I need a small LCD display for a digital thermometer-like device I am making. I need to be able to display 6 digits or letters only.The main constraint is the small size and rectangular shape.I cant have width more than a little over a centimeter and length appropriate for 6 characters. I am unable to figure out how and where I can get this type of LCD. I am also ok with other displays, e.g. LED-based.
The smallest standard product LCD glass I could find is one from Varitronix that is 20.3mm x 38mm. It offers eight digits instead of 6. According to the data sheet for this part it is available with pins attached which adds a very small amount of additional width.
Note that for smaller sizes it is generally required to work with a vendor such as this to get a custom LCD glass made to your size requirements. Smallest size will generally imply that you use zebra strip for connections and a custom tooled case / holder to bring the display into proper contact and orientation with the circuit board. Do note that for small form factor displays it is common that the digit height is approximately one third the overall width of the LCD glass with the rest being used up by the contacts and sealing area.
An alternative approach would be to take a look at a very small LCD graphic type display. The smallest modules use a technology called TAB where a graphics LCD controller is mounted on a flex circuit that goes between the display and your circuit board. The controller provides the drive excitation for the display so that you do not have to do that with your own circuitry. I found a web page (linked below) that lists products available from VS-Top Electronics. They show a graphic type display with 96x26 pixels with an active display area that is 25.9mm x 10mm. The module size is 33mm x 13mm but there is the flex strip with its "on flex" chip that has to fold in along side or under the display.
The graphic type display offers you a lot of flexibility to display more than just numbers. In a 96 pixel width you can easily display a six digit / character message using a font that is sized at 16x26. Smaller sized fonts could obviously display more - even two lines.
You would have to contact the manufacturer to get further information or to find local contact information.
Your small size device implies that you may also be after the lowest power consumption. LCDs offer this feature so that small battery operation is feasible. You did mention LED technology however so here is a small display recommendation for LEDs.
Avago offers a ultra mini seven segment display module that has a height of just 11mm. You could use six of these modules side by side to get your full display.