Proceedings of 14' International Conference on Dielectric Liquids (ICDL 2002), Graz (Austria), July 7-12, 2002

Experiments and modelling of conduction and charge accumulation in liquid crystal cells

A.R.M. Verschueren, R.A.H. Niessen, P.H.L. Notten, W. Oepts and E.M.L. Alexander-Moonen Philips Research Laboratories

Prof. Holstlaan 4,5656 AA Eindhoven, THE NETHERLANDS

Abstracc The combination of different electrical measurements on liquid crystal (display) cells yields a consistent model for charge transport and accumulation. At small timescales (ms) the charge transport is dominated by mobile ions, but on long timescales (hrs) it is demonstrated that the (bulk) generation of extremely low mobility ions determines the transport, These slow ions accumulate at an ionic double layer at the interface, giving rise to an electric tield over the polyimide alignment layer.

INTRODUCTION The application of liquid crystal displays in laptops, desktop- monitors and projection displays has sharply risen over the last decade. The demands for the front-of-screen performance are constantly set higher, making artefacts like image flicker and image retention [I] unacceptable. For understanding the basic effects that cause image retention, knowledge on transport and accumulation of charge in liquid crystal (display) cells [2] is essential. In this paper four different measurement techniques will be presented that characterise the electrical properties of liquid crystal cells. With the help of analytical models, parameters will be derived from the measurements that combine into a consistent and insightful electrical network model to describe the transpar! and accumulation of charge in liquid crystal cells.

EXPERIMENTAL Samples are fabricated by spincoating 20nm thin polyimide (PI) layers on top of aluminium and indium-tin-oxide (ITO) covered glass plates. The two electfode plates with PI are rubbed (to give LC alignment), cured and glued together after dispersion of quartz spacer balls (of 2 micron diameter). A small opening is left to evacuate and fill the cell with a commercial liquid crystal (LC) mixture of VAN type (with ~ ~ ~ 3 . 5 and e1=6.0). The cell is finished after plugging the filling hole. In this way a 50mmz pixel is defined consisting of a stack of IOOnm AI, 20nm PI, 2pm LC, 20nm PI and lOOnm ITO. Fifteen cells were constructed using the same materials in the same process, in clean-room facilities and give comparable results. The four types of measurements (voltage drop measurement, DC current-voltage measurement, DC stress measurement and impedance spectroscopy) will be discussed together with the results in separate paragraphs. All measurements described here are performed at room temperature.

VOLTAGE DROP MEASUREMENT The voltage drop measurement measures the voltage that "leaks" away through a cell in a certain frame-time. This measurement simulates the conditions of active matrix addressing. A cell is altematingly charged (in a line-time of several microseconds) with positive and negative voltage. During the frame-time (of several milliseconds) the cell is disconnected from the source and monitored with a voltmeter of extremely high (TQ) impedance. The resulting data for varied voltage and frame-time is indicated in Figure I .

7" .I

5 60

8 D DI 0 50

40

30

20

10

0

>

0 5 10 15 20 Frame tlme (ms)

Figure 1 - Plot ofthe voltage drop as a function of frame-time. Different curves correspond to different applied voltages (below optical threshold of the LC). The bias voltage is compensated

The physics behind the voltage drop is the movement of ions in the cell, moving to and from the electrodes with every change of polarity in the applied voltage. This can be modelled simply by considering an ionic concentration n (of univalent positive and/or negative ions of mobility I), that migrates completely (so neglecting difision) inside a cell of thickness d. Then one obtains:

0-7803-7350-2/02/$17,00 0 2002 IEEE 377

In which, e is the elementary charge, Y the applied voltage, EO the dielectric constant of vacuum and E~ the relative dielectric constant for the liquid crystal host (sub threshold).

Using the known values of the cellgap (&2pm) and the dielectric constant (&,=3.5), from Figure 1 one obtains:

n/= 3.0.10'8 m-' p,=4.7.10~10 mZNs (2)

These values are of the same order of magnitude as obtained elsewhere for purified liquid crystal mixtures [3] and represent fast mobile ions in the LC (therefore the suffixfis used). The corresponding Stokes radius [4] of these ions is about 0.3nm. From the low concentration of ions, it can be estimated that at 1 Volt migration dominates over diffusion by a factor of 40. So the ions indeed traverse the complete cellgap d. The impedance spectroscopy measurements (although taken at a low voltage, so where diffusion effects are important) will confirm the obtained values for concentration and mobility.

CURRENT-VOLTAGEMEASUREMENT The DC current-voltage (I-V) measurement is conceptually very simple. A DC voltage is applied and after the current has reached a steady-state level, the current is recorded. However, in practice there are three difficulties with this. In the first place, the current becomes very low, well into pico-Ampere regime, where care has to be taken to obtain reliable and reproducible measurements. Secondly, a real steady-state level is not reached within 10' seconds. Rather, the current decreases very gradually with a (small) power-law dependence IS]. This means that between IO2 and lo' seconds, the shape of the I-V curve remains identical and the magnitude remains in the same order (within factor of 3). For that reason the (quasi) steady-state current is recorded at a fixed settle time of 400 seconds. The third difficulty with the I-V measuremenis is that prolonged application of DC voltages on the cell influences the electric field. This effect is actually the topic of the next section (DC stress measurement). To minimise these effects, a stress-less relaxation period is introduced after every measurement point and care is taken to balance the applied DC voltages, by alternating the polarity around the zero-current voltage (bias voltage). The resulting I-V curve with this measurement procedure is plotted in Figure 2. In this plot, the definitions for the bias- voltage, s-current and linear conductance are included. It is interesting to notice that the zero current condition is reached for an extemal voltage (called bias voltage) of -0.7V. The origin of this voltage is the work function difference between the (positive) AI and (negative) IT0 electrodes 161. This was confirmed by Kelvin Probe measurements on the Pl coated electrodes before assembly of the cells, which showed that the AI work function is 0.7eV lower than for ITO. This same value for the bias voltage has also been taken into account for all other electrical measurements in this paper.

- 20 4p I

5 10

E

U - m w s o

-10

-20 6.0 4 . 0 -2.0 0.0 2.0 4.0

Extemal M: Voltage (VI

Figure 2 - Plot of the (quasi) steady-state I-V curve, taken at room temperature, afler a settle time of 400s. Indicated are the definitions

for bias voltage, linear conductance and s-current.

The I-V curve in Figure 2 is shaped like the letter S. Apart from the effect of the bias voltage, this shape was first reported for liquid crystal materials in [2]. For the quantitative explanation of this shape, the curve is decomposed into a straight S-shape (with constant s-current for high DC voltages), by subtracting the linear I-V defined by the linear conductance. The resulting curve is plotted in Figure 3. Later on it will be shown that the linear conductance is proportional to the s-current.

15

- 3 1 0

5 5 U m 2 0 a 4-5

-10

-1 5 4 0 -30 -20 - i o 00 1 0 2 0 30 4 0

Figure 3 - Plot of the (quasi) steady-state I-V curve, derived from the previous figure, by subtracting the measurement data with the linear conductance and subtracting the voltage with the bias voltage. The

indicated formulas are from (6), with A the pixel area.

With the following model of generation and recombination of ions this S-shape can be explained. Difision effects are again neglected, resulting in a uniform ion concentration n (equally divided into n12 positive and n/2 negative univalent ions of identical mobility p). The rate equation for generation and recombination of ions then becomes:

Extemal DC Voltatage - Bias Voltage (V)

378

1 dn -- = 2 dt (3) J = en@

In (3) the ion concentration n increases by generation (constant p times the Concentration no of ion-pairs), decreases by recombination (constant a times concentration product of positive and negative ions) and decreases by migration. Then the resulting (temporal) current density J can be calculated as a function of the (temporal) ion concentration n.

The steady-state solution of this current density is given by:

In which J, stands for s-current density, T~ for chemical relaxation time and T, for ion transit time. The solution (4) depends on three parameters pno, a and p. However, Langevin has demonstrated [7] that for ions the recombination constant a is proportional to the mobility p:

a=- 2eP

E&, (5)

Then the steady-state solution (4) becomes dependent on only two parameters: the eauilibrium ion concentration n (equal to &&) and the ion mobility p. With these parameters the

low- and high field limits of the current density can be derived:

ned J = J , 5 = ~ e n E forE <<-

T, % E ,

These expressions are also included in Figure 3. Notice that the low field steady-state conductance (6 ) is exactly equal to the initial value of the transient conductance derived from (1). This is because the generation process is constantly replacing the ions that have reached the electrodes. An excellent fit in Figure 3 is obtained.using the following values (taking into account that &,=6 above the threshold voltage of the LC):

n,= 5.2.1019 ni’ p,= 2.4.10-13 m2Ns (7)

This value for the mobility indicates a 2000 times slower ion species than the fast ions in (2). That is the reason for the

suffix s (for slow). Ions of this low mobility have not been reported before in liquid crystal literature. The corresponding Stokes radius is impossibly large, indicating that the assumptions for the Walden law [4] to calculate the Stokes radius may not be valid. Presumably this means that these ions are of similar size as the LC host molecules. This can lead to the speculation that these slow ions are dissociated or ionised LC molecules. Again, also for these slow ions, the impedance spectroscopy measurements will confirm the obtained values for concentration and mobility.

So far it is demonstrated that with generation and recombination of slow ions, the I-V curve (without the linear conductance) can be explained. Here, for the linear conductance the correlation with the s-current is plotted in Figure 4 for all the cells fabricated in the batch.

60

20

10

o k I I I I . -

0 2 4 6 8 linear conductance (PAN)

Figure 4 - Correlation between the s-current and the corresponding linear conductance for all the cells in the batch. The s-current and

linear conductance values were obtained from I-V curves.

Clearly there exists a strong linear relation between the s- current and the linear conductance. This is in agreement with the Onsager effect [SI that the generation of ions is enhanced by destabilisation of the ion-pairs in large electric fields. This leads to a field-dependent generation constant p:

e3 V 2 2 . - ) p = Po. (1 +

8 i ~ ~ ~ & , k T d

where k is the Boltzmann constant and T absolute temperature. Using an average ~~=(&,,+&~)/2=4.75 for the LC, one obtains that per volt the linear conductance increases the current by U%, which is in excellent agreement with the measurements of Figure 4.

DC STRESS MEASUREMENT In the DC stress measurement the bias voltage is monitored as a function of the prolonged application of DC voltages on the cell. The bias voltage is per definition the voltage that has to be applied to the cell in order to obtain zero conductance (see Figure 2), in other words to compensate the inner electric

379

field. This inner electric field is the combined result of the work function difference between the electrodes and the adsorbed ions on the electrodes (PI/LC interface). In the previous section (Figure 2) it was found that DC voltages applied to the cell cause generation of (slow) ions. Therefore, it is anticipated that these ions accumulate at the electrodes and influence the bias voltage, which is indeed the case and demonstrated in Figure 5.

0 2 4 6 8

Figure 5 - Bias voltage as a function of applying DC stress. Both the stress period (of 4 hours for various DC stress voltages) and the relaxation period (of 4 hours with the bias voltage -0.7V ) are indicated. The dashed lines indicate the simulation, with the

electric network model drawn in the upper right comer.

The bias voltage can be measured in several different ways. First of all, it can be determined from the I-V curves. Secondly it can be determined optically. Since the LC molecules will react to the inner electric field, this will lead to optical flicker (which will disappear at the bias voltage). And thirdly, related to this, also the capacitance will depend on the inner electric field. This last measurement method gives the most accurate (down to 10mV) and fastest (within 2s) results and is used for the measurements in Figure 5 .

From Figure 5 it can be derived that the increase of the bias voltage due to a stress of +1.3V (which is 2.0V above the bias voltage) is only 20% larger than due to a four times smaller stress of -0.2V (which is 0.5V above the b i b voltage). This very non-linear dependence is also seen in the I-V curve of Figure 2. In fact, using the currents derived from Figure 2 as a current source (with taking into account the small power-law time dependence) to charge a “Cs+W/Cp” electrical network model,,gives excellent fits of the bias voltage versus time. The used electrical network model is also indicated in Figure 5. Best fit is obtained with a series capacitance of 2.OpF. which corresponds to a Inm thick (with ~ ~ = 5 ) ionic double layer (Stern layer [9]). This, in series with a resistor of 30GQ in parallel with a capacitance of 70nF. corresponding to a PI layer of 18nm thickness (with s,=3) and 8.1013 Qm resistivity. Notice that these values should correspond to the total of the interfaces at both electrodes. but nevertheless the values are in

Time (hn)

a reasonable order of magnitude. Also these same parameters for the interface are consistent with the impedance spectroscopy results.

IMPEDANCE SPECTROSCOPY Impedance spectroscopy measures the complex impedance z‘ as a function of the angular frequency w. With a commercial AutolabTM PGSTAT-12 system, applying 60mV amplitude (and compensating for the bias voltage) the LC cell was measured in the mHz-MHz regime. ?om the complex impedance z‘ the complex capacitance C can be calculated, using the following definitions:

For finding optimal tit parameters, it is convenient to use both the complex impedance z‘ and capacitance 6. Both are plotted in Figure 6 and Figure 7.

For modelling this complex impedance the electrical network of Figure 8 is used. This electrical network consists of the electrode resistance (dominated by ITO), the total PI thickness and resistivity (equal to the DC stress results), the Stem ionic double layer thickness (also equal to the DC stress results) and the LC layer thickness and conductance. In this model the LC layer conductance results entirely from ions. The migration and diffusion effects for a (fixed) ion concentration n as a function of the angular frequency w are given by the space charge polarisation (SCP) equations [lo]:

1 . neM 1 1+2eRsin(R)-eZR cod R 1 + 2eR cos(R) + e2R

1 - 2eR sin(R) - elR (

c& =-*(1+ wd

e,,, =--

R(1+ 2eRcos(R) + -

2pkT

The low frequency limit of these SCP equations approaches a pure capacitance Cscp. The high frequency limit is a pure resistance RSCP:

lO@T foro<<-

ed2

for o >> - ed2

ne2&

d RSCP = -

n 4

C S C P == I o@T (1 1)

The physical interpretation of this is that for low frequency the ions build up a diffuse (Debye) double layer [9] at the interface (of capacitance Cscp). For high frequency the ions will not be able to reach the electrodes and behave as a pure ion conductor with resistance RSCP., in line with (1) and (6).

380

Incorporating the SCP equations (10) for three different ion species (slow, medium and fast) and taking the LC resistivity equal to the found low voltage generation (6) for slow ions, reasonable fits are obtained for both the complex impedance and capacitance. These fits are also plotted in Figures 6 and 7, together with reference fits without the SCP contributions of the three ion species.

The SCP values for ion concentration and mobility that give the best fit for the complex impedance are in excellent agreement with the other electrical measurements: slow ions with I-V measurements (7), and fast ions with voltage drop measurements (2).

CONCLUSION The results of four types of electrical measurements combine into a consistent and insightful model of the charge transport and charge accumulation in a liquid crystal cell. The charge transport on small timescales is dominated by fast ions, but on long timescales it is demonstrated that the (bulk) generation of very low mobility ions determines the transport. These slow ions accumulate at an ionic double layer at the interface, building up an electric field over the PI layer.

ACKNOWLEDGMENT Herbert De Vleeschouwer, Peter Kohsiek, Mark Johnson, Mireille Reijme and En It0 are acknowledged for fruitful discussions and their contribution to the measurement setups.

REFERENCES Chen, P.-L., Chen, S.-H., and Su, F.-C., Eurodisplay conference 1999, p.3 15-3 18 Verschueren, A.R.M, Kohsiek, P., Johnson, M.T. and Asselt, R. van, IDRC conference 2000, p. 55-58 Naemura, S., Nakazono, Y., Ichinose, H., et al. SID conference 1997, p. 199-202 Murakami, S., Naito, H., Okuda, M., Sugimura, A., Mol. Cryst. Liq. Cryst., 1994 De Vleeschouwer, H., Verschueren, A.R.M., et al, Jpn. J. Appl. Phys, Part 1, Vo1.41, No.3A (2002) Huang, H.-C., Cheng, P.-W., Jpn. J. Appl. Phys. Vol. 40 (2001) p.3448-3456 Debye P., Trans. Electrochem. Soc. Vol. 82 (1942), p

De Vleeschouwer, H., Verschueren, A.R.M., et al, Jpn. J. Appl. Phys. Vol. 40 (2001). p.3272-3276 lsraelachvili, J.N., “Intermolecular and Surface Forces”, Academic Press (1985),‘p.168 Sawada, A., Nakazono, Y., T a n ” , K. and Naemura, S., Mol. Cryst. Liq. Cryst. Vol. 318 (1998). p. 225- 242

262-272

I .E+lI

I.E+10 - c 1.€+09 t 5 I.E+08

x I.E+O~

TI 1.€+07

E - 1.€+05

I.E+04

1.E+03

1.EW2

-Z(fullsim) --

1.E43 1.E41 1.E+01 I.E+03 I.E+05 I.E+07 Angular frequency (ndhr)

Figure 6 - Real part (Z’) and imaginary part (T’) of the complex impedance Z’ as a function ofangular frequency, measured for the LC cell. Also indicated are the simulation results using the complete electrical network model (thick line, good tit) and without the SCP

elements (thin line).

1.E.07

r1.Eb8 - * e 1.E.09

4 l.E-10 0

X1.E-11

1.E-12

; I I 0

I.€-13 1.E.03 1.E.01 l.E+01 1.E+03 I.E+05 l.E+07

Angular frequency (ad ls )

Figure 7 -Real pari (C) and imaginary part (e’) of the complex capacitance C* as a function of angular frequency, derived from the

measured impedance.

PI I T 0 double

Figure 8 -Complete electrical network model for LC cell

381