The universal tight binding method based on sp 3 s * basis functions is used to calculate the electronic structure of the ternary alloy Si 1ÀxÀy Ge x C y . The dependences of the fundamental band gaps ðEðGÞ, EðDÞ, EðLÞ, and EðXÞÞ are obtained and investigated for small concentrations of carbon (0 y 0.05). It is found that the presence of carbon in the alloy Si 1ÀxÀy Ge x C y results in a very significant change (i.e., reduction) of the alloy bond length with a small change of the energy band gaps. The energy band gap increases upon adding carbon to the strained alloy. However, the energy band gap decreases upon adding carbon while keeping the alloy lattice matched to the substrate Si. The calculated band gaps are in good agreement with the limited available experimental data and ab initio results.The crystalline silicon-germanium-carbon (c-Si 1ÀxÀy Ge x C y ) alloys are promising semiconductor candidates for heterojunction devices. Incoporation of a low carbon concentration into substitutional sites of SiGe might be able to relieve the inherent strain of the SiGe layers grown on a Si substrate [1][2][3][4][5] while changing the band gap energy. This prospect would allow for tuning the lattice constant and band gap independently by adjusting the composition ratios and offers an additional degree of freedom for band gap engineering, which is not attainable by standard Si technology or SiGe heteroepitaxy [6]. However there are limitations on achieving complete substitution due to the low solubility of C in Si and the tendency of carbon to form silicon carbide, or C-C bonds [5].The energy band gaps and the lattice constants of the alloy are important parameters for device design. However, very little theoretical or experimental work on the alloy Si 1ÀxÀy Ge x C y has been reported. Limited experimental data is available with large intervals between the sampling points preventing the extraction of reliable information for low carbon concentrations [1]. Futhermore, some experimental reports suggest a decrease in the energy band gap if the C content is increased [7][8], but others suggest an increase in the energy band gaps [2][3][4]. Different theoretical methods [1,[9][10][11] or specimen preparation techniques [12] can lead to significantly different results. With this situation as background, the present work aims to provide reliable band gap calculations. The full electronic band structure of the alloy Si 1ÀxÀy Ge x C y is determined within the UTB method [13] based on sp 3 s* basis functions including the first nearest neighbor interactions, in which the excited s-like state s * is