A novel technique for measuring reflectivities in the near infrared

Volume 1, number 9

A NOVEL

OPTICS COMMUNICATIONS

TECHNIQUE IN

FOR THE

April 1970

MEASURING

NEAR

REFLECTIVITIES

INFRARED

M. BLI~TTE

Physikalisches lnstitut, University Frankfurt~MaDe, Germany Received 2 March 1970

A new measurement technique for reflectivity R in the near infrared is described. emissivity measurement technique in using only black bodies near room temperature A system is described which delivers directly a signal giving (I-R) in the wavelength about 5it and 25/2 for sample temperatures between 4°K and 400°K.

B l a c k - b o d y light s o u r c e s m a y be u s e d a d v a n t a g e o u s l y f o r s p e c t r o s c o p y in the n e a r i n f r a r e d . P o t t e r and S t i e r w a l t h a v e u s e d s u c h light s o u r c e s a s r e f e r e n c e l a m p s in o r d e r to m e a s u r e the e m i s s i v i t i e s of v a r i o u s s e m i c o n d u c t o r s [1,2]. T h i s t e c h n i q u e r e p r e s e n t s an a l t e r n a t e way to d e t e r m i n e a b s o r p t i o n c o e f f i c i e n t s by k e e p i n g the s p e c i m e n at a f i x e d t e m p e r a t u r e and c o m p a r i n g i t s t h e r m a l e m i s s i o n with that of a b l a c k - b o d y at the s a m e t e m p e r a t u r e . T h e m e t h o d is p a r t i c u l a r l y u s e f u l f o r a n a l y z i n g s e m i c o n d u c t o r s in s p e c t r a l r e g i o n s of v e r y low a b s o r p t i o n . R e f l e c t i v i t y m e a s u r e m e n t s can be o b t a i n e d with an e m i s s i v i t y s p e c t r o m e t e r by m a k i n g a few s i m p l e c h a n g e s in the s e t - u p . A s p o i n t e d out by P o t t e r and S t i e r w a l t an e m i s s i v i t y s p e c t r u m y i e l d s 1 - R f o r o p a q u e s a m p l e s [2]. H o w e v e r , the r e f l e c t i v i t y R at n e a r l y n o r m a l i n c i d e n c e can be m e a s u r e d e v e n f o r t r a n s p a r e n t s a m p l e s by i n s e r t i n g a b l a c k - b o d y behind the s a m p l e , h a v i n g the s a m e t e m p e r a t u r e as the s p e c i m e n . The s c h e m a t i c of the a r r a n g e m e n t is shown in fig. 1. T h e m a i n o p t i c a l c o m p a r t m e n t c o n s i s t s of an e v a c u a b l e and t e m p e r a t u r e - s t a b i l i z e d c h a m b e r with the s a m p l e - h o l d e r H and b l a c k - b o d i e s B. T h e s a m p l e S with p a r a l l e l s i d e s and o p t i c a l l y p o l i s h e d s u r f a c e s is at t e m p e r a t u r e T 1 and r e f l e c t s the i n t e n s i t y R(k) W(k, T2). H e r e W(~, T2) is the r a d i a t i o n d i s t r i b u t i o n a c c o r d i n g to P l a n c k ' s Iaw which is g e n e r a t e d by the b l a c k - b o d y B 2 at t e m p e r a t u r e T2. T h e n , the s a m p l e e m i t s E(;~) W(k, T1) and t r a n s m i t s a p o r t i o n T(k) W(k, T1) c o m i n g f r o m the b l a c k - b o d y B 1 and T 1 b e h i n d the s a m p l e . A c h o p p e r C with h i g h l y r e f l e c t i n g b l a d e s s w i t c h e s the o p t i c a l path b e t w e e n s a m p l e S and B2. A d i f f e r e n c e s i g n a l is finally obtained: 460

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Fig. 1. Schematic for the optical arrangement for r e fleetivity measurements in the near infrared. Sample S and black-body B1 are kept at temperature T1, the blaek-body B2 has the temperature T 2. S(~) = R(k) W(;% T 2) + + (E(~) + T(X)} W(k, T 1) - W(k, T2) . (1) C o n s e r v a t i o n of e n e r g y i m p l i e s :

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(2)

I

Volume 1, n u m b e r 9

OPTICS COMMUNICATIONS

R ( ; t , T ) t h e r e f l e c t a n c e , a n d T ( k , T) t h e t r a n s m i t t a n c e of t h e s a m p l e a t a g i v e n t e m p e r a t u r e and wavelength k. Using eq. (2) we get: S ( k ) = ( 1 - R ) { W ( k , T I ) - W(~,T2)} =(1-R)So(k)

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(3)

Eq. (3) s h o w s t h a t we o b t a i n t h e q u a n t i t y ( l - R ) m u l t i p l i e d b y t h e d i f f e r e n c e of two P l a n c k f u n c tions. T h e i n t e n s i t y So(h) c a n b e o b t a i n e d b y p u t t i n g R = 0, t h a t i s , b y a r u n w i t h o u t s a m p l e , a s i s d o n e in s t a n d a r d e m i s s i v i t y t e c h n i q u e s [2, 3]. A m i r r o r i n s t e a d of t h e s a m p l e m u s t r e d u c e t h e s i g n a l S(k) to z e r o . T h i s i s a n e x p e r i m e n t a l c h e c k for a balanced optical path and insures that the e f f e c t s of m i r r o r M 1 a n d t h e c h o p p e r b l a d e s a r e i n d e e d n e g l i g i b l e . T h e s i g n a l S(k) i s f e d i n t o a grating-monochromator, and detected with a Cu-doped Ge-detector. The detection system is d e s c r i b e d e l s e w h e r e [3]. A d i g i t a l r e g i s t r a t i o n of t h e f i n a l s i g n a l s i s useful for further computer calculations, to determine both the refractive index n and the

extinction coefficient k. The spectral region, covered by this method extends from 5~ to 25~, dependingsomewhat on the temperature used for the black-body B2 or the sample S. The sample temperature can be varied between liquidHe-temperature and 400°K. The advantage of this method for measuring R(k) lies in its simplicity, when combinedwith an emissivity measurement. Notice that the only difference between emissivity measurements and reflectivity measurements is the fact, that the reference black-body B1 is kept at the temperature of t h e s a m p l e . ( F o r a n e m i s s i v i t y r u n B1 i s a t t e m p e r a t u r e T2.) Table 1 gives a systematical listing for the d e t e r m i n a t i o n of t h e o b s e r v a b l e q u a n t i t i e s R ( ; t , T ) , E ( k , T) a n d T(~t, T ) , f o r t h e a r r a n g e m e n t of fig. 1 w i t h two t e m p e r a t u r e s T 1 a n d T 2. A s a n e x a m p l e f o r t h e u s e of a c o m b i n e d Table 1 O b s e r v e d quantity S(k) at detector for choice of t e m p e r a t u r e s of the black-bodies B1, B 2 and the sample S for configuration of fig. 1; for abbrevations see text B1

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April 1970

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F i g . 2 . (a) Reflectivity of a GaP single c r y s t a l at 77°K (solid line) and c o r r e s p o n d e n t e m i s s i v i t y data (dashed line). The t h i c k n e s s of the sample is 0.45 m m . (b) Ref r a c t i v e index n (solid line) and extinction coefficient k (dashed line), calculated f r o m the data of fig. 2(a). C i r c l e s indicate some of these calculated values for n to show s c a t t e r ; solid line is best smooth fit. e m i s s i v i t y a n d r e f l e c t i v i t y m e a s u r e m e n t we r e p o r t t h e o p t i c a l b e h a v i o u r of G a P in t h e r e g i o n f r o m 10~ to 2 0 # a t 7 7 ° K s a m p l e t e m p e r a t u r e . In t h i s s p e c t r a l r a n g e G a P s h o w s v e r y s t r o n g m u l t i p h o n o n a b s o r p t i o n b a n d s [4]. In fig. 2 a r e flectivity and emissivity data are drawn together. The dashed line is the emissivity spectrum and t h e s o l i d l i n e t h e c o r r e s p o n d e n t c u r v e f o r R (k). In fig. 2b t h e r e f r a c t i v e i n d e x n a n d t h e e x t i n c t i o n coefficient k are plotted as calculated from R a n d E. 461

Volume i , number 9

OPTICS COMMUNICATIONS

I thank Professor Queisser for many helpful d i s c u s s i o n s a n d m y c o l l e a g u e F. W i l l m a n n f o r a s s i s t a n c e , a l s o D r . H. V e r l e u r who k i n d l y donated a GaP sample. Financial support given by the Deutsche Forschungsgemeinschaft is gratefully appreciated.

REFERENCES [1] D. L. Stierwalt and R. F. P o t t e r , J . P h y s . Chem. Solids 23 (1962) 99. [2] D. L. Stierwalt and R. F. P o t t e r , in: Semiconductors and s e m i m e t a l s , Vol. 3, eds. R. K. Williardson and A . C . B e e r (Academic P r e s s , New York, 1967). [3] M.Bl~itte, in: Semiconductor silicon, eds. R . R . H a b e r e c h t and E . L . K e r n (New York, 1969). [4] D.A. Kleinman and W. G. Spitzer, Phys. Rev. 118 (1960} 110.

462

April 1970