Search for direct band gap in group IV semiconductor alloys and quantum wire structures

Interest in creating direct band gap group IV, semiconductor, particularly silicon based structures, has been stimulated with the discovery of the photoluminescence in electrochemically etched porous silicon. This work examines, theoretically, the possibilities of the existence of a direct band gap in group IV alloys and quantum wire structures using empirical pseudopotential method (EPM) for the calculation of the energy band structures.; The virtual crystal approximation has been used and the spin-orbit interaction has been taken into account for Ge, and {dollar}alpha{dollar}-Sn. The band structures for {dollar}rm Sisb{lcub}1-x-y{rcub}Snsb{lcub}x{rcub}Csb{lcub}y{rcub}{dollar}, {dollar}rm Snsb{lcub}1-x{rcub}Csb{lcub}x{rcub}{dollar}, {dollar}rm Gesb{lcub}1-x-y{rcub}Snsb{lcub}x{rcub}Csb{lcub}y{rcub}{dollar}, {dollar}rm Gesb{lcub}x{rcub}Csb{lcub}1-x{rcub}{dollar} and EPM band structures for {dollar}rm Sisb{lcub}x{rcub}Snsb{lcub}1-x{rcub}{dollar}, {dollar}rm Gesb{lcub}x{rcub}Snsb{lcub}1-x{rcub}{dollar}, {dollar}rm Sisb{lcub}1-x-y{rcub}Gesb{lcub}x{rcub}Snsb{lcub}y{rcub}{dollar}, and {dollar}rm Sisb{lcub}1-x-y{rcub}Gesb{lcub}x{rcub}Csb{lcub}y{rcub}{dollar}, have been computed for the first time. The band structure calculations show that a direct band gap of as much as 2.87 eV may be possible in {dollar}rm Snsb{lcub}x{rcub}Csb{lcub}1-x{rcub}{dollar} and {dollar}rm Sisb{lcub}1-x-y{rcub}Snsb{lcub}x{rcub}Csb{lcub}y{rcub}{dollar} alloys. Direct band gap values of 0.688 eV, 0.735 eV, and 2.26 eV are also predicted for {dollar}rm Gesb{lcub}x{rcub}Snsb{lcub}1-x{rcub}{dollar}, {dollar}rm Sisb{lcub}x{rcub}Snsb{lcub}1-x{rcub}{dollar}, {dollar}rm Gesb{lcub}1-x-y{rcub}Snsb{lcub}x{rcub}Csb{lcub}y{rcub}{dollar} alloys respectively. The effect of hydrostatic pressure and strain on the alloy band structure is also examined.; The EPM results also show that Si quantum wires in size regimes from 7.7 A to 40 A have direct band gap from 3.42 eV down to 1.3 eV in excellent agreement with the recently published tight binding, and density functional calculations. The band gap essentially approaches the bulk indirect limit beyond 60 A. The band structures of Ge and {dollar}alpha{dollar}-Sn quantum wires are computed for the first time, and direct band gap values of 1.56 eV and 0.773 eV are predicted for Ge and {dollar}alpha{dollar}-Sn quantum wires respectively. It was also found that the wire size window, over which the band gap is direct, shows a downward shift, as one goes down the group IV materials in the periodic table. {dollar}alpha{dollar}-Sn was found to become indirect below 32 A and it essentially approaches the bulk limit around 90 A wire size. Ge band gap was also found to go through a transition as a function of wire size; going from the bulk indirect gap to direct and finally becoming indirect again below 12 A wire size as the wire size was decreased. This can be attributed to the decrease in the {dollar}Gamma{dollar} point bulk conduction band electron effective masses in Si, Ge, and {dollar}alpha{dollar}-Sn, going down the group IV elements.