"specific description" is a correct and usable phrase in written English.
You can use it to describe a detailed account of something, either verbally or in writing. For example, "The witness provided a specific description of the suspect's clothing."
In response, the board asked for a more specific description of the information being requested.
Iggy I sent him a very technically specific description of exactly how The Idiot and Lust For Life were made.
And that is about as close as you'll come to a specific description of what happens in "Landscape".
Scientists said the main value Dr. Crowley's study was his specific description of the limited role of natural forces in recent decades.
Later, I asked Clark to e-mail me a more specific description of how she "drew" the album, and how it came to be named "Actor".
A general announcement – "some viewers may find the following upsetting" – seems justified, but a specific description of what a show contains risks both spoilers and, if the contentious element is small, misrepresenting the whole programme.
While Cantor's proof lacked any specific description of a transcendental number, it showed that algebraic numbers (such as the square root of two) are few and far between: they poke up like marker buoys through the sea of transcendental numbers.
Mr. Condit's goal was obviously to establish that he had done everything he could to help the police and the Levy family, while avoiding any specific description of his relationship with Ms. Levy.
Richard T. Sullivan, chief of police in Providence, said his department had received a call from police and federal officials in Boston to search for men meeting a specific description.
The letters furnish what may be the most specific description yet of Mr. Salinger's writing habits in the years after 1965, when he stopped publishing.
An necessary and specific description is given as follows.
