Higher moments of the implanted-ion profiles of bismuth in silicon

Abstract

In this paper, silicon wafers were implanted with bismuth ions ranging from 40 to 360 keV at room temperature. Secondary ion mass spectrometry was used to measure the implanted-ion profiles of bismuth in silicon. The first four moments of the implanted-ion profiles were experimentally determined through least-squares fitting the measured implanted-ion profiles to Pearson distributions. An extension of the Biersack theory up to the fourth order was combined with the Gibbons parabolic fitting formula in making theoretical predictions. A comparison of the measured with calculated values revealed a significant correlation between the calculated and measured values of both the lower (projected range and range straggling) and higher (skewness and kurtosis) moments of the implanted-ion profiles. In addition, the critical energy at which skewness equals zero is defined in this paper. An investigation of ion implantations over the whole range of incident ions reveals that skewness is negative if the incident-ion energy is greater than the critical energy, and vice versa. In addition, the depth profile of lighter ion implantation skews toward the target’s surface at lower incident-ion energies than with heavier ion implantation.