Stopping characteristics of boron and indium ions in silicon
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CTION OF PLASMA, PARTICLE BEAMS, AND RADIATION WITH MATTER
Stopping Characteristics of Boron and Indium Ions in Silicon D. S. Veselov* and Yu. A. Voronov National Research Nuclear University MEPhI, Kashirskoe sh. 31, Moscow, 115409 Russia *e-mail: [email protected] Received April 18, 2016
Abstract—The mean range and its standard deviation are calculated for boron ions implanted into silicon with energies below 10 keV. Similar characteristics are calculated for indium ions with energies below 200 keV. The obtained results are presented in tabular and graphical forms. These results may help in the assessment of conditions of production of integrated circuits with nanometer-sized elements. Keywords: theory of stopping of accelerated ions, nuclear stopping, electron stopping, boron, indium, mean range, standard deviation, impurity distribution. DOI: 10.1134/S1063778816140155
INTRODUCTION The progress in modern semiconductor electronics is governed by the Moore’s law, which states that the number of elements in an integrated-circuit chip should increase, while the minimum features (design rules) should get smaller [1, 2]. The reduction in feature size inevitably leads to a reduction in the depth of impurity implantation. The current 20–30 nm design rules imply the same (or lower) depth of impurity implantation. The implantation of accelerated ions is currently the basic processing method for semiconductor doping. The impurity distribution in a semiconductor subjected to ion implantation is characterized, in a first approximation, by a Gaussian function [3, 4]. This function is defined unambiguously by the following two parameters: the mean range and its standard deviation. These parameters are calculated on the basis of the theory of stopping of accelerated ions. The mean ranges and their standard deviations for various ions with energies falling within the interval of 20–200 keV are found in the scientific literature [3, 5, 6]. Data for lower energies and the stopping characteristics of indium are lacking. At the same time, the channel and the drain–source regions of MOS transistors with submicron design rules are often doped today with indium and boron with energies no higher than 10 keV. The aim of the present study was to calculate the range of boron ions with energies below 10 keV and the range of indium ions with energies below 200 keV in silicon. CALCULATION OF THE RANGE OF INDIUM AND BORON IONS IN SILICON The range of ions in matter is determined based on the energy losses of an ion in a solid body. This param-
eter is numerically equal to the ion energy loss per unit path length. The energy losses of an ion are commonly expressed in terms of the stopping power, which equals the ion energy loss per unit path length per a single atom of matter. The total energy loss results from the interaction of ions with nuclei of atoms of matter and their electron shells. It is commonly believed that the interactions with nuclei (nuclear stopping) and electrons (electron stopping) are independent. The total energy loss is
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