永久磁石を用いた半導体２次元電子系のホール測定

Title

永久磁石を用いた半導体２次元電子系のホール測定

Author(s)

鈴木　恭一

Citation

福岡工業大学総合研究機構研究所所報　第1巻 　P19-P22

Issue Date

2018-12

URI

http://hdl.handle.net/11478/1216

Right

Type

Departmental Bulletin Paper

Textversion

Publisher

福岡工業大学　機関リポジトリ　

FITREPO

Ӭٱ࣓ੴΛ༻͍ͨ൒ಋମ

2

࣍ݩిࢠܥͷϗʔϧଌఆ

ླ໦ɹګҰ

(

޻ֶ෦ిؾ޻ֶՊ

)

Hall Measurements with a Permanent Magnet for Semiconductor

Two-Dimensional Electron Systems

Kyoichi SUZUKI (Department of Electrical Engineering, Faculty of Engineering)

Abstract: Hall measurement is useful to investigate basic electronic properties of semiconductor wafers. Since

the invention of the strong permanent magnets, Hall measurement systems using permanent magnets have been commercially available. However, these systems include too many functions and therefore are too expensive for single laboratory use. We propose here a very simple Hall measurement system with a neodymium permanent magnet at low cost. Using this system, electron density and mobility in a Si-doped AlGaAs/GaAs single het-erostructure were measured. Obtained results are comparable to those found by using the commercially available system.

Keywords: Hall Measurement, Semiconductor Heterostructure, Two-Dimensional Electron System, Neodymium

1.

͸͡Ίʹ

൒ಋମσόΠε͸ɺߴ౓ͳूੵԽɾඍࡉԽ͕ͳ͞Εݱ ୅ͷ৘ใԽࣾձΛࢧ͍͑ͯΔɻใಓ౳Ͱ͸ɺूੵͨ͠τ ϥϯδελ਺΍ɺήʔτ͓Αͼ഑ઢͷඍࡉԽͳͲϓϩη εٕज़ʹ஫໨͕ू·͍ͬͯΔ͕ɺͦͷੑೳΛܾఆ͚ͮΔ ࠜݯ͸ɺ൒ಋମ΢ΣϋࣗମͷಛੑͰ͋Δɻ͜ͷ΢Σϋͷ ಛੑΛධՁ͢Δख๏ͷҰ͕ͭϗʔϧଌఆͰ͋Δɻϗʔϧ ଌఆͰ͸ɺ࣓৔தʹࢼྉΛஔ͖ɺిྲྀͱ࣓৔ͷ྆ํʹਨ ௚ํ޲ͷిѹ(ϗʔϧిѹ)Λଌఆ͢Δ͜ͱͰɺΩϟϦΞ (ిࢠ·ͨ͸ਖ਼޸)ೱ౓Λಉఆ͢Δɻ͞Βʹɺ͜ΕʹΑΓ ٻ·ͬͨΩϟϦΞೱ౓ͱɺ࣓৔͕ͳ͍ঢ়ଶͷଌఆʹΑΓ ٻΊͨ఍߅཰ΑΓɺ൒ಋମσόΠεͷੑೳΛେ͖͘ࠨӈ ͢ΔΩϟϦΞҠಈ౓͕ٻ·Δɻ ϗʔϧిѹ͸࣓৔ʹൺྫ͢ΔͨΊɺߴਫ਼౓ͷଌఆΛߦ ͏ͨΊʹ͸0.1 Tఔ౓Ҏ্ͷڧ͍࣓৔͕ඞཁͱͳΔɻै དྷɺ͜ͷΑ͏ͳڧ࣓৔Λൃੜͤ͞Δʹ͸ɺਫྫྷࣜͷి࣓ ੴ΍ۃ௿Թʹྫྷ٫ͨ͠௒఻ಋ࣓ੴΛ࢖͏ඞཁ͕͋Γɺඇ ৗʹେֻ͔Γͳ࣮ݧ૷ஔ͕ඞཁͰ͋ͬͨɻۙ೥ɺωΦδ Ϝ࣓ੴͷൃ໌ʹΑΓ0.1 Tఔ౓ͷ࣓৔͕༰қʹ࣮ݱͰ͖ ΔΑ͏ʹͳΓɺ૷ஔͷখܕԽ͕ਐΈɺݱࡏͰ͸ɺӬٱ࣓ ੴΛ༻͍ͨϗʔϧଌఆ૷ஔ͕͍͔ͭ͘ࢢൢ͞Ε͍ͯΔɻ ͔͠͠ͳ͕Βɺࢢൢͷϗʔϧଌఆ૷ஔ͸҆Ձͳ΋ͷͰ ΋50ສԁҎ্ͱɺେֶͷҰݚڀࣨͰಋೖ͢Δ͜ͱΛߟ͑ Δͱ·ͩ·ͩߴՁͰ͋Δɻ͜ͷߴՁʹͳΔཧ༝͸ɺ(1)ࢼ ྉʹਨ௚ํ޲ͷΈͷ࣓৔੒෼Λ࣋ͭɺ޿͘ۉҰͳ࣓৔ྖ ҬΛ࣮ݱ͢ΔͨΊʹɺ௚ܘ5 cmҎ্ͷେޱܘ࣓ੴΛࢼ ྉΛڬΉΑ͏ʹ2ݸ഑ஔ͍ͯ͠Δ͜ͱͱɺ(2)ଌఆΛࣗ ಈԽͤ͞Δ͜ͱͰ෇ՃՁ஋Λ෇͚͍ͯΔͨΊͰ͋Δɻ͜ ΕΒ͸͍ͣΕ΋࢈ۀతʹɺେޱܘ΢ΤϋΛߴ଎ͰධՁ͢ ΔͨΊʹඞཁͳػೳͰ͋Γɺ࣮ݧࣨϨϕϧͰɺ·ͯ͠΍ େֶʹ͓͍ͯڭҭ໨తͰ࢖༻͢Δ্Ͱ͸ա৒ͳػೳͰ͋ Δɻಛʹ্هཧ༝(1)ʹ͍ͭͯ͸ɺ൒ಋମσόΠε1ݸ ͷ੾Γग़͠αΠζ͸1 mm2ఔ౓Ͱ͋ΓɺۉҰͳ࣓৔ྖҬ ͸͜ΕΑΓ޿͚Ε͹े෼Ͱ͋Δɻ·ͨɺ Si-Metal-Oxide-Semiconductor (Si-MOSFET)΍൒ಋମϔςϩ઀߹ߏ଄ (ޙड़)Λݚڀର৅ʹ͢Δ৔߹ɺ2࣍ݩిࢠ(·ͨ͸ਖ਼޸) ܥͱͳΔͷͰɺࢼྉʹରͯ͠ਫฏํ޲ͷ࣓৔੒෼͕ଘࡏ ͯ͠΋ଌఆ஋ʹ͸Өڹ͠ͳ͍ɻ ࠓճզʑ͸ɺ൒ಋମϔςϩߏ଄ΛςʔϚͷҰͭͱ͢Δ ݚڀࣨͷ্ཱͪ͛ʹࡍͯ͠ɺࠓޙͷ൒ಋମ΢Τϋ͓Αͼ σόΠεධՁͷͨΊɺӬٱ࣓ੴ1ݸΛ༻͍ͨ୯७Ͱ͔ͭ Ӭଓతʹ࢖༻ՄೳͳϗʔϧޮՌଌఆ૷ஔͷ࡞੡Λߦͬͨɻ ຊ૷ஔΛ༻͍ͯSiมௐυʔϓAlGaAs/GaAs୯Ұϔς ϩߏ଄ࢼྉͷϗʔϧଌఆΛߦͬͨ݁Ռɺిࢠೱ౓ɺҠಈ ౓ͱ΋ʹࢢൢͷϗʔϧଌఆ૷ஔΛ༻͍ͨଌఆ݁Ռͱ΄΅ Ұக͠ɺຊ૷ஔ͕ࢢൢͷߴՁͳ૷ஔʹΑΔଌఆͱԿΒଝ

ླ໦ ګҰ ৭ͷͳ͍͜ͱ͕ࣔ͞ΕͨɻͪͳΈʹɺࡐྉඅ͸Ұສԁະ ຬͰ͋Δɻ

2.

૷ஔͷ֓ཁ

2.1

ߏ଄

ਤ̍ʹ࡞੡ͨ͠૷ஔͷ֎؍Λࣔ͢ɻిؾଌఆʹ͸16ϐ ϯICιέοτͷதԝ෦෼ͷ8ϐϯΛ࢖༻͠ɺ͜ΕΒ͸ ଆ໘ͷόφφ୺ࢠʹ઀ଓ͞Ε͍ͯΔɻ࣓ੴ͸ιέοτͷ Լ෦ʹ഑ஔ͞ΕΔɻ࣓ੴͷܘʹ߹Θ͕ͤͨ݀։͍͓ͯΓɺ ࣓ੴͷҐஔ͕ݻఆ͞ΕΔɻ࣓ੴ্໘ͱνοϓΩϟϦΞʹ ૷ண͞Εͨࢼྉͱͷڑ཭͸ 10.0 mmͰ͋Δɻ࣓ੴͷ޲ ͖ΛखಈͰม͑Δ͜ͱͰNۃͱSۃΛ੾Γସ͑Δɻ఍߅ ཰ͷଌఆ࣌ʹ͸࣓ੴΛऔΓ֎͢ɻ ☢▼ ヨᩱ

ਤ1: ૷ஔͷ֎؍/Photograph of the Hall measurement system

2.2

࣓ੴͷબผ

࣓ੴ͸ࢢൢͷɺ௚ܘ20 mmɺߴ͞20 mmͷԁபঢ়ω ΦδϜ࣓ੴΛ࢖༻ͨ͠ɻ͜ΕΒ͸ԁபͷߴ͞ํ޲ʹ࣓Խ ͞Ε͓Γɺ࢓༷ॻͰ͸ද໘࣓ଋີ౓͕࠷େͰ0.54 Tͱ ͳ͍ͬͯΔɻ࣮ࡍʹ͸ɺ࣓ଋີ౓΍ͦͷۭؒ෼෍ʹ͸ݸ ମ͕ࠩ͋ΔͨΊɺ͍͔ͭ͘ͷ࣓ੴʹ͍ͭͯɺද໘࣓ଋີ౓ ͷߴ͞ํ޲੒෼ͷۭؒ෼෍Λଌఆ͠(ਤ2)ɺ࣓ଋີ౓͕ ԁͷத৺෦ʹϐʔΫΛ࣋ͪɺ͔ۭͭؒ෼෍ͷภΓ͕͕ͳ Δ΂͘গͳ͍࣓ੴΛબΜͰϗʔϧଌఆʹ࢖༻ͨ͠(ਤ3)ɻ 㼄㼅㼆䝇䝔䞊䝆 ୖ䛛䜙 ☢▼ 䝩䞊䝹䝉䞁䝃䞊 ਤ2: ࣓ଋີ౓ͷۭؒ෼෍ଌఆ/ Measurement apparatus for the spatial variation of the magnetic field

㻞㻜 㻝㻡 㻝㻜 㻡 㻜 㻜 㻡 㻝㻜 㻝㻡 㻞㻜 䡔 㻔㼙㼙㻕 㼥 㻔㼙㼙㻕 㼥 㻔㼙㼙㻕 㼤 㻔㼙㼙㻕 㻮 㻔㼀 㻕 ᭱኱ 㻜㻚㻠㻡㻢㻌㻔㼀㻕 㻔㼍㻕 㻔㼎㻕 ਤ3: ࣓ଋີ౓ͷۭؒ෼෍ଌఆ݁Ռͷྫ/Spatial varia-tion of the magnetic field on a magnet

3.

࣮ݧํ๏

3.1

ϗʔϧଌఆ

Ұൠʹɺਫ਼ີͳϗʔϧଌఆʹ͸ɺਤ4ʹࣔ͢ϗʔϧόʔ ͱ͍͏ܗঢ়ʹ੒ܕͨ͠ࢼྉ͕࢖ΘΕΔɻ6ݸͷిۃΛ࣋ ͪɺిۃ1-4(xํ޲)ʹిྲྀ_I14Λྲྀ͠ిۃ2-3(xํ޲) ͷిѹ_V23Λଌఆͨ͠ͱ͖ɺ_R1423 =R_xx=V₂₃/I₁₄Λ ॎ఍߅ͱݺͿɻ࣓৔(࣓ଋີ౓_B)Λ͉ํ޲(ϗʔϧόʔ ͷ໘௚ํ޲)ʹҹՃ͠ɺిྲྀ_I14Λྲྀ͠ిۃ2-6(yํ޲) ͷిѹ_V26Λଌఆͨ͠ͱ͖ͷ_R1426=R_xy=V₂₆/I₁₄Λ ϗʔϧ఍߅ͱݺͿɻ୯Ґ͸྆ํͱ΋ΦʔϜ[Ω]Ͱ͋Δɻ3 ࣍ݩܥͷ৔߹ɺϗʔϧόʔͷ෯Λ_wɺిۃ2-3ͷִؒΛ lɺް͞Λ_tͱ͢Δͱɺిࢠೱ౓ͱϗʔϧ఍߅ͷؔ܎͸ Rxy= _netB (1) ͱͳΔ[1]ɻ2࣍ݩܥͷ৔߹ɺް͞ͷ࣍ݩ͕ফ͑ͯɺ Rxy= _neB (2) ͱͳΔɻ͜͜Ͱ_e͸ిؾૉྔͰ͋Δɻిࢠೱ౓ͷ୯Ґ͸ɺ 3࣍ݩܥͷ৔߹͸[m−3]ɺ2࣍ݩܥͷ৔߹͸[m−2]Ͱ͋ Δɻ2࣍ݩܥͰ͸ϗʔϧ఍߅ͱిࢠೱ౓ͷؔ܎ʹɺେ͖ ͞΍ࡐ࣭ʹؔ͢ΔύϥϝʔλΛؚ·ͳ͍ͱ͍͏େ͖ͳಛ ௃͕͋Δɻ ॎ఍߅ͱҠಈ౓(μ)ͷؔ܎͸3࣍ݩܥɺ2࣍ݩܥڞʹ Rxx=ρ · _wl (3)

σ = 1_ρ =neμ (4) ͱಋग़͞ΕΔɻ͜͜Ͱ_ρ͸఍߅཰ɺ_σ͸ಋి཰Ͱ͋Δɻ Ҡಈ౓ͷ୯Ґ͸[m2·V−1s−1]Ͱ͋Δɻ

㻔㼍㻕

㻔㼎㻕

㼂_㼤㼤 㼂_㼤㼥 㼘 㼣 㻵 㟁ᴟ 㻝 㻠 㻞 㻟 㻢 㻡

ਤ4: ϗʔϧόʔߏ଄/Hall bar structure

3.2 van der Pauw

๏

ϗʔϧόʔͷଌఆͰ͸ɺࢼྉܗঢ়ͷਫ਼ີͳՃ޻ͱ࠷௿

Ͱ΋5ݸͷిۃ͕ඞཁͰ͋Δ͕ɺ೚ҙܗঢ়ͷࢼྉʹ͍ͭ

ͯपғʹ4ݸͷిۃ͕͋Ε͹ɺղੳతʹిࢠೱ౓ɺҠಈ౓ ΛٻΊΒΕΔ͜ͱ͕van der PauwʹΑΓূ໌͞Εɺvan der Pauw๏ͱͯ͠޿͘ීٴ͍ͯ͠Δ[2]ɻҎԼɺvan der Pauw๏ʹΑΔଌఆखॱΛ؆୯ʹड़΂Δɻ ਤ5ͷΑ͏ͳAʙDͷ4ݸͷిۃΛ࣋ͭࢼྉΛߟ͑ Δɻ·ͣɺର֯ઢํ޲ACʹిྲྀ(IAC)Λྲྀ͠ɺBDͷ ిѹ(VBD)Λଌఆ͠ɺ఍߅_{RACBD(= VBD/IAC)}Λ ٻΊΔɻ࣓৔ΛҹՃͨ͠ͱ͖ͱ࣓৔͕ͳ͍ͱ͖ͷࠩΛ ΔRACBDͱ͢Δͱ ΔRACBD = B net (5) ͱͳΓɺ͇ࣜͱಉ༷ʹిࢠೱ౓͕ٻ·Δɻ ࣍ ʹ AB ʹ ి ྲྀ (IAB) Λ ྲྀ ͠ DC ͷ ి ѹ (VDC) Λ ଌ ఆ ͠ ɺ_{RABDC(= VAB/IDC)} Λ ٻ Ί Δ ɻಉ ༷ ʹ BC ʹ ి ྲྀ (IBC) Λ ྲྀ ͠ AD ͷ ి ѹ (VAD) Λ ଌ ఆ ͠ ɺ_{RBCAD(= VBC/IAD)} Λ ٻ Ί Δ ɻ͜ ͜ Ͱ RBCAD/RABDC < 1ͱͳΔΑ͏ʹిۃΛબఆ͢Δɻ ͜ͷଌఆ݁ՌΛ࣍ࣜ ρ = πt ln2 · RABDC + RBCAD 2 · f (6) ʹ୅ೖ͢Δͱ఍߅཰͕ٻ·Γɺͦͷٯ਺Ͱ͋ΔҠಈ౓͕ ٻ·Δɻ͜͜Ͱ_f ͸ɺ_RBCADͱ_RABDCͷؔ਺ͰɺҎ Լͷࣜ RABDC − RBCAD

RABDC + RBCAD = ln2f cosh

−1exp(ln2/f) 2  (7) Λຬͨ͢ɻ

㻭

㻮

㻯

㻰

㼂

㻭

㻮

㻯

㻰

㼂

㻔㼍㻕

㻔㼎㻕

_㻔㼏㻕

ਤ5: van der Pauwଌఆ/van der Pauw measurement (a)ࢼྉ/Sample. (b)ిࢠೱ౓ଌఆ࣌/For electron den-sity measurement. (c)఍ ߅ ཰ ଌ ఆ ࣌/For resistivity measurement.

3.3

ࢼྉ

ࠓճ༻͍ͨࢼྉ͸SiมௐυʔϓAl_0.3Ga_0.7As/GaAs ୯Ұϔςϩߏ଄ͱݺ͹ΕΔ΋ͷͰɺNTT෺ੑՊֶجૅݚ ڀॴʹͯɺGaAsج൘্ʹ෼ࢠઢΤϐλΩγʔ๏Ͱ࡞੡ ͞Εͨ[3]ɻਤ6͸ߏ଄அ໘ͱϙςϯγϟϧϓϩϑΝΠϧ Ͱ͋ΔɻAlGaAs૚ʹυʔϓ͞ΕͨSi͕ɺυφʔͭ·Γ ిࢠͷڙڅݯͱͳΓɺAlGaAs/GaAsք໘ʹ͓͍ͯϙς ϯγϟϧͷ௿͍GaAs૚ଆʹిࢠ͕஝ੵ͠ɺΩϟϦΞͱ ͳΓిؾ఻ಋΛ୲͏ɻిؾ఻ಋ૚(νϟωϧ)ͱҟͳΔ৔ ॴʹυʔϐϯάΛࢪ͢͜ͱΛมௐυʔϓͱݺͼɺΩϟϦ Ξ(͜ͷ৔߹ిࢠ)ͷෆ७෺ࢄཚ͕௿ݮ͞ΕΔɻ·ͨɺ෼ ࢠઢΤϐλΩγʔ๏͸ɺݪࢠ૚Ϩϕϧͷບް੍ޚͷԼͰ ݁থ੒௕͕ՄೳͰɺ૊੒༳Β͗ͷͳ͍ɺ໘ํ޲ʹۉҰͰ੒ ௕࣠ํ޲ʹٸफ़ͳϔςϩ(ҟछ൒ಋମ)ք໘ͷܗ੒͕Մೳ Ͱ͋Δɻ͜ͷͨΊɺϙςϯγϟϧ༳Β͕͗গͳ͘ɺ఻ಋి ࢠͷ߹ۚࢄཚ΍ք໘ߥ͞ʹΑΔࢄཚ͕௿ݮ͞ΕΔɻNTT ෺ੑՊֶجૅݚڀॴʹͯࢢൢͷϗʔϧޮՌଌఆ૷ஔΛ༻ ͍ͯଌఆͨ݁͠ՌɺࣨԹͰͷిࢠೱ౓͸2.5 × 1016m−2ɺ Ҡಈ౓͸0.70 m2·V−1s−1Ͱ͋ͬͨɻ ͜ ͷ ߏ ଄ ্ ʹ ɺή ʔ τ ͱ ͳ Δ ۚ ଐ Λ ৠ ண ͢ Δ ͱ ɺAlGaAs ૚ ͕ ઈ ԑ ૚ ͱ ͳ Γ ɺ Metal-Insulator-Semiconductor(MIS)ߏ଄͕ߏ੒Ͱ͖Δɻνϟωϧʹܨ ͕ΔిۃΛ࡞੡͢Δ͜ͱͰిքޮՌτϥϯδελͷҰ छͰ͋ΔMISFETͱͳΔɻ൒ಋମϔςϩߏ଄Λ༻͍ͨ MISFET͸ɺSi-MOSFETΑΓ΋2ܻఔ౓ߴ͍Ҡಈ౓͕ ࣮ݱ͞ΕΔ͜ͱ͔ΒɺҰൠʹߴిࢠҠಈ౓τϥϯδελ

(High Electron Mobility Transistor, HEMT)ͱݺ͹Εɺ ߴҠಈ౓͕ඞཁͱͳΔߴप೾σόΠεͱͯ͠ར༻͞Εͯ ͍Δɻ

ླ໦ ګҰ m2·V−1s−1ͱͳΓɺ࣓ଋີ౓͕5 Tఔ౓ͷ࣓৔Ͱ෼਺ྔ ࢠϗʔϧޮՌ͕؍ଌ͞ΕΔɻ 㻿㼕䝗䝘䞊䛛䜙 㟁Ꮚ䛜౪⤥ 㻿㼕䝗䞊䝥 㻭㼘_㻜㻚㻟㻳㼍_㻜㻚㻣㻭㼟 㻳㼍㻭㼟 㻳㼍㻭㼟 ⾲㠃ഃ ᇶᯈഃ 㻿㼕䝗䞊䝥㻭㼘㻜㻚㻟㻳㼍㻜㻚㻣㻭㼟 㻳㼍㻭㼟⾲㠃ಖㆤᒙ 㻳㼍㻭㼟 㻞ḟඖ㟁Ꮚ 㻳㼍㻭㼟ᇶᯈ 㻔㼍㻕 㻔㼎㻕 ਤ 6: Si ม ௐ υ ʔ ϓ ୯ Ұ ϔ ς ϩ ߏ ଄/Si-modulation doped AlGaAs/GaAs single-heterostructure

(a)ߏ଄அ໘/Cross section of the layered structure. (b)

ϙςϯγϟϧϓϩϑΝΠϧ/Potential profile.

4.

ଌఆ݁Ռͱߟ࡯

ઌʹड़΂ͨSiมௐυʔϓAlGaAs/GaAs୯Ұϔςϩ ߏ଄ࢼྉʹ͍ͭͯɺຊ૷ஔΛ༻͍ɺࣨԹʹͯvan der Pauw๏ʹΑΓిࢠೱ౓ɺҠಈ౓ΛٻΊͨ݁Ռʹ͍ͭͯ ड़΂Δɻిѹଌఆʹ͸ަྲྀϩοΫΠϯ๏Λ༻͍ͨɻ͜ͷ ํ๏͸ɺಛఆप೾਺ͷަྲྀిྲྀΛྲྀ͠ɺಉظͨͦ͠ͷप ೾਺ͷΈͷిѹ੒෼Λଌఆ͢Δ΋ͷͰɺඇৗʹS/Nൺ͕ ߴ͘ਫ਼ີଌఆʹద͍ͯ͠Δ͜ͱ͕஌ΒΕ͍ͯΔɻࠓճͷ ଌఆͰ͸ɺ13 Hzɺ1μAͷަྲྀిྲྀΛ༻͍ͨɻࢼྉҐஔ ʹ͓͍ͯଌఆ࣓ͨ͠ଋີ౓͸ɺ̣ۃͰ0.106 TɺSۃͰ 0.118 TͰ͋ͬͨɻ ·ͣిࢠೱ౓ΛٻΊΔʹ͋ͨΓNۃɺSۃΛ্ʹ޲͚ ࣓ͯੴΛ഑ஔ͠ɺର֯ํ޲ͷ఍߅_RACBDΛଌఆͨ݁͠ ՌɺͦΕͧΕRACBD = 1.379 ̺Ωɺ0.823̺Ωͱͳ Γɺ࣓ੴΛ഑ஔ͠ͳ͍ͱ͖͸_{RACBD = 1.099} ̺Ω Ͱ ͋ͬͨɻ͜ΕΑΓɺ྆ํͷۃͷଌఆΛฏۉͯ͠ٻΊͨి ࢠೱ౓͸2.51 × 1016 m−2ͱͳͬͨɻ ࣍ ʹ ɺ࣓ ੴ ͳ ͠ Ͱ ฒ ߦ ํ ޲ ͷ ఍ ߅ Λ ଌ ఆ ͠ ͨ ݁ Ռ RABDC=1.608 kΩɺ_{RBCAD= 0.506 kΩ}ͱͳͬͨɻ͜ ͷൺ͔Β_fʹ0.90ͱͳΓɺࣜ(6)ΑΓ఍߅཰͸4.28×102 Ω·m−1ͱٻ·ͬͨɻ্هిࢠೱ౓ɺ఍߅཰͔ΒҠಈ౓͸ 0.58 m2·V−1s−1ͱٻ·ͬͨɻ Ҏ্ͷΑ͏ʹɺࢢൢͷ૷ஔΛ༻͍ͯଌఆͨ݁͠Ռͱͳ ΜΒଝ৭ͷͳ͍݁ՌΛಘͨɻΘ͔ͣͳ૬ҧ͸ɺࣨԹͷҧ ͍΍ࢼྉͷܦ೥มԽʹΑΔ΋ͷͱߟ͍͑ͯΔɻ

5.

·ͱΊ

൒ಋମϔςϩߏ଄ΛςʔϚͱ͢Δݚڀࣨͷ্ཱͪ͛ʹ ࡍ͠ɺ൒ಋମͷಛੑͱͯ͠ॏཁͳ߲໨Ͱ͋ΔΩϟϦΞೱ ౓͓ΑͼΩϟϦΞҠಈ౓Λௐ΂ΔͨΊɺӬٱ࣓ੴͰ͋Δ ωΦδϜ࣓ੴΛ༻͍ͨϗʔϧޮՌଌఆ૷ஔΛ࡞੡ͨ͠ɻ ຊ૷ஔΛ༻͍ͯ൒ಋମ2࣍ݩిࢠܥࢼྉʹ͍ͭͯଌఆ͠ ͨ݁Ռɺࢢൢͷ૷ஔͱԿΒଝ৭ͷͳ͍ߴਫ਼౓ͳଌఆ͕Ͱ ͖͍ͯΔ͜ͱ͕ࣔ͞Εͨɻɻຊ૷ஔ͸ɺ௿Ձ֨ͷΈͳΒ ͣɺ୯७ͳߏ଄Ώ͑ʹݎ࿚Ͱ͋ΔͷͰ߃ٱతͳ࢖༻͕Մ ೳͰ͋Δɻ

ँࣙ

ຊ࿦จ͸ຊݚڀࣨͰߦΘΕͨฏ੒29೥౓ͷଔۀݚڀΛ ·ͱΊͨ΋ͷͰ͋Δɻଔۀੜͷ஑ా܆܅ɺྛޱ߽ਓ܅ɺ༗ Ҫ༗ش܅ɺࢁ಺༤౉܅ʹײँ͢ΔɻࢼྉΛఏڙͯ͘͠Ε ͨNTT෺ੑՊֶجૅݚڀॴͷळอو࢙ത࢜ʹײँ͢Δɻ ຊݚڀ͸ຊֶΤϨΫτϩχΫεݚڀॴͷฏ੒29೥౓৽೚ ڭһελʔτΞοϓݚڀඅͷࢧԉΛड͚ͨɻ·ͨɺՊݚ අج൫(B)16H03862(୅ද੺ࡔ఩໵ࢯ)ͷࢧԉΛड͚ͨɻ (ฏ੒30೥7݄31೔ड෇)

ࢀߟจݙ

[1] ޚࢠࣲએ෉ஶ ൒ಋମͷ෺ཧ[վగ൛](ഓ෩ؗ), ɹ pp.117-118 (1991).

[2] L. J. van der Pauw, Philips Res. Rep. 20, 220-224 (1958).

[3] T. Saku, Y. Hirayama and Y. Horikoshi, Jpn. J. Appl. Phys. 30, 902-905 (1992).