Possible causes of electrical resistivity distribution inhomogeneity in Czochralski grown single crystal silicon

Svetlana P Kobeleva,Vladimir S Berdnikov,Ilya M Anfimov,Tatyana V Kritskaya

doi:10.3897/j.moem.5.1.46315

Abstract

Electrical resistivity distribution maps have been constructed for single crystal silicon wafers cut out of different parts of Czochralski grown ingots. The general inhomogeneity of the wafers has proven to be relatively high, the resistivity scatter reaching 1–3 %. Two electrical resistivity distribution inhomogeneity types have been revealed: azimuthal and radial. Experiments have been carried out for crystal growth from transparent simulating fluids with hydrodynamic and thermophysical parameters close to those for Czochralski growth of silicon single crystals. We show that a possible cause of azimuthal electrical resistivity distribution inhomogeneity is the swirl-like structure of the melt under the crystallization front (CF), while a possible cause of radial electrical resistivity distribution inhomogeneity is the CF curvature. In a specific range of the Grashof, Marangoni and Reynolds numbers which depend on the ratio of melt height and growing crystal radius, a system of well-developed radially oriented swirls may emerge under the rotating CF. In the absence of such swirls the melt is displaced from under the crystallization front in a homogeneous manner to form thermal and concentration boundary layers which are homogeneous in azimuthal direction but have clear radial inhomogeneity. Once swirls emerge the melt is displaced from the center to the periphery, and simultaneous fluid motion in azimuthal direction occurs. The overall melt motion becomes helical as a result. The number of swirls (two to ten) agrees with the number of azimuthally directed electrical resistivity distribution inhomogeneities observed in the experiments. Comparison of numerical simulation results in a wide range of Prandtl numbers with the experimental data suggests that the phenomena observed in transparent fluids are universal and can be used for theoretical interpretation of imperfections in silicon single crystals.

Highlights

The growth of silicon single crystals with homogeneous impurity distributions using the Czochralski technique requires maintaining growth conditions providing for a flat crystallization front (CF), minimum radial temperature gradients at the crystallization front and absence of solutal undercooling of the melt under the crystallization front [1–3]
We studied electrical resistivity distribution maps for 17 wafers cut out at the distance X from the beginning of five boron-doped p-type 1 Ohm·cm (KDB 1) Grade single crystal silicon ingots grown using the Czochralski technique in REDMET type growth plants [14–15]
Except for one wafer cut from the ingot beginning at the edge of the growth cone, all the wafers were quite homogeneous but two inhomogeneity types could be traced from their electrical resistivity distribution patterns: azimuthal and radial

Summary

Introduction

The growth of silicon single crystals with homogeneous impurity distributions using the Czochralski technique requires maintaining growth conditions providing for a flat crystallization front (CF), minimum radial temperature gradients at the crystallization front and absence of solutal undercooling of the melt under the crystallization front [1–3]. This problem becomes increasingly complex with an increase in the crystal diameter. The aim of this work is to study the homogeneity of electrical resistivity distribution in Czochralski grown silicon single crystals and to analyze the causes of various inhomogeneity types on the basis of crystal growth physical simulation data

Materials and experimental

Results and discussion

Conclusion