Iodine insertion and dispersion of refractive index in organic single crystal semiconductor

Insertion of halogens such as bromine or iodine affects the electronic polarizability of ions and the local field inside the medium, and thus modifies the refractive index. Acquiring precise knowledge of the dispersion of refractive index and ultimately tailoring conventional semiconductors for wide-range refractive index control have been a vital issue to resolve before realizing advanced organic optoelectronic devices. In this report, dispersions of the refractive index of a single crystal tetramethyltetraselenafulvalene [C10H12Se4] (TMTSF) are thoroughly studied from broadband interference modulations of photoluminescence (PL) spectra at various temperatures and doping levels. A large enhancement of the refractive index, more than 20% of the intrinsic value, is achieved with inclusion of a small composition of iodide ions, while the structural and optical properties remain mostly intact. Nearly temperature independent dispersion of the refractive index suggests that, unlike most polymers in which the thermal expansion coefficient dominates over the change of polarizability with temperature, the latter enhances significantly and may become more or less comparable to the thermal expansion coefficient given by 1.71 × 10−4/K, when single crystal TMTSF is doped by iodine.

good optical qualities has been remained as a critical issue to resolve before realizing advanced organic optoelectronic devices. Unfortunately, however, the case study for small molecular organic semiconductors is currently very limited 13 . In this report, the dispersions of the refractive index of a small molecular semiconductor TMTSF [C 10 H 12 Se 4 ] and their temperature variations are thoroughly studied from the broadband interference modulation of PL spectra in which a pair of the parallel crystal facets takes a role as a cavity resonator of the Farby-Perot type. A large enhancement of the refractive index, more than 20% of the intrinsic value, is achieved with insertion of a small composition of iodide ions, while the structural and optical properties remain mostly intact. The refractive index, depending on its state of polarization and the direction of propagation, has been commonly measured with various techniques such as ellipsometry, interferometry, and prism or grating coupling methods. Our study strongly suggests that analysis of the interference modulation of the PL spectra is a simple but powerful tool for monitoring the dispersions and their temperature dependence of organic single crystal semiconductors in which the applications of these common techniques are not always straightforward.

Data and Discussions
The experimental setup for PL measurement is shown in Fig. 1(a). The excitation light was aligned normal to the (001)-plane of the single crystal TMTSF and the emission spectra was detected along the same direction (c*-axis). Figure 1(b) constructed based on single crystal x-ray diffraction measurements displays that the crystal structure is a triclinic with space group P-1. Unlike most studied organic semiconductors such as pentacene and rubrene which exhibit a herringbone packing motif 1 , the planar TMTSF molecules forms a slipped face-to-face arrangement along the a-axis with a pitch angle of ~39° and packs in a brick-wall pattern within the (010) plane providing an efficient two-dimensional network of charge transport. A possible orientation of transition dipole moment (TDM) which likely coincides with the long molecular axes is indicated with an arrow. Representative PL spectra taken from samples of different thicknesses, d = 29.14 ± 0.94 μm and d = 6.82 ± 0.71 μm, are displayed in Fig. 2(a,b), respectively. The data plotted on the right axis display the second derivative of the traces obtained from adjacent average of the normalized raw data. A fair level of objectiveness in determining the modulation  peak positions is maintained by taking the dips of the second derivative. The frequency of the intensity modulations which overlay a monotonic emission spectrum for the broad range of wavelength is highly dependent on the sample thickness. Data also indicate that there exist considerable surface emissions in the TMTSF system, which is somewhat unusual considering the fact that the surface emissions were negligible in similar measurements on common organic single crystals such as rubrene and thiophene/phenylene co-oligomers 4,8,9 . The propagation of the molecular light emission is associated with the orientation of the molecular transition dipole moments (TDM) 14,15 . Contrary to the common organic single crystals exhibiting nearly upright configuration of the TDM to the layered ab-plane, the planar TMTSF molecules intersect the (001)-plane at ~39°. The intersecting angle seems sufficiently large enough to allow the majority of the molecular light emissions to leak out through the (001)-facets resulting in the surface emission as observed. Moreover, it is expected that the intersecting angle being close to the critical angle for the total internal reflection would make intensity of the surface emission extremely sensitive to the modification of refractive index. The wavelength spacing between adjacent modulation peaks (Δλ), the so-called free spectral range, is inversely proportional to the thickness of the single crystal or, more precisely, the separation between two end-facets along the detecting direction of the light emission. In fact, a pair of parallel facets functions as a Fabry-Perot type resonator within which multiple reflections generate interferences resulting in the intensity modulation 4,8,9,14 . Only standing waves at discrete wavelength can exist in the self-cavity resonator. The condition for the constructive interference for the self-cavity of length L, which is essentially the longitudinal cavity multimode confined as standing waves, is given by where ν (=1/λ) is the wavenumber in vacuum, n is the phase refractive index, and N is the longitudinal mode order (integer). Thus, the longitudinal mode spacing is obtained as  estimated based on our single crystal XRD data taken at 200 and 298 K. The interlayer spacing L(001) = V/(ab sin γ) is obtained as 7.256 and 7.238 Å at 298 and 200 K, respectively. Thus the LTEC per K (i.e., (1/L) dL/dT) is given as 2.537 × 10 −5 /K from which all the sample thickness above 80 K are estimated using the known thickness at 298 K. The volume expansion coefficient is determined as β = 1.706 × 10 −4 /K based on lattice parameters). The dispersions determined from the thin sample with slower intensity modulations are more scattered than the data obtained from the thick sample, which is because the uncertainty involved in the estimate of the indices is associated with the modulation-width or the quality factor of the cavity resonator (see Fig. 2). Nevertheless, we notice that the dispersions of refractive index are obtained consistently for both samples independent of the sample thickness, which justifies the data analysis. Data from the thick sample with a better resolution are displayed in the main panel in which an average uncertainty ±0.023 is given in the estimate of the refractive indices. It is not clear at the moment whether the dispersions of the refractive index shift downward with increasing temperature, as expected for most polymers. We will discuss this issue in more detail later. The dispersion of light in medium is empirically described by Sellmeier formula. The phase refractive index is often calculated utilizing the first order Sellmeier equation 16,17 given by 2 where the fitting parameter A and B are dimensionless and the parameter C has a length scale associated with resonant absorption wavelength. At long wavelengths far from the absorption peak, the phase refractive index is approximately given by With the substitution of the Sellmeier formula for the phase refractive index in Eq. (2), the dispersion of the group refractive index in a function of the three fitting parameters is obtained 8,9 . The thin lines through the data points shown in upper panel of Fig. 3 are the outcomes of the least square fitting of the corresponding set of data points. Finally, the dispersion of the phase refractive index is calculated with application of the three fitting parameters to the Sellmeier equation Eq. (3), which is displayed in lower panel of Fig. 3. The phase refractive index is given as a monotonically decreasing function between n = 1.70 and 1.68 in the wavelength range of 640-810 nm. The refractive index at the sodium D-line (589.3 nm) and at the long wavelength limit are estimated by n D = 1.73 ± 0.023 and n(λ→∞) = 1.66 ± 0.01 at 270 K, respectively. The resonant absorption wavelength or the parameter C, which is closely related to the energy band gap, was obtain as 537 ± 40, 526 ± 60, and 542 ± 44 nm at 270, 210, and 80 K, respectively. The nominal value of C ≈ 535 nm corresponding energy gap of an order of 2.3 eV is close to that of the single crystal rubrene 8 , one of the most intensively studied organic materials.
Panel (a) and (b) of Fig. 4 display the dispersions of group refractive index taken at various temperatures after the samples are exposed to iodine vapor for 1 hour (panel (a)) and for 3 hours (panel (b)). Data displayed in panel (a) show that all the temperature variations of the group refractive indices are well described by the dispersion of the 1 hour-exposed taken at 270 K within a range of error ±0.034 at most. The resonant absorption wavelength is determined as C = 540 ± 20 nm and the phase refractive indices obtained at the sodium D-line and at the long wavelength limit are n D = 2.13 ± 0.024 and n(λ→∞) = 2.06 ± 0.024, respectively. Interestingly, a quasi-periodic beating pattern is observed when the sample is exposed for 3 hours as shown in panel (c). Both the envelope (beating) and modulation wavenumber slightly decrease as the wavelength increase. The clear beating behavior which consistently appears at different temperatures seems to suggest that there exist two different sets of broadband interference modes with slightly different free spectral ranges. The modulation wavenumber is given by 1/ Δλ M = (ν 1 + ν 2 )/2 and the beating wavenumber is obtained as λ ν ν Δ = | − | 1/ B 1 2 , in which ν 1 and ν 2 are defined by inverse of the free spectral range for corresponding each resonator modes. Then, the values ν 1 and ν 2 are given by the combination of the modulation and beating wavenumbers, that is 1/Δλ M ± 1/(2Δλ B ) in which the (+) sign is designated to the resonator 1 and the (−) sign is assigned to the resonator 2, respectively. In terms of the free spectral range, the group refractive index in Eq. (2) can be re-expressed by (1 ) 2 0, where f 1 is the volume fraction of the resonator 1. As an example, we show in Fig. 4(d) that, with a proper setting of the volume fraction in the range between 0.46 and 0.59, the dispersion of the effective index becomes coincident with that of the 1-hour data. When sample is further exposed by iodine vapor for 10 hours, in comparison with the 1-hour data, the beating wavenumber is enhanced, suggesting larger shifts in the dispersions. Indeed, one resonator with a higher set of indices closely follows the trace of the 1-hour data (1 h) and the other intimately matches the trace of the intrinsic data (0 h). The effective refractive indices become reduced as the duration of doping is increased from 3 to 10 hours. In other words, the optimum doping occurs with inclusion of a small composition of iodide ions in the range of 0.007.
The optical excitation of an organic semiconductor leads to the formation of excitons i.e., the tightly bound molecular excited states residing between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) levels. Doping of iodine introduces impurities and disorders, and provides additional nonradiative decay channels to diffusing excitons. Indeed, inset of Fig. 5(a) exhibits that the PL intensity decreases sharply upon the introduction of iodine vapor to the TMTSF single crystal. With 3 hours exposure to iodine vapor which corresponds to a small composition of iodide ions in the range of ~0.007, the integrated PL intensity decreases abruptly to a saturation, near 30% of the initial value. However, contrary to the acute sensitivity of the PL intensity to the iodine exposure, the PL linewidth and its shape remain more or less the same even with 10 hours of doping which gives the iodine composition in the range of 0.043. The interference modulations fade away as the duration of the exposure extends more than 10 hours. Taking a closer look at the PL spectra below the 10-hour trace, we notice that the spectra shift to higher energy side by ~11 meV with the doping. The small blueshift of the spectra can be attributed to the reduction of exciton binding energy with the increase of carrier density. A similar case was found in a 2D transition-metal dichalcogenide semiconductor in which doping was controlled by gate voltage in a configuration of the field effect transistor 19 . Unlike the electrical doping by gate voltage, the chemical doping inevitably induces disorders and even causes structural damage when doped excessively. When iodine vapor is introduced to organic crystal, it is known that iodide ions − I 3 and − I 5 are formed as a result of interactions with host molecules 18,20,21 . The iodide ions diffuse into interstitial sites in-between and alongside the host molecules 20,21 . The panel (b) of Fig. 5 showing x-ray diffraction experiments indicates that there occurs no noticeable change in the crystal structure accompanied by the introduction of iodine vapor with up to 14 hours of exposure. Data suggest that the iodide ions likely sit in the interstitial sites between the face of TMTSF molecules in (010)-plane under strong interaction with the Se atoms. When the specimen is doped for 48 hours, the spectrum linewidth increases due to the enhanced vibronic progression (sideband) of the main 680 nm band, or due to relatively stronger suppression of the main band. The resulting decrease in the peak ratio, i.e. the main 680 nm band over the progression, is consistent with a strong reduction of the exciton coherence length by disorders including structural defects 22,23 . Alternatively, we note that a similar suppression of the peak ratio can be described by a J-type aggregate in which the intensity of the main band decreases markedly with increasing disorders 24 . In fact, the molecular packing in the form of a slipped face-to-face with pitch angles less than 54° is consistent with the J-aggregates. When the samples are exposed by iodine vapor for less than 10 hours, the amount of induced disorder is sufficiently low and not enough to modify the lineshapes of the PL spectra. The case should be comparable to the carrier doping by gate voltage 19 , in which the blueshift of exciton energy as well as the gradual decrease of PL intensity are attributed to the increasing carrier density. Thus, it is expected that the PL intensity gradually decreases with doping duration within the low doping regime below 10 hours. On the contrary, as displayed in inset of Fig. 5(a), an acute drop in the PL intensity even with a small inclusion of iodide ion is observed, which cannot be explained by the increased carrier density alone. It must be associated with the enhancement of the refractive index which would effectively prevent the emissions from leaking out through the surface due to smaller critical angle for the total internal reflection. The abrupt decrease in the PL intensity in the early doing regime is a manifestation of the efficient confinement of light through active control of the refractive index of medium.
The refractive index, in relation with the density and polarizability, is described by the Lorentz-Lorentz equation: in which N is Avogadro's number, ρ is density, α is polarizability, M is molecular weight, and ε 0 is free space permittivity. The refractive index can be effectively increased by introduction of substituents with high molar refraction R which is related to the polarizability α of the molecules constituting the medium by α ε = R N /3 0 . Halogen elements, such as iodine and bromine, were utilized for developing high refractive index polymers in 1992 11 . The temperature dependence of refractive index (dn/dT), so-called thermo-optic coefficient, is determined by the combined contributions from the polarizability and thermal expansion coefficient. By differentiating the Lorentz-Lorentz equation Eq. (6), one obtains the following equation 25 : The thermo-optic coefficient is positive when the change of polarizability with temperature (polarizability coefficient) is larger than that of the thermal expansion coefficient. For common polymers, the thermal expansion coefficient dominates over the polarizability coefficient and the latter can be neglected 26 , which leads to a negative refractive index change with increasing temperature. For the intrinsic sample with the phase refractive index at the D-line n D = 1.70 ± 0.023 at T = 210 K and the volume thermal expansion coefficient β = 1.71 × 10 −4 /K, thermo-optic coefficient is determined by −4.47 × 10 −4 /K which places the TMTSF system in the high-end category among common polymers. The expected change in the refractive index is determined by Δn = 0.058 when temperature decreases to T = 80 K. When temperature increases to T = 270 K, the change of the refractive index is obtained as Δn = −0.027. The expected changes in the refractive index with the temperature variations are either an opposite direction or falling a bit short of the experimental data displayed in lower panel of Fig. 3. Nevertheless, it is important to account that the expected changes are comparable, well within the range of experimental uncertainty ±0.023. For the intrinsic sample, the expected changes of the refractive index with the temperature variations may have been not large enough to be identified above the experimental uncertainty. For the 1hour-doped sample, if we take the usual assumption for polymers that the polarizability coefficient is negligible in comparison to the volume expansion, the thermo-optic coefficient drastically increases to −1.40 × 10 −3 /K. The corresponding changes in the refractive index increase by threefold in comparison with the intrinsic case, i.e. Δn = 0.174 (from 210 to 80 K) and Δn = −0.081 (from 210 to 270 K) which should be large enough to be recognized above the experimental uncertainty. However, as displayed in Fig. 4(a) the dispersions are given nearly temperature independent, which imply that contrary to the common assumption the polarizability coefficient is enhanced dramatically and may even become more or less comparable to the volume expansion coefficient 1.71 × 10 4 /K, when the single crystal TMTSF is doped by iodine for 1 hour.
So far there has been only a few studies on the TMTSF system, all of which focus on electrical transport [27][28][29] . The latest study suggests that the system has a good electrical mobility in the range of μ ~ 4 cm 2 /V at room temperatrue 29 . With the added means to tune and monitor the optical characteristics that we have shown, we expect that the TMTSF single crystal should serve as a new benchmark system succeeding pentacene and rubrene semiconductors, both of which have provided significant insights into the fundamental understanding of organic semiconductors.

Conclusions
The dispersion of the refractive index and its temperature dependences of organic single crystal tetramethyltetraselenafulvalene (TMTSF) are systematically studied from the broadband interference modulation of photoluminescence (PL) spectra, which is essentially the emission spectra coupled to the longitudinal cavity multimode formed naturally between a pair of the parallel crystal facets. The dispersions of refractive index monotonically decrease in wavelengths between 640-810 nm, which are well described by the first order Sellmeier dispersion formula. With an exposure of iodine vapor for 1 hour which gives fractional compositions much less than 0.007, the refractive index of the singel crystal TMTSF is largely enhanced more than 20%, while the crystal maintains its structural and optical integrity. Non-uniform distribution of the dopant is manifested by the beating patterns in the interference modulations of the emission spectra when the system is exposed for extended durations. The effective dispersion of refractive index is reduced as the composition of iodine increases to 0.043 ± 0.012 with 10 hours of the exposure. It is demonstrated that the analysis of the interference modulation of PL spectra is a simple but powerful tool for understanding the dispersion of refractive index of organic single crystals at various temperatures and doping levels. The precise knowledge on various optical characteristics would be a vital prerequisite for design and fabrication of advanced optoelectronic devices.

Methods
As purchased powder form of TMTSF (>97%, Sigma-Aldrich) was purified by multiple sublimation and solidification under high vacuum. The purified powder was sublimated at 160 °C and carried by a continuous flow of Argon gas (ultrahigh purity Ar gas at a flow rate 80 cc/min) in quartz tube at ambient pressure. Single crystal TMTSFs were grown downstream in the gas flow at the range of temperature between 140 and 130 °C. The crystal structure was analyzed based on data taken at two temperatures of 298 and 200 K. Bruker SMART APEX CCD diffractometer was equipped with a graphite monochromator, which provided Mo K α line of λ = 0.7107 Å. Doping of TMTSF was performed in a upside-down U-shaped glass chamber. One end of the glass chamber containing iodine source (≥99.99%, Sigma-Aldrich) was cooled to 241 K, which essentially determined the iodine vapor pressure of ~1 mTorr that would be exposed to single crystal TMTSF. The other side of the diffusion chamber consisting of several doping cells was pumped below 1 mTorr before the iodine vapor was introduced to diffuse through the samples residing in each cell at room temperature. Each doping cell equipped with an independent valve allows us to stop the doping process on a specific cell, while we continue doping on other cells. All samples were pre-cleaned with isopropyl alcohol of HPLC grade and annealed at 60 °C for 2 hours before they were loaded to each cell. A single crystal of a uniform thickness was cleaved to several pieces of submillimeter-square in sizes and each piece was treated with different doping conditions, which essentially allowed us to isolate the doping effect from the data taken under various experimental conditions. The chemical compositions of iodine for given various durations of the exposure were determined by an electron probe micro-analyzer (EPMA-1600). With 5 and 10 hours of doping, the compositions of iodine were measured as 0.018 ± 0.006 and 0.043 ± 0.012, respectively. Measurements taken on 4 samples between 5 to 13 hours of exposure indicate that the composition of iodine depends linearly on the doping duration followed by ~90 minutes of lead time between openings of the doping cell and starting of the effective doping. Based on the doping pattern with the exposure time, a composition of ~0.007 is expected when the sample is exposed for 3 hours. The iodine composition was under the detection limit when sample was doped for 1 hour. We note from the measurements that the weakly bonded nature of the organic molecular single crystal inherently limits the detection of EPMA in the range of ~0.01. A micro PL/Raman measurement system, LabRAM HR UV/Vis/NIR spectrometer (by HORIBA Jobin Yvon) with a continuous 514 nm (2.41 eV) excitation line, was used for the PL measurements. The size of laser spot, approximately diameter of 1 μm, was aligned to one of samples mounted on a cold-stage which was capable of controlling a stable temperature between 10 and 298 K. The power of the laser excitation was varied from 0.05 to 2.5 mW at 14 K and no noticeable change was found in the PL lineshape. A typical power level of 1.5 mW was maintained throughout the PL measurements as long as it warranted a reasonable signal to noise ratio. In each measurement spot, multiple traces were obtained and carefully examined for possible degradation and/or spontaneous heating effect by the focused laser beam. Data availability. The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.