Piezoelectric FETs (PeFETs) are a promising class of ferroelectric devices that use the piezoelectric effect tomodulate strain in the channel. They present several desirable properties for on-chip memory, such as non-volatility, high-density, and low-power write capability. In this work, we present the first effort to design and evaluate cache architectures using PeFETs. Two key goals in cache design are to maximize capacity and minimize latency. Accordingly, we consider two different variants of PeFET bit-cells - a high-density variant (HD-PeFET) that does not use a separate access transistor, and a high-performance 1T-1PeFET variant (HP-PeFET) that sacrifices density for lower access latency.We note that at the application level, there exists significant heterogeneity in the sensitivity of applications to cache capacity and latency. To enable a better tradeoff between these conflicting design goals, we propose a hybrid PeFET cache comprising of both HP-PeFET and HD-PeFET regions at the granularity of cache ways.We make the key observation that frequently reused blocks residing in the HD-PeFET region are detrimental to overall cache performance due to the higher access latency. Hence,we also propose a cache management policy to identify and migrate these blocks from the HD-PeFET region to the HP-PeFET region at runtime.We develop models of HD-PeFET and HP-PeFET caches using the CACTI framework and evaluate their benefits across a suite of PARSEC and SPLASH-2X benchmarks.We demonstrate 1.11x and 4.55x average improvements in performance and energy, respectively, using the proposed hybrid PeFET last-level cache against a baseline with traditional SRAM cache at iso-area.