Electrical Simulation of Liquid Crystals

calculate a director configuration of the LC, it is necessary

n(

) = K n) + K(n × n + K(n × × n - (24)? (n? n + n × × n22(n × n

= ε

is the permittivity of vacuum, difference between the dielectric constant parallel and ver-tical to the director, and

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July, August, September 2015

is ε//=10.7 and ε⊥=3.7. LC material parameters can be specified in the SetLC statement in Clever, as follows:

setLC epsParaDir=10.7 epsV ertDir=3.7 splay=14.4e-12 twist=6.9e-12 bend=18.3e-12

The pretilt angles at the top and the bottom boundary of the LC layer are both 1?. The initial twist angle is 90?. Th ese alignment conditions can be defined in the following commands.

LCbndaryT partition(0 10) rubAngle(0) tiltangle(1)LCbndaryB partition(0 10) rubAngle(90) tiltangle(1)where LCbndaryT and LCbndaryB denote the statement for the top and the bottom boundary , respectively . The rubAngle sets the rubbing angle with respect to the x axis and tiltangle specifies the tilt angle measured from the x-y plane.

The LC cell structure consisting of a LC layer sandwiched by two electrodes was created in Victory Process and ex-ported with conformal tetrahedral mesh, as shown in Figure 1. The bias voltage on the electrode “Pix” was in-creased linearly from 0 to 6V in a 0.25V bias step through the following command in Clever:

Interconnect Capacitance \

domainboundarycondition=cyclic \

contact=”Pix” uservoltage=6 stevolt=0.25 strcture=”tn”

The solution was stored after each voltage step. The structure filename was generated in such a way that the current bias voltage is appended to the root file name “tn”. The director orientation of the TN-LC structure at 0 and 4V bias voltage is shown in Figure1(a) and 1(b), respectively. The arrows in the LC layer indicate the director orientation. Since Clever uses strong anchoring boundary condition for the LC simulation, the director orientation at the top and bottom boundaries will never change with the bias. Therefore, we can see as the bias is increased from 0 to 4V the director remains the same at the top and bottom boundaries while it becomes highly tilted in the middle of the LC layer.

The z component of the director n z was extracted along a line parallel to the z axis across the entire LC layer. The profile of n z at various bias voltages is shown in Figure 2. We can observe quantitatively how the director changes with increased bias. A nominal threshold voltage exists between 1.5V and 2V in this case. In order to identify the threshold voltage more clearly, the nz in the middle x-y plane (in terms of z axis) of the LC layer was extracted. The data was plotted as a function of the bias voltage with different twist angles of the director in Figure 3. We can see the transition region, i.e., the region where the nz goes from nearly 0 to nearly 1 becomes narrower and narrower with increased twist angle. Therefore the

Figure 1. The TN-LC cell structure biased at (a) 0V and (b) 4V, respectively. Arrows indicate the orientation of the director.

Figure 3. The director component nz in the middle x-y plane of the LC layer as a function of bias voltages with different twist angles.

Figure 2. The profile of the director component nz along the z direction with different bias voltages.

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threshold voltage becomes more distinct. This is a well-known phenomenon in TN LC. Because of their steep transition, TNs with twist angle larger than 90? (known as super-TNs) are used to make multiplexed displays on passive matrices.

Another example is an in-plane switching (IPS) cell with two coplanar zigzag electrodes shown in Figure 4. The LC layer of the structure has a lateral size of 10μm×10μm and a thickness of 3m. The whole structure was created in Victory Process with conformal tetrahedral mesh. The LC material parameters are the same as those used in the TN example. The initial rubbing angle of the director is 90 with respect to the x axis. As the applied voltage at the “Pix” electrode is increased, the director inbetween two electrodes turns to the x direction gradually due to the increased electric field along the x axis. The director above electrodes twists in a much smaller amount because the electric field is almost vertical to the electrode surface.

Shown in Figure 5 is the contour plot of the x component of the LC director, nx, in a x-z plane located at y=7.5 m at the (a) 4V and (b) 6V bias voltage. Shown in Figure 6 is the contour plot of the nx in a x-y plane 1m to the electrode plane at the (a) 4V and (b) 6V . We can see clearly from these two figures how the director reorients with bias in differ -ent regions of the LC layer. The n x profile was extracted along a line parallel to the z axis across the LC layer at x=4.5 m and y=5 m, the middle point between two zig-zag electrodes. The result is shown in Figure 7 where the electrodes are located in the left. The threshold voltage is estimated to be around 3V from the curve shape.

Figure 4. The IPS structure with zigzag electrodes.

Figure 5. The n x contour in a x -z plane at (a) 4V and (b) 6V.

Figure 6. The n x contour in a x -y plane at (a) 4V and (b) 6V.

Figure 7. The nx profile along the z direction with different bias voltages. The electrode plane is on the left side.

Figure 8. The capacitance-voltage curve of the IPS cell.

The capacitance of the LC cell between two electrodes can

be obtained during the voltage ramping simulation. The

calculation takes into account the anisotropic permittivity

of the LC director. To save the capacitance, one needs to add

the following command after the Interconnect statement:

save spice=”https://www.360docs.net/doc/702474971.html,”

The data in the netlist file can be viewed in Tonyplot. The

capacitance-voltage (CV) curve of the IPS cell is plotted in

Figure 8. The threshold voltage is a bit smaller than 3V, in

consistence with the director result shown in Figure 7.

Conclusion

In summary, three-dimensional static simulation of the

liquid crystal with user-definable material parameters

can be carried out in Clever. All vector components of

the LC director in the presence of the external electric

field (applied voltage) are solved by the finite element

method. The director data can be output at any stage of

the simulation for visualization or post-simulation pro-

cessing. The simulation on the TN and IPS structures has

been demonstrated. Other LC geometries such as vertical

alignment (VA) and fringe field switching (FFS) can be

analyzed as well.

References

[1] H. Mori et al, “Multidimensional Director Modeling Using the

Q Tensor Representation in a Liquid Crystal Cell and Its Ap-

plication to the π Cell with Patterned Electrodes”, Jpn. J.

Appl. Phys. Vol. 38 (1999) pp. 135–146.

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