Mobile traffic demand has been increasing exponentially over the last few years and forecasts show that this trend will continue in the foreseeable future. As a result, operators are forced to densify and upgrade their networks to meet this demand. This has created concerns, such as increasing greenhouse gas emissions, high capital expenditures, and associated energy costs. This paper uses tools from stochastic geometry to analyze and formulate energy-efficient deployment strategies for multi-tier heterogeneous networks (HetNets) using various user association schemes. We use simple approximations to combine the required base station (BS) density and associated transmit power per tier subject to both coverage probability and average user rate constraints. In this paper, this combination is called the deployment factor and it can be expressed in closed form for unbiased HetNets. We then formulate area power consumption (APC) minimization framework, which optimizes the deployment factor to derive specific optimal BS density and transmit power values. Furthermore, we perform a comprehensive study of the effect of biasing on the APC performance of biased HetNets. Our results show that for HetNets using the maximum average-biased-received-power association scheme, significant energy savings are possible with appropriate biasing.