本論文的主題是研究由不同烷基駢苯衍生物PTCDI-CnH2n+1(n = 7, 13)與併五苯(Pentacene)所構成的異質接面，使用電場調制光譜及低掠角X光散射儀分析內建電場與結構。
本實驗分為兩部分，第一部分我們將PTCDI-CnH2n+1(n = 7, 13)作為n-type有機半導體材料與p-type有機半導體材料Pentacene製作成異質接面(hetero-junction)，元件結構類似於平行板，如此可以形成均勻的內建電場。利用電場調制光譜分析PTCDI-CnH2n+1(n = 7, 13)/Pentacene異質結構，可以觀察到其內建電場的差異，由於內建電場對激子的分離具有顯著的影響，我們將實驗結果與文獻相互考證，探討將PTCDI-CnH2n+1(n = 7, 13) /Pentacene結構作為太陽能元件主動層其效率之差異，發現內建電場與元件短路電流具有高度的相關性，內建電場的提升，可以有效分離電子-電洞對，進而大幅度提高短路電流，也造成元件效率的提高。
第二部分為利用低掠角X光散射儀分析PTCDI-CnH2n+1(n = 7, 13)成長於Pentacene薄膜上其結構的差異，光源採用同步輻射中心的X光束，同步輻射光源具有高強度及較小的光束截面積，可以得到清晰的散射圖形。我們發現不同烷基的PTCDI在Pentacene上成膜，結構的有序性及晶格的匹配程度皆有顯著不同，分析結構特性並與第一部分結果相互對照，可以發現薄膜結晶程度及缺陷的多寡，對於形成均勻的內建電場具有極大影響。

PTCDI-CnH2n+1/pentacene interfaces studied by electro-reflectance spectroscopy and grazing angle X-Ray diffraction
Chong-Rong Wu
Wei-Yang Chou
Department of Photonics, College of Science, National Cheng Kung University
SUMMARY
This study investigated the built-in electric field and crystal structures of organic hetero-junction. Bilayer organic films were constructed using PTCDI–CnH2n+1(n = 7, 13) and pentacene.
Electro-reflectance (ER) spectroscopy was employed to analyze the built-in electric field existing in the organic hetero-junction. According to Franz–Keldysh oscillation period theorem and based on the ER spectroscopy results, the organic built-in electric field was calculated as 1.314 MV/cm for PTCDI–C7/Pentacene and 1.077 MV/cm for PTCDI–C13/Pentacene.
Grazing incidence X-ray diffraction (GIXD) was utilized to supplement the experimental results of the ER spectroscopy analysis. Given the differences in their lattice constant, PTCDI–C7 and PTCDI–C13 grown on top of pentacene exhibited different structural features. The results suggested that crystal structures could affect the intensity of the built-in electric field. The diffraction point from GIXD indicated that the structural feature of PTCDI–C7/pentacene was better than that of PTCDI–C13/pentacene, which reasonably explains the differences in the built-in electric field between the two structures.

Keywords: electro-reflectance spectroscopy, grazing angle X-ray diffraction, exciton, built-in electric field

INTRODUCTION
Electro-reflectance (ER) spectroscopy has been distinguished as a nondestructive and powerful technique for the characterization of semiconductors and their microstructure properties. In 1964, B. O. Seraphin pioneered the application of electro-reflectance technique in the investigation of germanium (Ge) inorganic materials and obtained spectral lines of differential form. Since then, related theorems and technologies have been widely developed. Modulation spectroscopy has become one of the most important measurement techniques for examining semiconductor characteristics. Electro-modulation spectrum could effectively suppress background signals and noise by showing in differential form. Therefore, it could provide considerable amount of information, such as semiconductor surface/interface field, energy band transition, exciton effect, and Fermi level, among others.
Interfacial electric field in hetero-structure, in particular, has become the mainstream that received much research attention. The measurement of the built-in field of organic materials was relatively insufficient compared with that of inorganic materials. Electro-modulation spectroscopy is an excellent approach in investigating the built-in electric field of semiconductors. A homogenous electric field is created at the PTCDI/pentacene interface. Therefore, the built-in electric field of a hetero-junction interface could be measured via ER spectroscopy, that is, Franz–Keldysh oscillations (FKO) for bulk-like transitions in layers. The electro-optic energy, which corresponds to the period of FKOs, is governed by the amplitude of the built-in electric field.
X-ray diffraction has been a well-established technique in the field of structural investigations. It is a powerful instrument used to analyze the crystal characterization of thin films. The properties of electronic devices are significantly determined by the crystal structure of a semiconductor layer. The degree of crystallinity is a key factor that defines important properties of a device, including photoelectric conversion efficiency, transport of carrier, energy band structure, and others.
This study proposed the use of ER spectroscopy to measure the built-in electric field at the hetero-junction interface of organic molecules and the use of the X-ray method on the degree of crystallinity to determine the difference in the built-in electric field between two structures.

MATERIALS AND METHODS
Hetero-junction structures of organic materials PTCDI–C7H15 (45 nm)/pentacence (45 nm) were grown on ITO substrate with 60 nm polyimide (PI) dielectric medium. PI has already been researched for application as a dielectric layer. Its remarkable insulation capability could effectively resist leakage current. The insulation layer was spun at 500 rpm for 10 s and then at 3000 rpm for 30 s to form a uniform coating. Afterwards, to evaporate the solvent, the PI layer was soft-baked at 90 ºC for 10 min and hard-baked at 220 ºC for 2 h.
Pentacene, a polycyclic aromatic hydrocarbon consisting of five linearly fused benzene rings, is an excellent p-type organic semiconductor. Pentacene (99.9 %, Aldrich Chemical Company), without further purification, was deposited on top of the PI layer at room temperature by thermal evaporation under 1×10−6 torr pressure.
PTCDI (N, N′-Dioctyl-3,4,9,10-perylene tetracarboxylic diimide) has been used extensively as an industrial pigment because of its brilliant color, strong absorption and fluorescence, and good thermal, chemical, and photochemical stability. PTCDI and its derivatives have been proven to be effective n-type organic semiconductors with various applications. Derivatives of perylene tetracarboxylic acid favor charge transfer because of large intermolecular coupling, which leads to the formation of charge-transfer excitons. PTCDI was deposited on top of pentacene and grown via the same method as that used for pentacene, with minor parameter modifications.
RESULTS AND DISCUSSION
ER is also known as differential reflectance spectroscopy (DRS), which arises from common reflectivity measurements. It is simply defined as:
(1)
It utilizes the change in reflectance between a sample with (R (E, d), d = film thickness) and without (R (E, 0)) adsorbate and is normalized by R (E, 0).
By FKO period theorem, an ordinary method was derived to determine the built-in electric field for the electro-reflectance spectroscopy, that is:
∆R/R~1/(E^2 (E-E_g ) ) exp⁡[-(Γ√(E-E_g ))/〖ℏΩ〗^(3/2) ]×cos⁡〖[〖2/3((E-E_g)/ℏΩ)〗^(3/2)+χ]〗 (2)
ℏΩ=2^(-2/3) ℏθ=〖((e^2 ℏ^2 F^2)/8μ)〗^(1/3) (3)
where ℏΩ is the electro-optic energy, is the line width, χ is the phase angle, F is the electric field, and is the electron–hole reduced mass that is assumed to be 0.458 m0.
The extrema of the FKO is given by the mathematical form expressed as:
nπ=4/3 〖[(E_n-E_g)/ℏθ]〗^(3/2)+χ (4)
where n is the index of the nth critical point, Eg is the energy gap, and En is the corresponding energy. A plot of (En−Eg)3/2 versus n yields a straight line with a slope proportional to F.
According to FKO theorem, FKO phenomenon is observed when the photon energy is greater than the energy band. Figure 1 shows the experimental results of the hetero-junction with PTCDI–C7/pentacene and PTCDI–C13/pentacene structures from ER, which was used for modulation at 260 Hz frequency and 1 V AC applied voltage. The results of this study completely satisfied the theorem because an oscillating behavior clearly appeared at the back of the energy band of pentacene, which is approximately equal to 1.86 eV.
To receive an accurate built-in electric field, formula (4) was utilized, and the maximum energy point was used to obtain a sketch of (En−Eg)3/2 and n. Figure 2 presents the fitting results of periodic oscillation, which indicates that the built-in electric fields in the PTCDI–C7/pentacene and PTCDI–C13/pentacene interface were 1.314 and 1.077 MV/cm, respectively. These values were larger than the field that appeared on inorganic semiconductor. The results demonstrated that the strong electric field in the organic hetero-junction could effectively separate the exciton because the binding energy of organic materials is relatively larger than that of inorganic materials.
In addition, the built-in electric field of PTCDI–C7/pentacene structure was larger than that of PTCDI–C13/pentacene, which suggests that the difference in the built-in electric field of the two hetero-junctions may result from the variation in their lattice structures. Therefore, grazing angle X-ray diffractometer was employed to further examine the degree of crystallinity of PTCDI grown on top of pentacene.

Figure 1. Schematic presentation of electro-reflectance spectra at room temperature with the modulation at a frequency of 260 Hz and a AC applied voltage 1V at PTCDI–CnH2n+1(n = 7, 13)/pentacene hetero-junction.

Figure 2. The built-in field from PTCDI–CnH2n+1(n = 7, 13)/pentacene structure determined by fitting FKO curve .
X-ray crystallography was carried out at the National Synchrotron Radiation Research Center using a wavelength λ = 1.5461 Å at an incident angle close to the critical angle of the substrate ≈ 0.20°. When the grazing angle X-ray was incident to the films, the crystal surface of films should display a diffraction pattern on the screen. The experimental grazing incidence X-ray diffraction (GXID) pattern is shown in Figure 3. The scattering intensity recorded by a 2D detector was plotted as a function of the momentum transfer qxy, qz parallel and perpendicular to the surface.
Figure 3(a) shows the GXID pattern of pentacene grown on the ITO substrate with 45 nm thickness. Figures 3(b) and 3(c) indicate that diffraction spots of PTCDI–C7 appeared in only 10 nm thickness, which suggests that PTCDI–C7 had its own lattice direction on the pentacene film at just 10 nm thickness. Therefore, PTCDI–C7 was able to grow on pentacene better than PTCDI–C13. Based on this result, we speculated that PTCDI–C7 exhibited a high degree of matching with the lattice constant with pentacene.
Further evidence, which prove that PTCDI film kept on growing to 45 nm, are displayed in Figures 3(d) and 3(e). The PTCDI–C7 that grew on pentacene had obvious diffraction spots, whereas PTCDI–C13 was characterized by diffraction rings. These observations reveal that the huge difference between the lattice constants of PTCDI–C13 and pentacene led to numerous defects in the crystal structure. The poor degree of lattice matching caused the presence of diffraction rings.
The results obtained from the X-ray method proved that the degree of lattice matching between PTCDI–C7 and pentacene was significant. Therefore, the growth of film could be ordered without numerous defects at the interface, thereby resulting in high built-in electric field.

Figure 3. Reciprocal space map of the surface of hetero-junction of PTCDI–CnH2n+1(n = 7, 13)/Pentacene measured in grazing incidence geometry using a 2D detector
CONCLUSION
The results showed that ER spectroscopy technique could be successfully applied to analyze the built-in electric field at the hetero-junction of organic semiconductors. In general, measurements of built-in electric field from a hetero-junction interface are difficult to achieve. However, the built-in electric field can be directly probed by means of ER techniques. Therefore, deriving the operating mechanism of single-layer solar cell from ER results was indeed possible.
Furthermore, grazing angle X-ray diffractometer is an efficient instrument for detecting surface crystal structures. An X-ray method was employed to verify the results of the built-in electric field of organic hetero-junction, which, based on ER results, was caused by the difference in degree of lattice matching. Compared with PTCDI–C13, PTCDI–C7 matched with pentacene better with larger built-in electric field at the interface.

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