黄昆固体物理总复习

Q02_02_001 Ƞ Ц Ƞ䜀 㠲 ⨕㕢 㐂 ⮳➨◨ȡ⻪ 㐂 喚ₒȠ䉎⻪ ͺ䬣䲏 Ѐ ҋ⩗㔻Ⱗρ䲏䔀喌 䲏䔀 ̯ ⼺ 喌⩠ν∐ ̼Ⱗ ⤵喌͓͙⻪ ⮳䬜 ⮳⩤ π⮳ϓ䔜щϖ⩎ ⮳ ȡ Ⱗρ 㶐 喌 ⽢ ⮳⻪ ҂喛Ц 㐂 喚䲏͓͙ 䉐⡝̯͙⩤ 喌 䅂⮳ Ц䩝喛䜀 㐂 喚㏳ ҂ ⃾͙ ⮳ ⩤ ͩ 喌 ₓ 㐂 䜀 ҂ 喌 ε 喈Ц喉⩤ ⮳ Ć↸⊧ć ⩠Ц⩤ ㏳ ⮳Ć⩤ πć͜ȡ 䔈⻼ ̺喌⩤ π ͺ䬣 Ѐҋ⩗喌҂⼞䊹 ⩤ π 䊹倇喌 ЀⰧρҋ⩗⮳ Ѐ㘬 ѽ喌㶗⣟ͩ 㖉 䊦 ⮳ҋ⩗ȡ㠲 ⨕㕢 㐂 喚 ㉏ ⮳⩤ ͩ8͙喌 ⤲ ⼟⮳⽢ 䬜㐂 ȡѵ ̯ⳛ ⩠νₒȠ䉎⩤͜ ̼䛼 㔻Ү ⣟ ⳛ ⴘ喌䔈 щҮ ϖ⩎ ⴘȡ䲍 ҂ ӌ䲏䔈ⳛ ⴘ⮳ρҋ⩗㔻㐂 ⮳ȡQ02_03_001ϯͷ 喟⮳㘬䛾䛾 ȡ ҂͜ ̼ ䷀⢶ ⮳ὐ 喌⼟ͩ 喌 㘬䛾 Д⩗ 䔟喌 Д㷚⓯ 喌Ύ Д⎝▜ȡQ02_03_002ϯͷ ҂℃☜⮳ ὐ 喟 ク䔟䃐テ㐂 ⮳ ͸ȡД䔍㐜Ϻ䉗⮳ ∑ В㶗 ∑喌 㤡 ⰺҋ ⮳䔍㐜Ϻ䉗喌 1͙㏤∑ 2͙⠛⿺⮳Ὑ∑ȡ䃐テ㐂 㶗 ѽ⍘ 䭿̺喚34)(1512)/(DD V T R T C 4 4S ā̽⍘ ⮳3⁐ ₒ℃ȡ⍘ ѽ喌 䔀ѫ 喌䄣 ⍘ ѽ 喌 䪮∑ ∑⮳⓯ ͪ㺰⮳ȡQ02_03_003ϯͷ ҂℃☜⮳❠ ὐ 喟 ク䔟䃐テ㐂 ⮳ ͸ȡν N ͙ ⮳ ҂喌 ҂͜ ⮳ ДⰧ ⮳䷀⢶Z 0 ȡ䃐テ㐂 㶗 ⍘ 䒲倇 喚āā̽ 䮵喍⣯ ̯㜣ȡB V NkC 3#⍘ 䲍 ѽ 喚T k B B V B e Tk Nk C 020)(3Z Z == āā ⍘ ⮳ 䭼ѽ喌̽ 侻㐂 ̼さȡ3AT C V ❠ ὐ ⪔ε ∑⮳䷀⢶ ȡQ02_04_001 㘬 ⤵䃩ク䔟䜀 Ƞ ҂ 㐌㑇҂⮳ ⩤ 喛ν䜀 喚⩤ 㘬 ͜⮳ Д ̼␐ 喌 喌 ₓ Л̯㝛 ҂ȡ ν ҂喚Ͻ㘬 㐂 ⰺ̽㐌㑇҂⮳Ⱗѫ喌ѵ ҂⺰ 䒲㐌㑇҂⮳⾳喌ӌ䲏☜⓯ Д ␐ ͜⮳⩤ ⓯ ͜喌 㔻 ⩤㘬 ȡν㐌㑇҂喚Ц⩤ ␐ε䃧 ⮳㘬 喌 ␐ ȡ Ц ͺ䬣 ̯͙ ⮳⺰ 喌 Д ⩤ ⮳ҋ⩗̺⇐ ⩤≰ϖ⩎ȡQ02_04_002ク䔟䔀㜙⩠⩤ 䔀ѫὐ Ƞ ∄ ⮳ͪ㺰㐂䃩ȡ㔲㮀䜀 ͜⩤ ㇁ ⮳ҋ⩗喌ն ⮳䊦о䒲 ȡҋͩ䰥㏖䔀ѫ喌 Д⩗ ⮳ իВ ⻪ ϖ⩎⮳ 喚)(r V V K ȡ ⮳䊦о䛾V V r V ' )(Kҋͩ ⤵ȡ ͓͙⩠Ⱗρ㜙⩠⮳ⴘ䭤 ⟥ k K n G k k K K K '⮳䰥㏖㘬䛾Ⱗへ 喌̯㏖ԝₒ∑ λ㏖㘬䛾ԝₒ䊺ν ⾦ ȡ 喚22n G k k K K K 喌 㔴0)21( n n G k G K K K 喌 䛻⌹ ⮳䓨⩻ 喌㘬䛾 ⾰ 喌 ̯㈪ ⮳㘬 ȡQ02_04_003ク䔟㉖ 㑉䔀ѫὐ ⮳ ͪ㺰㐂䃩ȡ㉖ 㑉䔀ѫ ∄⮳ 喚⩤ ̯͙ 喈 ◨喉䭳䔀 喌ͪ㺰 䄔 ⮳ҋ⩗喌㔻 喈 ◨喉 ⮳ҋ⩗ⰺҋ 喌 ҂͜⩤ ⮳∑ 䔀ѫⰺ 䒗䖂∑ ⮳㏮ ㏳ 喌䔈 Д 㘬㏖ ҂͜㘬 ͺ䬣⮳ ㈪ȡ̯͙ 㘬㏖H i ̯͙㘬 喌̼ ⮳ 㘬㏖ ̼ ⮳㘬 ȡ ҂ 喌 ε̯㈪ ⮳㘬 ȡ㘬䛾䒲ѽ⮳㘬㏖ ⩤ 喌 䒗䖂䒲 喌 ͺ䬣 ⩤ ⮳∑ Ⱗρ䛼 䒲 喌 Д ⮳㘬 䒲⾳ȡ㘬䛾䒲倇⮳㘬㏖ ⩤ 喌 䒗䖂䒲 喌 ͺ䬣 ⩤ ⮳∑ Ⱗρ䛼 䒲 喌 Д ⮳㘬 䒲 ȡQ02_05_001ϯͷ ⾩⾣喟̯͙⾩⮳1k K ⟥ ⮳䔀␐ ͜ ⩤ 䓿 ⮳⩤≰ ̯͙ ₒ⩤㢦喌Дe 1k K ⟥ ⩤ 䕎)(1k v e K K 䓿 ⮳㇁ ϖ⩎⮳⩤≰Ⱗ ȡ䔈͙⾩⟥ ⼟ͩ⾩⾣ȡQ02_05_002 ㇁ ⰺҋ ㏾ ㇁ 喌 ⮳䕎 䓿 ⼺ ϯͷ喟⩤ ⟥ 喚F dtk d K K = )(;⩤ ⮳䕎 喚E v k k =K 1Q02_05_003ク䔟 ͜⮳⩤ ҋ⩗̺ϖ⩎⩤≰⮳ ȡ͜ 䘗 ⟥ 㷚⩤ 喌 ⮳ҋ⩗щҮ 䛻⌹ ⮳⟥ ⩎ ȡ ⮳⩤ ⟥ ДⰧ ⮳䕎 ⇮Ɐ⩤ ⮳ 䓿 喌ѵ⩠ν㘬 ̼␐ 喌䔵⩤ ̹䓿 ⮳⩤ 䒲 喌 ₓϖ⩎⩤≰ȡE 喌 ⮳⩤ ⟥ ДⰧ ⮳䕎 ⇮Ɐ⩤ ⮳ 䓿 ȡ ␐ ⮳ ͜喌⩤ ⮳䓿 ̼ 䛻⌹ ͜⩤ ⮳ ȡ Д ҋ⩗⮳ 喌␐ ͜⮳⩤ ̼ϖ⩎ 㻱⮳⩤≰ȡQ02_06_001Ͻ⩤ ☜ 䛾 ⤵䃩ク䔟䜀 ͜⮳⩤ ҂☜ ⮳䉐⡝ȡ䛾 ⤵䃩͜喌 ⩤ ⮳㘬䛾䔋䔋ѽν䉨 㘬䛾喌⩠ν ∐ ⤵⮳䭿 ̼㘬 ̽☜⓯ 喌 䭳䔀㏕㠲 ⩤ ̽☜⓯ 喌 䜀 ⮳☜ 䛾 䉐⡝ȡ䃐テ㐂 㶗 ⩤ ⮳☜ 䛾̽⍘ ̯⁐ ₒ℃ȡ0F E 0F E T k B ~Q02_06_002ͩϯͷ⍘ 䒲倇 Д̼㔲㮀⩤ ҂☜ 䛾⮳䉐⡝喟䛾 ⤵䃩͜喌 ⩤ ⮳㘬䛾䔋䔋ѽν䉨 㘬䛾喌⩠ν ∐ ⤵⮳䭿 ̼㘬 ̽☜⓯ 喌 䭳䔀㏕㠲 ⩤ ̽☜⓯ 喌 䜀 ⮳☜ 䛾 䉐⡝ȡ ̯㝛⍘ ̺喌 ⮳☜ 䛾㺰℃⩤ ⮳☜ 䛾 喛 ⍘ 䒲倇̺喌☜ 䛾 ̯͙ ȡ0F E 0F E T k B ~Q02_06_003ͩϯͷ⍘ 䒲ѽ Д 䶪㔲㮀⩤ ҂☜ 䛾⮳䉐⡝喟ѽ⍘㠲 ̺喌 ⮳☜ 䛾 ⍘ ⮳3⁐ 䊺ν䰥喌㔻⩤ ⮳☜ 䛾̽⍘ 1⁐ ₒ℃喌䮾⍘ ̺䭼 ℃䒲㑂 喌ₓ ⩤ ⮳☜ 䛾 Д ⮳☜ 䛾Ⱗ℃䒲喌̼㘬 ⪔ȡQ02_06_004ͩϯͷ 㐌 䰥 喌䜀 ͜⮳⩤ ϼ♥ 䒲倇⮳㘬䛾喟⍘ 喚⩤ ⮳ 㘬䛾喈 㘬喉喚0 T 035Kin F E E 喌⩤ ϼ Ⱗ ⮳ 㘬䛾ȡ ͩ⩤ 䶪␐䋢∐ ̼Ⱗ ⤵喌⃾͙㘬䛾⟥ ̹ 㘬 䃧͓͙㜙 Ⱗ ⮳⩤ ȡ䔈 ⮳⩤ ̼ 㘬䘬 ѽ㘬䛾⟥ ȡQ02_06_005ク䔟ⵃ⾥䜀 ☜ 䛾⮳ ͸喌 Д䓶⍐ ㉏Mn ȠFe ȠCo Ni 䒲倇⮳⩤ ☜ 䛾ͩҺ䄣 䉨 㘬㏖䭳䔀㘬 ⮳ ȡ䃧 䜀 ⮳ 䉗 ν㘬䛾 䭳䔀⮳⩤ 喌⩤ ⮳☜ 䛾F E B B F V k T k E N C )])((3[02S ̽ₒ℃喌⩠⩤ ⮳☜ 䛾 Д㣦 䉨ㆢ䲑䭳䔀㘬 ⮳Ԑ ȡ)(0F E N 䓶⍐ ㉏Mn ȠFe ȠCo Ni 䒲倇⮳⩤ ☜ 䛾喌 ε Л 䉨ㆢ䲑䭳䔀 䒲 ⮳㘬 ȡ䓶⍐ ㉏⮳➨ d ⩤ ̼␐喌Ͻ㘬 ⤵䃩 喌 㷚⩤ ␐⮳d 㘬 ȡ⩠ν ⮳d ℃䒲䲏 ⮳䒗䖂喌 ҂ Ⱗρ䛼 䒲 喌 㔻ϖ⩎䒲⾳⮳㘬 喌 ̹⮳䒗䖂 5䛼ク ⮳喌 Д ⮳5͙㘬 ⩎̯ ⮳䛼 喌Ү d 㘬 ➨ ⮳㘬 ȡ䓶⍐䜀 䘗 d 㘬 喌 Д䉨 㘬㏖Ѽνd 㘬 ȡQ02_06_006ク䔟䜀 㼕⩤ ⮳ 喟͓ ̼ ⮳䜀 A B Ⱗρ 㼕喌⩠ν͓ 䜀 ⮳䉨ㆢ㘬㏖̼ 喌 Ⱗρ 㼕 Д ⩎⩤ ϓ 喌⩤ Ͻ䉨ㆢ㘬㏖䒲倇⮳䜀 ≰ 䉨ㆢ㘬㏖䒲ѽ⮳䜀 喌Ү̯ 䜀 ⮳ 㼕䲑 ₒ⩤喈⩤ ≰⮳䜀 喉喌Ү ̯ 䜀 ⮳ 㼕䲑 䉎⩤喈⩤ ≰ ⮳䜀 喉⮳䉨ㆢ㘬㏖喌⩤ ̼ ≰ ϓ ȡ ₓ ͓ 䜀 ͜ϖ⩎ε 㼕⩤ ȡQ02_07_001Д Si As ⮳N ҂ͩҺ喌ク䔟 ҂ ⩤㘬 ⮳ ȡ㏞⮳ ҂ 䔱 ⮳ 䉗喌Ύ㘬 ӊ䒬≰ ȡ Si As ⮳N ҂喌 䉗 䯈͜ ӊ ⩤ ⮳㘬㏖喌㘬㏖⪔ѽν ⮳㘬䛾喌 Ц ͜⮳⩤ Ⱗ℃䒲喌 ⓯ ͜ ⩤ 䒬≰ ȡQ02_07_002 XCH007_018_02 ⹩,ク䔟N ⇎䖂 ҂バ⮳ ҋ ⤵ȡ⩤ 喌⎿ S ␾ D 㷚P 䯃 喌Ү SD ͺ䬣 ̯ ⮳⩤ 喌ѵ⩠νSP DP͓͙ PN 㐂喌 ₓ ⮳PN 㐂⩤≰ȡ⩤ 䓭 䊴䓶̯ ⮳䬷ի喌 P ҂⅖ ➘㶗䲑 āā⩤ ⮳⊂ ν҂ ⾩⾣⮳⊂ 喌 ⎿ S ␾ D 䔍 䊦 喌ₓ SD̯͙⩤ 喌 щ ⮳⩤≰ϖ⩎ȡ䕉䓶 ⩤ ⮳ ի喌ҮMOS ҂バ ν䕉 ₑ⟥ 喌⎿ S ␾ D ͺ䬣⮳⩤≰⩤ ⮳䄲 āā䯵 ⩤䌞 ⩗ȡQ02_07_003 ҂ 䓨 ⮳∑䪮ͩ 喟⮳㘬䛾␐䋢喚g E t Z =喌O S Z c 2喌g E c t O S =2,䪮∑ 䭿喚g E c =S O 20 āā 䓨ȡQ02_07_004ク䔟 ҂ ⓯ ⮳➨◨ȡ䋢 倇⮳⍘ 喌⩠␐ ⮳⩤ ⓯ 喈 ⓯ 喉 ͪ㺰⮳ȡ ⓯ ⮳➨◨ ⃾ϖ⩎̯͙⩤ ϖ⩎̯͙⾩⾣: 喚pn |⩠T k E E B e N N np喌T k E B ge N N p n 2 |喌 ͜ E E E g ͩ 䯈 ȡͩ喚喌 ₓ ⓯ 䮾⍘ ͩ䮐 ȡ 䔈͙㠲 䛻喌≺䛾 䒬≰ 䮾⍘ ⮳ ㈪喌 Д⶝ 䯈 ȡi g E E !!Q02_07_005ϯͷ 䲍 㶐䒬≰ 喟☜ 㶐̺喌 ҂͜⮳ 䉗⩤ 喌 Ц ͜⮳⩤ 䕉䓶 ☜㘬喌⓯ ͜喈䒬≰ ⮳ϖ⩎喉喌 ⩤ Д 㥬 Ц ͜ ⾩⾣ ⩎ 喈䒬≰ ⮳ 喉喌 䓭 㶐 喌䒬≰ ⮳ϖ⩎⢶ ⢶Ⱗへ喌⩤ ⾩⾣⮳⊂ ε̯ ⮳ ȡ⩤ ⾩⾣⮳⊂ ␐䋢喚T k E B ge N N p n00 ⩻⮳ ҋ⩗̺喌⩤ ⾩⾣⊂ 㘬վ⻪ 㶐իȡ ϖ⩎⩤ ā⾩⾣ ȡ 喚00p p p ,n n n ''āā⼟ͩ䲍 㶐䒬≰Q02_07_006Д P ⮳PN 㐂ͩҺ喌ク䔟 ⩎о➨ ?⩗ ⮳ ∄喌 P ҂⮳㶗䲑 ̯͙㪳⮳N 喌 ⮳⚖ ̺喌 PN 㐂 䭳䔀ϖ⩎ 䛾⮳⩤ ⾩⾣ 喌 PN 㐂䭳䔀̯͙ 䪮 喌⩤ 喍⾩⾣ 䔇⇐ 㘬䕉䓶 䓭 PN 㐂⮳ ⩤ 喈PN 㐂㜙 ⩤ 喉喌⩤ 䓿 N 喌⾩⾣ 䓿 P 喌ҮN 䉎⩤ȠP ₒ⩤喌 ̹̺⩤ ϖ⩎⩤ āā ⩎о➨ ȡQ02_07_007ϯͷ 䉗㐂⮳⿆ 喟㘬䛾 ν 䯈⮳N 喌 N g E h )( Q 喌 Д䔾䓶N 喌 䯈䒲⾳⮳P 㷚 ȡ⩗ 䉗PN 㐂 ҋ ⩤↏喌 ⮳ 䘗 㶗䲑̯ 㷚 喌⩠ν㶗䲑㑩䮦 䊦⮳㶗䲑 倇 ͜䒬≰ ѽへ ㉏喌Ү ̯ϊ⩤ 喍⾩⾣ ̼㘬 䓭 ⩤ Д 喌 ⩎ε 喌䭼ѽε 䭢㘬⩤↏⮳ ⢶ȡ ⩗ 䉗㐂⮳⿆ 喌 Д ⩤ 喍⾩⾣⮳ ⢶喌 倇 䭢㘬⩤↏⮳ ⩤䒛 ⢶ȡQ02_07_008 ν ⮳N ҂ ☜ 㶐̺喌ͩϯͷ ͜⩤ ⮳⊂ 䊹倇喌Ц ͜⾩⾣⮳⊂ 䊹ѽ喟҂͜⮳⩤ 䜀 ͜⮳⩤ ̯ Ͻ䉨 āā⟳ 㐎䃐ȡ ͜⩤ ⊂ 喚T k E E B Fe N n Ц ͜⾩⾣⊂ 喚T k E E B F e N p喌Tk E E B e N N npN ҂͜喌 ͪ䊹 喌⓯ ͜⮳⩤ 䊹 喌⩤ 䋲䓰̽Ц ͜⾩⾣ ⩎ ⮳ ⢶䊹 喌 ₓ␐ ͜⮳⾩⾣䊹 ȡQ02_07_009ϯͷ 䋲䓰 ⩤ 喍⾩⾣ 喟喚 ⚖ Д Ц ͜⮳⩤ ⓯ ͜喌 ⩤ ā⾩⾣ 喌䔈̯䓶⼺⼟ͩ ȡ⩤ 喍⾩⾣ ⮳䔵䓶⼺喌 䘗⮳⩤ 䋲䓰 Ц 䶥䘗⮳⾩㘬㏖喌 㘬䛾㏕ͩ 䯈 ⮳ ȡQ02_07_010ͩϯͷ ҂ Д 倇 ⩤㘬 喟⤵ ⮳ ҂ ⇐ 㑩䮦 ⇐ 䉗喌 ҂͜⮳䒬≰ 㘬 ⓯ ͜⮳⩤ Ц ͜⮳⾩⾣ȡ ㏞⮳ ҂ 䔱 ⮳ 䉗喌Ύ㘬 ӊ䒬≰ ȡ ₓ 䭴⮳ ҂͜䮓ε̽㘬 ⮳⩤ ⟥ Д 喌䔇 ̯ϊ⩤ Дͩ 䉗 㔴㑩䮦 㑉喌 㑉⩤ ⶝ ⮳㘬㏖喌 䉗㘬㏖Ѽν 䯈͜ 䔀 ⮳Ѽ㒝喌 ̯㝛⍘ ̺ 㷚⓯ ͜喌Ͻ㔻 ҂⮳ ⩤㘬 ϖ⩎ ⮳ ȡQ02_07_011ϯͷ P N ҂喟㉏ ⩤⮳̼ 喌 䉗 ͓ͩ⻼ㆪ ȡ䉗 䯈͜ ӊ ⩤ ⮳㘬㏖喌㘬㏖⪔ѽν ⮳㘬䛾喌 Ц ͜⮳⩤ Ⱗ℃䒲喌 ⓯ ͜喌⼟ͩ⩤ 䒬≰ ȡͪ㺰 ͪ 䉗⮳ ҂喌ͪ㺰ӌ䲏 ͪ☜⓯ ⮳⩤ ⩤āāN ҂ȡ䉗 ӊ 䯈͜⾩⮳㘬㏖喌⩤ ⩠Ц ⓯ ͪ㘬㏖㺰℃⓯ ⮳ ȡͪ㺰 ͪ 䉗⮳ ҂喌 Ц ͜⮳̯ϊ⩤ 㷚⓯ ͪ㘬㏖喌㔻 Ц ͜ϖ⩎䃧 ⾩⾣喌ͪ㺰ӌ䲏䔈ϊ⾩⾣ ⩤āāP ҂ȡQ02_07_012 ҂͜ ⌠㘬㏖ 䉗喌 ҂⮳ ⩤ ҄ 喟1) Д ͩ ͜ 喌 䭼ѽ䒬≰ ⮳ 喛2) Д ͩ䲍䒿 ͜ 喌 ҂⮳ ⢶喛3) Дҋͩ㶔 䉗喌 倇 ҂ ⮳⩤䭪⢶ȡQ02_07_013Д Ge ҂ AsͩҺ喌ク䔟ͩϯͷㆪ⅑ 䉗㘬㏖⮳ ͪ㘬㏖Ѽν 䭳䔀喟̯͙せIV ㉏Ge喈4Ц ㉏喉㷚̯͙せV ㉏As喈5Ц ㉏喉 В⮳ 喌As 䔀䗪⮳Ge Ц䩝 ҈̯͙⩤ ȡ ͩ Ц䩝 ̯⻼Ⱗ ⮳ 䩝喌 㑉 Ц䩝̹⮳⩤ 㘬䛾 ѽ喌Ͻ㘬 ⮳㼁 䄣喌 νЦ ͜⮳⩤ ȡ ҈̯͙⩤ As+⻪ 䲈⩤ 喌 㑉ҋ⩗ Ⱗ ⮳喌 㘬 ͜喌 Ѽν 䯈ͺ͜喌̓䲍 䔀 ȡ䔈͙⩤ 㺰 ⮳㘬䛾喌 ДϽ 䯈䋲䓰 ͜ ͩ⩤ 䒬≰ ȡ3$57 7+5((Q03_01_001䃰 喚҂ ⿺ ⮳Ձ 䲑 ⿺ 喛䲑 ⿺ ⮳Ձ ҂ ⿺⩠Ձ ͸喚3213212a a a a a b G G G G G G u u S 喛3211322a a a a a b G G G G G G u u S 喛3212132a a a a a b G G G G G G u u S ҂ ⿺ 㘍 ⴑ喚123(),(),(222a a a a i j k a i j k a i j k )K K K K K K K K K K K K ҂ ⿺ 㘍҂⼞喚321a :Ձ ⴑ喚231123222()(222()()4a a a ab i j k a a a a i j k i j k )i j k S S S u u u : u : G G K K K K K K K G G G K K K K K K 12()b j k aS K K K ⤵喚31212322()a a b i k a a a a S S u u K K K K K G G G 喛12312322()a a b i j a a a aS S u u K K K K K G G G 㻰⩠321,,b b b K K K ͩ ⴑ ⮳ ͩ䲑 ⿺ ȡ䲑 ⿺ 㘍 ⴑ喚123(),(),(222a a a a j k a k i a i K K K K K K K )j K K 䲑 ⿺ 㘍҂⼞喚341a:Ձ ⴑ喚3213212a a a a a b G G G G G G u u S 喌12()b i j k a S K K K K ⤵22()b i j k a S K K K K 喌32()b i j k aS K K K K 㻰⩠321,,b b b K K K ͩ ⴑ ⮳ ͩ҂ ⿺ ȡQ03_01_002䃰 Ձ 㘍҂⼞ͩcv 3)2(S 喌 ͩ͜ₒ 㘍⮳҂⼞ȡc v Ձ ⴑ3213212a a a a a b G G G G G G u u S 喛3211322a a a a a b G G G G G G u u S 喛3212132a a a a a b G G G G G G u u SՁ ҂⼞喚)()()()2()(21133233321*a a a a a a v b b b v c cK K K K K K K K K u u u u u S CB A BC A C B A K K K K K K K K K )()( u u >@>@1211312132113)())()()(a a a a a a a a a a a a a K K K K K K K K K K K K K : u u u u u 33*231*(2)(2)()cc c v a a a v v S S u K K K Q03_01_003䃰 喚Ձ ⴑ䛾332211b h b h b h G K K K K Ⱓν ͩ(⮳ 䲑㈪)321h h h K K ͩ喌ij j i b a SG 2 332211b h b h b h G K K K KXCH_001_047 ⹩ȡ33223311,h a h a h a h a K K K K 䃰 喚0,0321321 CB G CA G h h h h h h KK G K ̽ 䲑㈪ₒϓȡ)(321h h h Q03_01_004 ⴑc ,b ,a KK K ク ₒϓ㈪喌䃰 䲑 ⮳䲑䬣䌌ͩ喚)(hkl 222)()()(1cl b k a h d 䄣 䲑 ク ⮳ 䲑喌 䲑 ℃䒲 喌 㼒⤵ȡνク ₒϓ㈪喚c b a K K K A A , 㘍⮳ ⴑ喚a kc a j b a i a K K K K K K 321,,Ձ ⴑ喚3213212a a a a a b G G G G G G u u S 喛3211322a a a a a b G G G G G G u u S 喛3212132a a a a a b G G G G G G u u S k c a j b a i a a K K K K K K 321,,В Ձ ⮳ ͸ 喚k cb j b b i a b K K K K K K S S S 2,2,2321 Ձ ⴑ䛾321b l b k b h G K K K K 喌k cl j b k i a h G K K K K S S S 222 䲑 ⮳䲑䬣䌌喚)(hkl 1222d G hb kb lb 3S S K K K K 喌2221()()()d h k l a b c䲑 䊹ク ⮳ 䲑喌 䲑⮳䬣䌌䊹 喌 䲑̹ ◨⮳ 䊹 喌䔈 ⮳ 䲑䊹 㼒⤵ȡQ03_01_005 ⿺ 喈111喉䲑̽喈100喉䲑喌喈111喉䲑̽喈110喉䲑⮳ϓ㏮⮳ ȡXCH_001_051_01 ⹩喈111喉䲑̽喈100喉䲑⮳ϓ㏮⮳ ͩABJJJ G JJJ G ⼪喌A ◨ ◨O 喌B ◨⮳Ѽⴑ喚AB B R aj akK K K ₓ喌喈111喉䲑̽喈100喉䲑⮳ϓ㏮⮳ 喚AB aj ak JJJ G K K āā[011]ABJJJ G XCH_001_051_02 ⹩喈111喉䲑̽喈110喉䲑⮳ϓ㏮⮳ ⼪喌A ◨ ◨O 喌B ◨⮳Ѽⴑ喚AB JJJ G B R ai ajK K K ₓ喌喈111喉䲑̽喈110喉䲑⮳ϓ㏮⮳ 喚AB ai aj JJJ G K K āā[110]Q03_01_006䄄 ク ⿺ Ƞ䲑 ⿺ ҂ ⿺⮳㐣 ㏢ā 㡗 㘍(Wingner-Seitz)ȡ㐣 ㏢ā 㡗 㘍喚⩠ ̯͙ ◨ͩ͜ 喌 䔀 ◨⁐䔀 ◨䔍㏮⮳͜ 䲑喌䔈ϊ ⮳⾩䬣ͩ㐣 ㏢ā㡗 㘍ȡ ⹩̯ͩ⻼λ㐣 ⮳㐣 ㏢ā 㡗 㘍ȡク ⿺ Ƞ䲑 ⿺ ҂ ⿺XCH001_002Ƞ007 003 ⹩ȡク ⿺ ⮳㐣 ㏢ā 㡗 㘍ͩ ◨ 6͙䔀䗪 ◨䔍㏮⮳ Ⱓ 䲑 ⮳⿺ₒ ҂ȡXCH001_058 ⹩ȡ䲑 ⿺ ⮳㐣 ㏢ā 㡗 㘍ͩ ◨ 12͙䔀䗪 ◨䔍㏮⮳ Ⱓ 䲑 ⮳ₒ λ䲑҂ȡ XCH001_059⹩ȡ҂ ⿺ ⮳㐣 ㏢ā 㡗 㘍ͩ ◨ 8͙䔀䗪 ◨䔍㏮⮳ Ⱓ 䲑 ⮳ₒ 䲑҂喌 ⇮⿺ 䒣⮳6͙⁐䔀䗪 ◨䔍㏮⮳ Ⱓ 䲑 䲑҂⮳ ͙㼁喌 ⮳14䲑҂ȡ ͙䲑 ₒ 䓨 喌 ͙䲑 ₒ 䓨 ȡ XCH001_060 ⹩ȡQ03_02_001䃰 ͓⻼̯Ц⻪ ㏳ ⮳̯㐣 ⮳供 䮵 ͩ喚2ln 2 D 供 䮵 喚¦ 321321,,2/1232221)()1('n n n n n n n n n D ν̯㐣̯Ц⻪ 喚¦ nnn )1('D 喌䔸 ̯͙⻪ ͩ 㔲⻪ 喌ն ⻪ Ⱍ 喌 㔲⻪ ͓䓨 ̯͙ ⻪ ȡ])1(615141312111[2NN"D 喌 f o N 喚2ln 2D Q03_02_002㠔̯ ҂͓͙͜⻪ 䬣⮳Ⱗρҋ⩗㘬㶗⹩ͩ喚()m u r r r n D Eȡ䃐テ喚1喉 㶐䬣䌌0r 2喉㐂 㘬喈 ͙ ⮳喉W 3喉҂ ὐ䛾4喉㠔 eV W nm r n m 4,3.0,10,20 喌䃐テE D ,⮳իȡ҂ ⮳ 㘬喚()()2m n N U r r rD E āā N ͩ ⮳ 1喉Г00r r dU dr 喌01010 n m r n r m E D āā 㶐 ⮳䬣䌌喚10()n m n r m E D2喉 ͙ ⮳㐂 㘬喚00011()()22m n W u r r r D Em n m n r 10)(D E В1(1)()2n m m n W n m DE D3喉҂ ὐ䛾喛0220)(V VU K V w w V r r U V U w w w ww w 喌 ҂⮳҂⼞喚āā ̯ͩ͜ 喌3NAr V A N ͩ ⮳ ȡ21131)(NAr r n r m V U n m w w E D 00]31)[(21122V n m V V NAr r n r m r V r V U w w w w w w E D ,][9100020220220n m n m V V r n r m r n r m V V U E D E D w w ͩ031)(2010100w w NAr r n r m VUn m V V ED āā 㶐Ѽ㒝␐䋢⮳ Х 喚n m r n r m 00ED 喌В ̹䲑⮳㶗䓭 喚][91020220220n m V V r n r m V V U E D w w ][9][91][91002000200020220n m m n n m V V r r V nm r m n r n m V r n n r m m V V UE D D E E Dw w n m r r U 000ED 喌)(902220U V mnV UV Vw w 0220)(V V U K V w w 喌09mn K U V 4喉eVW nm r n m 4,3.0,10,20 ⩠m n m n r 10)(D E mn m n n m W 1))(1(DE D 1004r WE 喌-96105.910eV m E u ][10020W rr ED 喌1924.510eV m D uQ03_02_003 ⴔ N ͙⻪ ㏳ ⮳NaCl ҂喌 㐂 㘬ͩ)4(2)(02n rr e N r U E SH D 喌⣟ДUrce В 䶨nr E喌̓ ҂ ν 㶐 喌䔈͓㔴 ρҋ⩗ 㘬⮳䉐⡝Ⱗ 喌䄄ⅱ n U ⮳ ㈪ȡ㐂 㘬 㶐Ѽ㒝 喚0r r " w w)()(21)()(000r r r U r U r U r r 䔸 㐂 㘬 喚)4(2)(02n rr e N r U E SH D " w w)()(21)()(000r r r U r U r U r r ДUrceВ n 0r E喌)4(2)('02U SH D rce r e N r U " w w)()'(21)(')('000r r r U r U r U r r ䷇ 喚喌)(')(00r U r U UE0r ncer㶐Ѽ㒝喚0)'()(00 w w w w r r r r r U r U 喌U U E02010rn er c r n ⩠UE0r ncer喌UE 00ln ln ln r c r n⩠UUE201r n er cr n喌UUE ln ln 2ln ln )1(ln ln 000r r c r n n UUE ln ln ln ln ln ln 000r c n r r n ДU ln ln ln 0 n r 喌U n r 0 U n r 0ВUE0r ncern nec n )(U E ,1()n e c n U EQ03_03_001䃗䃩N ͙ 㘍⮳̯㐣 䨭喈Ⱗ䗪 䬣䌌ͩa 喉喌 2N ∑㼒喌M m̯̽㐣 䨭⮳㐂 ̯̯ ȡXCH003_005 ⹩喌䉗䛾ͩM ⮳ Ѽν2n-1喌 2n+1喌 2n+3 ĉĉ䉗䛾ͩm ⮳ Ѽν2n 喌 2n+2喌 2n+4ĉĉ➊䶮䓿 ⼺喚)2()2(2221212121222n n n n n n n n M m P P P E PP P P E Pāā҂㈪N ͙ 㘍喌 2N ͙⠛⿺⮳ ⼺ ⼺㼒⮳ 喚])12([12])2([2aq n t i n q na t i n Be Ae Z Z P P䓿 ⼺ 喚])12([12])2([2aq n t i n q na t i n BeAe Z Z P P ¿¾½°¿°¾½0)2()cos 2(0)cos 2()2(2)(2)(2222B M A aq B aq A m B A e e B M A B e e A m iaq iaq iaq iaq Z E E E Z E E E Z E E Z 㠔A ȠB 䲍䰥⮳㼒喌㈪ 㵻 ␐䋢喚2cos 2cos 2222 ZE E E Z E M aqaq m 12222()4{1[1sin ]}()m M mM aq mM m M Z E r ͓⻼̼ ⮳ ∑⮳㞡 ㈪喚1222212222()4{1[1sin ]}()()4{1[1sin ]}()m M mM aq mM m M m M mM aq mM m M Z E Z Eaq a22SSdāāせ̯ 䛻⌹āāせ̯ 䛻⌹ 䃧q ⮳ Ⱍ喚/Na NaSS̯͙q ͓ ∑喚̯ ∑ ̯ ∑ȡ ⮳ ∑ Ⱍͩ2N ȡM m 喚12222{1[1sin ]}aq mZ E r22(1cos )aq m EZr 22aq aq Z Zāā͓⻼㞡 ㈪ XCH003_017 ⹩ 䪮∑ 䭿),0(a q !!o O ̺喚 q 喌0o 2)2sin(qa qa |喌q Z āā̯̽㐣 ∑⮳㞡 ㈪̯㜣ȡQ03_03_002䉗䛾Ⱗ ͓⻼ ̯㐣 䨭喌 䔀䗪 䬣⮳ ϓ䩈へν1c E210c E 喌 ̓ 䔀䗪⮳䬣䌌ȡ/2a 1喉ⅱ 㞡 ㈪ 䃐テ0,q q aS∑⮳䷀⢶ի喛2喉㜣⩪ 㞡 ㈪ ȡXCH003_018 ⹩喌䃭㨌㞡 䃟⮳ Ѽν2n-1喌 2n+1喌 2n+3 ĉĉȡ㏑㞡 䃟 Ѽν2n 喌 2n+2喌 2n+4 ĉĉȡ せ2n ͙ せ2n 喋1͙ ⮳䓿 ⼺喚21222211221122112222()()n n n n n n m m 1n n PE E P E P E P PE E P E P E P āā҂㈪N ͙ 㘍喌 2N ͙⠛⿺⮳ ⼺⼺㼒⮳ 喚1[(2)]221[(21)221i t n aq n i t n aq n AeBeZ Z P P ]喌 䓿 ⼺ 喚11222121211222121()(2()(i aq i aq i aq i aq m A e eB A m B eeA BZ E E E E Z E E E E ))喌Г221212,mmE E Z Z11222222212121122222221212()()()(i aq i aq i aq i aq A e e B eeA B Z Z Z Z Z Z Z Z Z Z 0)0㠔A ȠB 䲍䰥⮳㼒喌㈪ 㵻 ␐䋢喚11222222212121122222221212(),((),(0i aq i aq i aq i aq eeeeZ Z Z Z Z Z Z Z Z Z ))1111222222222222121212()()0()i aq i aq i aq i aq eeee Z Z Z Z Z Z Z 1c E 210c E 喌22201210,c c m m2010Z Z ZZ В22244000(11)20(10c 01)os aq Z Z Z Z㼒 喚220(1120cos 101)qa Z Z r āā͓⻼㞡 ㈪0q 喚22(11121)Z Z r 喚0220Z Z Z q aS喚220(1181)Z Z r 喚00202Z Z Z Z 㞡 ㈪ XCH003_019 ⹩ȡQ03_03_003䃐テ̯㐣 䨭⮳䷀⢶ )(Z U 䃭 䨭䪮 Na L ∑ⴑ իh Naq uS 2喌⃾͙∑ⴑ⮳ 喚Na q S 2 喌⟥S 2Na dq 䬣䯃 ⮳⟥ 喚dq NaS2喌 r 喌q Z Ⱗ ի ₓdq Na d SZ Z U 22)(u̯㐣 䨭㞡 ㈪喚)2(sin 422aq m EZГm EZ 40喌)2sin(0aq Z Z ͓䓨 dq aqa d )2cos(20Z Z2021)2cos(Z Z aq В dqaq a d )2cos(20Z Z dq a d 2202Z Z Z喌2202Z Z Zd a dq ZZZ S S d a Na dq Na 220122222 u u䷀⢶ 22021()N U Z SZ ZQ03_03_004䃭̸㐣 ⮳ 0 q 䭳䔀⮳䪮∑ 䭿 喚20)(Aqq Z Z 䃰 喚䷀⢶ °¯°®­! 002/102/320)(14)(Z Z Z Z Z Z S Z AV f ̸㐣 ⮳3)2(S V q d K䬣䯃 ⮳⟥ 喚dq q V 234)2(S S ͓䓨 20)(Aq q Z Z Aqdq q d 2)( Z 喌)(21q d Aqdq Z)(21q d Aq dq ZZ Z 01Aq В dq q V 234)2(S S)()(144)2(2/102/3223q d AV dq q V Z Z Z S S S Д1/223/21()()4V f A Z Z Z Z Z S0Z Z !喌ͩ㮉 喌 2/10)(Z Z ()0f Z Q03_04_001 ̯㐣䔀㜙⩠⩤ 䔀ѫ喌せn ͙㘬 喈1,2,3n 喉͜喌ク㏕∑ⴑak 2S⮳䰥㏖∑ȡ̯㐣䔀㜙⩠⩤ 䔀ѫ喌⩗ク㏕∑ⴑ㶗⹩⮳∑)]])2([211([)(22222x a ni n n mx aix k i k e a n k k mV L L ee x S S S \¦ u =せn ͙㘬 䰥㏖∑ 喚22()0211()i mx i m xikx a a nx e e eL LS S a S \ XCH004_006 ⹩ȡせ̯͙㘬 喚m 喌0 0211()i xa x e LS \ せλ͙㘬 喚2()02211,()i x a a e L S S \ m x 喌30221()i x ax e LS \ せ̸͙㘬 喚2()02311,()i x a a m x 喌e L S S \ 50231()i x ax e LS \ Q03_04_002⩤ ͜⮳ 㘬 喚°¯°®­ d d d d bna x b a n b na x b na na x b m x V )1(0])([21)(222Z ̓b a 4 喌Z ȡ1)⩪ ₓ 㘬 ㏮喌 䃐テ 㘬⮳ ի喛2)⩗䔀㜙⩠⩤ ὐ 喌䃐テ ҂⮳せ̯͙ せλ͙ 䯈 ȡ㘬 ㏮ XCH004_049⹩ȡ㘬⮳ ի喚³Likxikx dx e Lx V e L V 01)(1³bna bna ikx ikx dxe Lna x b m e L NV 1]})([21{1222Z ³ bna bna dxna x b m L NV ])([2222Z Гna x [喌NaL ³ bbd b m a V [[Z )(21222喌2296a V m Z 䔀㜙⩠⩤ 䔀ѫὐ ͜喌 㘬 ⮳せn ͙ 䛻 ㈪³ a k k i d V e a n V 0)'()(1)([[[,na k k S 2' ³ a n a i d V e a n V 02)(1)([[[S°¯°®­ d d d d bb b b b m V [[[Z [0)(21)(222В³ b b n a i d b m e a n V [[Z [S)(211)(2222喌³bbn aid b ea m n V [[Z [S )(2)(2222³bbaid b eam V [[Z [S )(22222142222()2biabm V eb aS [Z d [[³҂⮳せ̯͙⺰ 喚112g E V ҂⮳せλ͙⺰ 喚222g E V Q03_04_003̯㐣 ͜⩤ ⮳∑ ␐䋢 ≊䊚 ⤵ȡ ͩ ,⩤ ⮳∑ ͩa 1喉S \ax x k sin)( 2喉¦ffm mk ma x f i x )()()(\3喉S \ax i x k 3cos)( 4喉¦ffl k la x f x )()(\喌ⅱ⩤ 䔈ϊ ͜⮳∑ⴑȡ≊䊚 ⤵)()(r e R r nR k i n K K K KK \\ ̯㐣)()(x e na x inka \\ ,)()(x e a x ika \\ 1喉⩤ ⮳∑ 喚S \ax x k sin)( S S \a xa a x a x k sin sin)( 喌)()()(x e x a x k ika k k \\\ 1ikaek aS2喉⩤ ⮳∑ 喚¦ffm mk ma x f i x )()()(\¦ ff])1([)()(a m x f i a x mk \¦ ff])1([)(1a m x f i i m )()()(x i la x f i i k l \ ¦ ffД喚i eika2k aS3喉⩤ ⮳∑ 喚)(3cos )(3cos )(x axi a a x i a x k k \S S \ 1 ikaek aS4喉⩤ ⮳∑ 喚¦ffl k la x f x )()(\¦ ffl k a l x f a x ])1([)(\)()(x ma x f km \¦ ff喌 1ika e 0k Q03_04_004⩗㉖ 㑉䔀ѫⅱ 䲑 ⿺ ҂ ⿺ s㘬㏖Ⱗ ⮳㘬 ȡ䃐 䔀䗪 ◨ ⮳Ⱗρҋ⩗ 喌s 㘬㏖Ⱗ ⮳㘬 )(k E sKД㶗⹩ͩ喚¦NearestR Rk i s s ss se R J J k E K K K K)()(0H 䲑 ⿺ XCH_001_007 ⹩ȡЪ 䔸 ̯͙ ◨ͩ ◨ȡ12͙ 䗪䔀⮳ ◨喌 Ѽ㒝ͩ°°°°¯°°°°®­ 0,2,20,2,20,2,20,2,2a a a a a a a a 喌°°°°¯°°°°®­2,2,02,2,02,2,02,2,0aa a a a a a a 喌°°°°¯°°°°®­2,0,22,0,22,0,22,0,2a a a a a a aa k j a i a R s K K K K 022 へ12͙ ⴑВ ¦ NearestR R k i s s s s seR J J k E K K K K )()(0H s ∑ ⤲ ⼟ 喚0*01()()[()()]()}s i s i J J R R U V d M [[[M [³[K K K K KKK 01()ss ik R ss R NearestE k J J eH ¦K K K喌 k j a i a R s K KK K 022 В 䔊㵻䃐テȡ()(0)K 22s x y z a a k R k i k j k k i j k K K K K KK K 喌()2s x y a k R k k K K ()222(cos sin )(cos sin )222x y x y aa a i k k i k i k y y x x k a k a k a k aeeei i 2āāㆪѫ⮳㶗⹩ 12䶨㏾䓶 ク 喚01()4(coscos cos cos cos cos )222222y y sx x z z s k a k a k a k a k a k a E k J J H K҂ ⿺ XCH_001_003 ⹩喌Ъ 䔸 ̯͙ ◨ͩ ◨ȡ 8͙ 䗪䔀⮳ ◨喌 Ѽ㒝ͩ°°°°¯°°°°®­ 2,2,22,2,22,2,22,2,2a a a a a a a a a a a a喌°°°°¯°°°°®­ 2,2,22,2,22,2,22,2,2a a aa a a a a a aa a k a j a i a R s K K K K 222 へ8͙ ⴑВ ¦ NearestR R k i s s s s seR J J k E K K K K )()(0H s ∑ ⤲ ⼟ 喚0*01()()[()()]()}s i s i J J R R U V d M [[[M [ ³[K K K K K K K 01()ss ik R ss R NearestE k J J eH ¦K K K222s a a a R i j KK K K k В 䔊㵻䃐テȡ()()K 222s x y z a a a k R k i k j k k i j k K K K K KK K 喌()2s x y z a k R k k k K K ()2222(cossin )(cos sin )(cos sin )22222x y z x y z aa a a i k k k i k i k i k y y x x z k a k a k a k a k a k aeeeei i i 2z āāㆪѫ⮳㶗⹩ 12䶨㏾䓶 ク 喚01()8cos cos cos 222y sx z s k a k a k aE k J J H K Q03_04_005 ̯͙̯㐣 䨭喌 䬣䌌a 喌 䪮 L Na1喉⩗㉖ 㑉䔀ѫ ∄ⅱ ̽ s 㘬㏖Ⱗ ⮳㘬 )(k E sKȡ2喉ⅱ 㘬 ⮳㶗䓭⮳䉨 㘬㏖ ⮳㘬 ȡF E 0F E 3喉 ⃾͙ s ͜ ̯͙⩤ 喌䃐テT K 0䃐 䔀䗪 ◨ ⮳Ⱗρҋ⩗ 喌s 㘬㏖Ⱗ ⮳㘬 )(k E sKД㶗⹩ͩ喚¦NearestR Rk i s s ss s e R J J k E K K K K)()(0H āāЪ 䔸 ̯͙ ◨ͩ ◨ȡs ∑ ⤲ ⼟ 喚01()ss ik R ss R NearestE k J J eH ¦K K K͓͙ 䔀䗪⮳ ◨喌 ͩ喚¯®­ aaВ ¦NearestR Rk i s s ss s e R J J k E K K K K)()(0H 喚)()(10ika ika s s e e J J k E H 01()2cos ss E k J J kaH 㘬 喚̯㐣 ̺⮳㘬 喚喌ka J J k E s scos 2)(10 H dkka aJ k dE s)sin 2()(1 12)(cos J J k E ka s s H 喌210)2)((1sin J J k E ka s s H dk J J k E aJ k dE s s s2101)2)((12)( H 喌dkJ J k E aJ k dE s s s2101)2)((12)( H )())((412021k dE J k E J a dk s s sH ν̯㐣 喌∑ⴑͩk and k Ⱗ ⮳㘬䛾喌ₓ 㔲㮀 ⩤ 㜙 2⻼ 喌 ₓ 䬣⮳⟥ 喚dk 42NadZ dk S喌221021()4(())s s s N dZ dE k J E k J S H㘬 喚22102()()4(())s s s dZ NN E dE k J E k J S Hk ⮳⩤ āā ͜00()()Fk E s E E N NdE³001010()2cos 2s k s s k E k J J ka J J H H 0022102()4(())Fk E s s E s NN d J E k J SH³E k0020112()1()21()2Fk E s s E s dE k E k J J J H S ³Г喚102)(J J k E s s H [喌)(211k dE J d s[喌2211d [S [³0012arcsin2Fk E ss E E J J H S001112arcsin arcsin 222F s E J J J J H S 0012F s E J J H 喌0F s E J H 䉨 㘬㏖喚0T K ⮳䉨 㘬㏖喚00F s E J H āāВ 20102()4()F s NN E J E J S H2K 0T 䉨 㘬㏖ ⮳㘬 喚0F E 1()NN E J SQ03_04_006 䜀 ϓ ⮳㘬 喚22111122220022()(0),0.182()()(),0.062k E k E m m m E k E k k k m m m =K K = ͩ͜㘬 1⮳ 䶥喌ͩ㘬 2⮳ 喌ϓ 䘗 喚1(0)E 20()E k 120(0)()0.1E E k eV ⩠ν㘬 ⮳ϓ 喌㘬 1͜⮳䘗 ⩤ 䒛⼪ 㘬 2͜喌㔻 㘬 1͜ ⾩⾣喌䃗䃩 ⮳䉨 㘬㏖ȡ0TK 䜀 ⮳㘬 1 㘬 2 XCH004_050 ⹩ȡ㘬 1⮳㘬 13()2(2)k V dS N E ES ³21k kE m=喌 1112[(0)()]m E E k k =В 112[(0)()]/k E E E k =1m2131111()24(2)2[(0)()]/V N E kE E k m S S =312112222()()(0)()(2)V m N E E E k S=1 ⤵㘬 2⮳㘬 喚322222222()()()()(2)V m N E E k E k S =20 䜀 ̼ ⩎㘬 䛼 喌⩤ ␐̯͙㘬 喌 㐌㑇҂ȡѵ⩠ν㘬 ϓ 喌㘬 1͜⮳⩤ 㘬 2͜喌␐䋢01(0)02()012()()FFk E E E E N E dE N E dE³³01(0)02()03312221122022222222()(0)()()()()(2)(2)FFk E E E EV m V m E E k dE E k E k d S S ³³==E 01(0)02()03332221112220[(0)()][()()]F Fk E E E E m E E k m E k E k 320011220[(0)][()]F F m E E m E E k 01122012(0)()F m E m E k E m māā 120.18,0.06m m m m 120(0)()0.1E E k eV В 喚020()0.075F E E k eVQ03_04_007䃭 λ㐣ₒ 喌 ҂ ͩ喚)2cos()2cos(4),(y ax a U y x U SS ⩗䔀㜙⩠⩤ 䔀ѫ⮳ 䃩喌䔀ѫⅱ 䛻⌹䶥㼁),(aa SS ⮳㘬䯈ȡ҂ 䛻⌹䶥㼁),(aa SS ⮳㘬䯈喚112V E g 䔀㜙⩠⩤ 䔀ѫὐ ͜喌 㘬 ⮳せn ͙ 䛻 ㈪³aG i d V ean V n 02)(1)([[[KKK K ,n R r GK K[喌y x d d d [[[ K 喌nG k k K K K '))((),(2222y aiy aix aix aieeeeU y x U S S S S 喌 2211,[[ a n y a n x В))((),()(2)(2)(2)(22122221111[S[S[S[S[[ a n aia n aia n aia n aieeee U U ))((),(2211222221[S [S [S [S [[aiaiaiaieeeeU U 䛻⌹䶥㼁喚y x k ak a k K S S 喌y x n k a k a k G k K K K S S '喌y x n k a k a GK S S 2221b b G n K K K³³ a ayx a al a a b b i aiaiaiaid d eeeeeU a V y x y y x x 00)11()(22222122121)])(([1[[[[[S [S [S [S K K K K ³³ a ayx aa i aiaiaiaid d eeeeeU a V y x y y x x 00)22(222221)])(([1[[[S [S [S [S [S [S³³ a ayx aiaid d eeU a V y x 004421)]1)(1([1[[[S [SUV 1 䛻⌹䶥㼁),(aa SS ⮳㘬䯈喚12g E U Q03_04_008䭿 䓨䪮ͩL ⮳ₒ ͜⮳N ͙⩤ 喌⩤ ⮳㘬䛾ͩ喚)(2222y x k k mE =1喉ⅱ㘬2喉ⅱλ㐣㈪㐎 㐌 䰥 ⮳䉨ㆢ㘬䛾)(2222y x k k m E= ͩ2222=mE k k y x 喌 ν㐈 ⮳㘬䛾喌 ⼺ ∑ⴑ⾩䬣 ̯͙ ȡ k ⾩䬣喌 Ѽ䲑⼞ ⮳⟥ 喚22)2(2S L22=mE k ⮳ ⮳⟥ 喚222)2(2k L Z S S 喌E mL Z 22=S 㘬䛾E E+dE ͺ䬣⮳⟥ 喚dE mL dZ 22=S㘬 喚22()mL N E S=㘬䛾⩤ ⮳ Ⱍ喚喌dE E E o dE E f E N dN )()( dE E f mL dN )(22=S 㐌 䰥 喚0T 0220220F E E mL dE mL N F==S S ³㐌 䰥 ⮳䉨ㆢ㘬䛾喚202FN E mL S=Q03_04_009 2)()(2222=z z y y x x k m k m k m k E k E ,ⅱ㘬 ȡ2)()(2222=z z y y x x k m k m k m k E k E ͩ1][)(212222z z y y x x k m k m k m k E E =䔈 k ⾩䬣⮳̯͙Ṝ⤲ ⼺喌 䒣a, b, c ͩ212])(2[=k x E E m a 喌212])(2[=k y E E m b 喌212)(2[=k z E E m c Ṝ⤲ k ⾩䬣⮳҂⼞abc k S 34:k ⾩䬣⮳⟥ 3)2(2S L 喌Ṝ⤲ ⮳⟥ :2/32/322/13)()2()(34)2(2k z y x E E m m m L Z =S S dEE E m m m L dE E N dZ k z y x 2/12/12/323)()()2(34)2(223)( =S S 33/21/21/2222()()()()2x y z k L N E m m m E E S =Q03_05_001䃭̯㐣 ҂⮳⩤ 㘬 Д 喚)2cos 81cos 87()(22ka ka ma k E =喌 ͜a ͩ ȡ䃐テ1喉㘬 ⮳ 喛2喉⩤ ∑ⴑk ⮳⟥ ⮳䕎 喛3喉㘬 䘗 㘬 䶥䘗⩤ ⮳ 䉗䛾ȡ1喉㘬 䘗喚喌0 k 0)0( E 㘬 䶥䘗喚ak S 喌)2cos 81cos 87()(22S S Sma a E =,222)(ma a E = S㘬 喚222()(0)E E E a ma S'=2喉⩤ ∑ⴑk ⮳⟥ ⮳䕎 喚dkk dE k v )(1)(=喌1()(sin sin 2)4v k ka ka ma =3喉⩠222/*k E m w w =喌)2cos 84cos (222222ka a ka a ma kE w w =kaka mm 2cos 21cos *㘬 䘗⩤ ⮳ 䉗䛾喚喌0 k *2m m 㘬 䶥䘗⩤ ⮳ 䉗䛾喚ak S喌2*3m mQ03_05_002䃭⩤ へ㘬䲑ͩṜ⤲喚323222221212222)(m k m k m k k E ===K 喌 ⷰ B Ⱗ νṜ⤲ͪ䒣҈ ͩJE D ,,1) ⩤ ⮳ ㏾ 䓿 ⼺2)䃰 ⩤ 㐄ⷰ 䒛䷀⢶ͩ喚*m qBZ 喌 ͜232221321*J E D m m m m m m m ⷰ ͜⩤ 䓿 ⮳ ⼺喚B k v q dtk d K K K K =u )()(321J E D k k k B B K⩤ ⮳䕎 喚)(1)(k E k v k K =KK⩤ 㘬䛾喚323222221212222)(m k m k m k k E ===K332211)(k k E k k E k k E k E kK w w w ww w 喌333222221112)(k m k k m k k m k k E k = = =K ⩤ 䕎 喚333222111)(k m k k m k k m k k v= = =K K ⩤ 䕎 ⷰ В ⩤ 䓿 ⼺喚B k v q dtk d KK K K=u )(喌 ⩗321k k k u ㈪)}(){(321333222111J E D k k k k m k k m k k m k qB dt kd Ku 䓿 ⼺喚°°°¯°°°®­ )()()(221131133233221D E J D E J m k m k qB dtdk m k m k qB dt dk m k m k qB dt dk 喌123232313131212()0()0()0dk k k qB dt m m dk k kqB dt m m dk k k qB dt m m J E D J E D ­ °°° ®°° °¯Гti t i ti ek k e k k ek k Z Z Z 033022011,, В 䓿 ⼺ 喚000022011030110330203302201k m qB k m qB k i k m qB k m qB k i k m qB k m qB k i D E Z J D Z E J Z 030201,,k k k 䲍䰥㼒喌㈪ 㵻 ͩ䰥喚0213132ZD E DZ JE J Zi m qB m qB m qB i m qB m qB m qB i 0})()()({2312221223222213132E J D Z Z ZD E D Z J E J Z m m qB m m qB m m qB i i m qB m qB m qB i m qB m qB m qB i 0 Z ͸喌 ₓ 䒛䷀⢶喚212312322m m m m m m qBJ E D Z222123123m m m qBm m m D E J Z 喌 ͜*qB m Z123222123*m m m m m m m D E JQ03_06_001 ѽ⍘̺䜀 䧭⮳ ☜ 䛾⮳ 侻㐂 喚ȡ̯͙ ⮳䜀 䧭 ͙⩤ 喌ⅱ䧭⮳䉨ㆢ⍘ ⍘ K mol mJ TT C /57.208.2323106u N F T D 4ȡ ̯ ⮳⩤ ☜ ⮳䉐⡝喚BFB V k ETk N C )(2020S ̽ 侻㐂 ℃䒲 喚Kmol J T k T k Tk N k ETk N B FB B B FB u /1008.2)(2)(23-20020S S 䉨ㆢ⍘ 喚2-3196242 2.0810BF k T NKS u u 喚34)(512DB V T NkC 4 S ̽ 侻㐂 ℃䒲 喚43-3312() 2.5710/5B D Nk T T J mol KS u 4 ⍘ 喚41/3-312()915 2.5710B D Nk K S 4 u u Q03_06_002䃭N ͙⩤ ㏳ ク ⩤ ⅃喌҂⼞ͩV 喌䃰 K T 0 1喉⃾͙⩤ ⮳ 㘬䛾053F E U2喉㜙⩠⩤ ⅃⮳ ␐䋢U pV 32䜀 ͜㜙⩠⩤ ⮳㘬 喚2/12/32)2(4)(E hm V E N S K T 0 喌䉨ㆢ 喚¯®­!d )(0)(1)(0F F E E E E E f ⃾͙⩤ ⮳ 㘬䛾喚NdE E f E EN U ³f)()(dE E E h m V NU FE ³002/12/32)2(41S 喌2/502/32)2(452F E h m V N U S 䜀 ͜⮳⩤ 喚喌³f)()(dE E f E N N 2/302/322/12/32)2(432)2(40F E E h m V dE E h m V N FS S³N В 2/502/32)2(452F E h m V N U S喚035F U E⩤ ⅃ⰺҋ ⤵ ⅃҂喌 U n p 32喌U V N p 32 ,23pV NU Q03_07_001 InSb ⮳⩤ 䉗䛾0.015e m m 喌Ϻ⩤ 18H 喌 喌䃐テ0.6479a n m 1) ͪ⮳⩤⻪㘬2) ⮳䒗䖂3) ͪ 喌Ⱗ䗪 䉗 ⮳䒗䖂ͺ䬣 ⩎ϓ 喌 ⮳ ͪ 䉗⊂ 倇ν 喟⩤⻪㘬喚)2()4(*22204=H SH q m E i 喌422200.015(18)(4)(2)i mq E SH =喌46.310i E eV u ⮳䒗䖂 喚220002241841*0.0150.015a a m q mq S HH S H ==8喌62.4a nm Ⱗ䗪 䉗 ⮳䒗䖂ͺ䬣 ⩎ϓ 喌 䉗 ͺ䬣⮳䬣䌌喚2124.8d a nm ͪ⊂ 喚28331 5.110/n cm du。