As we know the number of different substrings has the upper bound $O(n^{2})$.
Consider the strings on $\{0,1\}$ alphabet. Can I build a string with $\Omega(n^{2})$ different substrings?
Actually I was thinking about the Thue-Morse sequence. We could use the fact that there are no two $s_1,s_2\in$ the Thue-Morse sequence, such that $s_1\cap s_2>0$.