Substitutional carbon defects in silicon: A quantum mechanical characterization through the infrared and Raman spectra

Abstract

The infrared (IR) and Raman spectra of eight substitutional carbon defects in silicon are computed at the quantum mechanical level by using a periodic supercell approach based on hybrid functionals, an all electron Gaussian type basis set and the CRYSTAL code. The single substitutional C _s case and its combination with a vacancy (C _s V and C _s SiV) are considered first. The progressive saturation of the four bonds of a Si atom with C is then examined. The last set of defects consists of a chain of adjacent carbon atoms C <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow></mml:mrow> <mml:mi>s</mml:mi> <mml:mi>i</mml:mi></mml:msubsup> </mml:math> , with i = 1-3. The simple substitutional case, C _s , is the common first member of the three sets. All these defects show important, very characteristic features in their IR spectrum. One or two C related peaks dominate the spectra: at 596 cm^-1 for C _s (and C _s SiV, the second neighbor vacancy is not shifting the C _s peak), at 705 and 716 cm^-1 for C _s V, at 537 cm^-1 for C <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow></mml:mrow> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn></mml:msubsup> </mml:math> and C <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow></mml:mrow> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn></mml:msubsup> </mml:math> (with additional peaks at 522, 655 and 689 for the latter only), at 607 and 624 cm^-1 , 601 and 643 cm^-1 , and 629 cm^-1 for SiC <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow></mml:mrow> <mml:mi>s</mml:mi> <mml:mn>2</mml:mn></mml:msubsup> </mml:math> , SiC <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow></mml:mrow> <mml:mi>s</mml:mi> <mml:mn>3</mml:mn></mml:msubsup> </mml:math> , and SiC <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow></mml:mrow> <mml:mi>s</mml:mi> <mml:mn>4</mml:mn></mml:msubsup> </mml:math> , respectively. Comparison with experiment allows to attribute many observed peaks to one of the C substitutional defects. Observed peaks above 720 cm^-1 must be attributed to interstitial C or more complicated defects.