An Analysis of Infrared Spectroscopic Geometries
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Source
Det ctor
0I~r
0ji,
63
y1x
y
6E2
3
63
I
Source
I
Detector
Detector
Transmission
External Reflection
Internal Reflection
Figure 1: Three infrared spectroscopic geometries. The spectroscopic geometry selected has a strong effect on the signal-to-noise ratio (SNR); if the sample is at all anisotropic, it will also have a strong effect on the relative intensities of the observed absorption bands. One purpose of this investigation has been to develop from experiment and from optical theory an understanding of the influences of spectroscopic geometry on SNR and relative band intensity, and to determine what is the optimal geometry to use for a given experiment.
353 Mat. Res. Soc. Symp. Proc. Vol. 477 0 1997 Materials Research Society
CALCULATIONS Relative sensitivity was calculated from expressions given by Chabal and co-workers[l, 2, 3, 4]. AI/Io expressions were calculated as a ratio normalized against AI/Io for Brewster-angle transmission spectrometry. These expressions were then numerically evaluated to provide the data discussed below. For the very small absorbances we are concerned with, it is valid to approximate the absorbance - log - as being proportional to Al. As the signal-to-noise ratio is proportional to A . I0, it can under these circumstances be approximated as AI. For Brewster-angle transmission, (A//Ia) = Wic [cos20BIm(gEd.) + sin-- ,m(a 8 )l (1)
COSlOB I=
los1---
And for s-polarization (Al/Ia)
2w/c Im(Eydy) cosOB(1 + e6)
(2)
While the intensity of absorption in transmission for p-polarized radiation as a function of angle is, more generally
(A/Io) = 27rd
1
Im([2)
( = n cos0 IT,
+ T,
n
±T
6
(3)
where 2 2 - (n/n 3) sin 0)1/2 2 2cos0(1 (n3 /n) + .1 - (n/n 3 )2 sin20 cos0
(4
Tn=
(5)
C(n3/n) +
COS 0
and n =E For external reflection: (AI/Io)~
/c
=
(AI/Io)P
SI•IIm (g .,d .)+ 1,.
.,-) Ira (jd,)_
(6 (6)
16V cos 0 [lezl (AI/Io)8 =
w/•
Iylm(Eydy)
(7)
where the electric field intensities I_ and I, are defined as
_
4E cos 2 0 [(e0/0) sin20 - 1] 2 EI E6 [(•+ 6 ± 68)/68) sin2 0 _ 1 2 'v cos 0 (Ev/ 3) sin 4 6 EV=6-
[(v+Es+)/6s)sin 2 0_1
I= •"- _
354
2
0
(8) ( (9) (10)
where -, is the dielectric constant of the substrate, 6, that of the vacuum, and 6x, ey, and 6c are those of the dielectric film in the x, y, and z coordinates. In internal reflection,
w/c V• Cos 0 LI.I (Al/)8 W/C
J2
1
~IyIm(44)
(2)
mo
-s V'loC where -
I..=
468cos 2 0 [(68/65) sin 2 2_] 8 - 6E [(R8 + e")/ev) sin 04e-cos 2 0 (E'/6) sin2 0 [(65 +6)/s) sin2 0-1 68E468 cos 2 0 IV=
68
1
(13) (14) (15) 1
The optical constants used were 68 - 11.56 for silicon, E' = 1 for air, and n - 1.5 - 0.1i for the dielectric film. EXPERIMENTAL Si(111) surfaces were prepared by cleaning the silicon in 1:3 (v/v) H 2 0 2 /H 2 SO 4 (J.T. Baker, CMOS electronic grade) for 10 minutes, followed by an etch in 40% (w/w) aqueous NH4 F (Ashland, cleanroom grade) for 15 minutes. Spectra were obtained in internal reflection and Brewster-angle transmission (73.80 for
silicon) modes using the same 50-refl
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