How should I write research description essay in my PhD application?
Normally, to be registered successfully for PhD project you have to write an abstract (10-20 pages) (and make a presentation). This should cover roughly and shortly:


state of the art 
state of knowledge
open questions
the very specialized niche of your work and what the motivation is(better understanding, prototype, measurement accuracy improvement...)
how you are going to achieve this (probably), i.e. a reasonable working and time plan


As you are still applying for a PhD position, it has to be much shorter, so show to the committee that you can identify above points analyzing literature and summarize them in 2-3 pages. 

To make things more easy, google similar current published PhD thesis related to this topic and read the preface (above points will often be summarized there within 2-3 pages). Don't write an essay, if the committee asks you to write 3 pages of decription of research area, write exactly 3 pages ;) 

PS: Oh forgot, why are you are motivated for this topic you don't know again? Maybe after writing the description of research you should polish up the statement of motivation also a bit based on that ;)