# Molecular Controlling the Transport Properties for Benzothiadiazole-Based Hole Transport Materials
## 3 Results and Discussion
### Hole Mobility Rate and Hole Mobility of HTMs  
The hole mobility is one of the most crucial parameters for HTM. Incoherent hopping and coherent band mechanism are the two main types of charge transport for organic material [44]. At room temperature, the charge transport type is viewed as the incoherent hopping type, that is to say, the carriers jump from one molecule (where they localized) to adjacent molecule [40; 43; 44]. And the Marcus theory is widely employed to estimate the rate of hole mobility (\(k_{h}\)) at room temperature, which can be expressed as [27; 45]:  
\[k_{h}=\frac{V^{2}}{\hbar}\left(\frac{\pi}{\lambda_{h}k_{B}T}\right)^{\frac{1}{ 2}}\exp\left(\frac{-\lambda_{h}}{4k_{B}T}\right) \tag{3}\]  
where \(V\) is the charge transfer integral, and \(\lambda_{h}\) is hole reorganization energy of HTM molecule, and \(k_{B}\) is the Boltzmann constant, and \(T\) is the temperature (here we use the room temperature \(T=300\) K). The charge transfer rate mainly depends on the two key parameters: \(V\) and \(\lambda_{h}\). According to the Marcus-Hush two state model, the charge transfer integral \(V\) between adjacent molecules can be estimated by following formula [46]:  
\[V=\frac{E_{HOMO}-E_{HOMO-1}}{2} \tag{4}\]  
where the \(E_{HOMO}\) and \(E_{HOMO-1}\) are the HOMO and HOMO-1 of face-to-face model in the HTM dimer. In theory, the hole mobility is usually evaluated from the Einstein-Smoluchowski equation, which can be expressed as [47]:  
\[\mu=\frac{e}{k_{B}T}D \tag{5}\]  
Particularly, when considering just one adjacent molecule, the diffusion coefficient can be expressed as [48]:  
\[D=\frac{1}{2}k_{h}r^{2} \tag{6}\]  
where the \(k_{h}\) and \(r\) are the rate of hole mobility and the centroid distance between adjacent dimer molecules, respectively. At room temperature, the hole mobility can be estimated by [27; 49]:  
\[\mu=\frac{er^{2}}{2k_{B}T}k_{h} \tag{7}\]  
Figure 6: UV-Vis absorption spectra of six investigated molecules in solution. The crucial parameters related to hole mobility of three experimental molecules Jy5-Jy7 have been listed in Table 6. From Table 6, the charge transfer integral \(V\) are 0.00016 eV for Jy5, 0.00141 eV for Jy6 and 0.01001 eV for Jy7, respectively. The hole organization energies of three molecules are quite close. The hole mobility rate of them are 2.69 \(\times\) 10\({}^{8}\) s\({}^{-1}\) for Jy5, 2.01 \(\times\) 10\({}^{10}\) s\({}^{-1}\) for Jy6, 1.01 \(\times\) 10\({}^{12}\) for Jy7. And the hole mobility of them are 1.24 \(\times\) 10\({}^{-5}\) cm\({}^{2}\)/(V\(\cdot\)s) for Jy5, 2.45 \(\times\) 10\({}^{-3}\) cm\({}^{2}\)/(V\(\cdot\)s) for Jy6 and 1.010 \(\times\) 10\({}^{-1}\) cm\({}^{2}\)/(V\(\cdot\)s) for Jy7. Both the hole transport rate and hole mobility for Jy5-Jy7 are in the following sequence: Jy5 \(<\) Jy6 \(<\) Jy7. Jy6 configuration corresponding to the replacement of one hydrogen atom in the core structure by one fluorine atom, and Jy7 is replacing two hydrogen atoms in the core structure by two fluorine atoms. The sequence indicates that the number of fluorine atoms (which is introduced in the core structure) is related to the hole mobility rate and hole mobility. In theory, along with the introduction of the more fluorine atoms in core structure of HTM, the hole mobility rate should be faster, and hole mobility should be larger. Experimentally, the hole mobility is in the following order: Jy5 \(<\) Jy7 \(<\) Jy6. The hole mobility of Jy6 and Jy7 are larger than Jy5, which is related to the introduction of the fluorine atom in the core structure, and the reason is due to the poor film quality of Jy7 (the hole mobility of Jy7 is smaller than that of Jy6). Furthermore, see that the hole mobility rate and hole mobility are in order of Jy5 \(<\) Jy6 \(<\) Jy7 because the charge transfer integral \(V\) is in the same order. The introduction of the fluorine atoms in the core structure increases the charge transfer integral \(V\) in the molecular face-to-face dimer structures.