## 1 Introduction  
The all-solid-state lithium battery is receiving significant attention as a next-generation lithium secondary battery because all the constituent materials, including the electrolyte, are made of solids, and it is safer and has a higher energy density than a liquid-type organic electrolyte-based lithium-ion battery [1, 2, 3]. However, the limited ductility of a solid electrolyte makes it difficult to cover the rough surface of the active material and penetrate the micropores of the electrode. Thus, the contact characteristics between the active material and solid electrolyte and the filling rate of the electrolyte in the electrode are relatively low compared to those of liquid electrolyte-based lithium-ion batteries [4]. This situation causes two significant problems. The first is poor contact, which increases the interface resistance between the active material and electrolyte. This causes an increase in the overvoltage during battery operation, which adversely affects vital performance parameters such as the capacity, energy density, and rate capability. The poor contact problem is a critical issue in all-solid-state batteries and has generated interest among many researchers [5, 6, 7, 8]. The other problem is that the transport of ions in the electrode is greatly limited by the low filling factor, as well as the distribution and connectivity problems of the solid electrolyte [9, 10]. It has been reported that the ion transport resistance in the electrode is a significant factor in the high-rate charge/discharge of the battery [11, 12, 13]. In relation to the kinetics, facile ion transport within the electrode is essential to the performance of an all-solid-state battery. Tortuosity is considered one of the most important parameters of porous media and there has been much effort to characterize the microstructure and ion transport propertiesof electrode composites in batteries by using it [14; 15; 16; 17; 18; 19]. Because higher tortuosity indicates a more complicated transport path for the ions in the electrode, the tortuosity is directly related to the high-rate charge/discharge characteristics of the battery. Therefore, previous studies have used the tortuosity to predict the ease of ion transport in the electrode and the battery output characteristics in relation to the design factors of the electrode (e.g., the thickness, density, composition, size, and shape of active material particles). [PERSON] et al. used the Bruggeman relation to derive the tortuosity of the ion transport path in an electrode according to the shape of the active material in a liquid-type lithium-ion battery [20], and [PERSON] et al. mathematically analyzed the shape and size of the active material particles, along with the tortuosity of the ion transport path, due to the pores formed as a result in a liquid-type lithium-ion battery [21]. The reports related to electrodes for all-solid-state batteries primarily discuss the distribution of the electrolyte and pores inside the electrode. [PERSON] et al. derived porosity and tortuosity values by modeling the interface characteristics and structural changes of solid particles in relation to the pressure applied during electrode manufacturing [22]. Assuming that the pores inside an electrode were entirely filled with a solid electrolyte, [PERSON] et al. used calculated the tortuosity values to analyze the effect on the filling factor of the electrolyte in an all-solid-state electrode [23]. However, most studies on tortuosity changes in relation to the microstructures of electrodes are conducted using computational simulation [20; 21; 22; 23; 24; 25]. Although computational simulation is suitable for simplifying and realizing complex microstructures, there is a limit to perfectly simulating the microstructure of an actual electrode because it is difficult to implement the non-uniform distribution of particles or closed pores in a solid electrode.