A Theoretical and Empirical Perspective of SiC Bulk Growth
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THEORY AND EXPERIMENTAL Vapor Composition In parallel with more detailed modeling of SiC crystal growth, new direct experimental methods for measuring technology optimization should be developed. One of these experimental methods is reconstruction of the vapor composition during crystal growth using the weight/fraction of the remaining carbon from the SiC vapor source sublimation, which can be measured post growth. The basis for this method is as follows. Sublimation of the SiC vapor source can be described using the following reactions:
,K1 = Psi ,K2 = Psi 2c/Psi ,K3 = PSiC2-PSi
SiC(s) = Si(g,l) + C(s) SiC(s) + Si(g,l) = Si 2C(g) 2SiC(s) = SiC2 (g) + Si(g,1)
(1)
Using the constants K1,K2 and K3 to calculate the equilibrium pressures of the vapor components, we can determine the temperature dependence of the ratio of Si to C in the vapor phase, Nsi/Nc: Nsi/Nc = (Psi + 2PSi 2C + Psic 2 ) / (2PSiC 2 + Psi2C).
(2)
This ratio can also be determined post growth by measuring the fraction of carbon, Fc, which remains after the source sublimes: Fc = nc/nsic
=
(Nsi-Nc)/Nsi = I - Nc/Nsi,
(3)
where nc is the number of atoms of the remaining carbon and nsic is the number of SiC molecules in the SiC source sublimed during growth (nsic = Nsi). From Eq. (1) and Eq. (2), the silicon vapor pressure can be expressed using the ratio Nsi/Nc and K 1, K2 and K3: Psi = [(K3 [1 - 2 Ns1/Nc]
) / (K2[Ns5 /Nc - 2
-
1)]0.5
(4)
Thus, using the experimental value of the ratio N5 /Nc, we can determine the silicon vapor pressure from Eq. (4) and from Eq. (1) the Si2C and Si2C vapor pressures during growth. Using this method, we can determine the influence on the vapor composition of such technological parameters as: a) temperature and pressure of argon/nitrogen during growth; b) temperature gradient; c) permeability of the growth cell and d) characteristics of the source material. Additionally, these measurements allow us to estimate the efficiency, E = Nc/nsic = Nc/Nsi, of conversion of SiC vapor source to a crystal during growth. The efficiency depends on the above-mentioned parameters and also on the presence of gases which can increase the fraction of carbon in the vapor phase (e.g., N 2, CO, H2, and hydrocarbons). Figure 1 shows the dependence of Ns/Nc, Fc and the efficiency of conversion of SiC source material to a single crystal, which was calculated based on thermodynamics.
90
2.5
†....... NsilNc - -Fc
2 ...
-E
"".
.......
1.5 1 0.5 0 2300
2400
2500
2600
2700
T, K Figure 1: Vapor composition and efficiency of SiC vapor source conversion where Ns/Nc is the ratio of Si to C in the vapor phase, Fc is the fraction of C remaining after source sublimation and E is the efficiency of conversion of source to bulk crystal. As can be seen from this dependence, efficiency increases with increasing growth temperature. This dependence is in good agreement with our experimental efficiency based on measurements of the remaining molecular fraction of carbon after growth. During our investigation of the influence of various tec
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