Orientation dependent complex bandstructure of Si<inf>1−x</inf>Ge<inf>x</inf> alloys

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Over the last decade, Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> has increasingly been used as a channel material in MOSFETs. Though many studies have dealt with the real bandstructure of Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> , the effect of germanium mole fraction x on complex bandstructure has been unexplored. Complex bands fundamentally determine band to band tunneling (BTBT) current. For example, using the orientation dependent complex bandstructure of silicon, it has been shown that the BTBT current in the [110] direction is an order of magnitude larger than that along the [100] direction. BTBT contributes significantly to off-current I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</sub> in conventional MOSFETs, via the mechanism of gate induced drain leakage (GIDL). Additionally, BTBT determines the on current I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</sub> in tunneling FETs, which have been suggested as next generation devices. Further, BTBT is more dominant in Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> than silicon, owing to a narrower bandgap. In this work, we determine the orientation dependent complex bandstructure of Si <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-x</sub> Ge <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> along common crystallographic directions and predict trends in BTBT current.