Evaporated Ga Amount Under the Consideration of Collision Inside the Crucible

The evaporated Ga amount with particle collisions can be obtained from the integration of the evaporation rate W in Eq. (8), with the function of receding length, over time. To integrate the evaporation rate for the infinitesimal change of length over time, the equation of receding length that is associated with time is necessary. However, K_{c} depends on the receding length that varies over time and there is no explicit solution for the integration of W over time. Therefore, the equation between the receding length L and time was derived numerically by the fitting data for each 1 h step of evaporation.

The fitting line for distillation for 16 h is, L = -0.0002t^{3} + 0.0065t^{2} - 0.078t, from the initial parameters of r = 0.95 cm, T = 1360 K and P = 4.50E-05 atm. The fitting line for growth for 400 h is, L = 10^{-9}t^{2} - 2 x 10^{-6}t + 0.006, from the initial parameters of r = 0.84 cm, T = 1160 K and P = 2.52E-07 atm. The equations of receding length for distillation and growth are shown in Figs. 6 and 7.

Fig. 6 Receding length for 16 h distillation as a function of time

Fig. 7 Receding length for 400 h growth as a function of time

The amount of evaporated Ga for both distillation and growth at whit the presence of collisions are summarized in Table 2 with the comparison to the evaporated amount at free evaporation. Since the crucible was tilted from vertical about 26°, the surface are for derivation of amount was projected to 3.14 cm^{2} from 2.82 cm^{2}.

The estimated result of 28.9 g was very close to the observation of 25 g. The difference of 3.9 g is because the consideration regarding the 26° tilt of Ga source crucible was not applied. The particles on the 90% of melt surface more probably

Time

(h)

Temperature

(K)

Ga

saturation

vapor

pressure

(atm)

Evaporation rate (kg/cm^{2 }• h)

Evaporated Ga without collision (g)

Evaporated Ga with collision (g)

Distillation

16

1360

4.50E-05

9.12E-02

45.8

23.2

Growth

400

1160

2.52E-07

1.76E-03

22.1

5.7

Sum

67.9

28.9

collide with the crucible wall and condense back to the melt surface in the tilted crucible. Therefore, smaller amount of Ga was evaporated in the observation than calculation. The degree of contribution by condensation in tilted port to the evaporation amount will be discussed in a follow-up paper.