First I will explain what "First Minima" is, and then I'll tell you why it's important.

What is "First Minima"?

A "First Minima" liquid crystal display is one that is optimized for the thinnest possible cell gap for a specific liquid crystal mixture and a specific wavelength of light. Gooch and Tarry (1) showed that the transmitted light intensity can be described by:

,         .

where d is the film thickness (cell gap), Dn is anisotropy of refractive index of the liquid crystal, and l is the wavelength of light. For a standard twisted nematic display, q = p/2 or 90 degrees and Dn will be fixed by the liquid crystal mixture.

We can determine the proper cell gap for a given liquid crystal if we know the wavelength of light that is being used. For most applications, a wavelength of 550 nm (Green) is used since this is the center of the visible spectrum, and it is also the photopic peak of the human eye. See the figure below for a plot of transmission versus cell gap for a 90 degree twist, a Dn of .18, and wavelengths of 400 nm (blue), 550 nm (green), and 700 nm (red). From this plot we can see that there are minima for 550 nm (green) light at 2.65 micron, 5.92 micron and 9.0 micron. The first minima for this liquid crystal is 2.65 micron.

The graph below shows that a display can be optimized for only one wavelength at a time. This is important to know if one is contemplating a normally black (transmissive) display with several different colored filters or a backlight behind the display. During the design process, it is necessary to fully specify all colors. We can then optimize the cell gap for the most important wavelength (color).

1  J Phys D: Appl. Phys., Vol. 8, 1975, 1575-84

Why is this important?

Simply put, a "First Minima" display will have the maximum contrast and viewing angle possible for a given LCD fluid. So if you want the best looking display you can get, specify that it be built at the "First Minima". This phenomenon is not very important for a positive image display, but for a negative image display the difference is dramatic.

A logical question might be, "Why don't you just build every display at the "First Minima" so every display looks as good as it possibly can?" Good question, and the answer has to do with a manufacturing problems that come about because of the small cell spacing required for these cells.

The glass that we use to build displays is extremely flat, but it does have slight imperfections in it. These imperfections tend to be small bumps on the glass about 2-3 microns high. As can be seen on the graph above, the TOTAL cell gap in this display (the distance between the top and bottom sheets of glass) needs to be about 2.7 microns. It is therefore possible that a small bump on the top glass will touch a small bump on the bottom glass, resulting in a front to back short in the display. There is no way to prevent or correct these shorts, and these displays are simply discarded.

The answer to this problem is to develop a fluid that has a "First Minima" of about 5 microns or greater. At this wide cell gap front to back shorts are not a problem. We therefore have a win-win situation where you get a display with maximum contrast and viewing angle, and we can manufacture it without any yield fallout. As an added bonus, the first minima fluids cost about the same as the others, so there is no increase in price!

We have a few first minima fluids, our #6 and our #16. For all new TN designs, we usually specify the #16 fluid, as it also has a wider temperature range, and a more even color.