೔ຊֶज़ৼ‫ڵ‬ձϝλϚςϦΞϧୈ 187 ҕһձ (2014 ೥ 6 ݄ 13 ೔)

1෼ޫΤϦϓιϝτϦʔɿ‫͔ૅج‬ΒԠ༻·Ͱాॴ ར߁ʢ༗‫ݶ‬ձࣾςΫϊɾγφδʔʣɹΤϦϓιϝτϦʔ͸ɼภޫΛར༻ͨ͠‫ܭ‬ଌ๏Ͱ͋Γɼ‫ۃ‬ബບ΍ද໘/ք໘ʹߴ͍‫౓ײ‬Λ༗͢Δ͜ͱ͔Βɼ൒ಋମΛ࢝Ίͱ͢Δ༷ʑͳ࢈‫ۀ‬෼໺ʹ͓͍ͯਫ਼ີບް‫͘޿ͯ͠ͱܭ‬ఆண͍ͯ͠Δɽۙ೥ɼίϯϐϡʔλʔͷ‫ٸ‬଎ͳൃୡɼϚϧννϟϯωϧ෼ޫ‫ث‬ͷߴੑೳԽʹࢧ͑ΒΕͯਐԽͨ͠෼ޫΤϦϓιϝτϦʔ͸ɼεϖΫτϧ༝དྷͷ๛෋ͳ৘ใྔΛ෢‫ʹث‬ɼബບࢼྉͷΞϓϦέʔγϣϯྖҬΛඈ༂తʹ֦େͨ͠ɽɹຊߘͰ͸ɼ෼ޫΤϦϓιϝτϦʔͷ‫ૅج‬ɾଌఆ‫ݪ‬ཧΛ֓આ͠ɼ෼ޫΤϦϓιϝʔλʔΛ༻͍ͨബບධՁԠ༻ྫΛ঺հ͢ΔɽΩʔϫʔυɿ෼ޫΤϦϓιϝτϦʔɼภޫɼ༠ిؔ਺ɼޫֶఆ਺ɼεϖΫτϧγϛϡϨʔγϣϯ

1 ɹ͸͡ΊʹภޫղੳΛບްܾఆʹԠ༻ͨ͠࠷ॳͷ࿦จ 1 ͔Β໿

120 ೥ɼ෼ޫΤϦϓιϝτϦʔʢspectroscopic ellipsometryʣٕज़͸ɼ࠷ۙͷ 20 ೥ఔͰ‫ʹܹٸ‬ਐา͠ɼ୯ͳΔਫ਼ີບް‫ܭ‬ͷ࿮Λ௒͑ͯɼ͞·͟·ͳࡐྉ‫ܥ‬ͷޫ෺ੑղੳʹԠ༻͞ΕΔΑ͏ʹͳͬͨɽ෼ޫΤϦϓιϝτϦʔൃలͷओཁҼ͸ɼίϯϐϡʔλʔͷߴ଎ԽͱϚϧννϟϯωϧ෼ޫ‫ث‬ͷߴ‫౓ײ‬Խɾ௿྿ԽͰ͋Δɽ͜ΕΒͷٕज़ʹࢧ͑ΒΕͯɼΤϦϓιϝτϦʔͷߴ‫౓ײ‬ੑΛଛͳ͏͜ͱͳ͘εϖΫτϧଌఆ࣌ؒͷେ෯ͳ୹ॖͱɼෳࡶͳղੳ‫ࢉܭ‬ͷߴ଎ॲཧ͕Մೳʹͳͬͨɽಛʹॏཁͳ͜ͱ͸ɼίϯϐϡʔλʔͷߴ଎ԽʹΑΓɼޫి৔ʹର͢Δ෺࣭Ԡ౴ΛϞσϧԽͨ͠༠ిؔ਺ʢdielectric functionʣΛ‫ͨ͠࢖ۦ‬ෳࡶͳεϖΫτϧϑΟοςΟϯάղੳ͕ɼ੍໿Λड͚ͣʹ࣮ߦͰ͖ΔΑ͏ʹͳͬͨ͜ͱͰ͋ΔɽຊߘͰ͸ɼ༠ిؔ਺Λ࢖ͬͨεϖΫτϧղੳͷॏཁੑɾ༗

Fig. 1. Schematic of polarization change upon light reflection ona sample surface, and definition of ellipsometric function.

ޮੑΛத৺ʹɼ෼ޫΤϦϓιϝτϦʔͷ‫͔ૅج‬ΒԠ༻·ͰΛ֓‫͍ͯ͘͠؍‬ɽೖࣹ໘಺ʹి৔ৼಈ໘͕͋Δ௚ઢภޫΛ p ภޫɼͦΕͱ௚ަ͢Δ௚ઢภޫΛ s ภޫͱ‫Ϳݺ‬ɽp ภޫͱ s ภޫ2 ɹΤϦϓιϝτϦʔͱ͸͸൓ࣹʹࡍͯ͠ภޫঢ়ଶ͕มΘΒͳ͍ภޫͰ͋Γɼશͯͷภޫঢ়ଶ͸ p ภޫͱ s ภޫͷϕΫτϧ߹੒ͱͯ͠‫ه‬ΤϦϓιϝτϦʔ͸ɼి࣓೾ͷ‫ج‬ຊతͳੑ࣭ͷҰͭड़͢Δ͜ͱ͕Ͱ͖ΔɽFig.1 ͷΑ͏ʹɼ͋Δ௚ઢภޫΛͰ͋ΔʮภޫʯΛར༻ͨ͠‫ܭ‬ଌ๏Ͱ͋Δ 2, 3 ɽΤϦϓιࢼྉද໘ʹࣼೖࣹ͢Δͱɼp ภޫͱ s ภޫͱͰෳૉৼ෯ϝτϦʔͰ͸ɼࢼྉʹೖࣹ͞Εͨภޫ͕ࢼྉද໘Ͱ൓൓ࣹ܎਺ʢৼ෯൓ࣹ܎਺ɼ൓ࣹҐ૬ʣ͕ҟͳΔͨΊɼ൓ࣹ͢Δࡍʹੜ͡ΔภޫมԽΛ‫؍‬ଌͯ͠ɼബບͷޫֶఆࣹޫ͸ҰൠʹପԁภޫͱͳΔɽࢼྉද໘ʹ͓͚Δ p ภ਺ʢ۶ં཰ nɼফਰ܎਺ κʣɼບް d Λߴ‫౓ײ‬ɾߴਫ਼౓ޫͱ s ภޫͷෳૉৼ෯൓ࣹ܎਺ΛͦΕͧΕ r p ɼr s ͱ͢ʹ‫ܭ‬ଌ͢Δ͜ͱ͕Ͱ͖ΔɽΔͱɼͦͷൺ ρ = r p /r s ͸ภޫղੳؔ਺ʢellipsometricFig.1 ʹɼࢼྉද໘Ͱͷޫͷ൓ࣹͱͦΕʹ൐͏ภޫมԽͷ༷ࢠΛࣔ͢ɽ

functionʣͱ‫ݺ‬͹ΕΔɽ

2ాॴར߁ɿʮ෼ޫΤϦϓιϝτϦʔɿ‫͔ૅج‬ΒԠ༻·Ͱʯρ ≡≡!

rpE pr=rsE pi"#!

"!

E pr
E sr
=
E si
E sr"#!

E pi
E sitan Ψ exp (i∆)େ͖͞͸༠ి཰ ε Ͱද͞ΕΔɽ

"Fig.2 ͸ɼޫ͕෼‫ۃ‬ΛҾ͖‫͕ͳ͜͠ى‬Β෺࣭தΛ఻೻
͢ΔΑ͏͢Λ͍ࣔͯ͠Δɽ

(1)(1) ࣜୈ࢛߲͔Βɼρ ͕ೖࣹޫͷภޫঢ়ଶ (E pi /E si ) ʹର͢Δ൓ࣹޫͷภޫঢ়ଶ (E pi /E si ) ͷൺͰද͞ΕΔ͜ͱ͕෼͔ΔɽΤϦϓιϝτϦʔͰ͸ɼρ Λ‫࠲ۃ‬ඪදࣔͯ͠ภޫղੳύϥϝʔλʔ Ψɼ∆ Λఆٛ͢Δɽ͜͜Ͱɼ∆ ͸ pภޫͱ s ภޫͷҐ૬ࠩ ∆ p − ∆ s Ͱ͋ΓɼΨ ͸ p ภޫͱ sภޫͷৼ෯ൺ tan Ψ = |r p |/|r s | ͔Β‫·ٻ‬Δ֯౓Ͱৼ෯ൺ
֯ͱ‫ݺ‬͹ΕΔɽ୯Ұ೾௕ͷΤϦϓιϝτϦʔͷ৔߹ɼ༩͑ΒΕͨബບͷບްॳ‫ظ‬஋ɼ۶ં཰ॳ‫ظ‬஋͔Βࢉग़͞ΕΔภޫղੳύϥϝʔλʔ Ψ sim ɼ∆ sim ͱɼଌఆ͞Εͨ Ψexp ɼ∆expͷ‫े͕ࠩޡ‬෼খ͘͞ͳΔΑ͏ʹϑϨωϧ൓ࣹৼ෯܎਺

Fig. 2. Schematic diagram of (a) oscillation of electric dipole
which is caused by electric field of light and (b) electric dipole
radiation in a dielectric.

‫ࢉܭ‬Λ൓෮ͯ͠ߦ͍ɼബບͷບް d, ޫֶఆ਺ʢ۶ં཰nɼফਰ܎਺ κʣͳͲͷऩଋ஋Λ‫ٻ‬ΊΔɽͨͩ͠ɼೋͭ

Fig.2(a) ͷࠨ͔Β఻೻͖ͯͨ͠ޫͷి৔ʹΑͬͯ෺࣭ͷଌఆྔ Ψexp ɼ∆exp ͔ΒࡾͭҎ্ͷະ஌਺Λ֬ఆ͢Δ಺ʹ෼‫͕ۃ‬ੜ͡Δʢ͜͜Ͱ͸ɼਖ਼ిՙɿ‫֩ࢠݪ‬ɼෛి͜ͱ͸Ͱ͖ͳ͍ͨΊɼೋະ஌਺Ҏ֎Λ༧Ίܾఆ͓ͯ͠ՙɿిࢠͷΠϝʔδͰඳ͍ͯ͋Δʣɽ෼‫ʹۃ‬Αͬͯ࡞͘ඞཁ͕͋Δɽయ‫ܕ‬తͳ࢖༻๏͸ɼޫֶఆ਺‫ط‬஌ͷ‫ج‬ΒΕΔిՙର͸ɼి‫ؾ‬૒‫ࢠۃ‬ʢelectric dipoleʣͱ‫ݺ‬͹൘্ʹ෇͚ΒΕͨಁ໌Ұ૚ບࢼྉΛର৅ʹɼບް d ͱ

ΕΔɽి‫ؾ‬૒‫ࢠۃ‬͸ɼޫͷి৔ৼಈʹಉ‫ͯ͠ظ‬όωͷ۶ં཰ n Λಉ࣌ʹ‫ٻ‬ΊΔਫ਼ີບް‫͋Ͱܭ‬ΔɽΑ͏ʹৼಈ͢Δɽৼಈ͢Δి‫ؾ‬૒‫ࢠۃ‬͸ɼޫͷަྲྀి৔ʹΑΓઈ͑ͣՃ଎౓͕มԽ͠ɼͦͷ݁ՌɼFig.2(b) ͷ3 ɹͲ͏ͯ͠෼ޫͳͷ͔

4෺࣭ͷޫֶఆ਺ʢ۶ં཰ nɼফਰ܎਺ κʣͷप೾਺ґଘੑɼ͢ͳΘͪɼnɼκ εϖΫτϧ͸ɼ‫ʹ͍ޓ‬ಠཱͰ͸ͳ͘ɼޫి৔ʹରͯ͠෺࣭͕Ԡ౴͢Δ͜ͱͰඞવతʹܾ·ΔҼՌ཯͕ଘࡏ͢Δɽ͜ͷ྆ऀͷؔ܎͸ɼΫϥϚʔεɾΫϩʔχοώͷؔ܎ࣜʢKramers-Kronig relationʣͰද͞ΕΔ 5 ɽͭ·Γɼ෼ޫεϖΫτϧʹ͸ࡐྉޫ෺ੑͷຊ࣭తͳ৘ใ͕‫·ؚ‬Ε͍ͯΔͷͰ͋Δɽ෼ޫΤϦϓιϝτϦʔ͸ɼ͜ͷΫϥϚʔεɾΫϩʔχοώͷؔ܎ࣜΛߟྀͨ͠εϖΫτϧղੳΛߦ͏఺Ͱɼ୯Ұ೾௕ͷΤϦϓιϝτϦʔΛଌఆ೾௕਺͚ͩฒ΂ͨ΋ͷͱ͸ຊ࣭తʹҟͳΔɽຊ߲Ͱ͸ɼ෼ޫΤϦϓιϝτϦʔղੳͷΑΓͲ͜Ζͱͳ͍ͬͯΔʮޫి৔ʹର͢Δ෺࣭ͷԠ౴ʯʹ͍ͭͯɼͦͷ‫ج‬ຊతͳϝΧχζϜΛௗᛌ͢ΔɽΑ͏ʹి‫ؾ‬૒‫͔ࢠۃ‬Β͸ಉ͡ৼಈ਺ͷి࣓೾͕์ग़͞ΕΔʢ์ग़͞ΕΔి࣓೾͸ɼυʔφπঢ়ͷ‫౓ڧ‬ύλʔϯͰ์ࣹঢ়ʹ֦͕Δ͕ɼ͜͜Ͱ͸લਐ͢Δޫ͚ͩΛඳ͍͍ͯΔʣɽ͜ͷి࣓೾ͷ࠶์ࣹΛɼి‫ؾ‬૒‫ࣹ์ࢠۃ‬ʢelectric dipole radiationʣͱ‫Ϳݺ‬ɽ‫ޙ‬ड़͢Δ༠ిମͷಁ໌ྖҬʢਖ਼ৗ෼ࢄྖҬʣʹ͓͍ͯɼ͜ͷ์ࣹաఔ͸Ґ૬஗ΕΛ൐͏ɽͦͷͨΊɼޫ͕ి‫ؾ‬૒‫ࣹ์ࢠۃ‬Λ‫܁‬Γฦ͠ͳ͕Β෺࣭தΛ఻ൖ͢Δͱɼε ͕େ͖͘෼‫͠ۃ‬΍͍͢෺࣭΄ͲɼޫͷҐ૬଎౓͕஗͘ͳΔɽҰํɼ۶ં཰͸ɼ෺࣭தͷޫͷ଎౓ v Λ༻͍ n ≡ c/v

ͱఆٛ͞ΕΔɽෳૉ۶ં཰ʢN = n − iκɼ࣮෦ n Λ۶ં཰ɼ‫ڏ‬෦ κ Λফਰ܎਺ɼ྆ऀΛ·ͱΊͯޫֶఆ਺ͱ‫ݺ‬Ϳʣͱෳૉ༠ి཰ʢε = ε1 − iε2 ʣͷؔ܎͸ɼMaxwell ͷํఔ͔ࣜΒɼN 2 = εʢε1 = n2 − κ2 ɼε2 = 2nκʣͱ‫ٻ‬ΊΒΕɼκ = 0 ͱ‫ͤͳݟ‬Δਖ਼ৗ෼ࢄྖҬͰ͸ɼn2 = ε1 ͱͳΓɼ༠ి཰͕େ͖͍΄Ͳ۶ં཰͕େ͖͘ɼޫͷҐ૬଎౓͕஗͘ͳΔͷͰ͋Δɽ

3.1 ɹ෼‫ͱۃ‬༠ిؔ਺ޫ͕༠ిମதΛ఻ൖ͢Δͱɼޫͷి৔ʹΑͬͯ෺࣭಺ʹిՙͷภΓɿ෼‫ۃ‬ʢpolarizationʣ͕ੜ͡Δɽ෼‫ۃ‬ͷ೔ຊֶज़ৼ‫ڵ‬ձϝλϚςϦΞϧୈ 187 ҕһձ (2014 ೥ 6 ݄ 13 ೔)

3.2 ɹ Lorentz ৼಈࢠ3ͦΕΛҟৗ෼ࢄͱ‫Ϳݺ‬ɽ·ͨɼFig.3(b) ͷ௨Γɼε1 ͱ ε2ి‫ؾ‬૒‫ৼࢠۃ‬ಈ͸ɼLorentz ৼಈࢠͰϞσϧԽͰ͖Δɽ

Lorentz ৼಈࢠ͸ɼ෼‫ʹۃ‬ΑΓੜ͡Δਖ਼ిՙͱෛిՙ͕όωͰଋറ͞Ε͍ͯΔ‫ݹ‬యతͳϞσϧͰ͋Δɽ‫ޙ‬ड़͢Δిࢠ෼‫Ͱۃ‬͸ɼޫͷి৔ৼಈʹରͯ͠ɼ࣭ྔͷେ͖͸‫ʹ͍ޓ‬ಠཱͰ͸ͳ͘ɼε1 εϖΫτϧͱ ε2 εϖΫτϧ͸ΫϥϚʔεɾΫϩʔχοώͷؔ܎ࣜʹै͏ɽ͜͏ͨ͠ޫͷ֯ৼಈ਺ʹର͢Δ ε ͷ෼ࢄΛɼ༠ిؔ਺ʢdielectricfunctionʣͱ͍͏ɽ͍‫֩ࢠݪ‬͸ಈ͔ͣɼిࢠ͚͕ͩ೪ੑྲྀମதΛόωৼಈ
͢Δ෺ཧϞσϧΛԾఆ͢ΔɽLorentz Ϟσϧͷӡಈํఔࣜ͸࣍ࣜͰ༩͑ΒΕΔɽ

me2d xdx+ me Γ+ me ω20 x = −eE0 exp(iωt)
dtdt23.3 ɹ༠ిؔ਺ͷप೾਺ґଘͱεϖΫτϧ࣮ࡍʹ‫؍‬ଌ͞ΕΔ༠ిؔ਺͸ɼ෺࣭಺ʹෳ਺छͷ෼

(2)‫͕ۃ‬ଘࡏ͠ɼͦΕͧΕͷ෼‫͕ۃ‬෼‫ిۃ‬ՙͷ༗ޮ࣭ྔʹґଘͨ͠‫ڞ‬໐‫ٵ‬ऩ೾௕ଳΛ࣋ͭͨΊɼޫͷ֯ৼಈ਺ʹ͜͜Ͱ me ͱ e ͸ɼͦΕͧΕిࢠͷ࣭ྔͱిՙͰ͋ΔɽΑͬͯେ͖͘มԽ͢ΔɽFig.4 ʹɼ෼‫ۃ‬ͷछྨͱϞσϧࠨลͷୈ 2 ߲͸ɼ೪ੑྲྀମதͷ೪ੑ఍߅Λද͓ͯ͠ΓɼԽͨ͠༠ిؔ਺Λࣔ͢ɽӡಈ଎౓͕஗͍৔߹͸଎౓ʹൺྫ͢ΔɽΓ ͸ɼ೪ੑ఍߅ͷൺྫ܎਺Ͱɼ‫ݮ‬ਰ܎਺ʢdamping coeﬃcientʣͱ‫ݺ‬͹ΕΔɽࠨลୈ 3 ߲͸ɼޫͷి৔ʹΑͬͯҠಈͨ͠ిࢠ͕ϑοΫͷ๏ଇʢF = −kF xʣʹैͬͯ෮‫͢ݩ‬Δ͜ͱΛද͠ɼω0 ͸όωͷ‫ݻ‬༗֯ৼಈ਺ɿω0 = (kF /me )1/2 Ͱ
͋ΔɽFig.3 ʹ Lorentz Ϟσϧ͔Β‫͞ࢉܭ‬ΕΔෳૉ༠ి཰ͷ࣮෦ ε1 ͱ‫ڏ‬෦ ε2 Λࣔ͢ɽ

Fig. 4. Schematic diagram of frequency dependence of the contributions of orientational, ionic, electronic polarizations to thedielectric function.

ϚΠΫϩ೾ྖҬͰ͸෼‫ͨ͠ۃ‬෼ࢠͷճసʢ഑޲෼‫ۃ‬ʣɼ੺֎ྖҬͰ͸෼‫ͨ͠ۃ‬෼ࢠɾ‫ࢠݪ‬ͷৼಈʢΠΦϯ෼‫ۃ‬ʣɼࢵ֎ՄࢹྖҬͰ͸෼‫ࢠిͨ͠ۃ‬ɾ‫֩ࢠݪ‬ͷৼಈʢిࢠ
Fig. 3. Dielectric function (real part ε1 and imaginary part ε2of the complex dielectric constant) calclated from the Lorentz
model. The inset shows a physical model of the Lorentz oscillator.

෼‫ۃ‬ʣͷ‫ڞ‬໐ʹΑΓޫ͕‫ٵ‬ऩ͞Εɼε2 ͸ϐʔΫΛ࣋ͭɽͳ͓ɼ༠ిମͳͲͷ‫ݻ‬ମͰ͸෼ࢠ‫͕ࢠݪ‬ಈ͚ͳ͍ͨΊʹ഑޲෼‫ۃ‬͸‫͜ى‬ΒͣɼSi ΍ Ge ͳͲΠΦϯੑΛࣔ͞ͳ͍݁থͰ͸ΠΦϯ෼‫ۃ‬͸‫͜ى‬Βͳ͍ɽޫͷ֯ৼಈ਺Λ૿Ճͤͯ͞ߦ͘ͱɼΠΦϯ෼‫ۃ‬ͷৼಈ͸ޫͷ֯ৼಈ਺ૠೖਤ͸ɼLorentz ৼಈࢠͷ෺ཧϞσϧͰ͋Δɽ(2) ࣜʹ௥ैͰ͖ͳ͘ͳΓɼε1 ͸ΠΦϯ෼‫ۃ‬ͷ‫د‬༩෼͚ͩ‫ݮ‬ʹࣔͨ͠ Lorentz Ϟσϧͷӡಈํఔࣜ͸ɼిࢠ͕ޫͷిগ͢Δɽ͞Βʹߴ͍֯ৼಈ਺Ͱ͸ɼ΍͕ͯిࢠ෼‫ۃ‬΋৔ৼಈ E0 exp(iωt) ͰՃৼ͞Ε͍ͯΔ‫ݮ‬ਰৼಈࢠΛද͠௥͍͚ͭͳ͘ͳΓɼ࠷ऴతʹ ε1 ͸ਅۭதͱಉ͡ 1 ʹͳ͍ͯΔɽLorentz Ϟσϧʹ͓͚Δ༠ి཰෼ࢄͰ͸ɼόωͷΔɽ‫ʹٯ‬ɼ௿֯ৼಈ਺ྖҬͰ͸ɼޫి৔ৼಈʹԠ౴Ͱ‫ݻ‬༗֯ৼಈ਺ ω0 Ͱ ε2 ͕࠷େʹͳΓɼε2 ϐʔΫͷ൒஋෯͖ΔΠΦϯ෼‫ۃ‬ɼిࢠ෼‫ۃ‬ͷ྆ํͷ‫د‬༩Λ‫ؚ‬ΉͨΊʹɼ͸‫ݮ‬ਰ܎਺ʢdamping coeﬃcientʣΓ Ͱܾ·Δɽε2 ϐʔΫε1 ͷ஋͸େ͖͘ͳΔɽ͔Βԕ͍ ε1 ͷޯ഑͕ਖ਼ͷྖҬʹ͓͚Δ෼ࢄΛਖ਼ৗ෼ࢄɼ

Fig.5 ͸ɼ༠ిମͷޫֶఆ਺εϖΫτϧͷϞσϧਤͰε2 ϐʔΫۙลͷޯ഑͕ෛͷྖҬʢ−Γ/2 < ω0 < Γ/2ʣͷ͋Δɽࢵ֎ྖҬʹ‫ݟ‬ΒΕΔେ͖ͳ κ ͷϐʔΫ͸ిࢠ෼4ాॴར߁ɿʮ෼ޫΤϦϓιϝτϦʔɿ‫͔ૅج‬ΒԠ༻·ͰʯFig. 5. Schematic diagram of optical constant spectra in the region from ultraviolet to infrared.

‫ۃ‬ʢ༠ిମ಺෦ͷిࢠόϯυؒભҠʣͷ‫ڞ‬໐‫ٵ‬ऩͰ͋Γɼ੺֎ྖҬʹ͸‫ࢠݪ‬෼‫ۃ‬ʢ෼ࢠ΍݁থ֨ࢠͷ෼‫ৼۃ‬ಈʣͷ‫ڞ‬໐‫ٵ‬ऩɼෆ७෺ͳͲΛ‫ݪ‬Ҽͱ͢ΔϑϦʔΩϟϦΞ͕͋Δ৔߹ʹ͸ɼ௿ΤωϧΪʔͷྖҬʹ͞Βʹͦͷ‫ٵ‬ऩ͕‫ݱ‬ΕΔɽ༠ిମͰ͸ɼ੺֎ྖҬʹ͓͚ΔΠΦϯ෼‫ۃ‬ͷ‫ڞ‬໐‫ٵ‬ऩͱࢵ֎ྖҬʹ͓͚Δిࢠ෼‫ۃ‬ͷ‫ڞ‬໐‫ٵ‬ऩͷؒʹɼେ͖ͳΤωϧΪʔΪϟοϓ͕ଘࡏ͠ɼՄࢹۙ੺֎ྖҬͰ κ ͕΄΅ 0 Ͱɼ֯ৼಈ਺ͷ্ঢʹ൐͍ n ͕ঃʑʹ૿Ճ͢Δޫֶఆ਺εϖΫτϧɼ͢ͳΘͪਖ਼ৗ෼ࢄΛࣔ͢ɽ͜ͷྖҬʹ͓͚Δޫֶఆ਺εϖΫτϧͷ‫ܗ‬ঢ়͸ɼࢵ֎ྖҬʹ͓͚Δిࢠ෼‫ۃ‬ͷ‫ڞ‬໐‫ٵ‬ऩʹΑ࣮ͬͯޮతʹܾఆ͞Ε͍ͯΔͱ͍ͬͯΑ͍ɽޫֶఆ਺εϖΫτϧ͸ଟ͘ͷ‫ʹऀڀݚ‬Αͬͯଌఆ͞ΕɼϥΠϒϥϦʔԽ͞Ε͍ͯΔͷͰɼޫֶఆ਺Λ‫ݻ‬ఆͨ͠ບްղੳʹར༻͢Δ͜ͱ͕Ͱ͖Δ 6 ɽ·ͨɼκ = 0ͱ‫ͤͳݟ‬Δ೾௕ྖҬʹ͓͚ΔղੳͰ͸ɼ͠͹͠͹ (3) ࣜFig. 6. Modeling the optical constants of SiO2 using Cauchy’sequation.

༻͞ΕΔ͕ɼCauchy ͷ෼ࢄࣜͷ࢖༻ʹ౰ͨͬͯ͸ΫϥϚʔεɾΫϩʔχοώͷؔ܎ࣜΛຬ଍͍ͯ͠ͳ͍͜ͱ
ʹे෼஫ҙΛ෷͏ඞཁ͕͋Δɽ
΋͠ɼ෺࣭ͷޫֶఆ਺Λ‫ٻ‬ΊΔ͜ͱ͕໨తͰ͋Ε͹ɼؔ਺Ͱ‫ه‬ड़͞ΕͨϑϨΩγϒϧͳ༠ిؔ਺ϞσϧΛ༻
͍Δඞཁ͕͋Δɽଟ͘ͷ෺࣭ͷ༠ిؔ਺͸ɼిࢠ෼‫ىྭۃ‬ʢLorentz ϞσϧɼTauc-Lorentz Ϟσϧ 7 ɼOJL Ϟσϧ 8 ͳͲʣɼΠΦϯ෼‫ىྭۃ‬ʢKim ৼಈࢠϞσϧ 9 ɼBrendel ৼಈࢠϞσϧͳͲʣɼϑϦʔΩϟϦΞྭ‫ى‬ʢDrude Ϟσϧͱͦͷ֦ுϞσϧʣͷ૊Έ߹ΘͤͰ‫ه‬ड़͢Δ͜ͱ͕Ͱ͖Δɽ͜͜ʹྻ‫ͨ͠ه‬୅දతͳৼಈࢠϞσϧͷଟ͕͘ Lorentz Λ‫֦ʹج‬ு͞Εͨ΋ͷͰ͋Δɽ༠ిؔ਺Ϟσϧͷબ୒ͱͦͷม਺ઃఆ͸ɼ෼ޫΤϦϓιϝτϦʔͷϑΟοςΟϯάղੳʹ͓͚Δ࠷΋ॏཁͳεςοϓͰ͋Δɽʹࣔ͢ Cauchy ͷ෼ࢄࣜ 10 ͕༻͍ΒΕΔɽ

n(λ) = A +BC++ ···,
λ2 λ4

κ(λ) = 0(3)4 ɹ෼ޫΤϦϓιϝτϦʔͱ෼ޫ‫ׯ‬ব๏ΤϦϓιϝτϦʔ͸ɼҰͭͷޫΛ p ภޫ/s ภޫͷೋ͜͜Ͱɼࣜதͷ Aɼ BɼC ͸ղੳม਺Ͱ͋Δɽͭͷ೾ಈ੒෼ʹ෼ׂͨ͠‫ׯ‬ব๏Ͱ͋ΓɼಉҰޫ࿏͕อ
6Fig.6 ͸ɼγϦίϯࢎԽບʢSiO2 ʣͷจ‫ݙ‬஋ ɼ͓Αূ͞Εͨೋͭͷ೾ಈํఔࣜͷ૬ରతͳؔ܎Ͱ͋Δ Ψ ͱͼղੳʹΑΓ‫ٻ‬Ίͨ SiO2 ͷ Cauchy ͷ෼ࢄࣜΛॏͶॻ∆ Λଌఆ͢ΔͨΊɼผʑͷޫ࿏Λ௨աͨ͠ޫΛ߹੒͖ͨ͢͠΋ͷͰ͋Δɽղੳม਺͸ୈ 3 ߲໨·Ͱ༻͍ɼ೾Δ௨ৗͷ෼ޫ‫ׯ‬ব๏ͱൺֱͯ͠ਫ਼౓ɼ‫ͱ౓ײ‬΋ʹ༏Ε௕ൣғɿ200 ∼ 1,000 nm ͰղੳΛߦͬͨɽղੳม਺஋͸͍ͯΔɽ೾௕ʹґଘ͢ΔͷͰɼղੳൣғͷऔΓํΛม͑Δͱҟ

Fig.7 ʹɼγϦίϯ‫ج‬൘্ͷγϦίϯࢎԽບʢSiO2 ʣͳͬͨ஋͕ಘΒΕΔɽCauchy ͷ෼ࢄࣜͰදͨ͠ SiO2 ͷͷບްมԽʹର͢Δ (a) ෼ޫΤϦϓιϝτϦʔʢೖࣹ֯ɿ۶ં཰෼ࢄϞσϧ͸ɼղੳ೾௕ൣғͰจ‫ݙ‬஋ͱྑ͘Ұ75◦ ʣɼ(b) ൓ࣹ෼ޫ‫ׯ‬ব๏ʢೖࣹ֯ɿ0◦ ʣͷεϖΫτϧม

க͍ͯ͠ΔɽԽγϛϡϨʔγϣϯΛࣔ͢ɽບްมԽൣғ͸ 0ʙ30 nmCauchy ͷ෼ࢄࣜ͸ɼκ = 0 ͱ‫ͤͳݟ‬Δղੳ೾௕ྖҬͰ

Ͱ͋ΔɽFig.7(a) ͷ ∆ εϖΫτϧʹ஫໨͠Α͏ɽ‫ج‬൘ͷບްଌఆΛ͢Δ৔߹ʹ༗ޮͰɼ෼ޫΤϦϓιϝʔλʔ∆ εϖΫτϧ͸ɼೖࣹ֯ɿ75◦ ͕ओೖࣹ֯ʢ∆ = 90◦ ʹΛ༠ిମບͷਫ਼ີບް‫͢༻࢖ͯ͠ͱܭ‬Δ৔߹ͳͲʹଟ

ͳΔೖࣹ֯ʣͱͳΔ೾௕ɿ780 nm ෇ۙΛ‫ʹڥ‬ɼ୹೾௕೔ຊֶज़ৼ‫ڵ‬ձϝλϚςϦΞϧୈ 187 ҕһձ (2014 ೥ 6 ݄ 13 ೔)

5ফޫ๏͸ɼภޫࢠͱ λ/4 ൘Λ༻͍ͯࢼྉ͔Βͷ൓ࣹޫ͕௚ઢภޫʹͳΔೖࣹପԁภޫΛ࡞Γɼ‫ࢠޫݕ‬௨ա‫ޙ‬ͷޫྔ͕ 0 ʹͳΔΑ͏ʹ‫ࢠޫݕ‬Λճసͤͯ͞௚ަχίϧʢcrossed Nicolsʣภޫࢠ഑ஔʹ͢Δ͜ͱͰɼΨɼ∆ͷଌఆΛߦ͏ɽফޫ๏͸ɼଌఆ෼ղೳ͕ߴ͍൓໘ɼଌఆʹ௕͍࣌ؒΛཁ͢Δͱ͍͏ܽ఺͕͋Δɽ·ͨɼଌఆʹλ/4 ൘Λ༻͍ΔͨΊɼ‫ج‬ຊతʹ෼ޫΤϦϓιϝτϦʔʹ͸޲͔ͳ͍ɽҰํɼޫֶ‫ܥ‬Λফޫঢ়ଶʹͤͣɼ‫ࢠޫݕ‬௨ա‫ޙ‬ͷޫ‫౓ڧ‬Λͦͷ··ଌఆ͢Δํ๏Λɼফޫ๏ʹରͯ͠ଌޫ๏ͱ‫Ϳݺ‬ɽଌޫ๏ʹ͸ɼภޫૉࢠΛ‫ػ‬ցతʹճసͤ͞Δճస‫ܕࢠޫݕ‬ʢrotating analyzerʣ͓Αͼճసิঈࢠ‫ܕ‬ʢrotating compensatorʣɼޫ஄ੑมௐ‫ث‬Λ༻͍ͨҐ૬มௐ‫ܕ‬ʢphase modulationʣͳͲ͕͋Δɽ‫ࡏݱ‬ɼࢢൢ͞Ε͍ͯΔ෼ޫΤϦϓιϝʔλʔͷ΄ͱΜͲ͸ɼଌޫ๏Λ࠾༻͍ͯ͠Δͱ͍ͬͯྑ͍ɽ
Fig. 7. Simulated (a) spectra of (Ψ, ∆) and (b) reflectance spectraof SiO2 on crystalline silicon substrate obtained from diﬀerent
thicknesses of the SiO2 layer.

Fig.8 ʹɼ୅දతͳଌఆํࣜͰ͋Δճస‫ܕࢠޫݕ‬෼ޫΤϦϓιϝʔλʔͷ‫ج‬ຊߏ੒ͱ‫ݕ‬ग़৴߸ͷ֓ཁΛࣔ͢ɽଆ ∆ ≈ 180◦ ͔Β௕೾௕ଆ ∆ ≈ 0◦ ʹେ͖͘มԽ͍ͯ͠

Δɽd = 0 nm ⇒ 2.5 nm ͷບްมԽΛ‫ݟ‬Δͱɼओೖࣹ֯લ‫Ͱޙ‬ඇৗʹେ͖ͳ ∆ มԽΛࣔ͢͜ͱ͕෼͔ΔɽΤϦϓιϝτϦʔͰ͸ɼৼ෯൓ࣹ܎਺ͷൺ rp /rs Λଌఆ͍ͯ͠Δ͜ͱ͔Βɼओೖࣹ֯෇ۙͰ࠷΋ଌఆ‫ͳ͘ߴ͕౓ײ‬ΔͷͰ͋Δɽ෼ޫΤϦϓιϝτϦʔ͕ɼ‫ۃ‬ബບʹඇৗʹߴ͍‫౓ײ‬Λ༗͢Δͷ͸ɼ͜ͷओೖࣹ֯෇ۙʹ͓͚ΔภޫมԽʹෛ͏ͱ͜Ζ͕େ͖͍ɽҰํɼd ʽ 10 nm ʹ͓͚Δ൓ࣹ཰εϖΫτϧมԽ͸‫ۃ‬Θ͔ͣͰɼ೾௕ɿ633 nmɼ

d = 0 nm ⇒ 2.5 nm ͷບްมԽʹର͢Δ൓ࣹ཰มԽ͸

0.0003 ʹա͗ͳ͍ʢFig.7(b)ʣɽ͜Ε͸ɼҰൠతͳ෼ޫ
ޫ౓‫Ͱܭ‬͸ଌఆ͕ࠔ೉ͳมԽྔͰ͋Δɽ͜ͷΑ͏ʹɼ਺ेφϊϝʔλʔΛԼճΔ‫ۃ‬ബບͷଌఆͰ͸ɼ෼ޫΤϦϓιϝτϦʔͷߴ͍‫͕౓ײ‬ඞཁʹͳΔɽ

Fig. 8. (a) Schematic of rotating-analyzer ellipsometer (RAE)
and (b) normalized light intensity in RAE; plotted as a functionof time.

5 ɹΤϦϓιϝʔλʔճస‫ܕࢠޫݕ‬͸ɼߏ੒͕ൺֱత؆୯Ͱਫ਼౓͕ग़͠΍ภޫղੳύϥϝʔλʔ Ψɼ∆ Λଌఆ͢Δ૷ஔΛΤϦϓ͘͢ɼࢢൢ૷ஔʹ΋޿͘࠾༻͞Ε͍ͯΔɽ෼ޫΤϦϓιϝʔλʔʢellipsometerʣͱ‫Ϳݺ‬ɽΤϦϓιϝʔλʔʹιϝʔλʔͰ͸ɼϋϩήϯϥϯϓͳͲͷന৭ޫ‫ͱݯ‬෼͸ɼภޫૉࢠ഑ஔ΍มௐ‫ߏػ‬ͷҟͳΔ͍͔ͭ͘ͷଌఆ๏͕ଘࡏ͢ΔɽΤϦϓιϝʔλʔ͸ɼͦͷଌఆ‫্ߏػ‬ɼେ͖͘ফޫ๏ʢnull ellipsometryʣͱଌޫ๏ʢphotometricellipsometryʣʹ෼͚ΒΕΔɽޫ‫ث‬Λ༻͍ͯ Ψɼ∆ ͷεϖΫτϧଌఆΛߦ͏ɽ࠷ۙͰ͸ɼ෼ޫଌఆͷߴ଎ԽΛ໨తͱͯ͠ɼϑΥτμΠΦʔυΞϨΠʢPDA: photodiode array) ‫ݕ‬ग़‫ث‬Λ༻͍Δͷ͕Ұൠతʹͳ͖͍ͬͯͯΔɽճస‫ܕࢠޫݕ‬ͷ৔߹ɼ‫ط‬஌6ాॴར߁ɿʮ෼ޫΤϦϓιϝτϦʔɿ‫͔ૅج‬ΒԠ༻·Ͱʯͷภޫʢయ‫ܕ‬తʹ͸ɼp ภޫͱ s ภޫʹಉ͡ৼ෯Λ༩͑ ʢ1ʣΨ, ∆ εϖΫτϧଌఆΔ 45◦ ํҐͷ௚ઢภޫʣΛೖࣹ͠ɼࢼྉ͔Βͷ൓ࣹପ෼ޫΤϦϓιϝʔλʔΛ༻͍ͯࢼྉͷ Ψɼ∆ εϖΫԁภޫΛճస‫ʹࢠޫݕ‬Αͬͯਖ਼‫ݭ‬೾ʹมௐ͠ɼͦͷ‫ݕ‬τϧΛଌఆ͢Δɽ‫ج‬൘ͷޫֶఆ਺͸ɼจ‫ݙ‬஋ 6 ͳͲΛࢀग़ޫ‫౓ڧ‬ͷ‫֨ن‬ԽϑʔϦΤ܎਺͔Β Ψ,∆ εϖΫτϧΛরͯ͠༻ҙ͢Δ͔ɼ༧ΊຊଌఆղੳखॱͰ‫ٻ‬Ί͓ͯ͘.

3‫ٻ‬ΊΔ ɽʢ2ʣޫֶϞσϧͷߏஙࢼྉͷ૚ߏ଄Λ‫ه‬ड़͠ɼ֤૚ͷ༠ిؔ਺ϞσϧΛબ

6 ɹଌఆղੳͷྲྀΕ୒͢Δɽޫֶఆ਺Ϟσϧͷ֤ύϥϝʔλʔॳ‫ظ‬஋ɼ֤૚ͷບްॳ‫ظ‬஋Λઃఆ͢ΔɽޫֶϞσϧͷͲͷύϥϝʔ෼ޫΤϦϓιϝτϦʔͰ͸ɼΨɼ∆ ͷଌఆεϖΫτϧλʔΛϑΟοςΟϯάม਺ʹ͢Δ͔Λબ୒͢ΔɽͱޫֶϞσϧ͔Β‫͞ࢉܭ‬ΕͨγϛϡϨʔγϣϯεϖΫτϧͱͷϑΟοςΟϯάʹΑΓɼບް΍ޫֶఆ਺ͳͲͷ ʢ3ʣγϛϡϨʔγϣϯ࡞੒ͨ͠ޫֶϞσϧ͔Β Ψɼ ∆ γϛϡϨʔγϣϯε෺ཧྔΛ‫ٻ‬ΊΔɽͦͷͨΊɼޫֶϞσϧͷཱͯํɼղੳͷਐΊํʹΑͬͯɼಘΒΕΔ݁Ռʹҧ͍͕ੜͣΔɽ͜͜Ͱ͸ɼFig.9 Λ࢖͍ɼ෼ޫΤϦϓιϝτϦʔʹ͓͚ΔσʔλղੳͷྲྀΕΛ֬ೝ͠Α͏ɽϖΫτϧΛੜ੒͢Δɽ
ʢ4ʣύϥϝʔλʔϑΟοςΟϯά
ଌఆσʔλͱγϛϡϨʔγϣϯεϖΫτϧͷ‫͕ࠩޡ‬࠷খʹͳΔΑ͏ʹɼϑΟοςΟϯάΛ࣮ࢪ͢Δɽ‫͕ࠩޡ‬ॴఆͷ஋ΛԼճΔ͔ɼ‫ࢉܭ‬൓෮ճ਺ͷ্‫ʹݶ‬ୡ͢ΔͱϑΟοςΟϯά͸ଧͪ੾ΒΕɼऩଋ݁Ռͱͯ͠ບͷޫֶఆ਺ɼບްͳͲͷ஋͕ಘΒΕΔɽʢ5ʣऩଋ݁ՌͷධՁऩଋ‫͕ࠩޡ‬େ͖͔ͬͨΓɼ݁Ռ͕෺ཧతʹෆ߹ཧͳ৔߹͸ɼ‫ॴہ‬తͳ‫ۃ‬খ஋ʹऩଋ͍ͯ͠ΔՄೳੑ͕͋Δ
ͷͰɼ(2) ʹ໭Γ‫ࢉܭ‬৚݅Λ࠶‫ݕ‬౼͢ΔɽޫֶϞσϧͷվળɼॳ‫ظ‬஋ͷదਖ਼Խɼύϥϝʔλʔͷ࠶બ୒ͳͲͷ‫ޙ‬ɼ࠶౓ϑΟοςΟϯάΛ࣮ߦ͢Δɽ߹ཧతͳऩଋ݁Ռ͕ಘΒΕΔ·Ͱɼ(2) ∼ (5) ͷखॱΛ‫܁‬Γฦ͢ɽϑΟοςΟϯάղੳͰ͸ɼʮγϯϓϧͳޫֶϞσϧ͔Βελʔτ͠ɼεϖΫτϧมԽʹ‫౓ײ‬ͷ͋Δখ਺ͷύϥϝʔλʔ͔ΒϑΟοςΟϯάΛ࢝Ίͯɼऩଋঢ়‫گ‬Λ‫ݟ‬ͳ͕Β࣍ୈʹࢼྉߏ଄ͷࡉ෦ʹ߹ΘͤͯޫֶϞσϧΛ
ਐԽͤ͞Δʯͱ͍͏ͷ͕࣮ફతͳղੳͷਐΊํͰ͋Δɽ

7 ɹԠ༻ബບղੳ
7.1 ɹޫֶബບ༻ߴ۶ં཰ࡐྉͷޫֶఆ਺ܾఆ
ࢎԽϋϑχ΢ϜʢHafnium oxide, HfO2 ʣࢼྉΛྫʹɼ
Fig. 9. Flow diagram of the data analysis procedure in spectroscopic ellipsometry.

ޫֶఆ਺ܾఆʹ͍ͭͯղઆ͢ΔɽHfO2 ͸ɼແ৭ͷແ‫ػ‬Խ߹෺Ͱɼࢵ֎ྖҬ͔Β੺֎ྖҬ·Ͱಁա͢Δ͜ͱ͔ΒɼޫֶίʔςΟϯάͷߴ۶ં཰ࡐྉͱͯ͠ར༻͞ΕΔɽࢎԽνλϯʢTiO2 ʣɼ‫ࢎޒ‬ԽλϯλϧʢTa2 O5 ʣͳͲͷޫֶίʔςΟϯά༻ߴ۶ં཰ࡐྉʹൺ΂ΔͱɼόϯυΪϟοϓ͕޿͘ɼࢵ֎ྖҬʹ͓͚Δಁաಛੑ͕༏Ε೔ຊֶज़ৼ‫ڵ‬ձϝλϚςϦΞϧୈ 187 ҕһձ (2014 ೥ 6 ݄ 13 ೔)

7͍ͯΔɽ·ͨɼHfO2 ͓Αͼͦͷෳ߹෺͸ɼߴ͍༠ి཰Λ࣋ͭ͜ͱ͔ΒɼೋࢎԽέΠૉʢSiO2 ʣʹ୅ΘΔήʔτઈԑບ༻ߴ༠ి཰ʢHigh-kʣࡐྉͱͯ͠஫໨͞Εͯ
͍Δɽ

Fig.10(a) ∼ (d) ʹεϖΫτϧϑΟοςΟϯάղੳ݁ՌΛࣔ͢ɽଌఆࢼྉʢ‫ࣜג‬ձࣾΦϓτΫΤετ༷͝ఏ‫ڙ‬ʣ

Fig. 11. Optical constants spectra of HfO2 layer.

Bruggeman Ϟσϧ 11 Ͱ͋ΔɽTauc-Lorentz ͸ɼΞϞϧϑΝεಛ༗ͷόϯυΪϟοϓʢTauc Ϊϟοϓʣʹ LorentzϞσϧΛֻ͚߹ΘͤΔ͜ͱͰɼε2 ͷඇରশͳϐʔΫ‫ܗ‬ঢ়Λ࠶‫͢ݱ‬ΔϞσϧͰ͋Δɽද໘ϥϑωε૚ʹ༻͍ͨBruggeman Ϟσϧ͸ɼ࠷΋Ұൠతͳ༗ޮഔ࣭ۙࣅϞσϧͰ͋Δɽ

Fig.10(b),(c) ͷ ऩ ଋ ݁ Ռ ͔ Β ɼද ໘ ϥ ϑ ω ε ૚ɿ3.89 nmɼHfO2 ɿ199.96 nm ͷບް஋͕ಘΒΕ͍ͯΔɽ

7.2 ɹಁ໌ి‫ۃ‬ͷ۶ં཰܏ࣼບղੳऎʢSnʣΛυʔϓͨ͠ࢎԽΠϯδ΢ϜʢIn2 O3 ʣ͸ɼ௨ৗɼITOʢIndium tin oxideʣͱ‫ݺ‬͹Εɼి‫఻ؾ‬ಋੑͱ
Fig. 10. (a) Stack of layers of the HfO2 sample and (b),(c) fitting
results of (Ψ, ∆) spectra.

ՄࢹޫͷಁաੑΛซͤ࣋ͭ͜ͱ͔ΒɼӷথσΟεϓϨΠͳͲͷΦϓτΤϨΫτϩχΫεσόΠεͷಁ໌ి‫ۃ‬ͱͯ͠޿͘ར༻͞Ε͍ͯΔɽ

͸ɼ୯݁থγϦίϯ‫ج‬൘ʢް͞ɿ0.5 mmʣ্ʹΠΦϯϏʔϜΞγετ๏ʢIAD: ion-beam assisted depositionʣͰ੒ບͨ͠ HfO2 ບͰ͋Δɽଌఆʹ͸ճసิঈࢠ‫ܕ‬෼ޫΤϦϓιϝʔλʔΛ༻͍ɼ೾௕ൣғɿ190 nm ∼ 1700 nmͰଌఆͨ͠ɽຊଌఆͰ͸ɼ୯݁থγϦίϯ‫ج‬൘ͷओೖࣹ֯ʢ∼ 75.3◦ ʣ෇ۙΛத৺ͱͨ͠ 3 ೖࣹ֯ʢ65◦ ɼ70◦ ɼ75◦ ʣଌఆΛߦ͏͜ͱͰਫ਼౓޲্Λਤ͍ͬͯΔ 12 ɽFig.11 ʹղੳͰಘΒΕͨ HfO2 ບͷޫֶఆ਺εϖΫτϧΛࣔ͢ɽϑΟοςΟϯάղੳͷ݁Ռɼए‫ׯ‬ͷද໘ϥϑωεΛԾఆͨ͠ํ͕ྑ͍ऩଋ͕ಘΒΕͨɽද໘ϥϑωε͸ɼ฼ମࡐྉɿਅۭதʹɼ‫ܗٿ‬ͷບࡐྉύʔςΟΫϧ͕෼ࢄͨ͠ϥϑωε૚ΛԾఆ͠ɼ༗ޮഔ࣭ۙࣅʢEMA:eﬀective medium approximationʣΛ༻͍ͯ૚ͷ༗ޮ༠ి཰Λ‫͢ࢉܭ‬Δํ๏͕औΒΕΔɽຊղੳͰ࢖༻ͨ͠༠ిؔ਺͸ɼHfO2 ૚ɿTauc-Lorentz Ϟσϧɼද໘ϥϑωε૚ɿ

ITO ͸ɼ੒ບ๏΍੒ບ৚݅ʹΑͬͯ݁থੑʹҧ͍͕ੜ͡қ͘ɼి‫ؾ‬ಛੑɼޫֶಛੑ͕มԽ͢ΔɽͦͷͨΊɼ੡඼ؒɾࢼྉؒͰޫֶಛੑ͕ҟͳͬͨΓɼࢼྉ಺ͷҟͳ
Δଌఆ৔ॴͰޫֶఆ਺͕ҧͬͨΓ͢ΔͨΊɼ෼ޫΤϦϓιϝτϦʔͷධՁର৅ͱͯ͠͸΍͔͍ͬͳࡐྉͷҰ
ͭͰ͋Δɽಛʹɼ݁থԽաఔͰੜ͡Δͱߟ͑ΒΕΔບްํ޲ͷີ౓෼෍͸ɼ෼ޫΤϦϓιϝτϦʔղੳΛ೉
͘͢͠ΔཁҼͷҰͭͰ͋Δɽ

Fig.12 ʹɼ୯७ͳ ITO ୯૚ບΛԾఆͨ͠৔߹ͷϑΟοςΟϯάղੳ݁ՌΛࣔ͢ɽࢼྉ͸ɼΨϥε‫ج‬൘ʢCorning7059ɼ1 mm ްʣ্ͷ ITO ບͰ͋Δɽଌఆ͸ɼճసิঈࢠ‫ܕ‬෼ޫΤϦϓιϝʔλʔΛ༻͍ɼ೾௕ൣғɿ320 nm ∼1690 nmɼೖࣹ֯ɿ50◦ ɼ60◦ ɼ70◦ ͰߦͬͨʢFig.12(a)ʣɽ
ITO ͸ɼࢵ֎ྖҬʹ͓͚ΔిࢠόϯυؒભҠͷ‫ڞ‬໐‫ٵ‬ऩͱۙ੺֎ྖҬ͔Β௕೾௕ଆʹ޿͕ΔϑϦʔΩϟϦΞ‫ٵ‬8ాॴར߁ɿʮ෼ޫΤϦϓιϝτϦʔɿ‫͔ૅج‬ΒԠ༻·Ͱʯ͘ɼ౷‫ܭ‬తʹฏ‫ࢄۉ‬ཚ࣌ؒ ⟨τ⟩ ఔ౓Ͱࢄཚ͞ΕΔ݁ՌɼΩϟϦΞͷҠಈ଎౓͸Ұఆ஋ʹམͪண͘ɽͦͷͨΊɼޫి৔ͷप೾਺͕͋Δఔ౓Ҏ্ʹߴ͘ͳΔͱɼΩϟϦΞ͕ి৔ৼಈʹ௥͍͚ͭͳ͘ͳΓɼITO ʹޫ͕ಁա࢝͠
ΊΔɽITO ͕ಋిੑΛ࣋ͪͳ͕ΒɼՄࢹྖҬͰߴ͍ޫಁա཰Λࣔ͢ཧ༝͸͜͜ʹ͋Δɽ‫࣭ۉ‬୯૚ບΛԾఆͨ͠ Fig.12(b),(c) ͷղੳ݁Ռ͸ɼશମతʹऩଋঢ়ଶ͕ྑ͘ͳ͍ɽಛʹɼۙ੺֎ྖҬͷ Ψ ͕େ͖ͣ͘Ε͓ͯΓɼϑϦʔΩϟϦΞΛ‫ه‬ड़͢Δ Drude Ϟσϧͷ 2 ͭͷύϥϝʔλʔɿϓϥζϚप೾਺ɼμϯϐϯά܎਺ʹదਖ਼ͳղ͕ಘΒΕ͍ͯͳ͍͜ͱΛ͍ࣔͯ͠Δɽ͜Ε͸ɼບްํ޲ʹີ౓෼෍Λ࣋ͭ ITO ບΛ୯७ͳ୯૚ບͱԾఆͨ͜͠ͱʹ‫ݪ‬Ҽ͍ͯ͠ΔɽຊྫͷΑ͏ʹບްํ޲ʹޫֶఆ਺͕෼෍͍ͯ͠ΔບΛҰൠʹ۶ં཰܏ࣼບͱ‫Ϳݺ‬ɽ

Fig.13 ʹ ITO ບΛ۶ં཰܏ࣼບͱԾఆͨ͠ϑΟοςΟ
ϯά݁ՌɼFig.14 ʹղੳʹΑͬͯಘΒΕͨ ITO ບͷޫֶఆ਺εϖΫτϧΛࣔ͢ɽ
Fig. 12. (a) Stack of layers of the ITO sample and (b),(c) fitting
results of (Ψ, ∆) spectra using a simple ITO layer model.

ऩͷؒʹ‫·ڬ‬ΕͨՄࢹྖҬͰಁ໌ͳޫֶఆ਺εϖΫτϧΛ࣋ͭɽຊղੳͰ͸ɼITO ບͷ༠ిؔ਺Λ Tauc-LorentzϞσϧʢࢵ֎ྖҬͷిࢠόϯυؒભҠʣͱ Drude ϞσϧʢϑϦʔΩϟϦΞ‫ٵ‬ऩʣͷ 2 ͭͷৼಈࢠΛ༻͍ͯϞσϧԽ͍ͯ͠ΔɽϑϦʔΩϟϦΞ‫ٵ‬ऩΛ‫ه‬ड़͢Δ Drude Ϟσϧ͸ɼ࣍ࣜͰ༩͑ΒΕΔɽm∗

d2 xdx+ m∗ Γ= −eE0 exp(iωt)
2dtdt(4)ͨͩ͠ɼm∗ ͸ΩϟϦΞͷ༗ޮ࣭ྔɼΓ ͸‫ݮ‬ਰ܎਺Ͱ͋
ΔɽDrude Ϟσϧͷ Γ ͸ɼΩϟϦΞͷฏ‫ࢄۉ‬ཚ࣌ؒͷ‫ٯ‬਺ ⟨τ⟩−1 Ͱ༩͑ΒΕΔɽLorentz Ϟσϧ (2) ࣜͱ Drude Ϟσϧ (4) ࣜͷҧ͍͸ɼDrude Ϟσϧʹ෮‫ྗݩ‬ͷ߲ me ω20 x͕ͳ͍͜ͱͰ͋Δɽ͜Ε͸ɼి৔ʹԠ౴ͯ͠Ҡಈͨ͠ΩϟϦΞʹରͯ͠ɼฏߧҐஔʹ໭ͦ͏ͱ͢Δ෮‫͕ྗݩ‬ಇ͔ͣɼΩϟϦΞ͕ଋറΛड͚ͣʹి৔Ԡ౴͢Δ͜ͱΛද͍ͯ͠Δɽप೾਺͕௿͘ΩϟϦΞ͕ࣗ༝ʹి৔Ԡ౴Ͱ͖Δ೾௕ྖҬʢλ > ∼ 1 µmʣͰ͸ɼITO தͰి৔ৼFig. 13. (a) Modified layer structure and (b),(c) fitting results of(Ψ, ∆) spectra using a graded ITO layer model.

ಈ͕‫ܧ‬ଓͰ͖ͳ͍ͨΊɼޫ͸ೖΓࠐΉ͜ͱ͕Ͱ͖ͳ͍ɽ಺෦తʹ͸ɼ۶ં཰܏ࣼບΛԾ૝తͳෳ਺૚ͷεϥͭ·Γɼλ > ∼ 1 µm ͷྖҬͰ͸ɼITO ͸ಋిੑ͕͋Γϒʹ෼ׂ͠ɼ۶ં཰͕ঃʑʹมԽ͢Δଟ૚ບͱͯ͠ղۚଐతʹৼΔ෣͏ɽ͔͠͠ɼʮϑϦʔΩϟϦΞʯͱ͸͍ੳ͢ΔɽFig.13(b),(c) Ͱɼे෼ʹখ͍͞ϑΟοςΟϯά͏΋ͷͷɼి৔ʹΑͬͯແ‫ʹݶ‬Ճ଎͞ΕΔΘ͚Ͱ͸ͳ‫Ͱࠩޡ‬ऩଋ͍ͯ͠Δ͜ͱ͕෼͔ΔɽϑΟοςΟϯάʹΑ

೔ຊֶज़ৼ‫ڵ‬ձϝλϚςϦΞϧୈ 187 ҕһձ (2014 ೥ 6 ݄ 13 ೔)

9Fig. 14. Optical constants spectra of ITO which depends on depthof ITO layer.

ΓಘΒΕͨ ITO ບͷऩଋບް஋͸ɼdIT O = 93.49 nm Ͱ͋ΔɽFig.14 ͔Βɼບͷද໘ͱఈ໘Ͱޫֶಛੑ͕େ͖͘ҧ͏͜ͱ͕֬ೝͰ͖ΔɽಛʹɼϑϦʔΩϟϦΞʹ‫ى‬Ҽ͢Δۙ੺֎ྖҬͷফਰ܎਺͕ɼບްํ޲Ͱେ͖͘෼෍͠
͍ͯΔɽ͜Ε͸ɼບͷް͞ํ޲Ͱి‫ؾ‬ಋిੑ΋େ͖͘มԽ͍ͯ͠Δ͜ͱΛҙຯ͍ͯ͠Δɽ

7.3 ɹ C60 ບͷޫֶఆ਺εϖΫτϧධՁ

Fig. 15. (a) Stack of layers of the C60 sample and (b),(c) fitting
results of (Ψ, ∆) and transmittance spectra.

ε2 Λ 7 ͭͷৼಈࢠΛ࢖ͬͯ‫ه‬ड़͍ͯ͠Δɽ·ͨɼ෼ޫΤ༗‫ػ‬τϥϯδελɼ༗‫ػ‬ଠཅి஑ͳͲͷ༗‫ػ‬൒ಋମϦϓιϝτϦʔͰ͸ɼখ͞ͳ‫ٵ‬ऩ܎਺ʢα < 100 cm−1 ʣ͸ɼ࣍ੈ୅σόΠεͱͯ͠‫ظ‬଴͞Ε͍ͯΔɽ༗‫ػ‬൒ಋΛਖ਼֬ʹܾఆ͢Δ͜ͱ͕೉͍ͨ͠Ί 3 ɼຊଌఆͰ͸ɼফମσόΠεͷੑೳ޲্ʹ͸݁থੑͷྑ͍‫ͳ࣭ۉ‬༗‫ػ‬ബਰ܎਺ͷܾఆਫ਼౓޲্Λ໨తͱͯ͠ɼ0◦ ೖࣹͷಁա཰ບͷ࡞੡͕ෆՄܽͰ͋Γɼ༗‫ػ‬ബບͷ෺ੑΛඇ઀৮ɾඇ

εϖΫτϧͱ 3 ೖࣹ֯ͷ෼ޫΤϦϓιϝτϦʔεϖΫഁյͰධՁ͢Δ͜ͱ͸ॏཁͰ͋Δ 13 ɽ͜͜Ͱ͸ɼ୅දτϧͷಉ࣌ϑΟοςΟϯάղੳΛߦ͍ͬͯΔɽతͳ༗‫ػ‬൒ಋମࡐྉͰ͋Δ C60ʢϑϥʔϨϯʣບͷޫֶ෺ੑධՁΛߦͬͨ݁ՌΛ঺հ͢Δɽଌఆࢼྉʢ‫ࣜג‬ձࣾΠσΞϧελʔ༷͝ఏ‫ڙ‬ʣ͸ɼ఍߅Ճ೤ࣜৠண૷ஔͰ੒ບ͞Εͨੴӳ‫ج‬൘্ͷ C60 ບͰɼߴ‫ࢎ౓ײ‬ૉηϯαʔ༻ʹ։ൃ͞Εͨ΋ͷͰ͋ΔɽC60 ບࢼྉͷ૚ߏ଄͸ɼBruggeman ϞσϧΛ༻͍ͨ༗ޮഔ࣭ۙࣅͷද໘ϥϑωε૚ΛՃ͑ɼੴӳ‫ج‬൘্ͷೋ૚ບ
ͱͨ͠ɽFig.15(b) ∼ (d) ͷϑΟοςΟϯά݁Ռ͸ɼ͍ͣΕ΋શ೾௕ྖҬͰඇৗʹྑ͘Ұக͓ͯ͠Γɼղੳ݁Ռͷ৴པੑΛཪ෇͚͍ͯΔɽ͸ɼ݁থମͰ͋Γͳ͕Β݁থؒͷܺؒαΠζ͕ࢎૉ෼Fig.16 ʹɼղੳʹΑΓಘΒΕͨޫֶఆ਺εϖΫτϧࢠ΍ਫૉ෼ࢠΑΓେ͖͍ͨΊɼΨε෼ࢠ‫ݕ‬ग़ʹ‫د‬༩͢Λࣔ͢ɽऩଋ݁Ռ͔Βɼද໘ϥϑωε૚ͷް͞ drough =Δද໘ੵ͕େ͖͘ɼηϯαʔͷߴ‫౓ײ‬Խ͕ՄೳͰ͋Δɽ

2.85 nmɼC60 ບͷް͞ dC60 = 304.02 nm ͕ಘΒΕͨɽ

Fig.15 ʹϑΟοςΟϯάղੳ݁ՌΛࣔ͢ɽଌఆʹ͸ճຊྫͷΑ͏ʹ‫ٵ‬ऩ͕͋Δࢼྉͷ৔߹ɼ༧Ίಁա‫ٵ‬ऩసิঈࢠ‫ܕ‬෼ޫΤϦϓιϝʔλʔΛ༻͍ͨɽଌఆೖࣹεϖΫτϧΛଌఆ͓ͯ͘͠ํ๏΋༗ޮͰɼ഑ஔ͢΂͖֯͸ɼੴӳ‫ج‬൘ͷओೖࣹ֯ʢ∼ 56◦ ʣ෇ۙΛத৺ͱͨ͠ৼಈࢠͷ਺΍‫ڞ‬໐प೾਺Ґஔɼৼಈࢠ‫౓ڧ‬Λ༧૝͢Δ3 ೖࣹ֯ʢ50◦ ɼ60◦ ɼ70◦ ʣʹઃఆͨ͠ɽଌఆ೾௕ൣғͷʹ໾ཱͭɽଌఆͨ͠ಁա‫ٵ‬ऩεϖΫτϧͷ৴པੑ͕͸ɼ245 nm ∼ 1700 nm Ͱ͋Δɽߴ͚Ε͹ɼFig.16 ͷಉ࣌ϑΟοςΟϯάʹ௥Ճ͢Δͷ΋C60 ບͰ͸ɼࢵ֎͔ΒՄࢹྖҬʹ͔͚ͯෳ਺ͷ‫ٵ‬ऩϐʔΫ͕͋ΔʢFig.16 ࢀরʣɽຊղੳͰ࢖༻ͨ͠ C60 ບͷ༠ిؔ਺͸ɼ‫ٵ‬ऩϐʔΫʹରԠ͢Δෳૉ༠ి཰‫ڏ‬෦ྑ͍ํ๏Ͱ͋Δɽ

10ాॴར߁ɿʮ෼ޫΤϦϓιϝτϦʔɿ‫͔ૅج‬ΒԠ༻·Ͱʯ[8] S.K. O’Leary, S.R. Johnson, and P.K. Lim, “The relationship between the distribution of electronic states and theoptical absorption spectrum of an amorphous semiconductor: An empirical analysis”, J. Appl. Phys., 82, pp.33343340 (1997).
[9] C.C. Kim, J.W. Garland, H. Abad, and P.M. Raccah, “Modeling the optical dielectric function of semiconductors:
Extension of the critical-point parabolic-band approximation”, Phys. Rev. B 45, pp.11749-11767 (1992).

[10] L. Cauchy, “Sur la dispersion de la lumiere”, bull.
des. sc. maht. 14, p.9 (1830).

Fig. 16. Optical constants spectra of the C60 layer.

8 ɹ͓ΘΓʹ
ภޫղੳΛ༻͍ͯບްΛܾఆͨ͠࠷ॳͷ࿦จ 1 ͔Β
໿ 120 ೥ͷ࣌Λ‫ͯܦ‬ɼ෼ޫΤϦϓιϝτϦʔ͸୯ͳΔ
ਫ਼ີບް‫ܭ‬ͷ࿮Λ௒͑ɼ෯޿͍෼໺Ͱɼ͞·͟·ͳࡐ

[11] D.A.G.
Bruggeman,“Berechnungverschiedener
physikalischer Konstanten von heterogenen Substanzen”,
Ann. Phys. (Leipzig) 24, pp.636-679 (1935).
[12] G.H. Bu-Abbud, S.A. Alterovitz, N.M. Bashara, and J.A.
Woollam, “Multiple-Wavelength-Angle-of-Incidence Ellipsometry: Application to Silicon Nitride-Gallium Arsenide Structures”, J. Vac. Sci. Technol. Al p.619 (1983).
[13] H. Oizumi, M. Saida, H. Sagami, K. Omote, Y. Mizobuchi,
Y. Kasama, K. Yokoo, S. Ono, and T. Tadokoro, “Noncontact Thickness Monitor of Organic and Molecular Films”,
The 35th F-NT Sympo. p.140 (2008).

ྉ‫ܥ‬ͷޫ෺ੑղੳʹԠ༻͞ΕΔΑ͏ʹͳͬͨɽ͞Βʹ࠷ۙͰ͸ɼෳ۶ંੑɼટޫੑɼ௚ઢೋ৭ੑɼԁೋ৭ੑɼภޫղফͳͲશͯͷภޫಛੑΛ‫ٻ‬ΊΔ෼ޫϛϡϥʔߦྻ‫ܭ‬ଌ๏ͳͲ΋։ൃ͞Ε͓ͯΓɼബບධՁͷ͞ΒͳΔ˞ຊߘ͸ɼ೔ຊֶज़ৼ‫ڵ‬ձϝλϚςϦΞϧୈ 187 ҕһձߨԋձʢ2014 ೥ 6 ݄ 13 ೔ʣͷ༧ߘ‫ߘݪ‬ΛվฤɼΧϥʔԽͨ͠΋ͷͰ͢ɽൃల͕‫ظ‬଴͞ΕΔɽຊߘͰ͸ɼࢴ໘ͷ౎߹͔Βৄࡉઆ໌͸লུͨ͠ɽ൓ࣹ/۶ંɼϑϨωϧ܎਺ɼ‫ׯ‬বɼ༠ిؔ਺ͳͲޫֶશൠʹ͍ͭͯ͸จ‫ ݙ‬3) Λɼ෼ޫΤϦϓιϝτϦʔશൠʹͭ————————————————————————ɹ ాॴ ར߁ʢToshiyasu TADOKOROʣ ത࢜ʢ޻ֶʣ͍ͯ͸จ‫ ݙ‬2) Λ͝ࢀর͍͖͍ͨͩͨɽ༗‫ݶ‬ձࣾςΫϊɾγφδʔ୅දऔక໾˟ 193-0832
౦‫౎ژ‬ീԦࢠࢢࢄాொ 2-46-16
ి࿩ & FAXɿ042-667-1992
tado@techno-synergy.co.jp
http://www.techno-synergy.co.jp/ࢀߟจ‫ݙ‬[1] P. Drude, “Ueber Oberflächenschichten”, Annalen derPhysik und Chemie, 36, pp.532-560 and pp.865-897(1889).
[2] R.M.A. Azzam and N.M. Bashara, “Ellipsometry and Polarized Light”, North Holland Press, Amsterdam (1977).

———————————————————————————ɹ

[3] ౻‫ݪ‬༟೭, “෼ޫΤϦϓιϝτϦʔ”, ‫ؙ‬ળ (2003)ɽ
[4] େ௡‫ݩ‬Ұɼాॴར߁, “ޫֶೖ໳”, ே૔ॻళ, pp.54-79(2008).
[5] Charles Kittel(ஶ), Ӊ໺ྑਗ਼ɼ௡԰ঢɼ৿ాষɼࢁԼ࣍࿠(༁), “‫ݻ‬ମ෺ཧֶೖ໳ (Լ)”, ‫ؙ‬ળ, pp.3-7 (1998).
[6] E.D. Palik (editor), “Handbook of Optical Constants ofSolids”, Academic Press, New York, (1985).
[7] G.E. Jellison, Jr., “Spectroscopic ellipsometry data analysis: measured versus calculated quantities”, Thin SolidFilms 313-314 pp.33-39 (1998).
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