三、 實驗部分
3.3 實驗結果
3.3.3 樣品 3 實驗結果
樣品 3 的各參數如下表 3-5：
等效電容（F） 1.48*10;9
cell gap（µm） 3.94
cell area（𝑐𝑚2） 0.9909
表 3-5 樣品 3 參數表
37
圖 3-6 樣品 3 𝑉
𝑖𝑜𝑛(𝑡) 實驗與理論比較圖
而圖 3-6 為樣品 3 的實驗數據與經由解析解計算得到的理論曲線比較 圖，其中實線部分為實驗得到的 𝑉𝑖𝑜𝑛(𝑡) 數據圖，而虛線部分則是由 解析解得到的數據圖。理論計算結果詳細如下表 3-6。
離子濃度(
個
𝑚3⁄ ) 離子遷移率.𝑚2⁄𝑉 ∗ 𝑠/
低解離率離子 2.848 ∗ 1018 8.679 ∗ 10;12
高解離率離子 少到無法正確估計
表 3-6 樣品 3 之計算結果
38
第四章 結論與未來展望
本論文首次用 VHR 量測系統來分析液晶盒中的高、低解離率離 子，利用一些可以調整的量測條件如：外加電壓小於液晶的臨界電壓、
分析數據為第一幀（first frame cycle）的圖形等，這些條件可以使得 分析簡單化進而可以推導出高、低解離率離子在 VHR 量測過程中之 解析解型式。藉由實驗數據、解析解以及分析實驗數據的方法，我們 可以求出此液晶盒的高、低解離率離子的初始濃度以及在 VHR 量測 期間的離子遷移率，並且藉由此解析解的理論圖形和實驗數據作比較 可以知道其理論之正確性。
在未來的研究中，可以將施加的外加電壓大於液晶的臨界電壓，
藉此來求出平行 TN LCD 液晶導軸的離子遷移率。並且可以藉由量測 不同溫度下之同一樣品來求得離子濃度和離子遷移率的各自活化能，
來瞭解離子濃度和離子遷移率與溫度之間的變化機制。本論文所推導 的理論模型，若加以適當的推廣，可以用來推算配向層內的離子濃度 及其遷移率。若再配合其它的電學量測時，更可求出配向層內的離子 濃度及其遷移率。
39
參 考 文 獻
[1]陳伯綸，「離子電荷效應對液晶盒物理特性之影響」，國立交通大 學，博士論文，民國八十九年六月。
[2] K. H. Yang, “Charge retention of twisted nematic liquid-crystal displays”, J. Appl. Phys., 67, pp. 36-39, January 1990.
[3] K. H. Yang, “The investigation of image formation in a large-area solid state x-ray receptor with electrophoretic display”, J. Appl. Phys., 54, pp. 4711-4721, September 1983.
[4] T. C. Chieu, K. H. Yang, “Transport Properties of Ions in Ferroelectric Liquid Crystal Cells”, Jpn. J. Appl. Phys., 28, pp. 2240-2246,
November 1989.
[5] Nobuyoshi Sasaki, “Simulation of the Voltage Holding Ratio in
Liquid Crystal Displays with a Constant Charge Model”, Jpn. J. Appl.
Phys., 37, pp. 6065-6070, November 1998.
[6] Takeo Nakanishi, Taiju Takahashi, Hitoshi Mada, Susumu Saito,
“Transient Behavior of Voltage Holding Ratio in Nematic Liquid Crystal Cells”, Jpn. J. Appl. Phys., 41, pp. 3752-3757, June 2002.
40
附 錄
以下為本論文作者在 2010 International Conference on Optics and Photonics in Taiwan 以及 2010 中國液態晶體學會年會暨研討會 發 表過的論文
“
Analytic Solution of Phase Transfer Function for aGeneral Twisted Nematic Cell.
”（“
一般扭曲向列型液晶之相位轉換函 數的解析解”）
。41
Analytic Solution of Phase Transfer Function for a General Twisted Nematic Cell
Chih Hao Kuo
1*, Wei Hsiang Liao
2, and Kei Hsiung Yang
31Institute of Imaging and Biomedical Photonics, College of Photonics, National Chiao Tung University, Guiren, Tainan
2Institute of Photonic System, College of Photonics, National Chiao Tung University, Guiren, Tainan
3 Institute of Imaging and Biomedical Photonics, College of Photonics, National Chiao Tung University,
Guiren, Tainan
Abstract---Analytic solution of phase transfer function for a general twisted nematic (GTN) cell has been derived. The solution can be applied to analyze data obtained by Heterodyne interferometry to derive important cell parameters such as cell gap, pretilt and twist angles.
Keywords: phase difference, Jones calculate, liquid crystal cell parameters
INTRODUCTION
LCDs (liquid crystal displays) become dominant from small-size mobile to large-size TV applications. To optimize the display qualities of LCDs, it is imperative to obtain optimized cell parameters such as cell gap, pretilt and twist angles. Recent publication [1] indicates that, by measuring the retardation of a GTN cell rotating along its cell normal is a Heterodyne interferometeric system. All the above three parameters can be obtained by fitting the experimental results to the calculated results by numerical computation of Jones calculation in a computer [1]. This paper presents analytical solutions to replace the published numerical computations of Jones calculation for faster calculation with more accurate results.
THEORETICAL CALCULATION
Assume that the polarization state of the incident light is .Exei∅1
Eyei∅2/, whose phase different δ between two Eigen modes can be expressed as (∅1− ∅2). After the light passes through a GTN cell,
we obtain the polarization state of the emerging light as (Ex′ei∅1′
Ey′ei∅2′+, whose phase difference δ′ is (∅1′ − ∅2′). We can measure the phase difference θ′=(δ′− δ) by a Heterodyne interferometeric
measurement system. If the polarization state of the incident light is (1
0), and after passing through the
GTN cell, the polarization state of the emerging light can be written as (Ex′ei∅1′
Ey′ei∅2′+, the phase difference of Ψ′= (∅1′ − ∅2′) should equal to θ′. In this case, we can carry out the following theoretical derivations.
42 We choose (1
0) to be the input Jones vector to incident upon a GTN cell with arbitrary rotation angle β, we can list the following formula to calculate twist angle ∅ of a GTN cell as shown in the Figure below.
β：t
he angle between the entrance LC director and the incident light light and ordinary light respectively43
The above equation shows the analytic solution of phase transfer function for a GTN cell.
CONCLUSIONS
We have derived an analytic solution of phase transfer function for a general TN cells. This analytic solution would contribute to derive the pretilt angle, cell gap, and twist angle of a TN or GTN cell from measured data with faster computation and more accurate.
REFERENCES
[1]
Ra Bin Li , Heng Cheng Tseng , and Kei Hsiung Yang , Determination of the cell parameters of a TNLC cell by phase-sensitive heterodyne interferometry, 2008 China FPD Conference.44
一般扭曲向列型液晶之相位轉換函數的解析解
郭智豪
1廖偉翔
2楊界雄
1國立交通大學光電學院
1影像與生醫光電研究所
2光電系統研究所
台南 台灣
E-mail address : [email protected] 摘要
derived. The solution can be applied to analyze data obtained by Heterodyne interferometry to derive important cell parameters such as cell gap, pretilt and twist angles.Keywords: phase difference, retardation, Jones matrix, liquid crystal cell gap, pretilt angle, twist angle
1.
.前言
45
46
47
所以利用此解析解和實驗數據擬合時只要把旋轉角度β限於區間[0，π]之間即可（如圖 3所示）。
圖 3 所示的模擬結果所使用與液晶盒相關的參數為：
ne= 1.597；no= 1.487；λ = 633nm；
∅ = 90o；d = 3.66μm；θ = 3.24o；
依照與解析解的運算和實驗數據做比較[1]，即可求得一般扭曲相列型液晶盒的重要參數∅、d、θ。
圖 3.解析解和實驗數據擬合曲線圖
3. 結論
本論文推導出一般扭曲相列型液晶之相位轉換函數的解析解。利用此解析解和實驗數據作比 較後，即可得到較準確的一般扭曲相列型液晶盒的重要參數如扭曲角、液晶盒厚以及預傾角。由 於這些參數對於液晶顯示器的光電效應有著相當重要的影響，所以準確的求得這些參數對於液晶 顯示器的設計和顯示品質是非常重要的。
4. 參考文獻
[1] Ra Bin Li , Heng Cheng Tseng , and Kei Hsiung Yang , "Determination of the cell parameters of a TNLC cell by phase-sensitive heterodyne interferometry", 2008 China FPD Conference.