Optical constants of lithium fluoride in far ultraviole

Roessler, D. M.

Walker, W. C.

English

NASA Technical Reports Server

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Optical Constants of Lithium Fluoride 
in the Far Ultraviolet* 
D. M. Roessler and W. C. Walker 
Department of Physics 
University of California 
Santa Barbara, California 93106 
I 4 
Lithium Fluoride is a very useful material for ultraviolet 
work because of its large band-gap. During research into the 
electronic spectrum of crystalline lithium fluoride, the optical 
parameters, n and k, were obtained in the course of the data 
analysis. Although the refractive index has been measured accu- 
rately in the transparent region (for example by Gyulai (1) and 
Schneider ( 2 ) ,  very few data are available beyond the transmission' 
limit at 12 ev. 
In the present work the near-normal-incidence reflectance of 
freshly cleaved crystals of lithium fluoride was measured from the 
near ultraviolet to 28 eV. The values of n and k were computed 
from the reflectivity, r, (where the ratio of the reflected and 
"Work supported by the National Aeronautics and Space Administration 
https://ntrs.nasa.gov/search.jsp?R=19670008807 2020-03-16T18:56:55+00:00Z
c 
. 
2 i n c i d e n t  l i g n t  i n t e n s i t i e s  i s  r ) through the ' expres s ions  
1 - r  2
n =. . 
2 1 + r - 2 r  cos 8 
2 r  s i n  8 
1 + r - 2 r  cos 8 ( 2 )  2 
k =  
The angle ,  8 ,  i s  t h e  absolu te  phase change on r e f l e c t i o n  and i s  
related t o  t h e  r e f l e c t i o n  spectrum through a Kramers-Kronig i n t e g r a l  
transform. A detailed d iscuss ion  of t h e s e  r e l a t i o n s h i p s  and t h e  
computation of 8 has  been given elsewhere (38 4, and references 
t h e r e i n ) .  
The e r r o r  involved i n  t h e  computation of 8 ,  which re l ies  
on an approximation procedure,  becomes important near  t h e  high 
energy l i m i t  of t h e  r e f l e c t a n c e  data. The va lues  of n and k are 
t h e r e f o r e  presented only  as f a r  as 25 e V .  B e l o w  t h i s  e n e r g y ' t h e  
primary source of u n c e r t a i n t y  a r i s e s  from t h e  experimental  determin- 
a t i o n  of  t h e  r e f l e c t a n c e .  Errors  i n  t h e  measurements themselves 
are less than 5% b u t  it i s  more d i f f i c u l t  t o  estimate how good 
t h e  c r y s t a l  surfaces w e r e .  The d a t a  given i n  Table 1 are from 
su r faces  g iv ing  t h e  h i g h e s t  r e f l e c t a n c e  a t  t h e  1 2 . 8  e V  exc i ton  
peak (about 40%), s i n c e  any sur face  contamination o r  d e f e c t s  tend 
t o  reduce u l t r a v i o l e t  r e f l e c t a n c e  s t r u c t u r e .  I n  practice a l l  the 
c r y s t a l s  w e r e  ob ta ined  from t h e  Harshaw Chemical Company, and 
f r e s h l y  cleaved su r faces  var ied  on ly  about 5% i n  peak r e f l e c t a n c e .  
- 2 -  
c 
The i n t e r v a l s  i n  t h e  photon ene rg ie s  w e r e  chosen so as t o  
de f ine  t h e  r e f l e c t a n c e  curve s u f f i c i e n t l y  w e l l  f o r  t h e  K r a m e r s -  
Kronig a n a l y s i s .  There i s  some v a r i a t i o n  i n  t he  l i t e r a tu re  i n  
the  use of ' k '  a s  a measure of absorpt ion;  i n  t h i s  work it rep- 
resents t h e  absorpt ion index, and i s  r e l a t e d  t o  the absorp t ion  
c o e f f i c i e n t ,  0 1 0  through t h e  expression Q = 477k/X. The s p e c t r a l  
v a r i a t i o n  of n and k i s  shown i n  Fig.  1. The e l e c t r o n i c  t r a n s i t i o n s  
r e spons ib l e  f o r  t h e  observed s t r u c t u r e  w i l l  be d iscussed  elsewhere.  
1. Z .  Gyulai, Z .  Physik, 46, 80 (1927) .  
2. E.  G. Schneider, Phys. R e v . ,  - 49, 341 (1936). 
3. D. M. Roessler,  B r i t .  J. A p p l .  Phys., 16, 1119 ( 1 9 6 5 ) .  
4. D. M. Roessler, B r i t .  J. Appl .  Phys., 17, 1313 (1966). 
TABLE CAPTION 
Table I Optical  cons tan ts ,  n and k,  of bu lk  l i th ium f l u o r i d e  
a t  300'K i n  t he  range 7 - 25 eV. 
~ 13 .20 
13.25 
13.30 
i 13.35 
I 13.40 
1 13.45 
I 13.50 
7.00 
8.00 
9.00 
10.00 
10.50 
11.00 
11.25 
11.50 
11.75 
12.00 
12.20 
12.30 
12.40 
12.50 
12.60 
12.65 
12.70 
12.75 
12.80 
12.85 
12.90 
12.95 
13.00 
13.05 
13.10 
1.46 
1.49 
1.53 
1.60 
1.67 
1 .77  
1.84 
1.94 
2.08 
2.28 
2.51 
2.68 
2.93 
3.34 
2.89 
2.57 
2.24 
1.92 
1.64 
1.42 
1.26 
1.13 
1.04 
0.97 
0 . 9 1  
0 . 0 0  0 .81  
0.80 
1.20 
1.10 
1.01 
0.92 
0.84 
0.76 
0.67 
0.58 
0.50 
0.43 
0.42 
0.46 
0 .52  
0.56 
0 . 5 9  
0.62 
0.64 
0.68 
0 . 7 1  
0.72 
0.73 
0.74 
0.74 
0.73 
0 .71  
0 . 0 0  
0 .00  0.80 
0.80 0 .00  
0.00 0 .81  
0 .00  0.82 
0.00 0.84 
0 .00  0.88 13.55 
0.04 13.60 0.95 
0 :1 13.65 1.05 
0.23 13.70 1.15 
0.33 
0.48 
13.75 
13.80 
1.24 
1.29 
1.17 13.85 
13.90 
1 . 3 1  
1.32 1.90 
2.08 13.95 1.32 
2.19 14.00 1.32 
2.20 14.10 1.32 
2.13 14.20 
14.30 
1.30 
1.27 2.02 
1.90 14.40 1.25 
1.22 14.50 1.77 
1.64 14.60 1.19 
1.17 1.53 14.70 
1.43 14.90 1.12 
13.15 0.84 1.33 I 15.10 1.08 0.68 
I 
n 
I 
15.30 
15.50 
15.70 
15.80 
15.90 
16.00 
16.10 
16.20 
16.40 
16.90 
17.30 
17.40 
17.50 
17.60 
17.70 
18.00 
18.30 
18.40 
18.50 
18.60 
19.00 
19.50 
20.00 
1 .04  
1.00 
0.98 
0.99 
1.02 
1.06 
1.09 
1 .12  
1.16 
1.20 
1 .19  
1.18 
1.16 
1.14 
1.13 
1.11 
1.13 
1.14 
1.15 
1.17 
1 .19  
1 .21  
1.20 
0.64 
0.59 
0.52 
0.47 
0.42 
0 .41  
0.39 
0.39 
0.40 
0.47 
0 .51  
0.52 
0.53 
0.52 
0.52 
0.48 
0.45 
0.44 
0.44 
0.44 
0.47 
0.53 
0.58 
20.50 
2 1  .oo 
21.40 
21.60 
21.80 
22 .oo 
22.20 
22.40 
22.60 
22.80 
22.90 
22.95 
23.00 
23.05 
23.10 
23.20 
23.30 
23.40 
23.60 
23.70 
24.00 
24.50 
25.00 
1.18 
1.14 
1.08 
1.04 
0.99 
0 . 9 1  
0.80 
0.70 
0.62 
0.55 
0 . 5 1  
0.50 
0.48 
0.47 
0.46 
0.45 
0.44 
0.43 
0.43 
0.42 
0.43 
0 .44  
0.47 
0.65 
0.73 
0.80 
* 0.84 
0.88 
0.93 
0 .94  
0 . 9 1  
0.87 
0 . 8 1  
0.78 
0.76 
0.74 
0.72 
0.70 
0.66 
0.62 
0 .59  
0.56 
0.50 
0.42 
0 . 3 1  
0.23 
FIGURE CAPTION 
Figure 1 Spectral dependence of the optical parameters, n and k, 
obtained from a Kramers-Kronig inversion of reflectance 
data. 
. . . .  
e . 
I 
0 
rc> 
\ 
\ 
I 
\ 
\ 
/’ 
I .\ 
4-=- 
-c--- ---- 
-+ ---0- 
L 1 I I I - m cu 
n 
> 
0 
3 


Optical Constants of Lithium Fluoride in the Far Ultraviolet

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