J. Inst. Electrostat. Jpn.
, 30, 6 (2006) 276 283

ធ⸅Ꮺ㔚޽ࠆ޿ߪ៺ᡂᏪ㔚ߒߚ⛘✼૕ਛߩᾲᐔⴧ㔚⩄ಽᏓᏒ Ꮉ ᕡ ᮸*,1
㧔2006 ᐕ 7 ᦬ 20 ᣣฃઃ㧘2006 ᐕ 9 ᦬ 30 ᣣฃℂ㧕Distribution of Electric Charge in Contact- or Tribo-Electrified
Insulating Materials under Thermal Equilibrium
Tsuneki ICHIKAWA*,1(Received July 20, 2006; Accepted September 30, 2006)

Spatial distributions of charge carriers in contact- or tribo-electrified insulating materials under thermal equilibrium
were estimated by solving the Poisson-Boltzmann equation under three conditions, namely, 1) inter-medium
migrations of both the positive and the negative charge carriers were allowed, 2) inter-medium migration of only the
positive charge carriers were allowed, and 3) inter-medium and intra-medium migrations of the positive and thenegative charge carriers, respectively, were allowed. In cases 1) and 3), the induced electric charges were localizedaround the contact surface, whereas in case 2) the charge distribution in a carrier-donating medium was broadened due
to freezing-out of the charge carriers. The theoretical results do not contradict the view that the triboelectricity and/or
contact charge of insulating polymers are induced by the migration of protons that are generated during the contact.

1.

ߪߓ߼ߦ

ሶ߇ᜂߞߡ޿ࠆߣߔࠆ᳿ቯ⊛ߥᩮ᜚ߪߥ޿㧚ੑߟߩ‛૕ࠍធ⸅ߒߡ↢ߓࠆធ⸅Ꮺ㔚߿㧘ᡂࠅวࠊߖߡ↢ߓ᦭ᯏ⛘✼૕ߪવዉᏪߩࠛࡀ࡞ࠡ࡯߇㜞ߊ㧘ࠪ࡝ࠦࡦ᮸⢽ߥࠆ៺ᡂᏪ㔚ߪ㧘ฎ᧪ᦨ߽りㄭߥ㔚᳇⊛⃻⽎ߩ৻ߟߛ߇㧘ߘߩߤࠍ㒰ߌ߫㧘વዉᏪߩᐩߩࠛࡀ࡞ࠡ࡯ߪ⌀ⓨḰ૏ㄭㄝ޽ࠆ޿

1)

ᧄ⾰ߪ޿߹ߛࠃߊಽ߆ߞߡ޿ߥ޿ 㧚ߘߩਥߚࠆේ࿃ߩ߭ߣ

ߪߘࠇࠃࠅ߽㜞ߊߥࠆ 2)㧚ࠃߞߡࡃࡦ࠼ࠡࡖ࠶ࡊߪ৻⥸ߦߟߪ㧘Ꮺ㔚ࠍᜂ߁㔚⩄ࠠࡖ࡝ࡗ࡯ߩỚᐲ߇ૐߔ߉ߡ㧘ߘߩታ

3eV એ਄ߣߥࠆߚ߼㧘ቶ᷷ㄭㄝߢߪ߶ߣࠎߤ㔚ሶ߇ሽ࿷ߒߥ

ᘒ߇ࠃߊಽ߆ࠄߥ޿ߎߣߦ޽ࠆ㧚100g㧘⋥ᓘ 6cm ߩࡐ࡝ࠛ࠴

޿㧚ߒ߆ߒߥ߇ࠄߎࠇߦ᡼኿✢ࠍᾖ኿ߔࠆߣ㧘વዉ㔚ሶߣᱜ࡟ࡦ߇⴫㕙㔚૏ 1 ਁࡏ࡞࠻ߦᏪ㔚ߒߡ߽㧘✚㔚⩄㊂ߪ㜞‫ޘ‬ሹ㧔ࠞ࠴ࠝࡦ㧕ࠍᄙ㊂ߦ⊒↢ߐߖࠆߎߣ߇ߢ߈ࠆ㧚᦭ᯏ⛘✼–13

3.5×10ࡕ࡞⒟ᐲߩᭂᓸ㊂ߛ߆ࠄ㧘৻⥸ߩ‛ℂൻቇ⊛ಽᨆᚻ૕ਛߢߩᱜሹߣવዉ㔚ሶߩ᜼േߦߟ޿ߡߪ᡼኿✢ൻቇߩಽᴺߢหቯߔࠆߎߣߪ㕖Ᏹߦ㔍ߒ޿㧚ߒߚ߇ߞߡ㕒㔚᳇ߩᧄ⾰㊁ߢ⦟ߊ⎇ⓥߐࠇߡ߅ࠅ㧘વዉ㔚ሶߣߩౣ⚿วࠍㅏࠇߚᱜሹ

ߢ޽ࠆ㔚⩄ࠠࡖ࡝ࡗ࡯ߩታᘒߦߟ޿ߡߪ㧘ផቯߦ㗬ࠄߑࠆࠍߪ㧘ᄙߊߩ႐วㅦ߿߆ߦਛᕈࡈ࡝࡯࡜ࠫࠞ࡞ߣࡊࡠ࠻ࡦߦ⸃

ᓧߥ޿㧚㔌ߒߡ቟ቯൻߔࠆߎߣ㧘↢ߓߚࡊࡠ࠻ࡦߪવዉ㔚ሶߣ෻ᔕߒ

Ꮺ㔚ࠍᜂߞߡ޿ࠆ㔚⩄ࠠࡖ࡝ࡗ࡯ߦߟ޿ߡߪ㧘2 ߟߩ⺑߇ߡ᳓⚛ේሶߣߥࠅ㧘ߎࠇ߇᦭ᯏ‛߆ࠄ᳓⚛ࠍᒁ߈ᛮ޿ߡ᳓⚛

޽ࠆ㧚ߘߩ߭ߣߟߪવዉ㔚ሶߢ޽ࠅ㧘ઁߩ৻ߟߪࠗࠝࡦߢ޽

ಽሶߣਛᕈࡈ࡝࡯࡜ࠫࠞ࡞ߦᄌࠊࠆߎߣ㧘ಽሶ㛽ᩰߦ㉄⚛ේࠆ㧚㊄ዻห჻ߩធ⸅Ꮺ㔚ߦ߅ߌࠆ㔚⩄ࠠࡖ࡝ࡗ࡯߇વዉ㔚ሶሶࠍ฽߻㜞ಽሶ߿㉄⚛ಽሶࠍਇ⚐‛ߣߒߡ฽߻㜞ಽሶߢߪ㧘ߢ޽ࠆߎߣߪ㧘ᾲ⿠㔚ജߥߤߩታ㛎߆ࠄ߽᣿ࠄ߆ߢ޽ࠆ㧚ߒવዉ㔚ሶߪCOO߿COߥߤߩࠕ࠾ࠝࡦߦߥߞߡ቟ቯൻߔ

߆ߒߥ߇ࠄ㧘⛘✼‛ห჻߇ធ⸅ߒߚࠅ៺ᡂߒ޽ߞߚࠅߒߚ㓙ࠆߎߣ㧘߹ߚႮൻࡆ࠾࡞ߩࠃ߁ߦࡂࡠࠥࡦේሶࠍ฽߻႐วߦ

ߦ↢ߓࠆ㕒㔚᳇ࠍ㧘⛘✼૕㧘ߣࠅࠊߌ᦭ᯏ⛘✼૕ਛߩવዉ㔚ߪ㧘ࡂࡠࠥࡦࠕ࠾ࠝࡦߣߥߞߡ቟ቯൻߔࠆߎߣߥߤ߇⍮ࠄࠇ
ߡ޿ࠆ 2)㧚ߒߚ߇ߞߡᏪ㔚ߒߚ‛૕ਛߩ㔚⩄ࠠࡖ࡝ࡗ࡯ߣߒ

ࠠ࡯ࡢ࡯࠼㧦ធ⸅Ꮺ㔚㧘៺ᡂᏪ㔚㧘ᾲᐔⴧ㧘㔚⩄ಽᏓ㧘Ꮺ㔚㊂* ർᶏ㆏ᄢቇᄢቇ㒮Ꮏቇ⎇ⓥ⑼㧔060-8628 ᧅᏻᏒർ඙ർ 13
᧦⷏ 8 ৼ⋡㧕Graduate School of Engineering, Hokkaido University Sapporo,
060-8628 Japan1ichikawa@eng.hokudai.ac.jpߡવዉ㔚ሶ߿ᱜሹ߇቟ቯߦሽ࿷ߔࠆߎߣߪ޽ࠅ߃ߥ޿㧚ߥ߅㧘ಽሶ㑆⋧੕૞↪߇ᒙ޿⛘✼૕ਛߩᱜሹ߿વዉ㔚ሶߪ㧘ᵄേ⊛ߣ޿߁ࠃࠅ߽߻ߒࠈฎౖ☸ሶ⊛ߦᝄ⥰߁ߎߣ߽⍮ࠄࠇߡ޿ࠆ 2)㧚
⛘✼૕ਛߩ㔚⩄ࠠࡖ࡝ࡗ࡯߇વዉ㔚ሶ߿ᱜሹߢߥ޿ߣߔ

277 (33)⴫㧝 㜞ಽሶߩធ⸅Ꮺ㔚㊂ߣ㧘ࡕ࠺࡞ൻว‛ߩࡊࡠ࠻ࡦ⸃㔌ቯᢙ߅ࠃ߮ࡊࡠ࠻ࡦⷫ๺ജߣߩ㑐ଥ
Table 1. Relation between triboelectric charges of polymers and proton dissociation constants and affinities of model compounds.

aPolymer

Charge / pC a[-CH2CH(C5H4N)-]n1.5[-CO(CH2)4CONH(CH2)6NH-]n1.2[-CH2CH(OH)-]n0.5[-CH2CH(OCOCH3)-]n0.2[-CH2C(CH3)(COOCH3)-]n0.14[-COC6H4COOC2H4O-]n0[-CH2CH(C6H5)-]n0[-CH2CH2-]n0[-CH2CHCl-]n-1.6[-CF2CF2-]n-2.8

pKb of model compoundin water b
CH3CH2(C5H4N)
5.89
CH3CONHC4H7
0.15
CH3CH(CH3)OH-4.1
CH3COOC2H5-5.1
CH3COOC2H5-5.1
C6H5COOC2H5-7.37
Naphthacene, C18H12-6.6

Gas phase proton affinity ofmodel compound / kJmol1 c
CH3CH2(C5H4N)
946
CH3CONHCH3889
CH3CH2OH
776
CH3COOC2H5
836
CH2CH(CH3)COOCH3836
C6H5COOCH3
850
CH3CH2C6H5
802
C6H12
687
CH3CH2Cl
707
CF4
527

Saturation charge after repeated contacts with a 2mm diameter sphere of Au in vacuum4).

b

Dissociation constant of protonated model compound9).

c

Data from NIST Chemistry WebBook, http://webbook.nist.gov/.

ࠇ߫㧘ߘࠇߪࠕ࠾ࠝࡦ߿ࠞ࠴ࠝࡦߣ޿߁ߎߣߦߥࠆ㧚Diaz ࠄ
3)޽ࠆߎߣ㧘߅ࠃ߮Ꮺ㔚㊂߇㘻๺ߔࠆߎߣߪ㧘㔚⩄ࠠࡖ࡝ࡗ࡯ߪ 㧘㜞ಽሶߩᏪ㔚೉ߪ㜞ಽሶߩ⵾ᴺ߿ጁᱧߦଐሽߒߥ޿ߎ

ߢ޽ࠆࡊࡠ࠻ࡦ߇ 2 ߟߩ‛⾰㑆ߢᾲᐔⴧ⁁ᘒߦ޽ࠆߎߣࠍ␜

ߣࠍ⏕⹺ߒ㧘Ꮺ㔚೉߇ਇ⚐‛ߢߪߥߊ㜞ಽሶߩൻቇ᭴ㅧߢ᳿

ໂߒߡ޿ࠆ㧚ᧄⓂߢߪ㧘⇣ߥࠆ⛘✼૕ࠍធ⸅ߐߖߚ႐วߦ↢߹ࠆߣ⚿⺰ߒߚ㧚߹ߚ㧘㊄ዻ⃿ࠍ㜞ಽሶ᧼ߦ᛼ߒઃߌࠆߎߣ

ߓࠆ㔚⩄ࠠࡖ࡝ࡗ࡯ߩ⒖േ߇㧘ᾲᐔⴧᤨߦߤߩࠃ߁ߥᏪ㔚⁁

4-8)㧘㜞ಽሶ߿㊄ዻ⃿ߩᘒࠍ߽ߚࠄߔ߆ߦߟ޿ߡ㧘ᾲജቇ⊛ߦ⠨ኤߒ㧘ធ⸅Ꮺ㔚߿៺઀੐㑐ᢙߦߪή㑐ଥߛ߇㧘᳓ਛߢࡊࡠ࠻ࡦઃടߒߚ㜞ಽሶ㘃ᡂᏪ㔚ߩታᘒߦㄼࠆߎߣࠍ⹜ߺࠆ㧚ߥ߅㧘㔚⩄ࠠࡖ࡝ࡗ࡯ߣ

ૃಽሶߩ⸃㔌ቯᢙߣᲧ଀㑐ଥߦ޽ࠆߎߣࠍ⷗಴ߒ㧘Ꮺ㔚߇ࡊߒߡߪ㧘ࡊࡠ࠻ࡦߦ㒢ࠄߕ㧘ࠗࠝࡦ৻⥸ࠍ⠨߃ߡ޿ࠆ߇㧘⛘

ࡠ࠻ࡦߩ⒖േߦࠃߞߡ↢ߓࠆߣ⚿⺰ߒߚ㧚᳓ࠍ߶ߣࠎߤ฽߹

✼૕ਛߩવዉ㔚ሶ߿ᱜሹߪ☸ሶ⊛ߦᝄ⥰߁ߩߢ㧘એᓟߩ⺰⼏ߥ޿㜞ಽሶߩᏪ㔚೉ࠍ᳓ਛߢߩ⸃㔌ቯᢙߣ㑐ㅪઃߌࠆߎߣ

ߪ㔚⩄ࠠࡖ࡝ࡗ࡯߇વዉ㔚ሶ߿ᱜሹߩ႐วߦߟ޿ߡ߽ᚑ┙ߦߪήℂ߇޽ࠆࠃ߁ߦᕁ߃ࠆ߇㧘⴫ 1 ߦ␜ߔࠃ߁ߦ㧘ൻว‛ߔࠆ‫ޕ‬ߩࡊࡠ࠻ࡦⷫ๺ജߣ⸃㔌ቯᢙߣߩ㑆ߦߪ⋧㑐߇޽ࠆߩߢ㧘Ꮺ

2.

㔚߇ࡊࡠ࠻ࡦߩ⒖േߦࠃߞߡ↢ߓࠆߣߒߚᩮ᜚ߪᅷᒰߥࠃ

૕Ⓧᄌൻ߇ή޿♽ߩ᷷ᐲ T ߦ߅ߌࠆࡈ࡝࡯ࠛࡀ࡞ࠡ࡯F ߪ㧘ߦࠃߞߡ㜞ಽሶߦ⺃⿠ߐࠇࠆᏪ㔚㊂ߪ

ℂ⺰߁ߦᕁ߃ࠆ㧚࠽ࠗࡠࡦߥߤ⓸⚛ࠍ฽߻㜞ಽሶߪᱜߦᏪ㔚ߒᤃU ࠍౝㇱࠛࡀ࡞ࠡ࡯㧘S ࠍࠛࡦ࠻ࡠࡇ࡯ߣߔࠆߣ F=UTS ߢ޿ߎߣ߇⍮ࠄࠇߡ޿ࠆ߇㧘ࡊࡠ࠻ࡦⷫ๺ജ߽㜞ߊߥߞߡ߅ࠅ㧘ਈ߃ࠄࠇࠆ㧚ᇦ૕ M ਛߦ㕒㔚ࡐ࠹ࡦࠪࡖ࡞Iߩ߽ߣߢ㔚⩄rqr

ᦨ߽⽶ߦᏪ㔚ߒᤃ޿࠹ࡈࡠࡦߪࡊࡠ࠻ࡦⷫ๺ജ߽ᦨૐߣߥ

ࠍ᦭ߔࠆỚᐲ Wrߩᱜ⽶㔚⩄ࠠࡖ࡝ࡗ࡯߇ሽ࿷ߔࠆ႐ว㧘ౝߞߡ޿ࠆ㧚ߥ߅㧘ࡐ࡝ࡆ࠾࡞ࠕ࡞ࠦ࡯࡞ߪ㧘ࡕ࠺࡞ൻว‛ߩㇱࠛࡀ࡞ࠡ࡯U ߪ㕒㔚ࠛࡀ࡞ࠡ࡯rqrIߣ㧘㈩૏ࠛࡀ࡞ࠡ࡯߿

ࡊࡠ࠻ࡦⷫ๺ജ߆ࠄ੍ᗐߐࠇࠆࠃࠅ߽ᱜߦᏪ㔚ߒᤃ޿߇㧘ߎṁᇦ๺ࠛࡀ࡞ࠡ࡯ߥߤ㧘☸ሶߦኻߔࠆᇦ૕࿕᦭ߩࡐ࠹ࡦࠪࡖ

ߩࡐ࡝ࡑ࡯ߪ⺃㔚₸߇ᄢ߈ߊ㧘ࠗࠝࡦߩಽᭂࠛࡀ࡞ࠡ࡯߽ᄢ

࡞ࠛࡀ࡞ࠡ࡯UMrߣߩ๺ߢਈ߃ࠄࠇࠆ㧚એᓟ UMrࠍ㔚⩄ࠠࡖ߈޿ߩߢ㧘ߘߩࡊࡠ࠻ࡦⷫ๺ജߪ᳇⋧ߢߩࡕ࠺࡞ൻว‛ߩࡊ࡝ࡗ࡯ߦኻߔࠆ㈩૏ࠛࡀ࡞ࠡ࡯ߣࠃ߱ߎߣߦߔࠆ㧚☸ሶ߇චࡠ࠻ࡦⷫ๺ജࠃࠅ߽߆ߥࠅᄢ߈ߊߥࠆน⢻ᕈ߇޽ࠆ㧚ಽᏗ⭯ߥ႐วߦߪ㧘♽ߩࠛࡦ࠻ࡠࡇ࡯ߪkTlogWrߢਈ߃ࠄࠇ

⛘✼૕ਛߢߩࡊࡠ࠻ࡦߩⷫ๺ജߣᏪ㔚㊂ߩ㑆ߦߪ⋧㑐߇ࠆ㧚ࠃߞߡ㔚⩄ࠠࡖ࡝ࡗ࡯ߩࡈ࡝࡯ࠛࡀ࡞ࠡ࡯ߪ

278 (34)

Fr

30

U  TSU M r r qr I  kT log Wr 㧔ⶄภห㗅㧕(1)ߢਈ߃ࠄࠇࠆ㧚ቯᏱ⁁ᘒߢߪࡈ࡝࡯ࠛࡀ࡞ࠡ࡯ߪߤߎߢ߽╬ߒߊ㧘ߘߩ൨㈩ߪ࠯ࡠߣߥࠆ߆ࠄ

kT
Wr   U M r r qr I
Wr

0

(2)

ߣߥࠆ㧚(2)ᑼߩ৻⥸⸃ߪ㧘W0,rࠍቯᢙߣߔࠆߣ

Wr

6

2006

⸅ὐ x=0 ߦ߅ߌࠆ㔚૏ࠍ 0 ߣߔࠆߣ‫ޔ‬Ⴚ⇇᧦ઙߣߒߡ

>I1 ( x)@x 0 >I2 ( x)@x 0ª d I1 ( x) º
«H1 dx »
¬
¼x 0

0

(6)

ª d I2 ( x) º
«H 2 dx »
¬
¼x 0

(7)

߇ᚑࠅ┙ߟ㧚ᱜ⽶㔚⩄ࠠࡖ࡝ࡗ࡯ߩଔᢙ߇⇣ߥࠆߣ㕒㔚ࡐ࠹ࡦࠪࡖ࡞ߦኻߔࠆ⸃ᨆ⸃߇ᓧࠄࠇߥ޿ߩߢ㧘એᓟଔᢙߪ╬ߒ§ U M ,r r qr I ·W0,r exp ¨ 
¸
kT
©
¹

(3)

޿߽ߩߣߔࠆ㧚
2.1

ᱜ⽶㔚⩄ࠠࡖ࡝ࡗ࡯߇ᇦ૕㑆ࠍ⒖േน⢻ߥ႐วߣߥࠆ߆ࠄ㧘ᾲᐔⴧᤨߩ㔚⩄ࠠࡖ࡝ࡗ࡯ߩỚᐲಽᏓߪࡏ࡞࠷

వߕᱜ⽶㔚⩄ߣ߽ᇦ૕ 1,2 㑆ࠍ⒖േน⢻ߥ႐วߦߟ޿ߡข

ࡑࡦಽᏓߣߥࠆߎߣ߇ࠊ߆ࠆ㧚(3)ᑼߩ㑐ଥߪ㧘⇣ߥࠆᇦ૕ࠍ

ࠅᛒ߁㧚㔚⩄ࠠࡖ࡝ࡗ࡯߇⒖േߔࠆߣ㕒㔚ࡐ࠹ࡦࠪࡖ࡞߇ᄌ

ធ⛯ߒߚ♽ਛࠍ㔚⩄ࠠࡖ࡝ࡗ࡯߇േ߈࿁ࠆ႐วߦ߽ᚑ┙ߔൻߔࠆ㧚x = fߢߩ㕒㔚ࡐ࠹ࡦࠪࡖ࡞ࠍI1,f㧘x = fߢߩ㕒㔚ࡐࠆ‫ߩߎޕ‬႐ว W0,rߪਔᇦ૕ߢ౒ㅢߩቯᢙߛ߇㧘UM,r߇૏⟎ߩ࠹ࡦࠪࡖ࡞ࠍI2,fߣߔࠆߣ㧘x = rfߢߪ㔚᳇⊛ਛᕈߩ᧦ઙ߇ᚑ

㑐ᢙߣߥࠆ‫ޕ‬ࠅ┙ߞߡ޿ࠆߪߕߛ߆ࠄ㧘㔚⩄ࠠࡖ࡝ࡗ࡯ߦኻߔࠆ⥄↱ࠛࡀ࡞ࠡ࡯߇⇣ߥࠆ 2 ߟߩᇦ૕߇ធ⸅ߔࠆߣ㧘ਔ⠪ߩ⥄↱ࠛࡀ࡞ࠡ࡯ࠍ╬ߒߊߔߴߊ㔚⩄ࠠࡖ࡝ࡗ࡯ߩ⒖േ߇↢ߓ㧘㔚૏߇⊒↢ߔࠆ㧚ᇦ૕ߩ⺃㔚₸ࠍHM ߣߔࠆߣ㧘ࠠࡖ࡝ࡗ࡯ߩ㔚⩄ኒᐲUߣ㕒㔚ࡐ࠹ࡦࠪࡖ࡞ߪ
એਅߩࡐࠕ࠰ࡦᣇ⒟ᑼߢ⚿߫ࠇࠆ㧚

 2I



U
1
{
(q W  qW )HM
HM  

(4)§ U1,  qI1,f ·§ U1,  qI1,f ·W0, exp ¨ ¸ W0, exp ¨ 
¸
kT
kT
©
¹
©
¹

(8)

§ U 2,   qI2,f ·§ U 2,  qI2,f ·W0, exp ¨ ¸ W0,  exp ¨ 
¸
kT
kT
©
¹
©
¹

(9)

ࠃߞߡ

ߎࠇߦ(3)ᑼࠍઍ౉ߔࠆߣࡐࠕ࠰ࡦ࡮ࡏ࡞࠷ࡑࡦᣇ⒟ᑼ

2

I

ª
§ U M ,  q I · º« qW0, exp ¨ 
¸ »
kT
1 «
©
¹ »

»
H M ««
U
q
I

§
M ,
 ·»
q W exp ¨ ¸»«  0,
kT
©
¹¼
¬

'U 

U 2,   U1, ,'U 

U 2,  U1, (10)ߣߔࠆߣ㧘(8)㧘(9)ᑼࠃࠅ
(5)

I2,f  I1,f

'U   'U 
2q

(11)

ߣߥࠅ㧘ធ⸅㔚૏Ꮕߪᱜ⽶㔚⩄ࠠࡖ࡝ࡗ࡯ߦኻߔࠆ㈩૏ࠛࡀ

ࠍᓧࠆ㧚ߎࠇ߇⒖േน⢻ߥᱜ⽶㔚⩄ࠠࡖ࡝ࡗ࡯ߩᐔⴧಽᏓࠍ
ቯ߼ࠆၮᧄᣇ⒟ᑼߣߥࠆ㧚࡞ࠡ࡯ߩᏅߦᲧ଀ߔࠆߎߣ߇ࠊ߆ࠆ㧚ធ⸅೨ᓟߢ㔚⩄ࠠࡖ࡝ࡗ࡯ߩ✚㊂ߪᄌൻߒߥ޿߆ࠄ㧘x 㧩࿑㧝ߦ␜ߔ㧘ෘߐߣ㕙Ⓧ߇ή㒢ᄢߢ㧘㔚⩄ࠠࡖ࡝ࡗ࡯ߦኻ

fߣ x = fߢߩᱜ߹ߚߪ⽶㔚⩄ࠠࡖ࡝ࡗ࡯ߩỚᐲߩ✚๺ߪធߔࠆ㈩૏ࠛࡀ࡞ࠡ࡯߇⇣ߥࠆ㧞ߟߩᇦ૕ࠍធ⸅ߐߖߚ㓙ߩ⸅೨ߩᇦ૕㧝㧘㧞ߩ㔚⩄ࠠࡖ࡝ࡗ࡯ߩỚᐲߩ✚๺ߣ╬ߒ޿ߪ㔚⩄⒖േࠍ⠨߃ߡߺࠃ߁㧚ធ⸅೨ߪਛᕈߛߞߚᇦ૕ߪ㧘ធ⸅ߕߢ޽ࠆ㧚ࠃߞߡ

ߦࠃߞߡᇦ૕㧝߇⽶ߦ㧘ᇦ૕㧞߇ᱜߦᏪ㔚ߔࠆ߽ߩߣߔࠆ㧚ᇦ૕ 1‫ޔ‬2 ߦ߅ߌࠆ㔚૏ࠍI1(x)‫ޔ‬I2(x)㧘ᱜ⽶㔚⩄ࠠࡖ࡝ࡗ࡯ߦ
ኻߔࠆ㈩૏ࠛࡀ࡞ࠡ࡯ࠍ U1,+㧘U1,߅ࠃ߮ U2,+㧘U2,ߣߒ‫ޔ‬ធMedium 1

Q
+Q

I1(x)

I2(x)

ߣߥࠆ߆ࠄ㧘

Medium 2

x=0§ U1,  qI1,f ·§ U 2,  qI2,f ·W0, exp ¨ ¸  W0,  exp ¨ 
¸
kT
kT
©
¹
©
¹
§ U1,  qI1,f ·§ U 2,  qI2,f ·W0, exp ¨ ¸  W0,  exp ¨ 
¸
kT
kT
©
¹
©
¹
W1,0  W2,0x࿑㧝 Ꮺ㔚ಽᏓߩ⸘▚ߦ૶↪ߒߚᐳᮡߣ⸥ภ
Fig. 1 coordinate and symbols used for the calculation of charge
distribution.

W0,rW1,0  W2,0
§ U1,r r qI1,f ·§ U 2,r r qI2,f ·exp ¨ ¸  exp ¨ 
¸
kT
kT
©
¹
©
¹
㧔ⶄภห㗅㧕

(12)

279 (35)ߣߥࠆ㧚qI1,f/kT >> 1㧘qI2,f/kT >> 1 ߩߣ߈㧘(20)ᑼߪ

߇ᚑࠅ┙ߟ㧚ߎࠇࠃࠅ㧘m ࠍ 1 ߹ߚߪ 2㧘

ym

qIm ( x)  qIm,f

(13)

kT

2 H1H 2 kT (W1,0  W2,0 )

Q|

exp

2

q (W1,0  W2,0 )Cmª§ ('U   'U  ) · º
H m kT «exp ¨ r¸  1»
2kT
©
¹ ¼
¬

(14)

2kT

ߣߥࠆ߆ࠄ㧘Ꮺ㔚㊂߇ធ⸅㔚૏Ꮕߦᜰᢙ㑐ᢙ⊛ߦଐሽߔࠆߎ
ߣ㧘߅ࠃ߮ធ⸅㔚૏Ꮕ߇หߓߢ޽ࠇ߫㧘qI2,f+qI1,f=0㧘ᓥߞ
ߡ'U+ = 'Uߩߣ߈ߦᦨᄢᏪ㔚㊂߇ᓧࠄࠇࠆߎߣ߇ࠊ߆ࠆ㧚ߣߔࠆߣ㧘(5)ᑼߪ

ోᏪ㔚㊂ߩ 1/2 ߇ሽ࿷ߔࠆ㗔ၞࠍᏪ㔚ᷓߐ'xm ߣቯ⟵ߔࠆߣ㧘d 2 ymCm ª¬exp ym  exp  ym º¼

dx 2

(15)

qI1,f/kT >> 1㧘qI2,f/kT >> 1 ߩߣ߈㧘'x1 | ߣߥࠆ㧚ߚߛߒ㧘m = 1 ߩߣ߈rߪ+ࠍ㧘m = 2 ߩߣ߈rߪࠍขࠆ߽ߩߣߔࠆ㧚x = rfߢ㔚૏൨㈩߇࠯ࡠߣߥࠆߣ޿߁᧦ઙ
ߩ߽ߣߢ(15)ᑼࠍⓍಽߔࠆߣ'x2 |2H 2 kT
qQ(22)

࿑ 2㧘3㧘4 ߦ㕒㔚ࡐ࠹ࡦࠪࡖ࡞ಽᏓ㧘㔚⩄ಽᏓ㧘߅ࠃ߮Ꮺ2Cm sinh ym / 2(16)ࠍᓧࠆ㧚ߎࠇߣႺ⇇᧦ઙ(7)߅ࠃ߮(11)ᑼࠃࠅ㧘Im,fߩ୯ߪª§ 'U  · º« H m  H1H 2 exp ¨ r¸»
kT© 2kT ¹ »«log«q
§ 'U  · »« H m  H1H 2 exp ¨ r¸»© 2kT ¹ ¼»
¬«

Im,f

2H1 kT,qQߣߥࠆ߆ࠄ㧘Ꮺ㔚ᷓߐߪᏪ㔚㊂ߦ෻Ყ଀ߔࠆߎߣ߇ࠊ߆ࠆ㧚

㔚㊂ߣ㈩૏ࠛࡀ࡞ࠡ࡯ߣߩ㑐ଥࠍ␜ߒߚ㧚㈩૏ࠛࡀ࡞ࠡ࡯ߩ
Ꮕ߇ዋߥ޿㔚⩄ࠠࡖ࡝ࡗ࡯߇ሽ࿷ߔࠆߣ㧘ߎࠇ߇㈩૏ࠛࡀ࡞
ࠡ࡯ߩᏅ߇ᄢ߈޿㔚⩄ࠠࡖ࡝ࡗ࡯ߩ⒖േߦࠃߞߡ↢ߓߚ㔚⩄ࠍᛂߜᶖߔߴߊ⒖േߔࠆߚ߼㧘Ꮺ㔚㊂߇⪺ߒߊᷫዋߔࠆ㧚

(17)

10
'U+/kT, 'U–/kTߣߥࠆ㧚Ⴚ⇇᧦ઙ(6)ߩ߽ߣߢ(16)ᑼࠍⓍಽߔࠆߣ

ªº§ qIm,f ·«1  tanh ¨ r¸ exp r 2Cm x »
4kT ¹
«
»
©
r2 log «»§ qIm,f ·« 1  tanh ¨ r
»
r
exp
2
C
x
¸
m
«¬
»¼
4kT ¹
©

Electrostatic potential / (kT/q)d ( ym / 2)dxym

qI2,f  qI1,f§ qI2,f  qI1,f ·exp ¨¸ (21)
4kT©
¹

5; –20, 20; –20, 10; –20,

00; –10, 10; –5, 5–5(18)
ߣߥࠆ㧚(4)ᑼ߅ࠃ߮(16)ᑼࠃࠅ㧘ᇦ૕ਛߩ㔚⩄ኒᐲߪ

U m ( x)Cm H m kTª¬exp  ym  exp ym º¼
q

–10

(19)

ߣߥࠅ㧘ᇦ૕ 1 ߅ࠃ߮ 2 ਛߩන૏㕙Ⓧᒰߚࠅߩ✚㔚⩄㊂ߪ

Q

³

f

0

U1 ( x) dx

f³ U2 ( x)dx
0

–10

2

0

Distance / [2q (W 1,0+W 2,0)/(HkT)]

1/2

࿑㧞 ᱜ⽶㔚⩄ߩᇦ૕㑆⒖േߢ↢ߓߚ㕒㔚ࡐ࠹ࡦࠪࡖ࡞ߩ
ಽᏓ㧔⸥ภߩቯ⟵ߦߟ޿ߡߪᧄᢥࠍෳᾖߩߎߣ㧕ª d I2 ( x) º»
¬ dx ¼ x 0

H2 «Fig. 2. Spatial distribution of electrostatic potential induced byinter-medium migration of positive and negative charge carriers.
The definitions of symbols are; kT: thermal energy, H: dielectric

H1H 2 kT (W1,0  W2,0 )ªºªº§ 'U  ·§ 'U  ·« H1 exp ¨¸  H 2 » « H1 exp ¨¸  H2 »© 2kT ¹© 2kT ¹¬¼¬¼

§ 'U  ·§ 'U  · exp ¨exp ¨¸¸
© 2kT ¹© 2kT ¹u§ 'U   'U  ·1  exp ¨
¸
2kT
©
¹

–20

constant, Wm,0: initial concentration of positive or negative charge
carrier in medium m, rq: charge of positive or negative charge
carrier, and 'Ur: difference between coordination energies for
positive or negative charge carrier in media 1 and 2, respectively.

(20)

280 (36)

30
6
2006
ធ⸅Ꮺ㔚޽ࠆ޿ߪ៺ᡂᏪ㔚ߒߚ⛘✼૕ਛߩᾲᐔⴧ㔚⩄ಽᏓ㧔ᏒᎹ
ᕡ᮸㧕

100

100
1/2

80
Charge / [HkT(W 1,0+W 2,0)]Charge density / [q(W1,0+W 2,0)]150

x 1/100

50
0'U+/kT, 'U–/kT–50; –20, 20; –20, 10; –20,–100

0; –10, 10; –5, 5

–150
–1

–0.5

2

0

0.5

Distance / [2q (W 1,0+W 2,0 )/(HkT)]

1/2–' U –

60

; 20
; 15

40

; 10
; 5
; 0

20

0
–20

1

–15

–10

–5

0

Energy difference / ('U+ / kT)࿑ 3 ᱜ⽶㔚⩄ߩᇦ૕㑆⒖േߢ↢ߓߚᏪ㔚ߩಽᏓ㧔⸥ภߩቯ࿑㧠 ᱜ⽶㔚⩄ߩᇦ૕㑆⒖േߢ↢ߓߚᏪ㔚ߩ㊂㧔⸥ภߩቯ⟵⟵ߦߟ޿ߡߪᧄᢥࠍෳᾖߩߎߣ㧕ߦߟ޿ߡߪᧄᢥࠍෳᾖߩߎߣ㧕

Fig. 3 Spatial distribution of electric charge induced by

Fig. 4. Amount of electric charge induced by inter-medium

inter-medium migration of positive and negative charge carriers.

migration of positive and negative charge carriers. See Fig. 1 for the

See Fig. 1 for the definition of symbols.

definition of symbols.

2.2ᑼ߆ࠄᓧࠄࠇࠆᣇ⒟ᑼ

⽶㔚⩄߇࿕ቯߐࠇߡ޿ࠆ႐ว

§ qI1,f · qI1,fªH2§ 'U  · º1¸« exp ¨ ¸  1» exp ¨kT© kT ¹ ¼¬ H1© kT ¹ᰴߦᱜ㔚⩄ࠠࡖ࡝ࡗ࡯ߩߺ߇ᇦ૕㑆ࠍ⒖േน⢻ߥ႐วࠍ⠨߃ߡߺࠃ߁㧚ߎߩ႐ว㧘x = rfߢ㔚᳇⊛ਛᕈߩ᧦ઙ߇ᚑࠅ
┙ߟߚ߼ߦߪ㧘x = rfߢߩᱜ㔚⩄ࠠࡖ࡝ࡗ࡯ߩỚᐲ߇⽶㔚⩄

H 2W2,0 ª qI1,f§ W2,0 · 'U  º 1  log ¨«»¨ W1,0 ¸¸
H1W1,0 «¬ kT
kT »¼
©
¹

ߩỚᐲ㧘ߔߥࠊߜធ⸅೨ߩᱜ㔚⩄Ớᐲ W1,0㧘W2,0 ߦ╬ߒߊߥࠆᔅⷐ߇޽ࠆ߆ࠄ

ࠍᢙ୯⊛ߦ⸃ߊߎߣߦࠃߞߡᓧࠄࠇࠆ㧚Im(x)ߩ⸃ᨆ⸃ߪᓧࠄ

§ U1,  qI1,f ·W0,  exp ¨ ¸ W1,0
kT
©
¹

(23)

§ U 2,   qI2,f ·W0, exp ¨ ¸ W2,0
kT
©
¹

(24)

ѕ I2,f  I1,fº
§ W2,0 ·1 ª
 'U  »« kT log ¨¸¨ W1,0 ¸
q «¬
»¼
©
¹

ࠇߥ޿߇㧘(27)ᑼࠍᢙ୯Ⓧಽߔࠇ߫Im(x)ߩᢙ୯⸃ࠍኈᤃߦᓧ
ࠆߎߣ߇ߢ߈ࠆ㧚㔚⩄ಽᏓߪ

Um ( x)

(25)

Q

dx 2



ªexp  ym  1º¼

H m kT ¬2q 2Wm,0H m kT§ qI1,f · qI1,f2H1 kTW1,0 exp ¨
1¸kT© kT ¹(30)ᣇᩮߦᲧ଀ߔࠆߎߣ߇ࠊ߆ࠆ㧚หߓធ⸅㔚૏Ꮕߩ႐ว㧘ᱜ㔚
(26)⩄ߩߺ߇⒖േน⢻ߥ႐วߩᏪ㔚㊂ߪᱜ⽶౒ߦ⒖േน⢻ߥ႐วߩᏪ㔚㊂ߦᲧߴߡߪࠆ߆ߦዋߥߊߥࠆ㧚W1,0 | W2,0 | W0㧘

H1 | H2 | H㧘'U+/kT>>1 ߩ႐วߦߪ㧘ߣߥࠅ㧘ߎࠇࠍⓍಽߔࠆߣ

dym
dx

(29)

ߣߥࠆ߆ࠄ㧘qI1,f/kT<<0 ࠃࠅ㧘Ꮺ㔚㊂߇߶߷ធ⸅㔚૏Ꮕߩᐔߔࠆߎߣ߇ࠊ߆ࠆ㧚U1,+ > U2,+ ߣߔࠆߣ㧘(5)ᑼߪ

q 2Wm,0qW0,m ª¬ exp  ym  1º¼

ߢਈ߃ࠄࠇࠆ㧚(7)ᑼࠃࠅ㧘Ꮺ㔚㊂ߪߣߥߞߡ㧘ធ⸅㔚૏Ꮕ߇㔚⩄ࠠࡖ࡝ࡗ࡯ߩೋᦼỚᐲߦ߽ଐሽ

d 2 ym(28)

exp  ym  ym  1

Q| 

(27)

2H kTW0 'U 
kT

(31)

ߣߥࠆ㧚࿑ 5㧘6 ߦ㕒㔚ࡐ࠹ࡦࠪࡖ࡞߅ࠃ߮㔚⩄ߩಽᏓࠍ㧘ࠍᓧࠆ㧚I1,f㧘I2,fߩ୯ߪ㧘Ⴚ⇇᧦ઙ(7)ߣ(27)ᑼ㧘߅ࠃ߮(25)࿑ 7 ߦᏪ㔚㊂ߣ㈩૏ࠛࡀ࡞ࠡ࡯ߣߩ㑐ଥࠍ࿑␜ߒߚ㧚࿑ 3 ߣ
5ធ⸅Ꮺ㔚޽ࠆ޿ߪ៺ᡂᏪ㔚ߒߚ⛘✼૕ਛߩᾲᐔⴧ㔚⩄ಽᏓ㧔ᏒᎹ ᕡ᮸㧕
30

0Charge density / ( qW1,0)Electrostatic potential / (kT/q)

10'U+/kT, W 2,0/W1,0–10; –20,

1; –20,

0.1; –20, 10; –10,; – 5,–20

281 (37)

–10

0

2

Distance / [2q W 1,0/(HkT)]

1/2

1
1

20

'U+/kT, W 2,0/W 1,0; –20,

1; –20,

0.1; –20, 1010; –10,; – 5,

1
1

0
–10

10

–5

2

0

Distance / [2q W 1,0/(HkT)]

1/2

5࿑ 5 ᱜ㔚⩄ߩᇦ૕㑆⒖േߢ↢ߓߚ㕒㔚ࡐ࠹ࡦࠪࡖ࡞ߩಽᏓ

࿑ 6 ᱜ㔚⩄ߩᇦ૕㑆⒖േߢ↢ߓߚᏪ㔚ߩಽᏓ㧔⸥ภߩቯ⟵㧔⸥ภߩቯ⟵ߦߟ޿ߡߪᧄᢥࠍෳᾖߩߎߣ㧕ߦߟ޿ߡߪᧄᢥࠍෳᾖߩߎߣ㧕

Fig. 5 Spatial distribution of electrostatic potential induced by

Fig. 6 Spatial distribution of electric charges induced byinter-medium migration of positive charge carriers. See Fig. 2 forinter-medium migration of positive charge carriers. See Fig. 2 forthe definition of symbols.

the definition of symbols.

5㔚⩄ࠠࡖ࡝ࡗ࡯ߩ⒖േࠍᅹኂߔࠆ߆ࠄ㧘৻ᣇߩ㔚⩄ߩߺ߇⒖േน⢻ߥ႐วߦߪᏪ㔚㊂߇⪺ߒߊૐߊߥࠆ㧚4

2.3

ߩߺࠍ⒖േน⢻ߥ႐ว

1/2

Charge / (2HkTW1,0 )ᱜ㔚⩄ߪᇦ૕㑆ࠍ⒖േน⢻ߛ߇㧘⽶㔚⩄ߪᇦ૕ౝ

3ᦨᓟߦᱜ㔚⩄ࠠࡖ࡝ࡗ࡯ߪᇦ૕㑆ࠍ⒖േߢ߈ࠆ߇‫⽶ޔ‬㔚⩄ߪห৻ᇦ૕ౝߩߺࠍ⒖േน⢻ߥ႐วࠍ⠨߃ߡߺࠃ߁㧚ή㒢㆙W 2,0/W 1,02ߦ߅ߌࠆ㔚⩄ਛᕈߩ᧦ઙ

; 0.01
; 0.1
;

1

1

§ U  qI1,f ·§ U1,   qI1,f ·W0,  exp ¨  1, ¸ W1,  exp ¨ ¸ { W1,0
kT
kT
©
¹
©
¹

; 10
; 100

0

–20

(32)
–10

§ U  qI2,f ·§ U 2,   qI2,f ·W0,  exp ¨  2, ¸ W2,  exp ¨ ¸ { W2,0
kT
kT
©
¹
©
¹

0

Energy difference / ('U+ / kT)(33)

࿑ 7 ᱜ㔚⩄ߩᇦ૕㑆⒖േߢ↢ߓߚᏪ㔚ߩ㊂㧔⸥ภߩቯ⟵ߦࠃࠅ㧘㔚૏Ꮕߪ

ߟ޿ߡߪᧄᢥࠍෳᾖߩߎߣ㧕
Fig. 7 Amount of electric charge induced by inter-medium

I2,f  I1,f

migration of positive charge carriers. See Fig. 2 for the definition ofsymbols.

º§ W2,0 ·1 ª
 'U  »« kT log ¨¸¨ W1,0 ¸
q «¬
»¼
©
¹

(34)

ߣ᳞߹ࠆ߆ࠄ㧘⽶㔚⩄ࠠࡖ࡝ࡗ࡯߇ᇦ૕ౝࠍ⒖േߒߡ߽㔚૏
࿑ 6 ߩᲧセ߆ࠄࠊ߆ࠆࠃ߁ߦ㧘ਔ㔚⩄ߣ߽ᇦ૕㑆ࠍ⒖േน⢻Ꮕߪᄌൻߒߥ޿ߎߣ߇ࠊ߆ࠆ㧚ߥ႐วߦᲧߴߡ,ᇦ૕ 1 ߦ߅ߌࠆ⽶㔚⩄ߩಽᏓ߇⪺ߒߊᐢ߇(32)㧘(33)ᑼߩ㑐ଥࠍ૶߁ߣ(5)ᑼߪ

ߞߡ޿ࠆ㧚ߎࠇߪធ⸅㕙ߩㄭறߦᱜ㔚⩄ࠠࡖ࡝ࡗ࡯ߩ಴ᛄ޿

d 2 ym㗔ၞ߇ߢ߈ߡߒ߹߁ߚ߼ߢ޽ࠆ㧚ᱜ⽶㔚⩄ࠠࡖ࡝ࡗ࡯߇౒ߦ

dx 2⒖േน⢻ߥ႐วߦߪ㧘ᱜ⽶㔚⩄ኻߩ⒖േߦࠃߞߡ಴ᛄ޿㗔ၞ

q 2Wm,0ªexp ym  exp  ym º¼

H m kT ¬(35)ߣߥࠆ߇㧘ߎࠇߪ(15)ᑼߣหߓᓸಽᣇ⒟ᑼߥߩߢ㧘⸃ߪߪᶖṌߔࠆ߆ࠄ㧘ߎߩࠃ߁ߥ⃻⽎ߪ↢ߓߥ޿㧚಴ᛄ޿㗔ၞߪ

6

282 (38)

30

6

2006

ធ⸅Ꮺ㔚޽ࠆ޿ߪ៺ᡂᏪ㔚ߒߚ⛘✼૕ਛߩᾲᐔⴧ㔚⩄ಽᏓ㧔ᏒᎹ ᕡ᮸㧕

ª§ 'U  · º
2« H mWm,0  H1H 2 W1,0W2,0 exp ¨ r¸»
kT© 2kT ¹ »log ««q
§ 'U  · »2
2« H mWm,0  H1H 2 Wm,0 exp ¨ r¸»«¬© 2kT ¹ »¼

Im,fߣߥࠆ㧚'U+/kT>>1㧘ᓥߞߡqI1,f/kT >> 1㧘qI2,f/kT >> 1 ߩ႐วߦߪ㧘ª§ qI2,f  qI1,f · º
Q | 2kT H1H 2W1,0W2,0 «exp ¨
¸»
4kT
©
¹ ¼»
¬«

(36)

ym

ߣߥࠆ㧚ߎߩᑼߪᱜ⽶㔚⩄ࠠࡖ࡝ࡗ࡯߇౒ߦᇦ૕㑆ࠍ⒖േน

ª§qIm,f ·2q 2Wm,0 · º«1  tanh ¨§ r
¨
¸»
x
r
exp
¸
«
»
¨
¸
kT
kT
4
H
m
©
¹
©
¹»
r2 log ««»§2q 2Wm,0 · »§  qIm,f ·«¨¸«1  tanh ¨ r 4kT ¸ exp ¨ r x H kT ¸ »
m
©
¹
«¬
©
¹ »¼

⢻ߥ႐วߩᦨᄢᏪ㔚᧦ઙ㧘'U = 'U+㧘ߦ߅ߌࠆᏪ㔚㊂ߣ╬
ଔߢ޽ࠆ㧚৻ᣇߩ㔚⩄ࠠࡖ࡝ࡗ࡯߇ᇦ૕㑆ࠍ⒖േน⢻ߢ㧘ઁᣇߩ㔚⩄ࠠࡖ࡝ࡗ࡯߇ᇦ૕ౝߩߺࠍ⒖േน⢻ߥ႐วߦᦨᄢ
Ꮺ㔚㊂߇ᓧࠄࠇࠆߎߣ߇ࠊ߆ࠆ㧚ߥ߅㧘Ꮺ㔚ᷓߐߪ㧘ᱜ⽶㔚⩄ࠠࡖ࡝ࡗ࡯߇ᇦ૕㑆ࠍ⒖േน⢻ߥ႐วߣห᭽

(37)

U m ( x) qWm,0 ª¬exp  ym  exp ym º¼'x1 | (38)

2H1 kT,qQ'x2 |2H 2 kT
qQ(41)ߢਈ߃ࠄࠇࠆ㧚࿑ 8㧘9 ߦ㕒㔚ࡐ࠹ࡦࠪࡖ࡞߅ࠃ߮㔚⩄ߩಽᏓࠍ㧘
࿑ 10 ߦᏪ㔚㊂ߣ㈩૏ࠛࡀ࡞ࠡ࡯ߣߩ㑐ଥࠍ࿑␜ߒߚ㧚ª§ 'U  ·§ 'U  · º
2H1H 2 kT «W1,0 exp ¨ ¸  W2,0 exp ¨¸»© 2kT ¹© 2kT ¹ ¼¬
H1W1,0  H 2W2,0

Q

(40)

ª
§ 'U  ·§ 'U  · º
 H1H 2 «W1,0 exp ¨ ¸  W2,0 exp ¨¸»© 2kT ¹© 2kT ¹ ¼
¬
(39)

20000

0

'U+/kT, W 2,0/W 1,0; –20,

1; –20,

0.1; –20, 10–10–5Charge density / (qW1,0)Electrostatic potential / (kT/q)

10; –10,; – 5,

02Distance / [2q W 1,0/(HkT)]

1/2

10000

0

'U+/kT, W 2,0/W 1,0; –20,

1; –20,

0.1; –20, 10; –10,; – 5,

1
1
x 100–10000x 100

1
1–20000
–0.2

5

–0.1

0

2

Distance / [2q W 1,0/(HkT)]

0.1

1/2

0.2

࿑ 8 ᱜ㔚⩄ߩᇦ૕㑆⒖േߣ⽶㔚⩄ߩᇦ૕ౝ⒖േߢ↢ߓߚ㕒

࿑ 9 ᱜ㔚⩄ߩᇦ૕㑆⒖േߣ⽶㔚⩄ߩᇦ૕ౝ⒖േߢ↢ߓߚᏪ㔚ࡐ࠹ࡦࠪࡖ࡞ߩಽᏓ㧔⸥ภߩቯ⟵ߦߟ޿ߡߪᧄᢥࠍෳᾖߩ

㔚ߩಽᏓ㧔⸥ภߩቯ⟵ߦߟ޿ߡߪᧄᢥࠍෳᾖߩߎߣ㧕ߎߣ㧕

Fig. 9 Spatial distribution of electrostatic potential induced by

Fig. 8 Spatial distribution of electrostatic potential induced byinter- and intra-medium migrations of positive and negative chargeinter- and intra-medium migrations of positive and negative charge

carriers, respectively. See Fig. 2 for the definition of symbols.

carriers, respectively. See Fig. 2 for the definition of symbols

7283 (39)ធ⸅Ꮺ㔚޽ࠆ޿ߪ៺ᡂᏪ㔚ߒߚ⛘✼૕ਛߩᾲᐔⴧ㔚⩄ಽᏓ㧔ᏒᎹ ᕡ᮸㧕

ⓍᒰߚࠅߩᏪ㔚㊂ߪ(40)ᑼߢਈ߃ࠄࠇࠆ㧚㔚⩄ࠠࡖ࡝ࡗ࡯߇

500

re ߩ㔚⩄ࠍ᦭ߒ㧘ਔᇦ૕ߩᲧ⺃㔚₸߇ 1 ߩ⒟ᐲߢ޽ࠆߣߔࠆ
ߣ㧘(41)ᑼࠃࠅ㧘㘻๺Ꮺ㔚㊂߇ 105C/m2 ߩ႐วߩᏪ㔚ᷓߐߪ400'x | 50 nm ߣߥߞߡ㧘Ꮺ㔚߇ធ⸅㕙ㄭறߩߺߦ↢ߓࠆߎߣ߇

Charge / (2HkTW1,0 )1/2ࠊ߆ࠆ㧚Ꮺ㔚ᷓߐࠍᱜ⏕ߦ᷹ቯߔࠆߎߣߪ࿎㔍ߛ߇㧘߅ߘࠄ
W 2,0 / W 1,0300

ߊ 1Pm એౝߢ޽ࠈ߁ 11,12)㧚ࠃߞߡ 50 nm ߩᏪ㔚ᷓߐߪਇ⥄ὼ; 0.01ߥ୯ߢߪߥ޿㧚⴫㕙߆ࠄߩᷓߐ 50nm ⒟ᐲߩ㗔ၞߪ㧘ធ⸅߿

; 0.1

200

100

0

; 1

៺ᡂߦࠃߞߡᄢ߈ߊᄌᒻߔࠆߢ޽ࠈ߁߆ࠄ㧘ߎߩㇱಽߩታല; 10᷷ᐲ߇㔚⩄ࠠࡖ࡝ࡗ࡯ߩ⒖േߦචಽߥ㜞᷷ߦߥࠆߣ⠨߃ߡ; 100߽ਇᕁ⼏ߢߪߥ޿㧚ធ⸅㔚૏Ꮕ߇ 0.5V ߣ઒ቯߔࠆߣ㧘(40)ᑼࠃࠅ㧘㘻๺Ꮺ㔚㊂߇ 105C/m2 ߦ㆐ߔࠆߚ߼ߩቯᏱ㔚⩄ࠠࡖ࡝ࡗ࡯Ớᐲߪ W0 | 1010 mol/dm3 ߣ㧘ᭂ߼ߡᏗ⭯ߣߥࠆߎߣ߇

–20

–10

ࠊ߆ࠆ㧚ធ⸅㕙ㄭறߩ᳓ಽሶ߇ធ⸅߿៺ᡂߩ㓙ߦ H+ߣ OH

0

Energy difference / ('U+ / kT)ߦ⸃㔌ߒ㧘േ߈ᤃ޿ࡊࡠ࠻ࡦ߇ਔᇦ૕㑆ߢᐔⴧಽᏓߔࠆߣ⠨࿑ 10 ᱜ㔚⩄ߩᇦ૕㑆⒖േߣ⽶㔚⩄ߩᇦ૕ౝ⒖േߢ↢ߓߚ߃ࠇ߫㧘㔚⩄ࠠࡖ࡝ࡗ࡯Ớᐲ߇ૐ޿ߎߣ߇ℂ⸃ߢ߈ࠆ㧚Ꮺ㔚ߩ㊂㧔⸥ภߩቯ⟵ߦߟ޿ߡߪᧄᢥࠍෳᾖߩߎߣ㧕એ਄㧘⇣ߥࠆ⒳㘃ߩ㜞ಽሶࠍធ⸅ߒߚࠅ៺ᡂߒߚࠅߒߚ㓙

Fig. 10 Amount of electric charge induced by inter- andߦ↢ߓࠆᏪ㔚ߪ㧘៺ᡂᤨ߿ធ⸅ᤨߦ↢ߓߚࡊࡠ࠻ࡦ߇ធ⸅㕙

intra-medium migration of positive and negative charge carriers,ㄭறߢᾲᐔⴧಽᏓߔࠆߎߣߦࠃߞߡ↢ߓࠆߣ⸃㉼ߒߡ߽⍦respectively. See Fig. 2 for the definition of symbols.

⋫߇ή޿ߎߣ߇᣿ࠄ߆ߣߥߞߚ㧚ߒ߆ߒߥ߇ࠄ㧘ᧄ⺰ᢥߢዷ
㐿ߒߚℂ⺰ߪ㧘㔚⩄ࠠࡖ࡝ࡗ࡯߇ฎౖ⊛☸ሶߣߒߡߺߥߖࠆ

3.

߶ߤචಽዪ࿷ߒߡ޿ࠇ߫㧘ߤߩࠃ߁ߥ㔚⩄ࠠࡖ࡝ࡗ࡯ߦኻߒ

⠨ኤ

ᧄⓂߦ߅ߌࠆߎࠇ߹ߢߩขࠅᛒ޿ߢߪ㧘ធ⸅ߒߡ޿ࠆ 2 ߟߡ߽ᚑ┙ߔࠆ‫ߚ߹ޕ‬㧘ᇦ૕㑆ߢ㔚⩄ࠠࡖ࡝ࡗ࡯߇⇣ߥࠆ႐วߩᇦ૕ਛߩ㔚⩄ࠠࡖ࡝ࡗ࡯ߪቢోߥᾲᐔⴧ⁁ᘒߦ޽ࠆߣ઒

ߦߟ޿ߡ߽㧘ਔ㔚⩄ࠠࡖ࡝ࡗ࡯ߩ㔚⩄߇╬ߒߌࠇ߫ߘߩ߹߹

ቯߒߡ߈ߚ㧚ᾲᐔⴧ⁁ᘒߦ㆐ߔࠆߚ߼ߦߪ㧘㔚⩄ࠠࡖ࡝ࡗ࡯

ᚑ┙ߔࠆ‫߫߃ߣߚޕ‬ᇦ૕ 1 ਛߩ㔚⩄ࠠࡖ࡝ࡗ࡯߇ࡊࡠ࠻ࡦߢ

ߪᇦ૕ਛ߅ࠃ߮ᇦ૕㑆ࠍ⥄↱ߦേ߈࿁ࠆᔅⷐ߇޽ࠆ㧚ߒ߆ߒ

ᇦ૕ 2 ਛߩ㔚⩄ࠠࡖ࡝ࡗ࡯߇࠽࠻࡝࠙ࡓࠞ࠴ࠝࡦߥࠄ㧘ᇦ૕ߥ߇ࠄ㧘Ꮺ㔚ᓟ߽㔚⩄ࠠࡖ࡝ࡗ࡯߇ᇦ૕ਛࠍ⥄↱ߦേ߈࿁ࠆ

1 ߢߩ㈩૏ࠛࡀ࡞ࠡ࡯ࠍࡊࡠ࠻ࡦߩߘࠇߦ㧘ᇦ૕ 2 ߢߩ㈩૏ߩߢ޽ࠇ߫㧘2 ߟߩᇦ૕ࠍᒁ߈㔌ߔߣ㧘Ꮺ㔚ߪㅦ߿߆ߦᄬࠊ

ࠛࡀ࡞ࠡ࡯ࠍ࠽࠻࡝࠙ࡓࠞ࠴ࠝࡦߩߘࠇߦขࠇ߫ࠃ޿‫ޕ‬ࠇߡߒ߹߁㧚Ꮺ㔚߇଻ߚࠇࠆߦߪ㧘㔚⩄ࠠࡖ࡝ࡗ࡯ߩ⥄↱ߥ
⒖േ߇ធ⸅㕙ㄭறߦ㒢ࠄࠇࠆᔅⷐ߇޽ࠆ㧚㔚⩄ࠠࡖ࡝ࡗ࡯ߩ

ෳ⠨ᢥ₂
A. G. Bailey: Journal of Electrostatics, 51-52 (2001) 82
Y. Tabata, Y. Ito, S. Tagawa (Eds.): Handbook of Radiation
Chemistry, CRC Press, Boca Raton (1991)
3) A.F. Diaz, R.M. Felix-Navarro: J. Electrostat. 62 (2004) 277
4) J. Lowell, A.R. Akande: J. Phys. D: Appl. Phys. 21 (1988) 125
5) J. Lowell, A. Brown: J. Electrostat. 21 (1988) 69
6) A.R. Akande, J.A. Adedoyin, J. Electrostat. 51& 52, (2001)
1057) E.M. Charlson, E.J. Charlson,S. Burkett: IEEE Trans Electr.
Insul. 27 (1992) 1144
8) A. Wåhlin, G. Bäckström: J. Appl. Phys. 25 (1974) 2058
9) D.D. Perrin: Dissociation Constants of organic Bases in
Aqueous Solution, Butterworths, London (1965)
10) ᧛↰㓶ม㧦㕒㔚᳇ࡂࡦ࠼ࡉ࠶ࠢ㧘㕒㔚᳇ቇળ✬㧘3 ┨㧘ࠝ࡯ࡓ␠ (1981)
11) F. Nordhage, G. Bäckström: Inst. Phys. Conf. Ser. 27 (1975) 84
12) W.J. Brennan, J. Lowell, M.C. O’Neill, M.P.W. Wilson, J.
Phys. D: Apply. Phys., 25 (1992) 151
1)
2)⒖േߦᔅⷐߥᵴᕈൻࠛࡀ࡞ࠡ࡯߇ᄢ߈޿႐ว㧘㔚⩄ࠠࡖ࡝ࡗ
࡯ߩ⒖േߦᔅⷐߥᵴᕈൻࠛࡀ࡞ࠡ࡯ߪ㧘ធ⸅ߒߚ⍍㑆㧘޽ࠆ޿ߪ៺ᡂ߇↢ߓߚߣ߈ߦߒ߆ଏ⛎ߐࠇߥ޿น⢻ᕈ߇޽ࠆ㧚ធ⸅߿៺ᡂߩ㓙ߦធ⸅㕙ㄭறߩታല᷷ᐲ߇߈ࠊ߼ߡ㜞ߊߥߞߡ㔚⩄ࠠࡖ࡝ࡗ࡯ߩዪㇱ⊛ᾲᐔⴧಽᏓ߇㆐ᚑߐࠇ㧘ធ⸅߿៺ᡂ߇⚳ੌߔࠆߣ㧘ߎߩಽᏓ߇ಓ⚿ߐࠇࠆߣ⠨߃ࠇ߫㧘㔚⩄ࠠࡖ࡝ࡗ࡯ߩᾲᐔⴧಽᏓ⩄ߦࠃࠆᏪ㔚⃻⽎ࠍℂ⸃ߢ߈ࠆ㧚ߎࠇ߹ߢߩ⸘▚⚿ᨐ߆ࠄ㧘㔚⩄ࠠࡖ࡝ࡗ࡯ߩ৻ᣇ߇ᇦ૕㑆ࠍ⒖േน⢻ߢઁᣇ߇ᇦ૕ౝߩߺࠍ⒖േน⢻ߥ႐ว㧘Ꮺ㔚㊂߇߽ߞߣ߽ᄙߊߥࠅ㧘Ꮺ㔚ᷓߐ߽ᵻߊߥࠆߎߣ߇᣿ࠄ߆ߣߥߞ
ߚ㧚ߎߎߢߪߎߩ♽ߦߟ޿ߡᏪ㔚ᷓߐࠍ⷗Ⓧ߽ࠅ㧘ធ⸅߿៺ᡂߦࠃߞߡዪㇱ⊛ᾲᐔⴧߦ㆐ߔࠆߎߣ߇น⢻߆ߤ߁߆ࠍ⺞ߴߡߺࠃ߁㧚៺ᡂᏪ㔚ߦࠃࠆ⛘✼‛ߩᏪ㔚㊂ߪ㜞‫ޘ‬105C/m2
㨪104C/m2 ⒟ᐲߢ޽ࠆߎߣ߇⍮ࠄࠇߡ޿ࠆ 10)㧚ធ⸅㔚૏Ꮕ߇ᾲࠛࡀ࡞ࠡ࡯㧔Ᏹ᷷ߢ 0.025V㧕ࠃࠅ߽චಽ㜞ߌࠇ߫㧘න૏㕙

8