Spectroscopic Ellipsometry. Determination of the Film Thickness and the Effective Medium Approximation Theories in Ellipsometry.

Abstract

Ellipsometry is an extremely high sensitive method for the film thickness determination. The complex amplitude reflection ratio of the sample is a basic formula for the analysis of the optical constants. The analytical methods of the complex amplitude reflection ratio are described for the both samples of single layer and multilayers. The calculation method for the simultaneous determination of the refractive index and the thickness of a single transparent film is described. We also describe the analytical method for the single absorbing layer of different film thickness. The algorithm for the calculation of the complex amplitude reflection coefficient of the multilayer samples is shown. The effective medium approximation theories of Maxwell-Garnett and Bruggeman are derived starting from the Clausius-Mosotti formula. 1. ‚Í ‚ ¶ ‚ß ‚É •@OEÅ 'Ì •\-Ê ‚É "-OE ‚ª ' ¶ •Ý‚· ‚é •ê • ‡,‚» ‚Ì "½ ŽË "Á •« ‚Í "-OE ‚Ì-OEOEú ‚É ‚ae ‚Á ‚Ä 'å ‚« ‚-ˆÙ ‚È ‚é •B-Ⴆ ‚Î,ƒK ƒ‰ƒX•\-Ê ‚É OEõ Šw-OE OEú(‹ü •Ü-¦ •~-OEOEú)‚ª ƒÉ/4‚AE ‚È ‚é ‚ae ‚¤ ‚É,MgF2‚Ì "-OE ‚ð •ö '…‚· ‚é ‚AE"g '· ƒÉ ‚Ì OEõ ‚É 'Î ‚µ ‚Ä ƒK ƒ‰ƒX•\-Ê ‚© ‚ç ‚Ì "½ ŽË ‚Í •Å •¬ ‚AE‚È ‚é("½ ŽË-h Ž~-OE)•B ‚Ü ‚½,OEõ Šw-OEOEú ‚ª ƒÉ/2‚Ì •ê • ‡ ‚Í ‹t ‚É,"½ ŽË '• ‰Á‚AE‚È ‚é •B ‚± ‚Ì ‚ae ‚¤ ‚É •¨ 'Ì •\-Ê ‚Å ‚Ì "½ ŽË ‚Ì-lŽq ‚Í "-OE‚Ì ' ¶ •Ý ‚É •q Š´‚ÅŠ´‚Å ‚ ‚é •B ‚± ‚ê ‚Í, ‹ó ‹Cˆê‹Cˆê-OE ŠE-Ê ‚Å ‚Ì "½ ŽË OEõ ‚AE-OEˆê•¨ 'Ì ŠE-Ê ‚Å ‚Ì "½ ŽË OEõ ‚AE‚̈ʂAE‚ÌˆÊ 'Š •· ‚É ŠÖOEW ‚µ ‚Ä ‚¢ ‚é •B OEõ‚Ì Š± •Â ‚É ‚ae ‚è 'ª 'è ‚Å ‚« ‚éˆÊ‚éˆÊ 'Š •· ‚Í 'å ŽG"c ‚É OE¾‚Á ‚Ä,ƒÉ/30'ö "x ‚Å ‚ ‚é •B ‚µ ‚© ‚µ,ƒG ƒŠ ƒv ƒ\ ƒ• ƒg ƒŠ •[ ‚Å ‚Í0.1•‹(=ƒÉ/3600)ˆÈ ‰º ‚ÌˆÊ‚ÌˆÊ 'Š •· ‚ð,•• 'Ê ‚É OEŸ•o ‚· ‚é ‚± ‚AE‚ª ‚Å ‚«,‚± ‚ê ‚ð Š± •Â ‚É ‚ae ‚é "½ ŽË-¦ 'ª 'è ‚AE 'P •ƒ ‚É "ä Šr ‚· ‚é ‚AE,‚» ‚Ì Š´"Š´"x ‚Í,‚¨‚ae ‚¨‚ae ‚»100"{ ‚Å ‚ ‚é •B ‚µ ‚½ ‚ª ‚Á ‚Ä,ƒG ƒŠ ƒv ƒ\ ƒ• ƒg ƒŠ •[ ‚Í ‹É ‚ß ‚Ä "-‚¢-OE‚Ì ' ¶ •Ý ‚É 'Î ‚µ ‚Ä "ñ •í ‚É •q Š´‚ÅŠ´‚Å ‚ ‚é •B ƒG ƒŠ ƒv ƒ\ ƒ• ƒg ƒŠ •[ ‚Å ‚Í •\-Ê ‚É ' ¶ •Ý ‚· ‚é1nmˆÈ ‰º‚Ì-OEOEú‚Ì 'ª 'è ‚à ‰Â "\ ‚Å ‚ ‚é •B •@ƒG ƒŠ ƒv ƒ\ ƒ• ƒg ƒŠ •[ ‚Í ‹É "-OE‚Ì-OEOEú'ª 'è-@‚AE ‚µ ‚Ä,•\-Ê ‚¨‚ae‚¨‚ae ‚Ñ ŠE-Ê ‚Ì OE¤‹ † ‚â "¼ "± ŽY‹AE ‚Å ‚Ì ŠJ "-OE¤‹ † ‚É 'å ‚¢ ‚É-˜-p ‚³ ‚ê ‚Ä ‚¢ ‚é •B ‚± ‚± ‚Å ‚Í,ƒG ƒŠ ƒv ƒ\ ƒ• ƒg ƒŠ •[ ‚É ‚ae ‚é-OEOEú'ª 'è ‚Ì ‰ð•Í Žè-@ ‚AE,•s ˜A '±-OE‚ ‚é ‚¢ ‚Í 'e ‚¢ •\-Ê ‹y ‚Ñ ŠE-Ê ‚Ì ‰ð•Í ‚É ‚¨‚¯‚¨‚¯ ‚é-LOEø"} Ž¿ ‹ß Ž-•˜_ ‚É ‚ ‚¢ ‚Ä ‰ð•à ‚· ‚é •B 2.'½ •d OEõ '© "½ ŽË Š± •Â •@ Fig.1‚É Ž¦ ‚· ‚ae ‚¤ ‚É,ŽŽ-¿•\-Ê ‚ª˜A‚ª˜A '± ‚È "-‚¢ 'P 'w ‚Ì-OE ‚Å •¢ ‚í ‚ê ‚Ä ‚¢ ‚é •ê • ‡,ŽŽ-¿‚É "ü ŽË ‚· ‚é OEõ‚Í,‹ó ‹Cˆê‹Cˆê-OEŠE-Ê ‚AE,-OEˆê‰ºOEˆê‰º'n ŠE-Ê ‚Å ‚» ‚ê ‚¼ ‚ê "½ ŽË,‹ü •Ü ‚ð ‚-‚è •Ô ‚· •B ‚» ‚µ ‚Ä,‚± ‚ê ‚ç ‚Ì OEõ•ü ‚Í OEÝ‚¢ ‚É Š± •Â ‚µ,ŽŽ-¿•\-Ê ‚© ‚ç ‚Ì "½ ŽË OEõ ‚AE‚È ‚é •B ‚± ‚Ì ‚ae ‚¤ ‚É,‚» ‚ê ‚¼ ‚ê ‚Ì ŠE-Ê ‚Å '½ •d ‚É "½ ŽË ‚ð ‚-‚è •Ô ‚µ ‚½ OEõ•ü ‚ª OEÝ‚¢ ‚É Š± •Â ‚· ‚é ‚± ‚AE‚ð,'½ •d OEõ'© "½ ŽË Š± •Â ‚AEOE¾‚¤ •B •@ŽŽ-¿‚É "ü ŽË Šp ƒÓ‚Å,OEõ ‚ª "ü ŽË ‚µ ‚½ ‚AE‚« ‚Ì,‹ó ‹Cˆê‹Cˆê-OEŠE-Ê ‚Å ‚Ì •U •• "½ ŽË-¦ ‚ðr1,•U •• " § ‰ß-¦ ‚ðt1,‚AE ‚µ ‹t •û OEü‚© 19