Home
Search
Collections
Journals
About
Contact us
My IOPscience
Optical and magneto-optical properties of metal phthalocyanine and metal porphyrin thin films
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 104201 (http://iopscience.iop.org/0953-8984/26/10/104201) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 131.156.59.191 This content was downloaded on 05/09/2014 at 09:16
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 104201 (12pp)
doi:10.1088/0953-8984/26/10/104201
Optical and magneto-optical properties of metal phthalocyanine and metal porphyrin thin films Tobias Birnbaum1 , Torsten Hahn1 , Claudia Martin1 , Jens Kortus1 , Michael Fronk2 , Frank Lungwitz2 , Dietrich R T Zahn2 and Georgeta Salvan2 1 2
Institute of Theoretical Physics, TU Bergakademic Freiberg, D-09596, Germany Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany
E-mail: [email protected] Received 15 August 2013, revised 5 November 2013 Published 19 February 2014
Abstract
The optical constants together with the magneto-optical Voigt constants of several phthalocyanine (Pc) and methoxy functionalized tetraphenylporphyrin (TMPP) thin films prepared on silicon substrates are presented. The materials investigated are MePc with Me = Fe, Co, Ni, Cu, Zn and MeTMPP with Me = Cu, Ni. We also compared our results to the metal-free H2 Pc, H2 TPP and H2 TMPP. The experimental results will be supported by electronic structure calculations based on density functional theory (DFT) and interpreted using the perimeter model initially proposed by Platt. The model allows for qualitative understanding of the forbidden character of transitions in planar, aromatic molecules, and is able to qualify differences between Pc and TMPP type materials. (Some figures may appear in colour only in the online journal)
1. Introduction
also TMPP results, since they have not been characterized with regard to different metal centers until now. Very recently an additional way to further engineer the magnetic properties by building phthalocyanine heterojunctions was discovered [8]. The possibility of producing well ordered films by thermal evaporation in vacuum makes them perfect model systems for preparing device-like structures. To understand the charge and spin transport properties of a material it is essential to know the electronic structure around the Fermi energy since typically only the few uppermost occupied and lowest unoccupied electronic levels define the transport characteristics. Therefore a clear understanding of the optical properties is an essential ingredient to reveal the electronic structure of a material. Additionally the anisotropy of the optical constants along different space directions can be used to obtain information about structural parameters of the sample [9, 10]. Reports on magneto-optical studies conducted by magnetic circular dichroism (MCD) spectroscopy in the typical energy range of electronic transitions of the porphyri-
Since the first reports of an organic spin valve [1, 2], novel devices such as spin-OLEDs (organic light emitting diodes) [3] and spin-OFETs (organic field effect transistors) [4] as well as sensors based on electrically detected magnetic resonance [5] have been developed. The rapid development of the field of organic spintronics is driven by the large spin life time in organic molecules, combined with the great diversity and flexibility of molecular synthesis and technological processing. The large range of molecules which has been integrated into spintronic devices to date comprises various diamagnetic molecules, e.g. [6], and individual single molecule magnets [7]. Among others, the groups of phthalocyanines (Pcs) and methoxy functionalized tetraphenylporphyrins (TMPPs) are very promising in terms of application in organic electronics and spintronics, due to their chemical and thermal stability and the possibility of tuning their electronic and magnetic properties by changing the central metal atom or substituting H-atoms of the ligands with functional groups. We present 0953-8984/14/104201+12$33.00
1
c 2014 IOP Publishing Ltd
Printed in the UK
J. Phys.: Condens. Matter 26 (2014) 104201
T Birnbaum et al
noids3
As shown in [15–19] this model makes valid predictions on the character of weakly dipole forbidden transitions. Even for porphyrins [20, 21] and derivates [22] the model could be applied with partial success. The prediction of OARNs requires only the knowledge of the real-valued representations of the molecular wavefunctions, which are existing whenever no external electric or magnetic field is present. Thus we would like to show how this electronic structure calculation information can be transformed by means of this simple model into useful data. In section 2 we present details on the experimental methods and section 3 outlines the theoretical background. The last two sections 4 and 5 contain the discussion and the summary of our results.
are numerous. Reference [11] provides an extensive overview on MCD measurements and spectral deconvolution analysis for several porphyrinoids. Early MCD spectral deconvolutions for porphyrinoids were performed in [12, 13]. From the lineshape of the MCD bands conclusions were drawn regarding the nature of the ground and excited states of the most prominent absorption bands of H2 Pc, CoPc, NiPc and CuPc. However, the commonly used absorption spectroscopy and MCD require the material to be dissolved in a liquid solvent or to be prepared as a film on transparent substrates. In this work films on silicon substrates have been investigated, which is much closer to the condition used in organic electronics and spintronics devices. The applied variable angle spectroscopic ellipsometry allows us to detect the anisotropy between the optical constants for light polarization in the plane of the film and the polarization perpendicular to the film plane. The magneto-optical Kerr effect (MOKE) spectroscopy setup used measures the full complex Kerr angle, i.e. both Kerr rotation and Kerr ellipticity were obtained. However, the shape of the raw MOKE spectrum is thickness dependent [10] due to optical interference within the film. Therefore, in contrast to MCD results, the MOKE data require numerical post-processing before they can be interpreted. From the measured complex MOKE spectra and from the optical constants determined from ellipsometry, the material-specific magneto-optical Voigt constant can be obtained [10]. The Voigt constant Q = −iε y /εx is part of the off-diagonal elements of the dielectric tensor in a magnetic field along z. The Voigt constant is material specific and the magnitude and lineshape of the features occurring in its energy dispersion spectrum in the near infrared to near ultraviolet spectral range can be used to extract information on the spin and/or orbital degeneracy as well as on the symmetry of the electronic levels involved in the measured electronic transitions. Moreover, with the knowledge of the complex Voigt constant, MCD as well as Faraday spectra can be predicted. The perimeter model is a qualitative model, which can be used for the characterization of the forbidden character of π → π ∗ transitions in planar, aromatic molecules. More specifically, it requires the π -system of interest to contain (4N + 2) electrons, which is the H¨uckel condition for aromaticity. The main point of the model is to approximate planar, aromatic molecules of arbitrary shapes by a 1D-quantum mechanical oscillator along the circumference of an appropriately chosen ring. It was first demonstrated by Platt in 1949 [14] and used for simple aromatic molecules such as benzene or anthracene. The idea behind it might be clarified by taking benzene as a small example. Benzene with its six delocalized π -electrons is a perfectly planar and regular hexagon which is replaced in the perimeter model by six free electrons in a 2D-disk. From this one can finally define hypothetical orbital angular ring quantum numbers (OARNs), which can be used in selection rules for possible excitations in the system.
2. Experimental details
The films, with three different thicknesses between 30 and 150 nm, were prepared by thermally evaporating the material from a Knudsen cell onto a silicon substrate using organic molecular beam deposition (OMBD). The growth rate of about (0.4 ± 0.1) nm min−1 was kept constant with little variation between the materials. The Si(111) substrates were cleaned by keeping them subsequently in acetone, isopropanol, and deionized water in an ultrasonic bath for 5 min each. After that they were dipped for 1 min in 5% hydrofluoric acid in order to remove the native oxide and afterwards once again rinsed in deionized water. This procedure was strictly applied to all metal phthalocyanines but the passivation step (dipping in HF) was omitted in the cases of H2 Pc and the porphyrins. For H2 Pc only two thicknesses were evaluated. The ellipsometry measurements were performed with either a VASE or M-2000 ellipsometer, both being variable angle spectroscopic ellipsometers from J A Woollam Co. Inc., Lincoln, NE. The 8 and 1 spectra were measured at the angles 50◦ , 60◦ , and 70◦ . For the data modeling the software WVASE32 and CompleteEASE from the same company were used. The MOKE spectra were measured using a home built spectrometer operating with a photoelastic modulator and lock-in amplifier after [23], as it is commonly used also in reflection anisotropy spectroscopy measurements [24, 25]. The magnetic field during the measurements was 0.35 T (H2 Pc, CuPc), 1.05 T (CoPc) and 1.69 T (MnPc, FePc, NiPc, ZnPc, H2 TPP, H2 TMPP, CuTMPP and NiTMPP). The MOKE spectra were measured in polar geometry, i.e. the magnetic field direction was perpendicular to the sample surface and quasi-parallel to the incident and reflected white light beam. The data shown in this work are normalized to 1 T by scaling the spectra magnitudes linearly with the applied field. This procedure is justifiable, since the strength of the applied magnetic field in our experiment does not influence the lineshape of the spectra. For the determination of the Voigt constant Q from the measured Kerr angle and from the ellipsometry data the numerical procedure described in [10] was applied. Briefly
3
Porphyrinoid refers to compounds with the porphyrin skeleton, i.e. porphyrins (Ps), meso-tetra-kis-(3-methoxy-phenyl)porphyrin and phthalocyanines are included besides others. 2
J. Phys.: Condens. Matter 26 (2014) 104201
T Birnbaum et al
summarized, the calculations are based on the formula for the complex Kerr angle 2K 2K = arctan
i(u + − u − ) i(u + − u − ) ≈ (u + + u − ) (u + + u − )
applied [27] with different material content in each single slice. The content was varied with an error function (erf), assuming a Gaussian height distribution over the area of the film within the measuring light spot. Therefore on the bottom of the ‘roughness slices’ the assumed content of Pc material was close to 100% and on the top close to zero. The assumption of a Gaussian profile also allows us to calculate the rms-roughness value. The obtained tilt angles and surface roughnesses will be discussed in section 4.
(1)
where u ± denotes the effective reflection coefficients of the sample for right and left hand circularly polarized light. These can be written as u=
rAF + a 2 · rFS . 1 + a 2 · rAF · rFS
(2)
3. Theoretical methods
In the formula the Fresnel reflection coefficient r and the phase propagation term a are appearing. The indices A, F, and S stand for air, film and substrate. r=
n˜ 1 − n˜ 2 , n˜ 1 + n˜ 2
h ω i a = exp i n˜ d . c
3.1. Technical details: DFT calculations
In order to support the experimental results and to further investigate the electronic structure of the materials we performed all-electron DFT calculations of all individual free molecules and for the bulk structures of the MePcs. The calculations for the individual free molecules were carried out using the NRLMOL program package [28]. NRLMOL combines large Gaussian orbital basis sets, numerically precise variational integration and an analytic solution of Poisson’s equation in order to accurately determine the self-consistent potentials, secular matrix, total energies and Hellmann– Feynman–Pulay forces. To include exchange and correlation effects, the generalized gradient functional developed by Perdew, Burke, and Ernzerhof (PBE) was applied [29]. First we relaxed the structures of the individual molecules by performing a full geometry optimization. The symmetries of the initial and the final state are of decisive character for the calculation of the possible optical transitions. The corresponding dipole matrix element is obtained for any possible transition and the intensity of every transition is weighted with the value of the dipole matrix element. This offers a direct mapping of the spectral signals to the electronic structure of the molecule. In order to reach qualitative understanding of our experimental data we added a Gaussian broadening of about 0.15 eV to the theoretical spectra. For the bulk structure calculations we used the ELK program which is an implementation of the all-electron full potential linearized augmented plane-wave (FP-LAPW) method [30]. The starting structures correspond to the α-phase of MePc and were obtained from the Cambridge Structural Database. The calculations were performed using a basis set with 440 valence states and an additional 562 local orbitals together with the same PBE functional as for the NRLMOL calculations. After geometry relaxation of the structures (Fmax < 0.05 eV Å−1 ) the full dielectric tensor was calculated according to [31]. The Voigt constant can be retrieved directly from the elements of the dielectric tensor. The effective k-point mesh size used for Brillouin-zone integration in the case of calculation of optical properties was 400. The effect of spin–orbit coupling and a magnetic field normal to the molecular plane were included in the calculations.
(3)
In equation (3) n˜ is the complex refraction index n˜ = n + ik, ω is the angular frequency of the light, c the vacuum light velocity, and d the thickness of the film. For Voigt constants Q = −iε y /εx much smaller than 1 the modification of the refractive indices for the circular light components can be written as n˜ ± = n(1 ˜ ∓ Q/2).
(4)
Thus, with the knowledge of Q, of the film thickness d, and of the ellipsometry result n˜ the complex Kerr angle can be calculated. To go the opposite way one has to invert the function 2K = f (Q) numerically. For proper modeling of the ellipsometry spectra of the investigated porphyrinoids, uniaxial anisotropy as well as surface roughness has to be taken into account. The main axis of anisotropy is the direction perpendicular to the substrate plane and linear light polarization in that direction experiences a different dielectric function (or optical constants) compared with light with a linear polarization parallel to the sample plane. The origin of the anisotropy stems from a preferential alignment of the molecules on the substrate [10, 26]. For estimating the average tilt angle α of the molecular plane with respect to the substrate plane we assume that all molecules adopt the same orientation and that the transition dipole moments of the electronic transitions in the Q-band (see later discussion) are degenerated and both parallel to the molecular plane. The molecular film is thus considered to consist of perfectly aligned disks. Under these assumptions we can employ the following formula [10]: s 2Ain − Aout α = arccos . (5) 2Ain + Aout Ain and Aout are the integrals over the area of the Q-band in the spectra of the in-plane and out-of-plane components of the extinction coefficient k, respectively. The surface roughness was modeled by introducing several (typically 11) slices of effective media on top of the Pc film in the model. Bruggeman mixing of the dielectric functions of the Pc and void was
3.2. Perimeter model
The basic assumptions within the perimeter model (PM) are as follows. 3
J. Phys.: Condens. Matter 26 (2014) 104201
T Birnbaum et al
(i) The π -system under investigation can be treated independently of the remaining electrons of the molecule. (ii) Spin–orbit coupling is negligible small. (iii) Full aromaticity of the investigated π -system (i.e. containing (4N + 2) electrons, with N ∈ N, with N being a natural number) is assumed, describing a closed path lying approximately in a plane. (iv) σ π ∗ and nπ ∗ state-mixing into π → π ∗ transitions will be ignored.
and final WFs and knowing how OARNs relate to the OANs, we are able to characterize transitions in optical absorption and MOKE spectra. The OARN becomes a measure of the OAN by defining the modulus of the OARN as half the number of nodes with sign change of the WF 9k (φ), along the outermost possible path of the investigated π -system. The sign of the OARN can be defined in two ways. The first possibility would be to identify the sign with the sign of the following equation: Z 2π 1 ˆ 9k (φ) dφ 9k∗ (φ) 4 2π 0 Z 2π h¯ ∂ 1 h¯ k 9k∗ (φ) = 9k (φ) dφ = . (6) 2π 0 i ∂φ 2π
Assumptions (i) and (ii) assure the separability of the molecular wavefunctions (WFs) into three components, one perpendicular to the plane of the molecule z, one polar angle φ in the molecular plane and an in-plane radius r . Assumption (iii) validates that outer shell π → π ∗ transitions are sufficient for the main part of the optical spectra. Note that the model is no longer valid if the number of electrons in the investigated π -system deviates from the number claimed above. The discussion may then be carried out for a stable aromatic anion or cation instead. Now that we know about the limitations of the PM and can ensure its validity, we will focus on the definition of the orbital angular ring quantum numbers (OARNs). The wavefunctions predicted by the PM are complex eikφ with the imaginary unit i, the angular variable φ and the OARN k. Commonly the PM is combined with classic molecular orbital theory, which the values of k to restricts k ∈ 0, ±1, ±2, . . . , ± n2 − 1 , n2 , where n is the number of electrons in the considered π -system. However, one has to note that the selection rules are defined with respect to orbital angular quantum numbers (OANs). If spin–orbit coupling is negligible, the selection rules split up in statements for spin s and angular momentum l resulting in the well known dipole selection rules 1l = ±1, if at the same time spin flips are not allowed. But why is it not possible to state that the OARN is equal to the OAN? Since an arbitrary closed path along a π -system never possesses a C∞ -symmetry, Lˆ z is not a constant of motion. In other words if there is no potential with circular symmetry, the OARN is not equal to the OAN. However, identifying the OARN as the OAN of Lˆ z is often misleadingly done in literature. The interpretation of the OARN as an eigenvalue of the linear momentum of the 1D problem along the circle is invalid, due to the periodic potential resulting from the atoms, along the polar coordinate φ. Hence the linear momentum is not a constant of motion in the 1D case. The molecular WFs are either linear combinations of eigenstates or not eigenstates at all of the angular momentum Eˆ That leaves basically three options: (1) direct comoperator L. putation of LEˆ applied on the molecular WF at distinct points,
ˆ := This gives the mean expectation value of the operator 4 h¯ ∂ ˆ . 4 can be interpreted either as linear momentum operator i ∂φ of the free electron model, i.e. along the circle with sufficient boundary conditions and the variable φ, or as Lˆ z of the restrained 3D problem. Note that the 3D problem can be substituted by a 1D problem with coinciding z-axes. Since the radius is fixed, the molecule is approximately planar and the cylinder coordinates are separable. The second way of determining the sign of the OARN is by using classic electrodynamics and Lorentz law. It follows that k < 0 if the magnetic moment, induced by the moving electrons, and the z-axis, are anti-parallel, and k > 0 otherwise. This suggests the illustration of the sign as the circulating sense of the electrons. Thereby the case of maximal k is implicitly defined as positive. Note that the OARNs k are adding up like scalars to a total ring quantum number K , which follows from the interpretation ˆ as a linear momentum operator in 1D or from power of 4 laws and the form of the molecular WF (a simple product of exponential functions) of n electrons. Therefore it is possible to apply the selection rules on k instead of l, corresponding to a replacement of LEˆ by Lˆ z , because Lˆ 2x + Lˆ 2y = const on the circle of the perimeter model. The change of the OARN 1k, resulting from a transition, can be recognized as a measure of the circular charge distribution. For example a greater OARN of the excited state can be interpreted as formation of a negatively charged particle. It is now clear that magnetic moments, induced by the circular currents, are proportional as well to 1k. In order to assign OARN one can start from the geometry of the molecule with the corresponding real-valued representations of the WF of interest and condense it using the following three steps. (i) Determine whether the molecule in question is aromatic or not. If it is not, use any stable aromatic anion or cation derivable from the molecule. (ii) Determine the number of electrons in the π -system under investigation. (iii) Plot the real-valued WFs and count the number of nodes with sign change along the path of the π-system of interest, this would equal figure 1. Now half the number of counted nodes equals the number of nodal planes, i.e. the absolute value of the OARN k.
(2) using linear combinations of atomic orbitals (LCAOs) to model the molecular WF at distinct points and obtain the linear combinations of the OAN or (3) using the perimeter model, to gain OARNs k, see [32]. In contrast to the first two, the third option is unique for a distinct WF, even if the WF is not Eˆ The an eigenstate or linear combination of eigenstates of L. OARN can be used instead of the OAN, since a one-to-one correlation exists. Thus knowing the OARNs for the initial 4
J. Phys.: Condens. Matter 26 (2014) 104201
T Birnbaum et al
Figure 1. For a (14)-annulene (phenanthrene; left), the ‘unfolded’ molecule (middle) and model perimeter (right) with atoms and nodal planes highlighted are shown. The two degenerate sets of nodal planes of every plot are shown for k = 2. (Analogous to [14].)
Figure 2. Measured extinction coefficients k of the Q-band. (a) Typical lineshapes for MeTMPP for Cu (S = 21 ) and Ni (S = 0). (b) Effect of introducing methoxy sidegroups into TPPs. The slight redshift of the H2 TMPP films may indicate a higher degree of crystallinity of H2 TMPP.
in agreement with theory, the B-band being related to π → π ∗ transitions of the aromatic system, nearly independent of the center atom(s) (see [33, 22]). Also the methoxy sidegroups do not influence the lineshape of the B-band significantly. The Q-band is lower in energy at ∼2.25 eV for TMPPs and based on an a2u → eg transition. It was also found that the Q-band is dependent on the central atom(s), since a WF of a2u symmetry has no nodal point at this location. Figures 2 and 5 show this dependence by comparing H2 - and the MeTMPPs. The former shows a four-fold splitting of the Q-band, since the total spin is 0 and the unoccupied states are approximately degenerated within 10 meV. This can be related to the C2 symmetry of the molecule. Please note that the definition of Q- and B-band by using the energy can be misleading, as in the case of Pcs the character of the two features exchanges with the a2u → eg transition occurring at higher energy in that case. The influence of the methoxy sidegroups on the shape of the Q-band is shown in figure 2(b). One can see a slight redshift of the functionalized molecule and a change in the ratio between in-plane and out-of-plane components of the extinction coefficient. The redshift of the H2 TMPP absorption is most probably an effect of stronger intermolecular interactions, an
Finally we are going to remark on possible influences of the center atoms, which will support our discussion and can be understood with the help of the WF symmetry. All metal atoms have lower electronegativities than hydrogen and therefore the binding σ -electrons will be shifted towards the ring. This will increase the electron densities on the nitrogen sites and increase the energies of states with electron density there by Coulomb interaction. This effect is known as the inductive effect. The next effect is known as the conjugative effect and influences primarily the π -system of the TMPPs. As the p orbitals, especially pz , of the d-block elements are empty, transition group elements increase the size of the π -system by conjugation. The energy of a WF with according symmetry, i.e. without nodal points on the center atom, is lowered. 4. Results and discussion 4.1. Optical properties: B- and Q-band
The B-band was defined as the energetically higher feature rising at ∼2.8 eV for TMPPs in the optical spectrum based on an a1u → eg transition. For porphyrins, experiments indicate, 5
J. Phys.: Condens. Matter 26 (2014) 104201
T Birnbaum et al
Figure 3. Molecular orbital scheme of selected orbitals of the ground state for CuPc, CuTMPP and as reference CuP with indicated Q- and B-band transitions.
Figure 4. Optical constants of the Pcs under investigation. (a) Real parts and (b) imaginary parts of the dielectric tensor. Solid lines are the in-plane and dotted lines are the out-of-plane components. (c) Comparison of the DFT calculated imaginary parts εx x (dash-dotted), ε yy (solid) and εzz (dashed) of the dielectric tensor compared with the measured out-of-plane component (dotted).
effect known as crystallochromy, which might be an indication of a better degree of crystallinity of these films. As can be seen from DFT calculations, each of the a1u → eg and a2u → eg transitions ends in the same final pair of states with eg symmetry. This is true for all investigated molecules, see figure 3. The reversal of Q- and B-band ordering between TMPP and Pc is related to a change in level ordering of the corresponding occupied states. Accordingly the a1u orbital is once above (TMPP) and once below (Pc) the a2u orbital, as was already observed in the case of manganese derivates [34]. These four states account for the Q- and B-bands of porphyrins [35] and the description is known as Gouterman’s four orbital model [36], which was used successfully for various porphyrinoids [19, 22, 33, 36–38].
In figure 4(b) it can be seen that the Q-band of all Pcs consists of at least two main features. H2 -, Co-, Ni-, Cu-, and ZnPc all show significant splitting of the Q-band into main features at ∼1.75 and ∼2.1 eV. The Q-bands of Mn- and FePc show an even more complex character and in contrast to the other Pcs significant absorption at low energies (
Search
Collections
Journals
About
Contact us
My IOPscience
Optical and magneto-optical properties of metal phthalocyanine and metal porphyrin thin films
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2014 J. Phys.: Condens. Matter 26 104201 (http://iopscience.iop.org/0953-8984/26/10/104201) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 131.156.59.191 This content was downloaded on 05/09/2014 at 09:16
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 26 (2014) 104201 (12pp)
doi:10.1088/0953-8984/26/10/104201
Optical and magneto-optical properties of metal phthalocyanine and metal porphyrin thin films Tobias Birnbaum1 , Torsten Hahn1 , Claudia Martin1 , Jens Kortus1 , Michael Fronk2 , Frank Lungwitz2 , Dietrich R T Zahn2 and Georgeta Salvan2 1 2
Institute of Theoretical Physics, TU Bergakademic Freiberg, D-09596, Germany Institute of Physics, Chemnitz University of Technology, D-09107 Chemnitz, Germany
E-mail: [email protected] Received 15 August 2013, revised 5 November 2013 Published 19 February 2014
Abstract
The optical constants together with the magneto-optical Voigt constants of several phthalocyanine (Pc) and methoxy functionalized tetraphenylporphyrin (TMPP) thin films prepared on silicon substrates are presented. The materials investigated are MePc with Me = Fe, Co, Ni, Cu, Zn and MeTMPP with Me = Cu, Ni. We also compared our results to the metal-free H2 Pc, H2 TPP and H2 TMPP. The experimental results will be supported by electronic structure calculations based on density functional theory (DFT) and interpreted using the perimeter model initially proposed by Platt. The model allows for qualitative understanding of the forbidden character of transitions in planar, aromatic molecules, and is able to qualify differences between Pc and TMPP type materials. (Some figures may appear in colour only in the online journal)
1. Introduction
also TMPP results, since they have not been characterized with regard to different metal centers until now. Very recently an additional way to further engineer the magnetic properties by building phthalocyanine heterojunctions was discovered [8]. The possibility of producing well ordered films by thermal evaporation in vacuum makes them perfect model systems for preparing device-like structures. To understand the charge and spin transport properties of a material it is essential to know the electronic structure around the Fermi energy since typically only the few uppermost occupied and lowest unoccupied electronic levels define the transport characteristics. Therefore a clear understanding of the optical properties is an essential ingredient to reveal the electronic structure of a material. Additionally the anisotropy of the optical constants along different space directions can be used to obtain information about structural parameters of the sample [9, 10]. Reports on magneto-optical studies conducted by magnetic circular dichroism (MCD) spectroscopy in the typical energy range of electronic transitions of the porphyri-
Since the first reports of an organic spin valve [1, 2], novel devices such as spin-OLEDs (organic light emitting diodes) [3] and spin-OFETs (organic field effect transistors) [4] as well as sensors based on electrically detected magnetic resonance [5] have been developed. The rapid development of the field of organic spintronics is driven by the large spin life time in organic molecules, combined with the great diversity and flexibility of molecular synthesis and technological processing. The large range of molecules which has been integrated into spintronic devices to date comprises various diamagnetic molecules, e.g. [6], and individual single molecule magnets [7]. Among others, the groups of phthalocyanines (Pcs) and methoxy functionalized tetraphenylporphyrins (TMPPs) are very promising in terms of application in organic electronics and spintronics, due to their chemical and thermal stability and the possibility of tuning their electronic and magnetic properties by changing the central metal atom or substituting H-atoms of the ligands with functional groups. We present 0953-8984/14/104201+12$33.00
1
c 2014 IOP Publishing Ltd
Printed in the UK
J. Phys.: Condens. Matter 26 (2014) 104201
T Birnbaum et al
noids3
As shown in [15–19] this model makes valid predictions on the character of weakly dipole forbidden transitions. Even for porphyrins [20, 21] and derivates [22] the model could be applied with partial success. The prediction of OARNs requires only the knowledge of the real-valued representations of the molecular wavefunctions, which are existing whenever no external electric or magnetic field is present. Thus we would like to show how this electronic structure calculation information can be transformed by means of this simple model into useful data. In section 2 we present details on the experimental methods and section 3 outlines the theoretical background. The last two sections 4 and 5 contain the discussion and the summary of our results.
are numerous. Reference [11] provides an extensive overview on MCD measurements and spectral deconvolution analysis for several porphyrinoids. Early MCD spectral deconvolutions for porphyrinoids were performed in [12, 13]. From the lineshape of the MCD bands conclusions were drawn regarding the nature of the ground and excited states of the most prominent absorption bands of H2 Pc, CoPc, NiPc and CuPc. However, the commonly used absorption spectroscopy and MCD require the material to be dissolved in a liquid solvent or to be prepared as a film on transparent substrates. In this work films on silicon substrates have been investigated, which is much closer to the condition used in organic electronics and spintronics devices. The applied variable angle spectroscopic ellipsometry allows us to detect the anisotropy between the optical constants for light polarization in the plane of the film and the polarization perpendicular to the film plane. The magneto-optical Kerr effect (MOKE) spectroscopy setup used measures the full complex Kerr angle, i.e. both Kerr rotation and Kerr ellipticity were obtained. However, the shape of the raw MOKE spectrum is thickness dependent [10] due to optical interference within the film. Therefore, in contrast to MCD results, the MOKE data require numerical post-processing before they can be interpreted. From the measured complex MOKE spectra and from the optical constants determined from ellipsometry, the material-specific magneto-optical Voigt constant can be obtained [10]. The Voigt constant Q = −iε y /εx is part of the off-diagonal elements of the dielectric tensor in a magnetic field along z. The Voigt constant is material specific and the magnitude and lineshape of the features occurring in its energy dispersion spectrum in the near infrared to near ultraviolet spectral range can be used to extract information on the spin and/or orbital degeneracy as well as on the symmetry of the electronic levels involved in the measured electronic transitions. Moreover, with the knowledge of the complex Voigt constant, MCD as well as Faraday spectra can be predicted. The perimeter model is a qualitative model, which can be used for the characterization of the forbidden character of π → π ∗ transitions in planar, aromatic molecules. More specifically, it requires the π -system of interest to contain (4N + 2) electrons, which is the H¨uckel condition for aromaticity. The main point of the model is to approximate planar, aromatic molecules of arbitrary shapes by a 1D-quantum mechanical oscillator along the circumference of an appropriately chosen ring. It was first demonstrated by Platt in 1949 [14] and used for simple aromatic molecules such as benzene or anthracene. The idea behind it might be clarified by taking benzene as a small example. Benzene with its six delocalized π -electrons is a perfectly planar and regular hexagon which is replaced in the perimeter model by six free electrons in a 2D-disk. From this one can finally define hypothetical orbital angular ring quantum numbers (OARNs), which can be used in selection rules for possible excitations in the system.
2. Experimental details
The films, with three different thicknesses between 30 and 150 nm, were prepared by thermally evaporating the material from a Knudsen cell onto a silicon substrate using organic molecular beam deposition (OMBD). The growth rate of about (0.4 ± 0.1) nm min−1 was kept constant with little variation between the materials. The Si(111) substrates were cleaned by keeping them subsequently in acetone, isopropanol, and deionized water in an ultrasonic bath for 5 min each. After that they were dipped for 1 min in 5% hydrofluoric acid in order to remove the native oxide and afterwards once again rinsed in deionized water. This procedure was strictly applied to all metal phthalocyanines but the passivation step (dipping in HF) was omitted in the cases of H2 Pc and the porphyrins. For H2 Pc only two thicknesses were evaluated. The ellipsometry measurements were performed with either a VASE or M-2000 ellipsometer, both being variable angle spectroscopic ellipsometers from J A Woollam Co. Inc., Lincoln, NE. The 8 and 1 spectra were measured at the angles 50◦ , 60◦ , and 70◦ . For the data modeling the software WVASE32 and CompleteEASE from the same company were used. The MOKE spectra were measured using a home built spectrometer operating with a photoelastic modulator and lock-in amplifier after [23], as it is commonly used also in reflection anisotropy spectroscopy measurements [24, 25]. The magnetic field during the measurements was 0.35 T (H2 Pc, CuPc), 1.05 T (CoPc) and 1.69 T (MnPc, FePc, NiPc, ZnPc, H2 TPP, H2 TMPP, CuTMPP and NiTMPP). The MOKE spectra were measured in polar geometry, i.e. the magnetic field direction was perpendicular to the sample surface and quasi-parallel to the incident and reflected white light beam. The data shown in this work are normalized to 1 T by scaling the spectra magnitudes linearly with the applied field. This procedure is justifiable, since the strength of the applied magnetic field in our experiment does not influence the lineshape of the spectra. For the determination of the Voigt constant Q from the measured Kerr angle and from the ellipsometry data the numerical procedure described in [10] was applied. Briefly
3
Porphyrinoid refers to compounds with the porphyrin skeleton, i.e. porphyrins (Ps), meso-tetra-kis-(3-methoxy-phenyl)porphyrin and phthalocyanines are included besides others. 2
J. Phys.: Condens. Matter 26 (2014) 104201
T Birnbaum et al
summarized, the calculations are based on the formula for the complex Kerr angle 2K 2K = arctan
i(u + − u − ) i(u + − u − ) ≈ (u + + u − ) (u + + u − )
applied [27] with different material content in each single slice. The content was varied with an error function (erf), assuming a Gaussian height distribution over the area of the film within the measuring light spot. Therefore on the bottom of the ‘roughness slices’ the assumed content of Pc material was close to 100% and on the top close to zero. The assumption of a Gaussian profile also allows us to calculate the rms-roughness value. The obtained tilt angles and surface roughnesses will be discussed in section 4.
(1)
where u ± denotes the effective reflection coefficients of the sample for right and left hand circularly polarized light. These can be written as u=
rAF + a 2 · rFS . 1 + a 2 · rAF · rFS
(2)
3. Theoretical methods
In the formula the Fresnel reflection coefficient r and the phase propagation term a are appearing. The indices A, F, and S stand for air, film and substrate. r=
n˜ 1 − n˜ 2 , n˜ 1 + n˜ 2
h ω i a = exp i n˜ d . c
3.1. Technical details: DFT calculations
In order to support the experimental results and to further investigate the electronic structure of the materials we performed all-electron DFT calculations of all individual free molecules and for the bulk structures of the MePcs. The calculations for the individual free molecules were carried out using the NRLMOL program package [28]. NRLMOL combines large Gaussian orbital basis sets, numerically precise variational integration and an analytic solution of Poisson’s equation in order to accurately determine the self-consistent potentials, secular matrix, total energies and Hellmann– Feynman–Pulay forces. To include exchange and correlation effects, the generalized gradient functional developed by Perdew, Burke, and Ernzerhof (PBE) was applied [29]. First we relaxed the structures of the individual molecules by performing a full geometry optimization. The symmetries of the initial and the final state are of decisive character for the calculation of the possible optical transitions. The corresponding dipole matrix element is obtained for any possible transition and the intensity of every transition is weighted with the value of the dipole matrix element. This offers a direct mapping of the spectral signals to the electronic structure of the molecule. In order to reach qualitative understanding of our experimental data we added a Gaussian broadening of about 0.15 eV to the theoretical spectra. For the bulk structure calculations we used the ELK program which is an implementation of the all-electron full potential linearized augmented plane-wave (FP-LAPW) method [30]. The starting structures correspond to the α-phase of MePc and were obtained from the Cambridge Structural Database. The calculations were performed using a basis set with 440 valence states and an additional 562 local orbitals together with the same PBE functional as for the NRLMOL calculations. After geometry relaxation of the structures (Fmax < 0.05 eV Å−1 ) the full dielectric tensor was calculated according to [31]. The Voigt constant can be retrieved directly from the elements of the dielectric tensor. The effective k-point mesh size used for Brillouin-zone integration in the case of calculation of optical properties was 400. The effect of spin–orbit coupling and a magnetic field normal to the molecular plane were included in the calculations.
(3)
In equation (3) n˜ is the complex refraction index n˜ = n + ik, ω is the angular frequency of the light, c the vacuum light velocity, and d the thickness of the film. For Voigt constants Q = −iε y /εx much smaller than 1 the modification of the refractive indices for the circular light components can be written as n˜ ± = n(1 ˜ ∓ Q/2).
(4)
Thus, with the knowledge of Q, of the film thickness d, and of the ellipsometry result n˜ the complex Kerr angle can be calculated. To go the opposite way one has to invert the function 2K = f (Q) numerically. For proper modeling of the ellipsometry spectra of the investigated porphyrinoids, uniaxial anisotropy as well as surface roughness has to be taken into account. The main axis of anisotropy is the direction perpendicular to the substrate plane and linear light polarization in that direction experiences a different dielectric function (or optical constants) compared with light with a linear polarization parallel to the sample plane. The origin of the anisotropy stems from a preferential alignment of the molecules on the substrate [10, 26]. For estimating the average tilt angle α of the molecular plane with respect to the substrate plane we assume that all molecules adopt the same orientation and that the transition dipole moments of the electronic transitions in the Q-band (see later discussion) are degenerated and both parallel to the molecular plane. The molecular film is thus considered to consist of perfectly aligned disks. Under these assumptions we can employ the following formula [10]: s 2Ain − Aout α = arccos . (5) 2Ain + Aout Ain and Aout are the integrals over the area of the Q-band in the spectra of the in-plane and out-of-plane components of the extinction coefficient k, respectively. The surface roughness was modeled by introducing several (typically 11) slices of effective media on top of the Pc film in the model. Bruggeman mixing of the dielectric functions of the Pc and void was
3.2. Perimeter model
The basic assumptions within the perimeter model (PM) are as follows. 3
J. Phys.: Condens. Matter 26 (2014) 104201
T Birnbaum et al
(i) The π -system under investigation can be treated independently of the remaining electrons of the molecule. (ii) Spin–orbit coupling is negligible small. (iii) Full aromaticity of the investigated π -system (i.e. containing (4N + 2) electrons, with N ∈ N, with N being a natural number) is assumed, describing a closed path lying approximately in a plane. (iv) σ π ∗ and nπ ∗ state-mixing into π → π ∗ transitions will be ignored.
and final WFs and knowing how OARNs relate to the OANs, we are able to characterize transitions in optical absorption and MOKE spectra. The OARN becomes a measure of the OAN by defining the modulus of the OARN as half the number of nodes with sign change of the WF 9k (φ), along the outermost possible path of the investigated π -system. The sign of the OARN can be defined in two ways. The first possibility would be to identify the sign with the sign of the following equation: Z 2π 1 ˆ 9k (φ) dφ 9k∗ (φ) 4 2π 0 Z 2π h¯ ∂ 1 h¯ k 9k∗ (φ) = 9k (φ) dφ = . (6) 2π 0 i ∂φ 2π
Assumptions (i) and (ii) assure the separability of the molecular wavefunctions (WFs) into three components, one perpendicular to the plane of the molecule z, one polar angle φ in the molecular plane and an in-plane radius r . Assumption (iii) validates that outer shell π → π ∗ transitions are sufficient for the main part of the optical spectra. Note that the model is no longer valid if the number of electrons in the investigated π -system deviates from the number claimed above. The discussion may then be carried out for a stable aromatic anion or cation instead. Now that we know about the limitations of the PM and can ensure its validity, we will focus on the definition of the orbital angular ring quantum numbers (OARNs). The wavefunctions predicted by the PM are complex eikφ with the imaginary unit i, the angular variable φ and the OARN k. Commonly the PM is combined with classic molecular orbital theory, which the values of k to restricts k ∈ 0, ±1, ±2, . . . , ± n2 − 1 , n2 , where n is the number of electrons in the considered π -system. However, one has to note that the selection rules are defined with respect to orbital angular quantum numbers (OANs). If spin–orbit coupling is negligible, the selection rules split up in statements for spin s and angular momentum l resulting in the well known dipole selection rules 1l = ±1, if at the same time spin flips are not allowed. But why is it not possible to state that the OARN is equal to the OAN? Since an arbitrary closed path along a π -system never possesses a C∞ -symmetry, Lˆ z is not a constant of motion. In other words if there is no potential with circular symmetry, the OARN is not equal to the OAN. However, identifying the OARN as the OAN of Lˆ z is often misleadingly done in literature. The interpretation of the OARN as an eigenvalue of the linear momentum of the 1D problem along the circle is invalid, due to the periodic potential resulting from the atoms, along the polar coordinate φ. Hence the linear momentum is not a constant of motion in the 1D case. The molecular WFs are either linear combinations of eigenstates or not eigenstates at all of the angular momentum Eˆ That leaves basically three options: (1) direct comoperator L. putation of LEˆ applied on the molecular WF at distinct points,
ˆ := This gives the mean expectation value of the operator 4 h¯ ∂ ˆ . 4 can be interpreted either as linear momentum operator i ∂φ of the free electron model, i.e. along the circle with sufficient boundary conditions and the variable φ, or as Lˆ z of the restrained 3D problem. Note that the 3D problem can be substituted by a 1D problem with coinciding z-axes. Since the radius is fixed, the molecule is approximately planar and the cylinder coordinates are separable. The second way of determining the sign of the OARN is by using classic electrodynamics and Lorentz law. It follows that k < 0 if the magnetic moment, induced by the moving electrons, and the z-axis, are anti-parallel, and k > 0 otherwise. This suggests the illustration of the sign as the circulating sense of the electrons. Thereby the case of maximal k is implicitly defined as positive. Note that the OARNs k are adding up like scalars to a total ring quantum number K , which follows from the interpretation ˆ as a linear momentum operator in 1D or from power of 4 laws and the form of the molecular WF (a simple product of exponential functions) of n electrons. Therefore it is possible to apply the selection rules on k instead of l, corresponding to a replacement of LEˆ by Lˆ z , because Lˆ 2x + Lˆ 2y = const on the circle of the perimeter model. The change of the OARN 1k, resulting from a transition, can be recognized as a measure of the circular charge distribution. For example a greater OARN of the excited state can be interpreted as formation of a negatively charged particle. It is now clear that magnetic moments, induced by the circular currents, are proportional as well to 1k. In order to assign OARN one can start from the geometry of the molecule with the corresponding real-valued representations of the WF of interest and condense it using the following three steps. (i) Determine whether the molecule in question is aromatic or not. If it is not, use any stable aromatic anion or cation derivable from the molecule. (ii) Determine the number of electrons in the π -system under investigation. (iii) Plot the real-valued WFs and count the number of nodes with sign change along the path of the π-system of interest, this would equal figure 1. Now half the number of counted nodes equals the number of nodal planes, i.e. the absolute value of the OARN k.
(2) using linear combinations of atomic orbitals (LCAOs) to model the molecular WF at distinct points and obtain the linear combinations of the OAN or (3) using the perimeter model, to gain OARNs k, see [32]. In contrast to the first two, the third option is unique for a distinct WF, even if the WF is not Eˆ The an eigenstate or linear combination of eigenstates of L. OARN can be used instead of the OAN, since a one-to-one correlation exists. Thus knowing the OARNs for the initial 4
J. Phys.: Condens. Matter 26 (2014) 104201
T Birnbaum et al
Figure 1. For a (14)-annulene (phenanthrene; left), the ‘unfolded’ molecule (middle) and model perimeter (right) with atoms and nodal planes highlighted are shown. The two degenerate sets of nodal planes of every plot are shown for k = 2. (Analogous to [14].)
Figure 2. Measured extinction coefficients k of the Q-band. (a) Typical lineshapes for MeTMPP for Cu (S = 21 ) and Ni (S = 0). (b) Effect of introducing methoxy sidegroups into TPPs. The slight redshift of the H2 TMPP films may indicate a higher degree of crystallinity of H2 TMPP.
in agreement with theory, the B-band being related to π → π ∗ transitions of the aromatic system, nearly independent of the center atom(s) (see [33, 22]). Also the methoxy sidegroups do not influence the lineshape of the B-band significantly. The Q-band is lower in energy at ∼2.25 eV for TMPPs and based on an a2u → eg transition. It was also found that the Q-band is dependent on the central atom(s), since a WF of a2u symmetry has no nodal point at this location. Figures 2 and 5 show this dependence by comparing H2 - and the MeTMPPs. The former shows a four-fold splitting of the Q-band, since the total spin is 0 and the unoccupied states are approximately degenerated within 10 meV. This can be related to the C2 symmetry of the molecule. Please note that the definition of Q- and B-band by using the energy can be misleading, as in the case of Pcs the character of the two features exchanges with the a2u → eg transition occurring at higher energy in that case. The influence of the methoxy sidegroups on the shape of the Q-band is shown in figure 2(b). One can see a slight redshift of the functionalized molecule and a change in the ratio between in-plane and out-of-plane components of the extinction coefficient. The redshift of the H2 TMPP absorption is most probably an effect of stronger intermolecular interactions, an
Finally we are going to remark on possible influences of the center atoms, which will support our discussion and can be understood with the help of the WF symmetry. All metal atoms have lower electronegativities than hydrogen and therefore the binding σ -electrons will be shifted towards the ring. This will increase the electron densities on the nitrogen sites and increase the energies of states with electron density there by Coulomb interaction. This effect is known as the inductive effect. The next effect is known as the conjugative effect and influences primarily the π -system of the TMPPs. As the p orbitals, especially pz , of the d-block elements are empty, transition group elements increase the size of the π -system by conjugation. The energy of a WF with according symmetry, i.e. without nodal points on the center atom, is lowered. 4. Results and discussion 4.1. Optical properties: B- and Q-band
The B-band was defined as the energetically higher feature rising at ∼2.8 eV for TMPPs in the optical spectrum based on an a1u → eg transition. For porphyrins, experiments indicate, 5
J. Phys.: Condens. Matter 26 (2014) 104201
T Birnbaum et al
Figure 3. Molecular orbital scheme of selected orbitals of the ground state for CuPc, CuTMPP and as reference CuP with indicated Q- and B-band transitions.
Figure 4. Optical constants of the Pcs under investigation. (a) Real parts and (b) imaginary parts of the dielectric tensor. Solid lines are the in-plane and dotted lines are the out-of-plane components. (c) Comparison of the DFT calculated imaginary parts εx x (dash-dotted), ε yy (solid) and εzz (dashed) of the dielectric tensor compared with the measured out-of-plane component (dotted).
effect known as crystallochromy, which might be an indication of a better degree of crystallinity of these films. As can be seen from DFT calculations, each of the a1u → eg and a2u → eg transitions ends in the same final pair of states with eg symmetry. This is true for all investigated molecules, see figure 3. The reversal of Q- and B-band ordering between TMPP and Pc is related to a change in level ordering of the corresponding occupied states. Accordingly the a1u orbital is once above (TMPP) and once below (Pc) the a2u orbital, as was already observed in the case of manganese derivates [34]. These four states account for the Q- and B-bands of porphyrins [35] and the description is known as Gouterman’s four orbital model [36], which was used successfully for various porphyrinoids [19, 22, 33, 36–38].
In figure 4(b) it can be seen that the Q-band of all Pcs consists of at least two main features. H2 -, Co-, Ni-, Cu-, and ZnPc all show significant splitting of the Q-band into main features at ∼1.75 and ∼2.1 eV. The Q-bands of Mn- and FePc show an even more complex character and in contrast to the other Pcs significant absorption at low energies (
