The deployment of femtocells in a conventional cellular network is a promising way to increase network capacity, whereas the main bottleneck is the interference between and within tiers. Previous work proposed channel splitting and F-ALOHA to manage the cross-tier and co-tier interference, respectively. However, such spectrum allocation scheme is not efficient given the often scenarios where part of the macro-tier spectrum is vacant but the femto-tier spectrum is overused. In this paper, a cognitive spectrum access scheme is proposed, where femtocells can access both femto-tier and macro-tier spectrum with certain probabilities, to increase the area spectral efficiency (ASE). The closed-form expressions of the optimum spectrum access probabilities in maximizing the ASE are derived for two scenarios where macrocell base stations (MBSs) are modeled as Poisson point process (PPP) and periodic grid. Analytical results reveal that for most cases, the ratio between the optimum probabilities for femtocells to access the femto-tier and macro-tier spectrum is equal to the ratio between the number of subchannels in the femto-tier and idle macro-tier spectrum. Simulation results show that with both models, the proposed scheme outperforms previous work in terms of the ASE.