A poster? Ha ha, solid! I don't know anyone who's had to make a poster for Physics! Lucky you!
As to the topic, it's easy in itself, and, from what I imagine, so too should be the poster. The 'shortcomings' mentioned basically refer to the, now obsolete, thermionic valves and triodes used in devices such as the telegram and portable radio devices of the pre-1980s (and when I say portable, I mean running on 12 D-sized batteries, very fragile and so cumbersome that a small child wouldn't even be able to carry them - exaggerating a little, of course
). So, you might decorate your poster with photos of some of these ancient relics, and the inventors and/or companies associated with them, and some short speals on their significance to the time.
Solid state devices outstrip their thermionic counterparts in almost every respect, and this is where your 'properties of materials' and 'reference to the transistor' will come in. Their advantages run as deep as the atomic level, so some diagrams illustrating p-n junctions or interfaces, electron-hole migrations and a pictorial representation of the transistor would probably be appropriate. I won't get too caught up in explaining to you the operation of solid state devices and the physics it involves, since you probably already have that in the bag, so I'll just mention that a transistor is analogous, in function (not appearance), to a thermionic amplifier, and also that the fact that energy inputs are lower, the speed of signal transmission is much higher, they are far more durable and resilient, are incredibly reliable with a long lifetime, and lend themselves to miniaturisation make them a suitable substitute for modern communication applications.
Good luck, man, and just remember, being a poster, your work should be as vibrant and colourfully engaging as can be
