Analytical expressions which permitted a direct determination of the equilibrium concentrations of self-interstitials and vacancies, on the basis of measured impurity diffusion profiles, were deduced from the equations for kick-out and Frank-Turnbull diffusion mechanisms. In order to deduce the equilibrium point-defect concentrations, it was necessary only to measure the diffusion profiles. As a test, the equilibrium vacancy concentration in Si was determined by means of Pt diffusion. A value of about 4.4 x 1013 /cm3 at 770C was deduced for the equilibrium vacancy concentration. The vacancy diffusion coefficient was estimated to be equal to 2.2 x 10-11cm2/s. The rate of generation of vacancies by internal sources appeared to be lower than 10-5/s at 770C.
H.Zimmermann, H.Ryssel: Physical Review B, 1991, 44[16], 9064-7
Diffusion of 35S in Si as a Function of Temperature
T (K) | D (cm2/s) |
1671 | 1.8 x 10-7 |
1633 | 1.3 x 10-7 |
1590 | 9.2 x 10-8 |
1554 | 6.8 x 10-8 |
1516 | 4.7 x 10-8 |
1484 | 4.0 x 10-8 |
1463 | 3.1 x 10-8 |
1432 | 2.2 x 10-8 |
1380 | 1.2 x 10-8 |
1328 | 7.1 x 10-9 |
Table 203
Diffusivity of Sb in Si
Temperature (C) | D (cm2/s) |
1100 | 2.21 x 10-14 |
1000 | 1.28 x 10-15 |