Online proceedings - EDA Publishing Association

24-26 September 2008, Rome, Italyn . cos ϕ− n0 0r S=n0. cos ϕ0+n11. cos. coswith r P , amplitude reflection coefficient of parallel axe and r S ,amplitude reflection coefficient of perpendicular axe. Paralleland perpendicular axes are defined by the incidence plane.The ellipsometry principle consists of measuring the ratio ofthose two coefficients (p) :with :tanp=rrPSr=tanj . D( Psi ).eϕϕP( Psi ) = et D = dP− dSrSwith d P and d S the phase of the parallel and perpendicularpolarisation axes respectively.This relationship yields simple expression of the refractiveindex :n= sin2⎛ 1 − ρ ⎞2( ϕ ).1 + ⎜ ⎟ . ( ϕ )⎠⎝ 1 + ρ1 0tanBecause only one wavelength measure is needed (632 nm),the decision to mount an ellipsometer in this wavelength hasbeen made. Some results have already been get with thissystem.110(6)(7)(8)measuring the state of polarization after reflection, lightintensity is measured for 4 angles (0°, 45°, 90° and 135°) bythe linear analyser (A) and the photo-detector. Then, analgorithm using the least squares method, can determine thestate of polarization with great accuracy [12],[13].J∑ ( I n , MEASURED− In , MODEL)= 4 n = 1and 2I = A.( k + B ) Cn MODELn +, sinwith, J, the criterion of the least squares method, I MEASURED ,the light intensity measured for 0, 45, 90 and 135°, I MODEL , themathematic function of light intensity, and, A, B and C,respectively the amplitude, phase shift and offset of lightintensity.From (9) and (10), we can find the parameters A, B and C :A =2( I − I ) + ( I − ) 21 32 I 4⎡arctan ⎢⎣ 1B =2( I 2 − I 4)( I − I )3⎤⎥⎦I + I2+ I3+ I4C =+41 Awith I 1 , I 2 , I 3 and I 4 , respectively the optical intensity at 0, 45,90 and 135°.22(9)(10)(11)(12)(13)LASERHe-NePAPhotoDetectorThe ellipticity (E) and the orientation (O) of the polarizationafter reflection can be calculated with the equations below :⎛ minE = arctan⎜⎝ max( I ) ⎞MODREL( I ) ⎟⎟ MODREL ⎠(14)O=angle( max( I ))MODREL(15)MUTTemperatureControllerAs orientation before reflection is oriented at 45°, theparameters D and tan(Psi) are respectively :tan ( Psi ) = tan( O ) and D = 2.E(16)Fig. 4. Optical system of null ellipsometry. P and A are linear polarizer andanalyser respectively. The temperature controller is a Peltier module.Some noise are present on the measures. So, averages (aboutone hundred for each temperature) of polarization parametersare done, for reducing the noise impact.The linear polarizer is fixed at 45°. So the non-polarizedoptical signal emitted by the laser is linearly polarized. Thispolarization state is, next, transforms by the MUT. For©EDA Publishing/THERMINIC 2008 29ISBN: 978-2-35500-008-9