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In this paper, we analyze a hybrid Heterogeneous Cellular Network (HCNet) framework by deploying millimeter Wave (mmWave) small cells with coexisting traditional sub-6GHz macro cells to achieve improved coverage and high data rate. We consider randomly-deployed macro base stations throughout the network whereas mmWave Small Base Stations (SBSs) are deployed in the areas with high User Equipment (UE) density. Such user centric deployment of mmWave SBSs inevitably incurs correlation between UE and SBSs. For a realistic scenario where the UEs are distributed according to Poisson cluster process and directional beamforming with line-of-sight and non-line-of-sight transmissions is adopted for mmWave communication. By using tools from stochastic geometry, we develop an analytical framework to analyze various performance metrics in the downlink hybrid HCNets under biased received power association. For UE clustering we considered Thomas cluster process and derive expressions for the association probability, coverage probability, area spectral efficiency, and energy efficiency. We also provide Monte Carlo simulation results to validate the accuracy of the derived expressions. Furthermore, we analyze the impact of mmWave operating frequency, antenna gain, small cell biasing, and BSs density to get useful engineering insights into the performance of hybrid mmWave HCNets. Our results show that network performance is significantly improved by deploying millimeter wave SBS instead of microwave BS in hot spots.