Review of Driving Waveform for Electrowetting Displays

Electrowetting display (EWD) is the most potential technology among new electronic paper technologies. It not only has the advantages of electrophoretic display (EPD) technology but also can realize color video playback. Therefore, this technology has been widely studied in recent years. Driving waveform is a voltage sequence which can drive pixels to display gray scales in EWDs. As one of the key technologies, it directly affects the display effect of pixels. In this paper, we give a review of the display principle of EWDs and the research status of driving waveforms. At the same time, the contact angle hysteresis, charge trapping, and oil splitting are also reviewed, which can provide a reference value for designing driving waveforms.


INTRODUCTION
Display is one of the most important modes of human-computer interactions, and display devices play a key role in daily life. Along with the rapid increase of network information, people expect better displays to meet various requirements. At present, the most common displays are liquid crystal displays (LCD) and light-emitting diode (LED) displays [1,2]. These self-luminous displays have the defect of high power consumption which can severely limit the using time of electronic products. Nevertheless, electronic paper displays, such as electrophoretic displays (EPDs) and electrowetting displays (EWDs), have the advantages of paper-like reading experience and low power consumption due to its reflective display. EPDs are the most widely used electronic paper. It has been widely used in e-books, e-labels, etc. However, it cannot achieve video playback and the luminance of color is not enough [3][4][5][6]. As a result, many scholars began to pay attention to EWDs for obtaining better paperlike display performance in recent years.
The principle of EWDs was first proposed by Beni in 1981 [7]. In 2003, Hayes and Feenstra have successfully demonstrated that the electrowetting technology can be used to form a basis of a new reflective display. Its display principle is to utilize the voltage-controlled movement of a colored oil [8]. As a new reflective electronic paper display, EWDs have excellent display characteristics, such as paper-like reading experience [9,10]; low power consumption [11,12]; color display [13][14][15][16]; fast response speed which can meet the requirements of video playback [17]; low manufacturing cost because part of the manufacturing process is the same as LCDs [18,19]. Hence, EWD technology becomes the most potential paper-like display technology. The voltage sequence which can control gray scales in EWDs is driving waveform [20][21][22][23]. The earliest driving waveform of EWDs is a pulse width modulated (PWM) square wave [24]. However, some defects are caused by this driving waveform, such as gray scale distortion which is caused by contact angle hysteresis [25][26][27][28]; maximum aperture ratio is reduced due to oil splitting [29][30][31]; oil backflow caused by charge trapping in the hydrophobic insulator [32][33][34][35][36]. The movement of oil is directly controlled by the driving waveform, the optimization of driving waveform can affect the display effect of EWDs. Hence, the equivalent circuit models, capacitor-voltage (C-V) characteristics and contact angle hysteresis characteristic of EWDs have been studied by scholars, and some new driving waveforms were proposed for better performance of EWDs.
In this paper, driving waveforms of EWDs are summarized, and classified with different categories according to functions. It includes optimizing contact angle hysteresis, reducing charge trapping and oil splitting. The display quality of EWDs was greatly improved by these driving waveforms. Furthermore, it provided an important reference for the further study of EWDs.

Principle of Electrowetting Displays
EWD is essentially an optical switch [37,38]. Its structure is shown in Figure 1A. Each pixel is composed of a hydrophobic insulating layer, colored oil, polar liquid, pixel walls, a electrode which is made by ITO (Indium tin oxide) glass, a substrate. The colored oil is controlled by driving voltage to turn pixels on or off. The state of oil shrinkage can be described by the contact angle. The Lippmann-Young equation is considered as the basic theory of electrowetting technology. As shown in Eq. 1 [39][40][41][42]. The relationship between the voltage and the contact angle can be described by this equation.
Where θ is the contact angle when the driving voltage is V. θ 0 is the contact angle when the driving voltage is 0 V ε 0 is a vacuum dielectric constant and ε r is a relative dielectric constant. d is the thickness of a hydrophobic insulation layer, c is interfacial tension between oil and electrolyte solution. V is the driving voltage. When the driving voltage is 0 V, the contact angle is approximately equal to zero due to Lippmann-Young equation. At this stage, because the oil is spread on the substrate, the pixel displays the color of colored oil, as shown in Figure 1A. With the increase of driving voltage, the electric field force is increased. Therefore, the oil original force balance is broken and oil begins to shrink to one corner of a pixel. The oil completely shrinks in one corner of the pixel when the voltage increases to V max . The aperture ratio cannot become bigger when the voltage is greater than V max [43]. The value of V max depends on the size of the pixel and the thickness of hydrophobic The blue curve is the aperture ratio when the driving voltage is increased from 0 to 30 V, and the red curve is the aperture ratio when the driving voltage is decreased from 30 to 0 V. (C) Phenomenon of charge trapping. When the oil shrinks to one corner of a pixel, the charge distribution in a pixel. Charge trapping would be caused when the interaction between ions and hydrophobic insulating layer is stronger than that between ions and conductive liquid. (D) Phenomenon of oil splitting. A is the colored oil which shrinks to one corner of a pixel. B and C are oil which is split into two parts.

Contact Angle Hysteresis
Ideally, in the process of driving voltage rise or fall, the aperture ratio of the same driving voltage value should be the same. But experimental result is completely inconsistent with the expectation. The relationship between aperture ratio and voltage when the driving voltage rises from 0 to 30 V and falls from 30 to 0 V can be tested, respectively. As shown in Figure 1B [48]. The blue curve represents the relationship between the aperture ratio and the voltage when the driving voltage is rising. The red curve represents the relationship between the aperture ratio and the voltage when the driving voltage is falling. When the driving voltage is close to 0 and 30 V, the aperture ratio of these two curves almost coincide. But the difference of the aperture ratio is big when the driving voltage is in the middle stage. When the aperture ratio increases as the voltage increases, the contact angle is called as advancing angle. On the contrary, when the aperture ratio decreases as the voltage decreases, the contact angle is called as receding angle. Therefore, this distortion is called contact angle hysteresis [48]. The accurate gray scale display cannot be achieved because of this phenomenon.

Charge Trapping
Theoretically, the aperture ratio of a pixel is related to the applied voltage due to Lippmann-Young equation. But the oil can backflow when the same voltage is applied continuously. Thus, the aperture ratio is reduced. It has been found that some charge is trapped in the hydrophobic insulator when driving voltage is applied to EWDs [49]. The charge distribution is shown in Figure 1C. A three-phase contact line is formed where the oil, water and hydrophobic insulator are in contact. Positive ions gather on the three-phase contact line, and then, the nearby electric field can be distorted. The backflow can be caused due to the imbalance between Laplace pressure and Maxwell pressure at the three-phase contact line [50]. It can also reduce the maximum aperture ratio of EWDs.

Oil Splitting
Ideally, the oil shrinks in one corner of a pixel when driving voltage is applied to EWD in the process of oil shrinkage. However, oil may be split to two or more parts. The reason is that the charges in the hydrophobic insulator can cause a sudden change in electric field. When the capacitance value of a pixel increases rapidly, it is likely to cause oil splitting [51]. As shown in Figure 1D, the oil is divided into B and C from A in a pixel. The areas covered by oil are S A , S B , S C . The sum of S B and S C is greater than S A . Therefore, the aperture ratio becomes smaller when the oil is divided into two parts. The more the oil is divided, the smaller the aperture ratio.

Driving Waveforms for Optimizing Contact Angle Hysteresis
The fundamental reason of contact angle hysteresis is the rough surface of hydrophobic insulation layer and the viscous resistance of two-phase liquid [52]. The precise gray scale cannot be displayed by EWDs because of contact angle hysteresis. The contact angle hysteresis can be reduced by optimizing driving waveforms. A multi-waveform adaptive driving scheme was proposed [53]. In this scheme, the contact angle hysteresis curves of EWDs driven by a square wave, a sine wave and a triangle wave were tested. Then, the optimal waveform of each stage could be selected by superimposing the three hysteresis curves, and an activation voltage sequence was added in front of the first stage. The maximum distortion caused by contact angle hysteresis could be effectively reduced by this driving scheme. Besides, the inhibitory effect of alternating current (AC) voltage on contact angle hysteresis was proved in another driving scheme [48].

Driving Waveforms for Reducing Charge Trapping and Oil Backflow
With an applied constant voltage, the shrinking oil cannot be maintained in a stable state because of charge trapping. This defect can also be solved by optimizing driving waveforms. A method showed that charge trapping can be reduced by a reverse electrode pulse voltage which takes a few milliseconds, and the proposed driving waveform is shown in Figure 2A [54]. Furthermore, the influence of oil backflow caused by charge trapping can also be reduced by the reset signal [55], as shown in Figure 2B. The proposed driving waveform was divided into a driving signal and a reset signal. The driving signal S 0 and S 3 were direct current (DC) signals. They were used to drive the pixel to a target gray scale, and the reset signal was used to release trapped charges. S 2 in the reset signal was a driving recovery phase. It was used to obtain a faster gray scale response speed. But it has been proved that the higher the brightness of the target gray scale, the more serious the charge trapping [56]. Therefore, the dwell time of the reset signal needed to be adjusted according to the gray scale. However, the additional power consumption of EWDs caused by charge trapping and oil backflow cannot be reduced by these methods. A driving waveform with a rising gradient and a sawtooth wave was proposed to reduce the power consumption by reducing charge trapping [57]. The power consumption of various waveforms was compared, and the driving waveform is shown in Figure 2C. It was proved that the sawtooth wave can prevent oil backflow caused by charge trapping, and lower power consumption can be obtained by sacrificing the maximum aperture ratio. Besides, charge trapping can slow down the turn-off time of EWDs, which makes it difficult to achieve high quality video playback. It is important to solve this problem when the driving waveform is designed for video playback. The earliest two methods for video playback were amplitude modulation and pulse width modulation. These methods can divide the driving waveform into a display phase and a reset phase. The Charge trapping can be reduced due to the reset phase. But a multi-gray scale video could not be obtained in previous studies [58]. An improved multi-gray scales dynamic symmetrical driving waveform was proposed [59]. In this method, the display stage was divided into two identical parts. The probability of applying a constant voltage for a long time can Frontiers in Physics | www.frontiersin.org July 2021 | Volume 9 | Article 728804 be greatly reduced. Thus, this method could achieve 16 gray scales and reduce oil splitting and charge trapping.

Driving Waveforms for Reducing Response Time
In order to obtain a higher frame rate video playback and a better display effect, it is necessary to shorten the response time of EWDs. There are several different methods to achieve this goal. First, although some defects are caused by contact angle hysteresis, the hysteresis curve can help to design new waveforms. An amplitude-frequency mixed modulation driving system was proposed according to the contact angle hysteresis, as shown in Figure 2D [60]. The driving voltage and driving time of each stage were determined by the hysteresis curve of a target gray scale. Next, a driving waveform based on an exponential function was proposed to reduce the response time [51]. The optimal time constant of the exponential function was designed by testing the influence of the time constant on the aperture ratio oscillation range. Then, it has been proved that excessive reverse voltage can cause a chemical reaction between water and ITO [50]. In order to solve this problem, a mixed DC and AC waveform was proposed, as shown in Figure 2E. The driving waveform was composed of two parts. The first part was a DC driving stage. It was used to drive pixels to reach target aperture ratios. The second part was an AC driving stage, and a reverse voltage was used to prevent oil backflow. This scheme could effectively reduce the response time. Lastly, due to the response speed of the oil was increased when the driving voltage was increased, the work showed that overdriving voltage can reduce the response time [61]. The influence of different overdriving voltages on response time was tested in this work.

Driving Waveforms for Reducing Oil Splitting
The reset frame is often used to solve the problem of charge trapping in EWDs. However, the reset frame could affect the instantaneous display state, such as flickers and the decrease of reflective luminance [57]. Therefore, a separated reset waveform was proposed to solve this problems [62]. The instantaneous reverse driving voltage can be achieved by adjusting the voltage of the common electrode. The charges can be released quickly with the overdriving voltage, and another lower instantaneous reverse driving can keep the oil active. In addition, DC balance is not complied in the improved multi-gray scales dynamic symmetrical driving scheme, which may cause polarization in EWDs. Therefore, a DC balanced driving waveform was proposed [63]. In this work, a long frame was divided into two short frames. In the two short frames, DC balance can be complied due to the reversal of polarity.
Generally, the oil splitting caused by the sudden change of electric field force could be prevented by a rising voltage. In a previous study, the sinusoidal waveform could reduce oil splitting effectively [64]. Therefore, a novel driving scheme was proposed to reduce oil splitting [65]. The driving voltage increased gradually from a value which was below the threshold voltage to a final voltage with a sinusoidal curve. It was proved that this driving waveform could reduce oil splitting and increase the aperture ratio of pixels.

CONCLUSION
The design of driving waveform plays a key role for improving the display quality of EWDs. In this paper, we reviewed new driving waveforms. At first, the shortcomings of EWDs were described, including contact angle hysteresis, charge trapping phenomenon and oil splitting. Then, driving waveforms for improving these shortcomings were classified. It provide a reference value for reducing response time, increasing aperture ratio and improving oil stability of EWDs. In the future, driving waveforms design would become an important part of driving system design with the development of EWDs, and an excellent driving waveform design is expected to achieve higher quality performance for EWDs.

AUTHOR CONTRIBUTIONS
ZY and HZ discussed and wrote the manuscript together. WZ, HF, ZL, LL, and YH discussed and corrected the manuscript. XZ and CZ also helped with drawing the figures. All authors have read and agreed to the published version of the manuscript.