I checked the dependent of coatings properties with the uncertainty in x (amount of Al in Al_x Ga_(1-x) As). The effect is already within the uncertainties in materials parameters we did before and will not be a problem.
G. Cole told us about the variations in Al contents in the coatings. Right now the values are 92% +/- 0.6%.
(92.10, 91.43, 91.34, 91.57, 92.73, 92.67). Although the deviation is small, the Al content does not always hit 92%, but 92+/- sigma%. So I decided to check the effect of x on the optimization.
The materials properties that change with x are heat capacity, alpha, beta, heat conductivity and n. The values of those as functions of x can be found on ioffee except n. So I looked through a couple of sources ( rpi, sadao) to get n as a function of x, (Note: E0 and D0 are in eV, they have to be converted to Joules when you calculate chi and chi_so). GaAs (nH) has a well defined value ~ 3.48+-0.001, nL has a bit more uncertainty, but it is within the approximated standard deviation of 0.03 . The table below has numbers from the sources. For RPI, I use linear approximation to get nL for x = 0.92 @ 1064nm.
| source |
nL(x=0.92) |
nH |
| G.Cole |
2.977 |
3.48 |
| RPI |
3.00 |
3.48 |
| Sadao |
2.989 |
3.49 |
| |
|
|
The dependent of n on x is about -0.578 *dx. The numbers from RPI and Sadao are about the same. This means that for the error of 0.6% in Al. nL can change by 0.578*0.006 = 0.0035. The number is almost a factor of ten smaller than the standard deviation of nL and nH I used in previous calculation (0.03). For examples,
- x = 0.914, nL = 2.993,
- x=0.92, nL = 2.989
- x=0.926 nL = 2.986 (From Sadao's fit)
This means that the uncertainty in nL/nH (+/- 0.03) we used are much larger than the effect coming from uncertainty in x. This is true for other parameters as well. |