We report on observations of transient behavior of currents induced by the polarity reversal of a dc voltage applied across a nematic liquid-crystal cell. The curve of the time-evolved transient current reveals two peaks for the external voltage larger than a characteristic value. The temperature dependence of drift mobility of ion carriers implies that both the first and second peaks are caused by the director orientation in the bulk.
© 2004 Optical Society of America
Over the years, considerable attention has been directed toward the interpretation of various transient currents in nematic liquid crystals (NLCs). The transport behaviors of ions in NLC displays influence critically the device performance, causing flickering as well as image sticking and decreasing voltage holding ratio [1,2] and, in turn, degrade the image quality of the display. In order to explain the motion of charges in NLC cells, theoretical and experimental investigations on the transient current in differently prepared samples induced by various forms of applied voltages were reported [3–9]. A peak of transient current resulting from a step voltage in a cell without the alignment layers was observed and the origin of the peak has been discussed on the basis of the space-charge-limited current, which is caused by injection of charges into the NLC layer from the electrodes . However, the transient-current phenomenon of a NLC cell with alignment layers is explained more completely by the double-layer effect and asymmetry in the transient depletion-layer fields, which arise from a difference in mobility of the positive and negative charges . In a polarity-reversal field, transient currents originate from the spatial distribution of carrier mobility, which is dependent on the director orientation in NLCs [5,6] and on the electric double-layer thickness . A special transient behavior has been observed for the externally applied voltage below a characteristic value . The transient current is dominated by the time-evolved, applied electric field and by the internal electric field induced by the adsorbed charges on the substrates . The effect of the impurity ions is particularly manifested through the behavior of transient discharging current  and in the double-pulse experiment . All of these experimental and theoretical works together have provided a fundamental explanation for the nature of the transient current under various circumstances; however, some interesting details have yet to be studied for fully understanding of the transient phenomenon.
In this paper, we report on observations of transient currents characterized by two peaks under certain experimental conditions for a polarity-reversal field. We show the experimental results on temperature-dependent transient currents and discuss the transient behavior of current peaks in nematic cells, which is dependent strongly on the temporal length of the electric field prior to the polarity reversal; namely, prefield. Besides the peak reported previously [4–7, 9], a second peak is observed when the prefield applied is shorter than 10 s in general in cells of NLCs in mesophase. The longer the duration of the prefield, the shorter the time between the occurrences of the two peaks. This unusual behavior of the transient current, induced by the polarity-reversal field, can be explained by the uneven temporal and spatial distribution of the liquid-crystal molecular orientation along the field direction; such molecular orientation is related to the duration of the prefield. The prefield modifies the charge distribution, which, in turn, alters the liquid-crystal director orientation. Consequently, the time evolution of the transient current exhibits its unique shape due to the varied carriermobility distribution in the bulk. The onset of the observed peaks is generated by the molecular reorientation due to the polarity reversal.
Transient current in the polarity-reversal field can be described by carrier mobility distribution, which depends on the director orientation of NLC [5–7]. In the following theoretical approach, we shall assume that the z axis is taken as normal to the substrates and the director orientation is influenced by the electric field varying merely with z.
The charge-adsorbed layers are formed by the immobilized charges, which are introduced by impurities in NLC and by the electric decomposition of liquid-crystal molecules, with the same sign on each substrate. The charge-adsorbed layers produce an asymmetric internal electric field E a(z) in the liquid-crystal bulk. Consider that the substrates are located at z=+d/2 and z=-d/2. From the Poisson equation, the distribution of the internal electric field can be written as 
where σ - denotes the surface-charge density on the surface of substrates and LD(z) represents the thickness of the layer of diffused charges compensating the surface adsorbed charges . The time-evolved external electric field across the NLC cell is caused by the polarity reversal of the applied voltage V and is expressed as
where d is the cell gap and τ 0 is the RC time constant, which is equal to the multiplication of resistance and capacitance of the NLC.
When an electric field applied is larger than Fréedericksz threshold, liquid crystals with a positive dielectric anisotropy Δε will start to align themselves in the direction of the electric field. The director rotation, which can be obtained using the torque-balance equation with the known field, will then induce transient current in the cell. The behavior of the director rotation is primarily described by the one-dimensional torque-balance equation in the equal-elastic-constant approximation,
where θ(z, t) is the director tilt being measured from the z axis, K 11 is the first Oseen-Frank elastic constant, ε 0 is the permittivity of free space, E(z, t) is the sum of a time- and position-independent electric fields, defined as E(z, t)=E a(z, t)+E P(z, t), and γ 1 is the rotational viscosity. The transient current density is given by
where C(t)=∫d/2-d/2[1/ε 0 ε(z,t)]dz is the capacitance per unit area and ε is the z, z component of the dielectric tensor, which is expressed as ε=ε‖ sin2 θ(z, t)+ε ⊥cos2 θ(z, t) in our system. It is obvious that the behavior of the transient current is governed by the change in the effective dielectric constant, which is dominated by the temporal and spatial distribution of the director rotation. Likewise, the behavior of the transient current can also be interpreted by the dynamic change in the average mobility along the z axis, which, again, is determined by the director rotation.
The NLC used for this experiment was the commercial eutectic NLC mixture E7 (from Merck), whose Δε=213.1 at 1 kHz, bulk resistivity ρ=2.4×1011 Ω-cm, and clearing point is 58.5°C. Each empty cell was manufactured with two flat glass substrates coated with indium–tin oxide (ITO). The overlapped area of the electrodes was 1 cm2. Polyimide films were layered on the ITO glasses and rubbed in antiparallel to promote a planar alignment with a small pretilt angle (~2°). The 5.7-µm-thick cell was filled with E7 in the isotropic phase.
Transient currents of homogeneously aligned E7 were measured through a series resistor (1 MΩ) by means of a digital oscilloscope (Hitachi VC-5810, with the horizontal and vertical resolutions of 10 ns and 20 µV, respectively). The external voltage in the range from ±0.1 to ±10 V, resembling a signum function between -t 0 and +t 0, was applied to a cell along the cell normal by an arbitrary waveform function generator (Tektornix AFG310). The cell temperature was controlled by means of a thermoregulator. In order to check the phase of E7 at various temperatures, a crossed-polarizer configuration was employed, in conjunction with a light beam from a 650-nm diode laser as a probe. The phase of either isotropic or nematic could be identified from the characteristic curve of transmission.
4. Results and discussion
Figure 1 reveals the behavior of the transient current induced by the polarity-reversal field at various temperatures. At first, normal charging current appears, and then transient-current peaks are observed. A close look at this figure allows one to identify two peaks in the transient-current curve of a lower-voltage-biased cell at a lower temperature. Not shown in the figure, the unusual (i.e., double-peak) phenomenon was also observed in NLC cells without polyimide as the blocking layers, which would hinder charge injection from the electrodes. Moreover, the double-peak phenomenon disappears for all cells under a step voltage (from a null value). These observations suggest that the occurrence of the transient current induced by a polarity-reversal field cannot be explained by the space-charge-limited current. The second peak of transient currents in the low-voltage regime, as shown in Fig. 1, was not observed at high temperature near the clearing point, indicating that the orientation of the director of the NLC molecules in the direction of the electric field plays an important role in the transient-current behavior.
The occurrence of the second transient-current peak has not been reported before. There are several possible reasons to explain why the second-peak feature was not observed in the previous studies [4–7, 9]. First, the duration of the prefield, t 0, influences the distribution of the charges in a NLC cell and modifies the intensity of the internal electric field. According to our experimental results, if t 0 is too large (longer than 10 s in this study), the double-peak phenomenon will not be observed. Second, the temporal overlap is actually more or less serious and the current of the first peak covers the transient effect of the second peak. As a result, the signal of the second peak is weaker than the first one, causing it difficult to be distinguished from the first peak. In this paper, we intend to pay attention to explaining how the second peak occurs in the polarity-reversal field, which is not discussed in the pervious works.
As can be seen from Fig. 2(a), there are two distinct transient behaviors associated with the first polarity-reversal current peak for the applied voltage less or larger than the temperature-dependent characteristic voltage V c, which is slightly larger than Fréedericksz threshold voltage V th=π (k 11/Δεε 0)1/2=0.93 V. For V<V c, the time of occurrence of the first peak current, t 1, decreases with deceasing voltage applied. Note that the second peak was not observed in this voltage regime. The special behavior cannot be explained by v=µE, where v is the carrier velocity, µ is the carrier mobility, and E is the external electric field. Such behavior has been previously explained by Sugimura et al.  through a simple model in accordance with the polarity-reversal field, which causes the time-evolved electric-field E P(t) across the cell as presented in Eq. 2.
For V>V c, the occurrence of the first peak in the transient current, I 1, originates in the carrier-mobility distribution dependent on the director orientation in NLCs and the electric double-layer thickness [5–7]. The time of occurrence of either the first or the second peak current, t 1 or t 2, respectively, decreases with increasing voltage applied due to the fast rotation of the NLC directors in the anisotropic phase as shown in Fig. 2. The two peaks of a transient current get closer as the voltage increases. It is clear from Fig. 2 that the voltage dependence of the peak time of transient currents of a NLC cell in the isotropic phase is different from that in the anisotropic phase. This indicates that there are two distinct mechanisms underlying the polarity-reversal transient currents for the anisotropic and isotropic cases.
The voltage dependence of the peak current at various temperatures is shown in Fig. 3. For an applied voltage larger than V c, the first polarity-reversal peak current I 1 varies nearly with V 1.3 in the anisotropic phase and with V 3 in the isotropic phase. The relationship between the second peak and the applied voltage is expressed as I 2~V 1 in anisotropy and as I 2~V 1.5, satisfying the Child-Langmuir law, in isotropy. All of the above-mentioned results discussed in this section for V>V c imply that the nature of transient currents in the anisotropic phase results from the spatial distribution of charge mobility which is determined by the profile of director orientations.
The data shown in Figs. 2 and 3 were directly extracted from the original experimental results (i.e., measurements of transient current vs. time). When an applied voltage is larger than the characteristic voltage, the two peaks become close to each other in time. In order to confirm those data associated with the partially temporal overlap of peaks, we additionally used the multiple-peak fitting technique after subtracting the baseline from the original data. The baseline is a non-instantaneous feature and can be expressed by an exponential function. As a matter of fact, we found that the results from both methods—direct extraction and multiple-peak fitting—are very similar within uncertainty. Certainly, using the multiple-peak fitting technique will help better decompose the first and second peaks when they are overlapped.
The peak times of the transient current in Fig. 2 represent the time needed for a charge to cover the thickness d between alignment layers in a NLC cell. If a constant voltage V is applied to the cell, we can estimate the mobility from the slope of the t P-V curve using µ=d 2/t p V in the various temperature, where the subscript P represents 1 or 2. The magnitude of drift mobility as a function of temperature of cells is illustrated in Fig. 4 and displayed in Table 1. Note that the mobility corresponding to the first current peak, µ 1, is greater than that corresponding to the second current peak, µ 2. One confirms that the mobilities at various temperatures are indeed caused by director orientation in that µ 1 is comparable to the magnitude of the mobility parallel to the liquid-crystal director, µ ‖, and that µ 2 is of the order of and slightly greater than the mobility perpendicular to the director, µ ⊥, derived from the diffusion constants reported in Ref. . Upon the onset of an externally applied voltage, part of liquid-crystal molecules in a cell start to align in the electric-field direction, the charges experience the mobility along the molecular director and their flow produces the first transient current peak. The second transient current peak is associated with the smaller charge mobility µ 2, which is dominated by µ ⊥ owing to the slow molecular rotation. The spatial distribution of the director orientation in the cell is presumably caused by a nonuniform internal electric field determined by the sequential distribution of charges in the bulk governed by the application time of the prefield.
Figure 5 presents the transient current for different durations of the applied prefield. We elected to present Fig. 5 as an overlay of 4 single plots with arbitrary units for clarity. The vertical range of each plot displayed is actually identical, all from 0 to 2 µA/cm2. The transient current evolves from two peaks to one peak as t 0 is increased to ~10 s. Clearly, the application time of the prefield influences the distribution of charges in a NLC bulk. The distribution of charges builds up an internal electric field in a cell and affects the director orientations. A longer t 0 can modify the distribution of overall charges and form a uniform internal electric field in the cell while a shorter t 0 can only affect the charge in the boundary efficiently. Sugimura et al. studied the transient current in NLCs excited by a single- and double-voltage pulse techniques . The theoretical and experimental results showed that the application of the prepulse to the NLC before the measurement of the transient current altered the shape of the peaks due to the modified carrier distribution by the prepulse . In the present study, the effect of the polarity-reversal field applied to a NLC cell is similar to that in the double-pulse experiment. The prefield causes the liquid-crystal molecules near both electrodes to rapidly orient parallel to the field, resulting in the first peak upon the action of polarity reversal. A shorter duration of the prefield allows one to detect the second peak in the transient current because of the slow molecular rotation in the middle of the cell. The liquid crystals in the middle region of the entire cell experience a smaller net electric field and rotate more slowly compared with the ones in the boundary. The time of occurrence of the second peak gets closer to that of the first peak as the duration of the prefield becomes longer until they coincide together for t 0>10 s.
From the measured features, the total transient current I(t) could be understood as I(t)=I 1(t, t 0)+I 2(t, t 0) for a given voltage applied. As t 0 increases, I 1(t, t 0) increases in strength and moves slightly towards the +t direction, while I 2(t, t 0) shifts to the -t direction without much change in its amplitude. Therefore, with increasing t 0, I 1(t, t 0) becomes dominant and eventually cover the effects associated with the second peak completely because the internal electric field becomes more uniform for a larger t 0, enhancing the first peak of transient current in terms of both its strength and width.
It is known that cyano compounds, such as 5CB or E7, have low resistivity and relatively higher concentration of impurity ions. This is the reason why these compounds are not currently employed in the active-matrix display industry . Replacing E7 with a CF2O-based TFT-grade liquid crystal, which possesses a very high bulk resistivity of 4.6×1014 Ω-cm at 25°C, no transient currents were observed at a voltage as high as 10 V in our experiment, presumably due to its high purity with little impurity ions in the bulk. Moreover, the cell-thickness dependence of the transient current was examined using additional 15- and 25-µm-thick samples. As expected, a thicker NLC requires a higher externally applied voltage for one to observe an apparent transient current. The peak times of the transient current increase with increasing cell gap. Besides, for a thicker cell, the signal of the second peak is only observed in a high-voltage region (higher than ~7 V), because the diffusion layer is too small in comparison with the cell gap and the double-layer mechanism, in turn, becomes less effective. This result is consistent with an earlier theoretical analysis dealing with the double-pulse field condition .
The resistivity of a NLC cell has previously been found to depend on the material of aligning layers . Although the influence of the aligning layers is not the focus of this study, we envision that similar double-peak effects will hardly be observed for NLC cells with SiO2 alignment layers because polyimide and MgF2 alignment layers, owing to their greater tendency to adsorb ions, give rise to higher values of sample resistivity than SiO2 alignment layers do . The higher surface-adsorbed charge density σ, which induces stronger double-layer effects, will manifest the behavior of transient current in the NCL cell, allowing one to observe the double-peak phenomenon.
5. Concluding remarks
In summary, we have examined the behavior of transient currents induced by the polarity reversal of an applied dc voltage in homogeneous NLC cells at various temperatures. The experimental results show that the polarity-reversal transient current is characterized by the charge mobility, which is dependent of director orientations of NLC molecules due to the internal field of charges. The distribution of charges in the bulk is substantially modified by the prefield. The occurrence of the observed two peaks of the transient current originates in the difference in speeds of orientation of the directors in the boundary and central regions of the entire cell. Because the transient current comes from the impurity ions in a liquid crystal, no appreciable transient current was observed at a voltage as high as 10 V in an ultrapure CF2O-based TFT-grade liquid crystal. Furthermore, the thinner the NLC cell, the more pronounced the transient current observed in this study.
This research was supported by National Science Council, Taiwan, Republic of China, under Grant No. NSC-92-2112-M-033-008.
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