Gibbs–Thomson effect on aluminum doping during trench-filling epitaxial growth of 4H-SiC

Abstract

Diffusion equations were solved to examine how the aluminum concentration in 4H-SiC grown on a trenched substrate is influenced by the Gibbs −Thomson (GT) effect. The GT effect increases or decreases the equilibrium gas-phase concentration of growing species in the vicinity of the top or bottom of the trench, respectively, which results in a part of the incident growing species, excluding the central area of the trench, diffusing inward. After fitting activity coefficient of a conditional constituent AlC in solid solution AlSiC and surface free energy of 4H-SiC, we determined the aluminum fluxes toward the top and bottom in such a way that the flux ratio of aluminum to silicon equals the AlC mole fraction at the top (X s t ) and bottom (X s b ), respectively. Calculated X s b was lower than X s t and almost agreed with the measured X s b in filled trenches, showing the GT effect on AlC being weaker than that on SiC.

Estimation of surface-diffusion length of aluminum-containing species on 4H-SiC (0001)

“…By fitting the standard molar Gibbs free energy (G Al °= −500 kJ mol −1 ), 16) Segal et al reproduced the reported dependences of x in Al x Si 1-x C on growth temperature T g , total pressure, TMA flow rate, and R g 18) up to x = 0.01. 15) This quasi-thermodynamic model has also been used to quantitatively analyze aluminum doping during trench-filling epitaxial growth of 4H-SiC.…”

“…15) This quasi-thermodynamic model has also been used to quantitatively analyze aluminum doping during trench-filling epitaxial growth of 4H-SiC. 16,19) The maximum x analyzed in this study is 5.8 × 10 -5 , 20) which is much less than 0.01. 15) Accordingly, the same model is employed to quantitatively analyze the reported x in Al x Si 1-x C on misoriented (0001) substrates.…”

“…14) Relying on this feature, Segal et al 15) considered the aluminum impurity as a highly diluted solid solution of a conditional constituent AlC in a dominant SiC and characterized it by the activity coefficient γ AlC (=6.5 × 10 8 ). 16) According to Cavallotti et al, 17) the gas-phase reaction mechanism includes trimethylaluminum (TMA) pyrolysis, giving rise to AlCH 3 and monoatomic Al, whereas AlH 2 comes into the reactor via desorption from the growth surface. The quasi-equilibrium pressures of the aluminum-containing species then satisfy the mass-action law equations for the following reactions:…”

“…3, however, decreases over one to two orders of magnitude when C/Si increases from 4 to 6. To discuss this difference, computational fluid dynamics analysis 16) is required because C/Si at growth position is strongly influenced not only by fluid dynamics, but also by the temperature and reactive/nonreactive boundary conditions. 24) In the case of 6H-SiC, λ Si on (0001̅ ) was determined to be one order of magnitude longer than λ Si on (0001).…”

“…Under this condition, aluminum segregation can be observed because segregation coefficient is less than unity. 16,19) An impurity can segregate not only at the surface site, 25) but also at the step-edge 26,27) and kink 28,29) sites. According to Yamamoto et al, 20) the aluminum concentration in 4H-SiC (0001̅ ) decreased with increasing θ.…”