Gooch-Tarry minimum

With regard to the dye-related parameter measurements, the dye concentration is usually kept at about 0.5-2%, depending on its absorption coefficient. For azo dyes the dye concentration is about 0.25-1% for dye doped TN, about 2-4% for Heilmeier displays, and about 2-5% for phase change displays. The cell thickness is usually about 5 pm for dye-doped TN at the first Gooch Tarry minimum [ 15,16,88], about 7-10 pm for dye-doped TN at the second Gooch Tarry minimum [15, 16, 88], about 5-15 pm for Heilmeier, and about 10-20 pm for phase change dichroic displays. Usually, the dye concentration is increased by a factor of about 1.5-2 when anthraquinone dyes are used instead of azo dyes, as anthraquinone dyes have less absorbance than azo dyes. Sometimes combinations of azo and anthraquinone dyes are used [16, 54]. 

For the lowest order m = 1, dAnJX = Vlll. This is the Gooch-Tarry s first minimum condition for the 90° TN cell. For the second order m = 2 and dAn = v/l5/2. The second minimum condition is used only for low-end displays such as wrist watches, because a large cell gap is easier to fabricate, and the cyano-biphenyl LCs are less expensive. For notebook TFT-LCDs, the first minimum is preferred because fast response time is required. 

Table 1. Necessary birefringence values to fulfill the 1st, 2nd and 3rd minimum condition according to the Gooch and Tarry curve for layer thickness d=6 pm and d=S pm.

For the NB mode, intensity minima of the transmitted luminance are calculated for dAn=0.48 pm, 1,09 pm and 1.68 pm which correspond to the minima of the Gooch and Tarry transmitted intensity for a wavelength A=0.55 pm. Operation in the 1 st minimum is mostly used in TFT displays as it offers a wider viewing angle [15, 16]. The 2nd minimum condition is used in watches and calculators. 

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