LCD screens don't get burn in images like cathode ray tube type monitors since they don't involve phosphor based displays like tubes (CRTs).
The following is an excerpt from this
article. This article was written about televisions, but the same technology hold true with monitor screen.
"It is a fact that LCD displays are immune to phosphor wear, simply because LCD televisions do not use phosphor to create a television image. Otherwise, it would be like saying an electric car can run out of gas.
However, LCD displays have certain characteristics that do not make them completely immune to static images. On LCD displays it's kindly referred to as "video memory." LCD panels use a complicated process of organizing liquid crystal molecules into a twisted or untwisted state, which allows polarized light to pass through the liquid crystal substrate. Over time, it is possible the liquid crystals can "get used to" the state of twist they are in, causing a static image, similar to phosphor burn-in, appear on the screen.
Some say that simply turning off the display for 24-48 hours eliminates the effect, while others have claimed the effect is permanent in extreme cases. Nonetheless, home users of LCD televisions have little to fear.