The a pplication of ellipsomctr y to t hc dcterm ination of t he op tical proper t ies of t hin film s ,?r~ transparent s ubstrates b y t h e usc of intcl'l1al r efiection and a ngles of incidence ncar the cl'ltlcal an gle for total r efi ection is dcs cribed a nd illust rated. Foul' cases are co ns idcrcd : 1. t he angle of i ncidence, (J;, is less t han eithcr t he cr itical a n IT le for total r eflection bctween t he s ubstrate, a nd the film , 0e " ' , a nd t he criti cal a ngle betw~e n t he substrate and t he surroundll1& mec\ll~m , (Je ' · 3 ; 2. 8e , · 3 > Oi>.(J , I.,; 3. 0,1,3< Oi< O, " '; and '!. 0, 1.3 < 0,>11,1,2. For case 1, fit ce r ta~!1 Cri tICal ~l aili es of . film t hl ck ncss d iln.d ref l:a ctive index n" t he refi ected li gh t mfly be p ola ll zed WIth .Its electl'l c v e~t r eltll er e nt irely Hl or normal to t he plan e of in cid en ce . N ear thcs? co nd it io ns t he se ns l t l v~ty of cll ipso met l'l c meas ure men ts is extrem ely high, but ~h e Intensity of the refl ect.crll igh t IS very low . Except under t hese condition s t hc in tcns itv IS adeq ua te for eXIJerim cnt a l meas urem en ts, as it is a lso in Cfl SC 2. For casc 1 it is alway"s po.sslbl c to determ ine on, a nel d by a Single m e~s urcm c n t ; for casc 2 th is is possib lc o nl y tor t hin fi lms , For cases .) a nd 4, il nel CflSC 2 fo r t hi ck fi lms, only one of t hesc may be determincd . Under t hese concli tlOn s, howc ver , t hc rc fl cct ivity is 100 pcr ce n t .
Introduc tionThe determination of the op tical const,lll ts or surfaces and the thickness and refractive index of thin films bv measurement of t he chan O'es in t he J b s~ate. of polarihation of polarized light upon r eflectIOn IS based on t he well-known equati ons of Drude (1),1 The tecbnique for carr ying out t hese measuremen ts is frequ~ntly. refel'l'~d to as ellipsometry and has b een descn~ed 111 .detaIl elsewb ere [e.g., 2, 3, 4J. lV10st work WIth ellIpsom etry has b een concerned with s.tu.dies. OI~ n~etallic surfaces [2,3], either because of the!!' mtrmSIC mtere~t or because t hey form hig hly refiectmg substrates for t he study of thin films. However, it is sometimes desirable to measure the properties of thin films on transparent surfaces in which case the low intensity of the reflected light makes accurate analysis of its state of polarization difficult.There are two possible systems which would in general, incr ease the intensity of the reflected b~am over that obtained by direct external reflection from a transparent surface. In one, a thin layer of the transparent material which is to be used as a subs trate for the film is placed in intimate contact with a metal, which is used as the reflectin o' substrate.The traJ?sparen t material may be placed ~s a film on a. J:?1etalhc plate, for example by evaporatin g a film of SIlIca on a metallIC substrate in a vacuum evaporator.1 Figures in brackets indicate ihe literat ure reference at the end of this paper.
601It is necessary, of course, to determi ne t he optical proper ties of...