Supporting Information

Transcription

1 Supporting Information Fluorination of Metal Phthalocyanines: Single-Crystal Growth, Efficient N-Channel Organic Field-Effect Transistors, and Structure- Property Relationships Hui Jiang 1*, Jun Ye 2, Peng Hu 1, Fengxia Wei 1, Kezhao Du 1, Ning Wang 1, Te Ba 2 Shuanglong Feng 1, and Christian Kloc 1* 1 School of Materials Science and Engineering, Nanyang Technological University, Singapore Jianghui@ntu.edu.sg; Ckloc@ntu.edu.sg 2 Institute of High Performance Computing, Agency for Science, Technology and Research, Singapore 1. Molecular packing of F 16 ZnPc 2. Molecular packing of F 16 CoPc. 3. Molecular packing of F 16 CuPc. 4. Field-effect transistor based on individual single crystal of F 16 CoPc. 5. Electron-phonon coupling calculations. 6. Population and molecular orbital analysis of F 16 MePcs and the role of superexchange mechanism in contributing to electron transfer integral. 7. Theoretical calculation of electron mobility 8. Reference 1

2 1. Molecular packing of F 16 ZnPc. Figure S1 Molecular packing of F 16 ZnPc from different view directions. 2

3 2. Molecular packing of F 16 CoPc. Figure S2 Molecular packing of F 16 CoPc from different view directions. 3

4 3. Molecular packing of F 16 CuPc. Figure S3 Molecular packing of F 16 CuPc from different view directions. 4

5 4. Field-effect transistor based on individual single crystal of F 16 CoPc. Figure S4 (a) Device structure and (b) typical transfer curve of field-effect transistor based on individual single crystal of F 16 CoPc. The inset of (b) is the optical image of the real device. 5

6 E pol (mev) g 2 5. Electron-phonon coupling calculations. (a) (b) F16ZnPC F16CuPC F16CoPC ~740cm -1 ~1240cm -1 ~1350cm -1 ~1520cm (cm -1 ) F16ZnPC 12 F16CuPC 10 F16CoPC (cm -1 ) Figure S5 (a) Electron-phonon coupling strength g 2 for different vibrational modes in F 16 MePcs. (b) Contributions of different vibrational modes to the polaron binding energies of F 16 MePcs. The electron-phonon coupling calculations adopted the method given [S1]. Both electron-phonon coupling strength and polaron binding energies of different vibrational modes were calculated. We are able to point out a few major modes with large values of polaron binding energies. All F 16 MePcs studied in this paper share similar features such that the normal modes around 740, 1240, 1350 and 1520 cm -1 are found to give largest contributions to the overall polaron binding energies. To gain further insights into the electron-phonon coupling in these molecules, detail atom vibrational patterns of these 4 major normal modes are given in Figure S5-S7 for F 16 ZnPc, F 16 CoPc and F 16 CuPc, respectively. All four major modes strongly coupled to electronic transition in F 16 MePcs correspond to in-plane stretching modes of C=C and C=N bonds. 6

7 Figure S6 (a)-(d) Important normal modes in the F 16 ZnPc molecule, where the vibrational frequencies of these modes are given in respective figures. All vectors in the figures are scaled by displacement of atoms. 7

8 Figure S7 (a)-(d) Important normal modes in the F 16 CoPc molecule, where the vibrational frequencies of these modes are given in respective figures. All vectors in the figures are scaled by displacement of atoms. 8

9 Figure S8 (a)-(d) Important normal modes in F 16 CuPc molecule, where the vibrational frequencies of these modes are given in respective figures. All vectors in the figures are scaled by displacement of atoms. 9

10 6. Population and molecular orbital analysis of F 16 MePcs and the role of superexchange mechanism in contributing to electron transfer integral. The spin population analysis results are given in Table S1. The Mülliken spin population of Co and Cu for F 16 CoPc and F 16 CuPc were calculated as 0.93 and 0.66, respectively. Mülliken reduced spin populations further suggest dz 2 orbital of Co contribute most to the spin population in F 16 CoPc, while dx 2 -y 2 orbital of Cu is a major source of the spin population in F 16 CuPc. Without singly d-orbital occupation, electron transfer integral of F 16 ZnPc alone [001] is clearly mainly contributed by overlap of -orbital of neighboring molecules. Higher electron transfer integral in F 16 CoPc may be only understood as a result of additional super-exchange mechanism [S2] due to singly occupied Co dz 2 orbital compared to that of F 16 ZnPc without singly d-orbital occupation. In addition, singly occupied Cu dx 2 -y 2 orbital in F 16 CuPc was previously found to contribute less to electron transfer integral due to lack of super-exchange mechanism [S3], which further support the possible role of dz 2 orbital in contributing to electron transfer integral in F 16 CoPc. Orbital Co-Spin Cu-Spin s pz px py dz dx-z dy-z dx 2 -y dx-y Table S1 Comparison of Mülliken reduced spin populations for major metallic ions in F 16 CoPc and F 16 CuPc. 10

11 7. Theoretical calculation of electron mobility The transport of electron is calculated based on a temperature dependent canonical transformation of Holstein Hamiltonian, specific formalism can be found [S4]. Charge carrier mobility is related to the diffusion coefficient through Einstein relationship as:, where e is the charge of the electron,. The diffusion coefficient can be obtained with: D a (R1) 2 2 k / kk kk where a is the nearest neighbor distance, k is the wave vector and is the polaron band velocity. The double bracket denotes the thermal average of the polaron states, where and are the scattering and hopping rates.: 1 kk N kk' W k, k; k ', k ' kk 2q Re 2Wk, k; k ' q, k ' q Wk, k q; k ', k ' q q0 W crucial to the calculation of diffusion coefficient are given by: where k, k q; k ', k ' q Wk, k q; k ', k ' q dt V 0 k ' q, k qvk, k '( t) exp i Ek ' q Ek q t Vk ' q, k q ( t) Vk, k ' exp i Ek Ek ' t The single bracket indicates the average of the residual interaction. Here the single angular bracket denotes the average of the residual interaction ( ) over phonon states. This residual interaction originates from the temperature dependent canonical transformation. Owing to limited space, interested readers are suggested to refer to the reference for more details [S4]. Here we wish to further demonstrate how physical parameters affect mobility critical quantities, i.e., the scattering and hopping rates. The overall effects of electron-phonon coupling and temperature for the parameters 11

12 used to perform our calculations on scattering and hopping rates can be found in the Figure S9 as follows. Figure S9 (a) reciprocal of scattering rates and (b) hopping rates for F 16 MePc calculated with parameters presented in the Table 1 of the main text. The band velocity for all three types of molecular crystals fall within the order of magnitude of 10-4, therefore it is clear that the first term of equation R1 contributes most to the final value of D. Although we can observe a much increased hopping rate for F 16 CoPc in Figure S9(b), a much decreased contribution from scattering term limits the overall value of D. Therefore, even we have a very promising electron transfer integral for F 16 CoPc, we are still not able to obtain highest mobility among all F 16 MePcs. Results here have suggested the importance of electron-phonon coupling in determining charge transport properties of organic crystals. The organic crystals are known to be very sensitive to electron-phonon coupling and temperature. Such interesting interplay between transport properties and specific physical parameters has finally resulted in the trend we have obtained for the three F 16 MePcs studied. 12

13 8. Reference [S1] Coropceanu V. et al. Charge Transport in Organic Semiconductors. Chem. Rev. 107, (2007). [S2] Anderson P. W. New Approach to the Theory of Superexchange Interactions. Phys. Rev. 115, 2-13 (1959). [S3] Wu, W. et al. Magnetic Properties of Copper Hexadecaphthalocyanine (F 16 CuPc) Thin Films. J. Appl. Phys. 113, (2013). [S4] Chen, D. et al. On the Munn-Silbey Approach to Polaron Transport with Off- Diagonal Coupling and Temperature-Dependent Canonical Transformations. J. Phys. Chem. B 115, (2011). 13