Step-edge and kink segregation models for analysis of reported step-velocity dependences of carbon concentration in GaN

Abstract

The correlation between step velocity and carbon incorporation during the step-flow growth of GaN was analyzed from the standpoints of the meantime until a carbon atom incorporated at the kink site moves through the step-edge site to the surface site, τ, and the length of time before the carbon concentration at the step-edge site reaches its equilibrium value, τ step . Reported step-velocity dependences of carbon concentration in GaN were successfully reproduced with the assumption of τ ? τ step or τ < τ step . Due to the difficulty in estimating τ step , additional experiments are needed to tell which segregation is dominant for carbon in GaN.

Analysis of step-velocity-dependent concentration of magnesium in GaN based on Burton−Cabrera−Frank theory and step-edge segregation model

“…23) Impurity segregation during MOVPE, on the other hand, has been quantitatively analyzed as a function of step velocity V step in the case of carbon in GaN. 25) Accordingly, in this paper, we first estimate the values of V step on the gently and sharply sloped surfaces and then apply the reported stepedge segregation model 25) to quantitatively analyze the magnesium segregation reported in Ref. 23.…”

“…23) According to the experiments by Benzarti et al, 37) D is 3.0 × 10 −14 cm 2 s −1 at T g = 1100 °C. With this D value, a of 0.30 nm, 25) and Eq. ( 8), we fitted the normalized N s , taking N step /N surf as a parameter.…”

Step-edge segregation model for step-velocity dependences of carbon and oxygen concentrations in GaN layers grown on m-plane GaN

“…As suggested by Šichman et al, 19) residual stress in GaN can influence residual carbon impurity. Considering a large strain around the carbon occupying a gallium site (C Ga ) in GaN (because of the bond length of C Ga being 18%-26% shorter than the Ga-N bond length), 4,[20][21][22] the present authors assumed that the segregation coefficient k of C Ga is less than unity 23) and that the concentration ratio of carbon adatoms to gallium adatoms around step-edge site is about the same as that at the surface site. They rewrote the equation for the step-edge segregation model 24,25) as 23)…”

“…When τ step > τ, on the other hand, the kink segregation model 26,27) applies. If the impurity concentration at the kink site is an equilibrium value of N kink , N is expressed in the kink segregation model as 23)…”

“…(2′). 23) With respect to the m-plane growth, 28) however, the correlation coefficient monotonically increases with N kink [Fig. 2…”