Cognitive radio and small cells are the promising techniques to minimize energy consumption and satisfy the exponentially increasing data rates for the heterogeneous cellular network (HCN). In this paper, a theoretical framework is developed to calculate the outage probability of the HCN based on the opportunistic utilization of the traditional cellular bandwidth and television white space (TVWS) for the cognitive femto base stations. This work investigates overlay, underlay, mixed overlay-underlay based two tiers cognitive HCN. It also investigates the impact of the TVWS in the overlay-TVWS mixed spectrum sharing technique (SST). Tools from stochastic geometry are used to model cognitive HCN. Furthermore, the tier selection probability, average ergodic rate, area spectral efficiency (ASE), and energy efficiency (EE) of the HCN are also calculated for different SSTs. Numerical results show that mixed SST achieves a significant reduction in tier outage probability and total outage probability as compared to underlay and overlay techniques alone. It is also demonstrated that compared to the traditional single tier network, cognitive based HCN can improve the total ASE and EE of the order of \(10^{2}\) and 10, respectively.