Electrostatic loudspeaker. It is a fairly old technique. Yet not play very low frequencies and as well he has a pretty low life time.
This type of speaker is thin itself, but transformers that you need to raise the voltage can not be thin. There are very heavy.
An example:

This type of speaker seems to be from a story:
It is under 1mm thickness and can be shaped in various forms.

http://technabob.com/blog/2012/06/20/hannes-harms-flat-boombox/
They give us assurances that there is this prototype and it works

Another option may be piezoelectric speaker.

Another option, it would be a very flat type of electrodynamic speaker, but very expensive.

I want to find a simple and cheap solution, to buy or build such a thin speaker.

 

Your pic is an electrostaitc speaker combined with a conventional sub-woofer.

Conventional amplifiers operate into 8 ohms, so the "voltage out" is pretty much set my the load. You don;t need that much current to drive the electrostatics, so you can build your own amp with a smaller current power supply. Search for the "Leach amp". It's very nice. I made one in the early 80's.

 

Your pic is an electrostaitc speaker combined with a conventional sub-woofer.

Yes, because they need a box for the high voltage for electrostatic speaker. And also offers low frequencies that I think we can not convey the electrostatic speaker.

 

A Korean company 'Fils' is supposed to be making them. Have had a hard time finding an elusive piezofilm product vendor.

----> http://film.koreasme.com/pro_03.htm