Primary energy consumption is one of the key drivers of global CO2 emissions that, in turn, heavily depends on the efficiency of involved technologies. Either improvement in technology efficiency or the expansion of non-fossil fuel consumption requires large investments. The planning and financing of such investments by global policy makers or global energy firms require, in turn, reliable measures of associated global spread and their evolution in time, at least from the point of view of the principles for responsible investment (PRI). In this paper, our main contribution is the introduction of index measures for accessing global spread (that is, measures of inequality or inhomogeneity in the statistical distribution of a related quantity of interest) of technology efficiency and CO2 emission in primary energy consumption. These indexes are based on the Gini index, as used in economical sciences, and generalized entropy measures. Regarding primary energy sources, we consider petroleum, coal, natural gas, and non-fossil fuels. Between our findings, we attest some stable relations in the evolution of global spreads of technology efficiency and CO2 emission and a positive relation between changes in global spread of technology efficiency and use of non-fossil fuel.