We present a rigorous electrical and optical analysis of a highly scaled, graded-base, SiGe heterojunction bipolar transistor (HBT) electrooptic (EO) modulator. In this study, we propose a 2-D electrical model and a 3-D optical model for a graded-base SiGe HBT structure that is capable of operating at a data bit rate of 250 Gbit/s or higher. In this structure, apart from a polysilicon/low doped emitter <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$( \hbox{width} = 90\ \hbox{nm})$</tex></formula> and a strained SiGe graded base <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$( \hbox{depth} = 8.5\ \hbox{nm})$</tex></formula> , a selectively implanted collector (SIC) <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(\hbox{depth} = 26\ \hbox{nm})$</tex></formula> is introduced. Furthermore, at a base-emitter swing of 0 to 1.0 V, this model predicts a rise time of 3.48 ps and a fall time of 0.55 ps. Optical simulations predict a <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\pi$</tex></formula> phase shift length <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$(L_{\pi})$</tex></formula> of 204 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu \hbox{m}$</tex></formula> , with an extinction ratio of 13.2 dB at a wavelength of 1.55 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\mu\hbox{m}$</tex></formula> .
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