The energy efficiency of ICT has become a major issue with the growing demand of Cloud Computing. More and more companies are investing in building large datacenters to host Cloud services. These datacenters not only consume huge amount of energy but are also very complex in the infrastructure itself. Many studies have been proposed to make these datacenter energy efficient using technologies such as virtualization and consolidation. Still, these solutions are mostly cost driven and thus, do not directly address the critical impact on the environmental sustainability in terms of CO2 emissions. Hence, in this work, we propose a user-oriented Cloud architectural framework, i.e. Carbon Aware Green Cloud Architecture, which addresses this environmental problem from the overall usage of Cloud Computing resources. We also present a case study on IaaS providers. Finally, we present future research directions to enable the wholesome carbon efficiency of Cloud Computing.