Consider the sample covariance matrices of form $W=n^{-1}C C^{\top}$, where $C$ is a $k\times n$ matrix with real-valued, independent and identically distributed (i.i.d.) mean zero entries. When the squares of the i.i.d. entries have finite exponential moments, the moderate deviations for the extreme eigenvalues of $W$ are investigated as $n\to\infty$ and either $k$ is fixed or $k\rightarrow \infty$ with some suitable growth conditions. The moderate deviation rate function reveals that the right (left) tails of $\lambda_{\max}$ is more like Gaussian rather than the Tracy-Wisdom type distribution when $k$ goes to infinity slowly.

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