the valence band/HOMO discontinuity of 1.07 eV and thus indicates similar driving forces for excited electron hole pairs from the dye to the silicon. As mentioned above, sometimes the onsets rather than the maximum positions of the molecular orbitals are taken for further evaluation. From the literature it is known that for perylene derivatives the distance between the HOMO and LUMO onsets as determined by UPS and IPES is slightly larger than the optical gap.11 In our case, the onset of the PA-PTCDI HOMO is at a binding energy 0.45 eV above its maximum. Assuming a comparable value for the LUMO and taking into account the optical gap of 2.09 eV, we would reach a UPS/IPES gap larger than 2.99 eV and thus a similar LUMO position compared to the procedure described above and thus also similar discontinuities between the silicon bands and the molecular orbitals. The widths of the molecular orbitals in Figure 10 are drawn to scale. After subtraction of spectrometer broadening, the fwhm of the HOMO is 430 meV. The position of the optical gap is determined assuming that the exciton binding energy is distributed symmetrically between the exciton electron and hole. The electronic lineup shows that the HOMO and LUMO levels of PA-PTCDI are well within the silicon bands and that the band discontinuities are roughly of the same size. This is a very good premise for a charge transfer of photogenerated electron hole pairs from the molecule to the silicon. In addition, the band bending at the interface is small enough so that neither charge

species should be hindered at transferring the interface, which is of major importance if the PA-PTCDI is used for bulk sensitization in a solar cell. PA-PTCDI Adsorbed on Si(111):H: Theoretical Analysis. Based on our calculations, we analyze the electronic properties of the molecule/surface interface. In the theoretical analysis we have assumed a chemical bond between the PA-PTCDI and the Si(111):H surface since a proper description of the van der Waals interactions at the DFT level of theory is lacking and therefore the adsorption position of a physisorbed molecule can only be determined approximately by, e.g., using empirical force fields. Thus in the present work, we adopt the chemisorption geometry, which shows only weak chemical interactions between the frontier orbitals of the molecule and the substrate. A chemisorption process may occur if a dangling bond is available upon deposition of the molecule.58 Furthermore, in the calculations, the peripherical phenoxy groups of PA-PTCDI have been replaced by methoxy groups to optimize the computational costs. This reduction is not expected to influence the photophysical properties, because the phenoxy groups do not participate in the photophysics of the first excited state, as described in the theoretical optical characterization above. Figure 11 shows the energy-level line-up of the PA-PTCDI/ Si(111):H interface at the HSE06-level of theory, including the valence band maximum (VB) and the conduction band minimum (CB) of Si(111):H, the energies of the molecular resonance states related to the adsorption of PA-PTCDI at the Si(111):H surface as well as the corresponding orbitals. For comparison, the energy levels and the orbitals of the isolated molecule are also depicted. Note that all values given for the isolated molecule were obtained 21147

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Figure 11. Calculated energy levels and frontier orbitals of PA-PTCDI in the gas phase and chemisorbed at the Si(111):H surface using the HSE06 functional. The left panel shows the S1 excitation energy for the isolated molecule. Figure 10. Band diagram of the Si(111):H/PA-PTCDI interface as determined from the photoelectron spectra in Figure 9. The size of the gap of silicon was taken from the literature,13 whereas the size of the optical PA-PTCDI gap was taken from the transmittance measurement described above. The photoemission gap was calculated using an empirical formula relating optical gaps to UPS/IPES gaps.56

for the reduced molecule without the phenoxy groups. Furthermore, the orbital energies have been obtained using a plane wave basis in a large supercell for this purpose. To allow a direct comparison, all energies are given with respect to the vacuum reference. In order to determine this reference, the electrostatic potential was averaged in planes parallel to the surface. The value at the asymptotic region has been chosen as a reference value and set to zero. Upon adsorption, the character of the molecular orbitals remains unchanged except for the HOMO-1 orbital. The positions of the molecular levels with respect to the vacuum level are uniformly shifted to lower energies. The rather small value of the energy shift (≈ 0.4 eV) indicates a weak interaction/hybridization of the optically active states with the silicon substrate, despite the covalent bonding of the linker group. Thus a similar alignment of the frontier orbitals is also expected for a physisorbed molecule where the interaction is assumed to be even weaker. The resonance associated with the HOMO level of the isolated molecule is located 1.03 eV below the VB edge and 5.94 eV below the vacuum level, which is in remarkable agreement with the experimental photoemission values of 1.07 and 6.39 eV obtained for Si(111):H. The HSE06 calculation also yields a highly accurate description of the band gap of 1.16 eV. TD-DFT excitation energies for the HOMO
LUMO transition of the reduced isolated molecule yield to an excited state at 2.08
2.05 eV for both B3LYP and HSE06 functionals. As the HOMO
LUMO gap hardly changes upon adsorption, the excitation energy of the adsorbed molecule may be estimated by the TD-DFT gas phase value. This locates the photoexcited state of the absorbed molecule, which is relevant for the photoinduced electron injection process, at
3.89 eV and thus close to the silicon conduction band edge. Note, however, that the position

of the LUMO resonance predicted by the HSE06 calculation (
4.18 eV) appears to be too low as judged from a comparison of the HSE06 and B3LYP results for the HOMO
LUMO gaps of the isolated molecule. Despite the agreement of the HOMO
LUMO excitation energies, this value is 0.4 eV larger for the latter functional and in better agreement with the experiment. The discrepancy indicates the known difficulty of the DFT to precisely predict in particular the LUMO level position. A more accurate characterization of the resonance position requires the calculation of quasiparticle energies employing many-body perturbation theory, e.g., within the GW approximation, using a dynamically screened Coulomb interaction.59,60

’ SUMMARY AND CONCLUSION The investigation of PA-PTCDI for use as a sensitizing molecule in hydrogenated microcrystalline silicon led to promising results. First experiments on the dye in solution showed that the optical properties should allow for a bulk sensitization of the μcSi:H as the absorptivity of PA-PTCDI is very high in the range of 500
600 nm where the absorptivity of μc-Si:H is comparatively low. The calculated absorption maximum matches the experimental one quite well. From the calculation it could be deduced that the HOMO and the LUMO stretch out over the whole perylene core and thus form a large conjugated π-system. The electrochemical properties as measured with cyclovoltammetry gave a first indication that the PA-PTCDI HOMO and LUMO are within the silicon bands. Under UHV conditions, PA-PTCDI sublimes at a temperature above the temperature needed for producing microcrystalline silicon. The shape of the transmittance spectra is roughly preserved when compared to the molecules in solution, but shifted slightly to higher wavelenghts. Detailed photoemission spectra proved that the molecule is intact after sublimation as the molecular stoichiometry is preserved according to the structural formula. In a detailed peak fit analysis, the identification of the differently bound atomic species in the molecule was made possible. 21148

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The Journal of Physical Chemistry C The electronic lineup was measured on the model system Si(111):H with an SXPS interface experiment. It shows that the HOMO and LUMO levels of PA-PTCDI are indeed within the silicon bands. With an estimate on the LUMO position, we could predict that the band discontinuities are of roughly the same size. This is a good precondition for a charge transfer from an excited molecule to the silicon. The calculations of the HOMO lineup, which were conducted on a similar molecule for reasons of simplicity are in good agreement with the experimentally determined band diagram. The combined results presented in this paper make PAPTCDI a very good candidate for producing sensitized thin film silicon solar cells. In future experiments composite structures with HWCVD silicon will be prepared. Enhancement of photoconductivity and/or photocurrent is expected.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The authors would like to thank the BMBF for funding the project “OPV-Hybride” under Contract Number 03SF0339, within which this work has been conducted. O.R.-P. and M.T. acknowledge partial support by the DFG within the cluster of excellence “Munich Center of Advanced Photonics” as well as the generous allocation of computing time at the computing centers in Erlangen (RRZE), Munich (LRZ), and J€ulich (JSC). ’ REFERENCES (1) Mayer, T.; Weiler, U.; Kelting, C.; Schlettwein, D.; Makarov, S.; W€ohrle, D.; Abdallah, O.; Kunst, M.; Jaegermann, W. Sol. Energy Mater. Sol. Cells 2007, 91, 1873–1886. (2) Moser, J. Monatsh. Chem. 1887, 8, 373. (3) Mayer, T.; Weiler, U.; Mankel, E.; Jaegermann, W.; Kelting, C.; Schlettwein, D.; Baziakina, N.; W€ohrle, D. Renewable Energy 2008, 33, 262–266. (4) Mayer, T.; Hunger, R.; Klein, A.; Jaegermann, W. Phys. Status Solidi B 2008, 245, 1838–1848. (5) Weiler, U.; Mayer, T.; Jaegermann, W.; Kelting, C.; Schlettwein, D.; Makarov, S.; W€ohrle, D. J. Phys. Chem. B 2004, 108, 19398–19403. (6) W€urthner, F. Chem. Commun. 2004, 1564–1579. (7) Chen, Z.; Lohr, A.; Saha-Moller, C. R.; W€urthner, F. Chem. Soc. Rev. 2009, 38, 564–584. (8) Higashi, G. S.; Chabal, Y. J.; Trucks, G. W.; Raghavachari, K. Appl. Phys. Lett. 1990, 56, 656–658. (9) Higashi, G. S.; Becker, R. S.; Chabal, Y. J.; Becker, A. J. Appl. Phys. Lett. 1991, 58, 1656–1658. (10) Yablonovitch, E.; Allara, D. L.; Chang, C. C.; Gmitter, T.; Bright, T. B. Phys. Rev. Lett. 1986, 57, 249–252. (11) Zahn, D. R.; Gavrila, G. N.; Gorgoi, M. Chem. Phys. 2006, 325, 99–112. (12) Shah, A. V.; Schade, H.; Vanecek, M.; Meier, J.; Vallat-Sauvain, E.; Wyrsch, N.; Kroll, U.; Droz, C.; Bailat, J. Prog. Photovoltaics: Res. Appl. 2004, 12, 113–142. (13) Sze, S. M.; Ng, K. K. Physics of Semiconductor Devices; John Wiley & Sons: Hoboken, NJ, 2006. (14) Ensling, D.; Thißen, A.; Gassenbauer, Y.; Klein, A.; Jaegermann, W. Adv. Eng. Mater. 2005, 7, 945–949. (15) Mayer, T.; Lebedev, M.; Hunger, R.; Jaegermann, W. Appl. Surf. Sci. 2005, 252, 31–42. (16) Himpsel, F. J.; McFeely, F. R.; Taleb-Ibrahimi, A.; Yarmoff, J. A.; Hollinger, G. Phys. Rev. B 1988, 38, 6084–6096.

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