  We study the vacuum structures of four-dimensional $\mathcal{N} = 1$ old
minimal supergravity with higher derivative corrections. We find that
$\mathcal{N} = 1$ supergravity with Riemann curvature square corrections and
higher derivative matter chiral multiplets induces a non-trivial de Sitter
vacuum, even in the absence of superpotentials. This vacuum generically breaks
supersymmetry. We show that the auxiliary fields in the gravity and the chiral
multiples play important roles to generate a potential in supersymmetric higher
derivative theories.
