triu makes a copy of the matrix with the lower-half set to zero. So it makes no sense to call triu(zeros(n, n)) since zeros(n,n) already has a zero lower half. You are just making an unnecessary copy of the matrix.
Furthermore, note that the output of triu(zeros(n, n)) is simply another ordinary Matrix, so there is no performance effect to using it compared to any other Matrix (= 2d Array).
In contrast, if you have an upper triangular matrix T and you are solving a system of equations via T \ b or similar, then you are much better off wrapping it in the UpperTriangular type, i.e. using UpperTriangular(T) \ b, since that dispatches to a different algorithm that exploits the UpperTriangular shape. (And there are a few other functions that have specialized UpperTriangular variants.)