EPD has become the most widely used paper-like display due to its good market potential. As a reflective display technology, the light reflection characteristic provides it with a paper-like comfortable reading experience [1–4]. In addition, EPDs also have the advantages of ultra-low power consumption and a good bistable characteristic [5, 6]. Therefore, EPDs have been widely used in electronic labels, e-books, etc. But video playback cannot be achieved due to the long response time of EPDs [7]. Particles in microcapsules of EPDs are driven by voltages, and pixels can display different gray scales by adjusting the position of particles [7–10]. The voltage sequence which can drive particles to display gray scales is called the driving waveform. Hence, it is of great significance to reduce the response time and improve the display effect by optimizing the driving waveform design [11, 12].

A traditional driving waveform can be divided into four stages: erasing the original image, resetting to the black state, clearing to the white state, and writing a new image [13–15]. When a particle is in a same position for a long time, its mobility is much lower than that of other particles. The particle activity can be improved by resetting to the black state and clearing to the white state [16–18]. This driving process may be continued from hundreds of milliseconds to 1 s [19, 20]. Therefore, there are some scholars who have conducted a series of research on the driving waveform, and some principles and methods of driving waveform editor are put forward to shorten the driving time or reduce flickers. Kao et al. [21] studied the property of the suspension viscosity, characterized the response latency of the EPD, and put forward a new driving waveform, which set the white gray scale as a reference gray scale, to shorten the driving time and reduce the number of flickers. However, the proposed driving method did not take into account an important factor-DC balance. Moreover, the reference gray scale is unstable. Wang et al. [22] used four kinds of screen update modes to update the EPD according to different images, and it could improve the update speed. However, the form of driving waveforms in four modes was not changed, and it could not improve the refresh speed fundamentally. In a traditional driving waveform, stages of resetting to the black state and clearing to the white state are longer than the other two stages [23, 24], so some scholars have studied new driving schemes to reduce the driving time of these two stages. Yi et al. [25] found that high-frequency voltage can be used to activate particles, and the new driving waveform could effectively reduce the ghost image and flicker. But it is difficult to get a stable gray scale display. He et al. [26] proposed a driving waveform based on the optimization of particle activation by analyzing the electrophoresis performance of particles. It can effectively reduce the driving time. However, the DC balance is not considered in the design of the driving waveform, which may cause damage to the EPD [27].

In this article, a new driving waveform, which is based on the black reference gray, is proposed to reduce the driving time. The new driving waveform obeys the rule of DC balance and is divided into two stages: reset to black state and write the new image. The first stage is used to get an accurate reference gray, and some principles are proposed to get a uniform reflectance value for black state at the same time. The second stage is used to write a new gray value by comparing it with the black reference gray.

The introduction of microcapsule technology is an important breakthrough in EPD technology. There are two kinds of particles in a microcapsule [28]. Here, the microcapsule is a pixel in EPD. It solves the long-term display instability problem in EPD. The movement and aggregation of particles are limited in microcapsules, and the different gray scales could be realized by controlling the voltage which is applied on electrodes. In the display process, the white SiO₂ particles of the EPD are charged with a negative charge and black carbon particles are charged with a positive charge. The structure of an EPD is shown in Figure 1. In Figure 1A, the electrode of a pixel in the upper left part is provided with a negative voltage and the positively charged white particles move upward, the EPD shows white, the lower right part is provided with a positive voltage and the negatively charged black particles move upward, and the EPD shows black.

In the interior of a microcapsule, as is shown in Figure 1B, in order to ensure the good electrophoretic performance of electrophoretic particles, a charged control agent is injected into the display capsule, which can effectively prevent the accumulation of charged particles and deposit on the capsule wall. The display particles in the capsule are mainly affected by gravity, buoyancy, electric power, and the viscosity of nonpolar solvent. In order to avoid the settlement of display particles, gravity is equal to buoyancy, as shown in Eq. 1. [ ( 3 m − 4 π R 3 ρ ) g 3 ] = 0 . (1) Here, m is the mass of a particle, R is the radius of a particle, ρ is the density of nonpolar solvents, and g is the gravity constant. The electric force can be expressed by Eq. 2. F E → = q E → + m → ∇ E → + 1 6 ∇ ( Q → : ∇ E → ) + O ( ∇ 3 E ) . (2) Here, F E → is the electric force, q is the charge of the particle, E → is electric field, and Q → is the total charge of particles. The first term of Eq. 2 is the Coulomb interaction between particles and electric field, and the other term is the interaction of dielectric polarization components induced by particles. The viscosity can be expressed by Eq. 3 [29, 30]. F S → = 6 π η R v → . (3) Here, F S → is the viscosity, η is the viscosity coefficient of the nonpolar solvent, and v → is the velocity of the particle. v → can be obtained by solving Eq. 3, and it is shown in Eq. 4 [31]. v → = q F E → 6 π η R ( 1 ± e − 6 π η R t m )   . (4) In general, the charged particle zeta potential could reach a level which could make a particle whose radius is 1 μm with 50–100 charges by using the charge control agent, at the same time, the electrophoretic mobility reaches 10 − 4 − 10 − 5   c m 2 / V s . The expression of response time is shown as Eq. 5. T = 6 π d 2 η V ξ ε , (5) where T is the response time, d is the distance between the common electrode and the pixel electrode, V is the voltage applied between two kinds of electrodes, ξ is the particle zeta potential, and ε is the dielectric constant of suspension liquid. Generally speaking, the voltage of the driving waveform could be set as 15, 0, or −15 V, and the EPD may spend 1 s or so on updating the image.

In this article, a new driving waveform based on two stages is proposed, and the driving process of gray scales is effectively fused. The first stage of the driving waveform can erase the original image, and the second stage is used to realize a multilevel gray scales display. In addition, the black state is used as the reference gray scale according to the mechanical analysis of particles in microcapsules. The driving waveform proposed by us has the advantages of short driving time and less voltage conversion times. It can effectively reduce the flicker sense and improve the reading comfort while shortening the screen switching time. What is more, the DC balance rule is applied to the design, which can effectively prevent the display breakdown caused by charge trapping. So, the proposed driving waveform provides a reference for the continuous improvement of the EPD display quality.