Internal Gettering in Silicon: Experimental and Theoretical Studies Based on Fast and Slow Diffusing Metals

An in depth evaluation of internal gettering effectiveness in Si wafers has been run based on iron and nickel intentional contamination followed by minority carrier recombination centers measurements. The paper demonstrates the relevance of oxygen clusters density and stability as well as thermal treatment cooling phase conditions on gettering mechanism activation. A theoretical model is proposed taking into account both homogeneous and heterogeneous nucleation of metals at oxygen clusters and surface sites. Introduction Evaluation of silicon wafer gettering efficiency is of great importance for practical purposes like new product or process developments and yield optimization [1,2]. For the same reasons, models of gettering processes are also receiving increasing attention due to the interest in computer simulation as a tool for a preliminary evaluation and better understanding of gettering mechanisms as well as reduction of cost effective experimental trials. This work covers both these aspects of gettering studies and focuses on internal gettering, that is gettering effects mostly depending on characteristics and distribution of oxygen clusters. The paper will investigate gettering behavior in case of two metals, nickel and iron, chosen for their different characteristics of fast and slow diffuser, respectively. Contamination level has been set in the range representative of the present device manufacturing cleanliness levels. This study will focus on the effect of thermal treatments, that is oxygen cluster characteristics, and final cooling. Baselines of the relaxation gettering model here proposed will be described in a dedicated section and then computer simulation results will be compared to experimental data in the result discussion section. Theoretical model Gettering kinetics in silicon has been modeled taking into account the following elements: (a) Metal diffusion inside the wafer (Fick's equation); (b) Formation of supercritical metal silicide clusters: (b1) from supersaturated metal solution. Using a classical nucleation model, this homogeneous process can be described by a nucleation rate of the form ( ) ( ) ( ) [ ] kT G kT C f D T C J Mo o M M M M M o / exp , * 2 / 1 ∆ − ⋅ = − σ ρ , (1) with CM , ρM metal concentration in solution and in precipitate, DM diffusivity, ( ) * / ln M M M C C kT f ⋅ = (CM is the solubility),σo precipitate-silicon interface energy and ( ) [ ] 2 3 * 3 16 M M o Mo f G ρ πσ = ∆ critical energy in a spherical cluster approximation. σo can be estimated by a best fit of metal nucleation data. 2 Title of Publication (to be inserted by the publisher) (b2) around oxygen precipitates. The heterogeneous nucleation rate is similar to Eq.1, with ρM replaced by the density. Ne of oxygen precipitates and σo replaced by a different value σe, which can be estimated by a best fit of available experimental data (usually nucleation is favoured on the heterogeneous site, so σe<σo). (b3) on the wafer surface. The surface nucleation rate can be expressed as ( ) ( ) [ ] kT G C D J T C J Ms Ms M so M s / exp , * ∆ − = , (2) with CMs as the surface metal concentration. A best fit of experimental data shows that Jso depends only on the surface characteristics while the critical energy can be treated as a linear function of temperature. (c) Growth of metal silicide clusters. Since metals diffuse fast in silicon it is necessary to take into account that precipitate growth occurs together with cluster formation, so the metal flux, which is usually expressed as 4 π DM (CM CM), must be written in the more complete form ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ] ∫ ∫       − − = t t t M M M o M M M M o dt dt t C t C t D t J t C t C t D t Q 0 2 / 1 ' * * ' ' ' ' ' ' ' ' ' ' 2/ 4 ) ( ρ π , (3) where the inner integral is the radius at time t of the metal precipitates formed at time t'. The most relevant feature of this approach is the analysis of metal nucleation kinetics, which allows a more accurate analysis of metal gettering phenomena, since most model based only on precipitate growth have no time-lag and tend to overestimate the gettering effect. Experimental 150 or 200 mm CZ wafers, boron doped with resistivity in the range of 5-15 ohm-cm and oxygen content in the range of 11-12 ppma or 14-15 ppma, have been used for this study. A group of P/P epi wafers has been also included, previously pretreated to have oxygen precipitate density of 3E10 cm-3. Wafers were contaminated with a controlled amount of metal, iron or nickel, in acid solution at two concentration levels targeted after drive-in to 1E13 cm and 1E12 cm. Contamination was deposited on polished silicon surface as a drop of controlled diameter in the center and R/2 positions. Ad hoc thermal treatments have been applied according to Table 1. Drive in duration and temperature (1000°C for Fe, 800°C for Ni) were fixed taking into account the different diffusivity of the two examined metals and targeted to reach a concentration profile uniform in depth. In some cases, oxide clusters stabilization and growth steps were added before the drive in. Care has been taken to control cooling ramp rate as relaxation gettering occurs when supersaturated metal concentration is present. Low temperature treatments were also applied at the end of the thermal cycles on sample subsets in order to test the effect of a prolonged treatment in supersaturation conditions. TREATMENT DESCRIPTION TTA 1000oC, 1h TTB 1000oC, 1h; ramp-down 1000-600oC, -4oC/min TTC 800oC, 40 min; ramp up 800-1000oC, 4oC/min;1000oC, 1h; ramp-down 1000-600oC, -4oC/min TTD 800oC, 40 min; ramp up 800-1000oC, 4oC/min;1000oC, 2.5h; ramp-down 1000-600oC, -4oC/min; followed by TTC LTT (Fe)/(Ni) 600 or 400oC, 2h / 300 or 400oC, 1h Ni drive-in 800 oC, 7 min