?’ Ò ×-± n ǎ ì Å= k-Œ £ ?’ Ò × } º 8 ý  ˜ m× DT c l V R ËX ê s U ê s0 n É; c  \ ¥ '

Œ

£

?’ Ò ×-± n ǎ ì Å= k-Œ £ ?’ Ò × } º 8 ý  ˜ m× DT c l V R ËX ê s U ê s0 n É; c   \ ¥ '

[, f Ç S Ë  ¹ Å üX ê sä Ä — ¤V R Ë Ž ì ŏ Œ

+ ä

g ` @?  ·  ™ » ÷ 7 B * > · + ä ¦ ‡ Ú ·  ™ »g ` @  ™ ¸ ^∗ · + ä ] ï B ^†

1 l

x² D G @ /† < Ɠ § ì ø ͕ ¸^ ‰õ † < Æõ , " fÖ  ¦ 100-715



™ »0 ï F„ ç ¡ ^‡

1 l

x² D G @ /† < Ɠ § Ó ü t o † < Æõ , " fÖ  ¦ 100-715 (2008¸   9 Z 4 22{ 9  ~ à Î6 £ §)

‘

: r ƒ  ½ ¨\ " f  H ' V , a A „  À Ó t C & h Ü ¼– Ð
 
  H 2 nm s  _  · û ª“ É r í ß – o} Œ •`  ¦ ”   tunnel junc- tion \ " f í ß – o} Œ • $ í  © œ ~ ½ ÓZ O \    É r F K5 Å q/ í ß – o} Œ • ] X ½ + ˀ  \ " f_  „  0 A © œ# 4  : £ ¤$ í `  ¦ › ¸  l  0 AK  e  ¦   Ý

¼  í ß – o ~ ½ ÓZ O õ  \ P  í ß – o ~ ½ ÓZ O `  ¦ s 6   x # Œ Al/AlO

^x

/Al x 9  Al/AlO

x

/Nb ] X ½ + Ë ™ è \  ¦ ] j Œ • % i  .

Image force ´ òõ \  ¦ “ ¦ 9ô  Ç € ª œ % i † < Æ& h “   Transfer matrix > í ß –Z O `  ¦ s 6   x # Œ ' V , a A „  À Ó\  ¦ > í ß – 

“

¦ 8 £ ¤& ñ  ) a   õ ü < q “ § # Œ Al(¢ ¸  H Nb)/AlO

x

] X ½ + Ë\ " f_  ' V , a A  © œ# 4 _  Z  } s , ¿ ºa  x 9  AlO

x

Ä »„   © œ Ã

º\  ¦ Æ ÒØ  ¦ % i  . € ª œ % i † < Æ& h “   transfer matrix > í ß –Z O `  ¦ s 6   x ô  Ç — ¸4 S qa A   õ   H tunnel junction _  8 £ ¤

&

ñ  ) a ' V , a A „  À Ó : £ ¤$ í õ   Å Ò Z  }“ É r & ñ S X ‰ • ¸\  ¦ t “ ¦ { 9 u  % i Ü ¼ 9, s    õ \ " f Al (¢ ¸  H Nb)/AlO

x

] X

½ + ˀ  \ " f ' V , a A  © œ# 4  Z  } s   H „  F G Ü ¼– Ð  6   x ) a F K5 Å q Ó ü t| 9 \  ß ¼>  % ò † ¾ Ó`  ¦ ~ à Ît ë ß – AlO

x

í ß – o} Œ •_ 

$ í

 © œ ~ ½ ÓZ O \   H › ' a > \ O s  1 l x{ 9 ô  Ç „  0 A © œ# 4  Z  } s \  ¦ ”     H  כ `  ¦ · ú ˜ à º e ” % 3  .

PACS numbers: 68.55.L, 73.40, 85.30.M Keywords: ' V , a A, È Òõ > à º, „  5 Å x' Ÿ § > =

I. " e  ] Ø

ì

ø ͕ ¸^ ‰\  ¦ Ÿ í† < Êô  Ç „    ™ è  / B N& ñ s  & h  
” ¸p '  % ò

%

i Ü ¼– Ð ] X   H † < Ê\     ' V , a A „  À Ó : £ ¤$ í \  @ /ô  Ç ƒ  ½ ¨  H '

V , a A ¾ º[ O  „  À Ó\  ¦ þ j™ è o l  0 Aô  Ç ] X ƒ  ^ ‰ Ó ü t| 9  ƒ  ½ ¨ ì

 r  ü < (: £ ¤ y  Si`  ¦ l ì ø ÍÜ ¼– Ð   H ì ø ͕ ¸^ ‰ í ß –\ O \ " f) & h  F G& h Ü ¼– Ð ' V , a A ´ òõ \  ¦ s 6   x  9  H 6 £ x6   x ì  r  – Ð ß ¼> 

Ð ü t à º e ”   [1]. l ‘ : r& h Ü ¼– Ð  © œ ´ ú §s   6   x ÷ &  H ' V ,  a A] X ½ + Ë ™ è   H F K5 Å q õ  F K5 Å q í ß – o} Œ •`  ¦ s 6   x ô  Ç ½ ¨› ¸s  9,

~ Ã

Ì} Œ • $ í  © œ l Õ ü t õ  / B N& ñ l Õ ü t s  µ 1 τ  † < Ê\      € ª œô  Ç F K 5

Å q/] X ƒ  ^ ‰/F K5 Å q (metal/insulator/metal) ½ ¨› ¸_  ' V , a A ] X

½ + Ë ™ è  ½ ¨› ¸ ] jî ß –÷ &“ ¦ e ” Ü ¼ 9 s [ þ t \  @ /ô  Ç ' V , a A

¾

º[ O  „  À Ó 8 £ ¤& ñ x 9  ì  r$ 3 “ É r ™ è  : £ ¤$ í x 9  à º5 Å x ‰ & ³ © œ_  l 

‘

: r& h “   ƒ  ½ ¨ ~ ½ ÓZ O s  ÷ &% 3  . Õ ª Q
 & h   í ß – o} Œ •_  ¿ ºa 

 · û ª f ” \     8 £ ¤& ñ  ) a „  À Ó-„  · ú š : £ ¤$ í “ É r í ß – o} Œ • x 9  F K 5

Å q/ í ß – o} Œ • ] X ½ + ˀ  \ " f_  Ó ü t| 9  : £ ¤$ í \  ß ¼>  _ ” > r  9,  



" f l ” > r \  ´ ú §s   6   x ) a Wentzel, Kramers, Brillouin \ 

∗

E-mail: [email protected]

†

E-mail: [email protected]

‡

E-mail: [email protected]

_

K  ] jî ß –  ) a WKB > í ß –Z O  x 9   y Œ • „  0 A  © œ# 4    H  \  ¦ : Ÿ x K

 — ¸4 S qa A ½ + É Ã º \ O >  ÷ &% 3 “ ¦ 7 á §  8 & ñ S X ‰ ô  Ç ì  r$ 3 s  € 9 כ ¹

>  ÷ &% 3   [2,3].

‘

: r  7 Hë  H \ " f  H Al/AlO x /Al ( ¢ ¸  H Nb) ' V , a A] X ½ + Ë ™ è



\  ¦ ] j Œ • # Œ „  À Ó-„  · ú š : £ ¤$ í `  ¦ 8 £ ¤& ñ % i “ ¦, € ª œ % i † < Æ

&

h “   transfer matrix > í ß –Z O `  ¦ s 6   x # Œ % 3 “ É r ' V , a A „   À

Ó-„  · ú š : £ ¤$ í õ  q “ § # Œ AlO x x 9  AlO _x /Al ] X ½ + ˀ  \ 

"

f_  Ä »„    © œÃ ºü < ' V , a A  © œ# 4  Z  } s  1 p x`  ¦ Æ ÒØ  ¦ % i  .

AlO _x   H Aluminium s  í ß –™ èü < ~ 1 >  ì ø Í6 £ x # Œ í ß – o} Œ • + þ A

$ í

s  6   x s  “ ¦, ç  H{ 9  “ ¦ î ß –& ñ & h Ü ¼– Ð $ í  © œ÷ &  H Ó ü t| 9 – Ð, AlO _x  6 eV_   H  ½ ™× ¼Ì “ s \  -t \  ¦ 4 R · û ª“ É r ~ à Ì} Œ •Ü ¼– Ð

$ í

 © œ  8 • ¸ a % ~“ É r „  l & h  ] X ƒ   : £ ¤$ í `  ¦
 ? /# Q œ í„  

•

¸^ ‰ x 9   $ í ^ ‰\  ¦ Ÿ í† < Êô  Ç „   ™ è \  V , o   6   x “ ¦ e ” 



. 8 £ ¤& ñ  ) a „  À Ó-„  · ú š : £ ¤$ í õ  — ¸4 S qa A ì  r$ 3 `  ¦ : Ÿ x K  Al (¢ ¸



 H Nb)/AlO x ] X ½ + ˀ  \ " f_  „  0 A © œ# 4  Z  } s   H AlO x õ    

½

+ Ë÷ &  H F K5 Å q „  F G _  7 á x À Ó\     ß ¼>  ² ú ˜ t t ë ß – í ß – o }

Œ

• $ í  © œ ~ ½ ÓZ O \    É r s   H ˜ Ðs t  · ú §  H  כ `  ¦ · ú ˜ à º e ” 

% 3  .

-296-

Fig. 1. SEM image of Al/AlO _x /Nb tunnel junction.

II. S z » < gX c l õ m Í M-I-M ± n ɶ  ¥ Œ º; c" e8 ý potential profile

1. S z » < gX c l õ m Í ÷ m Ç] M ö U ê s0 n É í

ß – o} Œ • $ í  © œ ~ ½ ÓZ O õ  í ß – o} Œ •/„  F G ] X ½ + ˀ  \    É r „   0

A © œ# 4 _  : £ ¤$ í s \  ¦ › ¸  l  0 AK  Al/AlO x /Al õ  Al/AlO _x /Nb ' V , a A ] X ½ + Ë ™ è \  ¦ Õ ªa Ë >  7 £ x ‚ à ÌZ O `  ¦ s  6

 

x # Œ ] j Œ • % i   [4]. Fig. 1“ É r ] j Œ •  ) a ™ è  ×  æ Al/AlO x /Nb _  Secondary Electron Microscopy (SEM) s

p t \  ¦ ˜ Ð# Œï  r  . AlO ^x ] j Œ • ~ ½ ÓZ O “ É r % ƒ6 £ § 7 £ x ‚ Ã Ì  ) a Al

„

 F G`  ¦ e  ¦  Ý ¼  í ß – o ~ ½ ÓZ O `  ¦ s 6   x # Œ 70 V_  5 Å q„  

· ú

šõ  35 uA/cm2_  „  À Óx 9 • ¸, 0.003 mbar_  í ß –™ èÛ ¼ ¨ 8 Š

 â

\ " f 3œ íü < 10œ í 1 l x î ß – í ß – o r (  Ü ¼ 9, \ P  í ß – o ~ ½ ÓZ O _ 

 â

Ä º  © œ“ : r \ " f 0.1 mbar_  í ß –™ èÛ ¼ ¨ 8 Š â \ " f 20ì  r í ß –



o r (   . r « Ñ_  „  l & h  : £ ¤$ í `  ¦ › ' a ¹ 1 Ï l  0 AK  Keith- ley4200 parameter analyzer ü < 10 KÍ ‰ ty Œ • © œu \  ¦  6   x 

%

i Ü ¼ 9, 280 K ∼ 10 K “ : r • ¸ % ò % i \ " f 2 mV ç ß –  Ü ¼– Ð break-down „  · ú š“   ±0.7 V # 3 0 A t  8 £ ¤& ñ % i  .

2. M-I-M ± n ɶ  ¥ Œ º; c" e8 ý potential profile

@

/ Òì  r _  tunnel junction ì  r$ 3 \ " f potential dia- gram“ É r Fig. 2 (a) _  & h ‚  õ  ° ú  s  ç ß –é ß –ô  Ç f ”  y Œ •+ þ A — ¸

€

ª œ_  „  0 A © œ# 4 Ü ¼– Ð & ñ # Œ M ® o  . t ë ß – z  ´] j ] X ½ + ˽ ¨

›

¸\ " f  H image force ´ òõ \  _ K  F K5 Å q/ í ß – o} Œ • ] X ½ + ˀ  



 H % ƒ\ " f Ä »• ¸ „    + þ A$ í ÷ & 9 % ò  © œ (image) „   ç ß –_  Coulomb  © œ  ñ Œ •6   x Ü ¼– Ð í ß – o} Œ •? /\  „  >  Ò q t$ í  ) a  . s 



Qô  Ç image force ´ òõ – Ð “  K  „   _  tunneling õ & ñ \ " f Ä

»´ òô  Ç „  0 A © œ# 4 _  ¿ ºa ü < Z  } s  y Œ ™™ è H † d \     (Fig.

2 (a) z  ´‚  Ü ¼– Ð ³ ð‰ & ³ ) a potential) „   _  È Òõ  S X ‰Ò  ¦ s  7 £ x

 >  ÷ &“ ¦, ' V , a A „  À Ó\  ¦ 7 £ x r v >   ) a  . z  ´| 9 & h Ü ¼

Fig. 2. (a) Potential profile of a tunnel junction at zero bias. The solid line represents a potential profile with an image force correction. (b) Calculated potential dia- grams with various dielectric constants.

–

Ð image force ´ òõ \  ¦ “ ¦ 9 l  0 AK  Simmon“ É r bias 

“

   ) a  © œI \ " f insulator_  ¿ ºa ü < Z  } s  Õ ªo “ ¦ Ä »„   © œ Ã

º\  ¦ “ ¦ 9ô  Ç potential`  ¦  6 £ § õ  ° ú  s  Ä »• ¸ % i   [5].

φ(x) = φ ₀ − eV _a x

d − 1.15λ d ²

x(d − x) (1) d ”

 (1)\ " f λ  H _8πε ^e

²

^{ln 2}

0

ε

r

d – Ð Å Ò# Qt “ ¦, φ 0   H image force ´ ò õ

 “ ¦ 9÷ &t  · ú §“ É r f ”  y Œ •+ þ A „  0 A © œ# 4 _  Z  } s , d  H „  0 A



© œ# 4 _  ¿ ºa , V a   H “    ) a bias\  ¦
 ? / 9, Fig. 2 (a)\ 

"

f φ ^m “ É r zero -bias \ " f_  Ä »´ òô  Ç þ j@ / „  0 A © œ# 4  Z  } s \  ¦

  · p . Image force ´ òõ   H 0 A à ºd ” õ  Fig. 2 (b) \ " f

•

¸d ”  ô  Ç  ü < ° ú  s  Ä »„  ^ ‰ Ó ü t| 9 _  Ä »„   © œÃ º (ε ^r ) \  ß ¼>  _

” > r  9, Ä »„   © œÃ º  Œ •`  ¦ à º2 Ÿ ¤, V a  7 £ x † < Ê\     „   0

A © œ# 4 _  ß ¼l  / å L  y  ± ú  t >  ÷ &# Q  8 ´ ú §“ É r ' V , a A

„

 À Ó â ìØ Ô>   ) a  .

3. Transfer matrix õ u § T “ Ó Þ” X ¢ ' [, f Ç S Ë  ¹ Œ ½ 4  ˜ m

F

K5 Å q-] X ƒ  ^ ‰-F K5 Å q (M-I-M) ' V , a A] X ½ + Ë ½ ¨› ¸\ " f „  



_  \  -t  E x \    É r È Òõ > à º\  ¦ T (E x )  “ ¦ ½ + É M : „   À

Ó x 9 • ¸  H  6 £ § õ  ° ú  s 
 è ­ q à º e ”   [6].

J = 4πm ^∗ ek B T h ³

Z E

_m

0

T (E x ) ln

 1 + exp[(E F − E x )/k B T ] 1 + exp[(E F − E x − eV a )/k B T



dE x (2)

s

 d ” \ " f E ^m “ É r þ j@ / „  0 A © œ# 4  Z  } s , E ^f “ É r F K5 Å q _  ` …Ø Ô p

 ï  r 0 A, V ^a   H “  ô  Ç biass  .

‘

: r ƒ  ½ ¨\   6   x ) a r « Ñü < ° ú  s  í ß – o} Œ •_  ¿ ºa  F  g  © œ y

 · û ª“ É r  â Ä º È Òõ  S X ‰Ò  ¦`  ¦ & ñ S X ‰ y  > í ß – l  0 AK   6   x

÷

&  H ~ ½ ÓZ O  ×  æ  © œ @ /³ ð& h “   ~ ½ ÓZ O s  „  5 Å x' Ÿ § > = (transfer matrix)`  ¦ s 6   x # Œ È Òõ  > à º\  ¦ ½ ¨   H  כ s  . (Ä »• ¸ õ

& ñ “ É r Appendix ‚ à Л ¸). s  ~ ½ ÓZ O “ É r Fig. 2 (a) ü < ° ú  s  image force  “ ¦ 9  ) a z  ´] j& h “   potential`  ¦ · û ª“ É r  y Œ • potential – Ð
¾ º# Q   H   o r ( ” Ü ¼– Ð+ ‹  6 £ § õ  ° ú  “ É r „   5

Å x' Ÿ § > = (TM) › ' a > d ” `  ¦ s 6   x # Œ

 A _n B n



= T M n × T M n−1 · · · T M 2 × T M 1

 A ₁ B 1



(3)

„

 ^ ‰ ½ ¨ç ß –\ " f_   1 l x † < Êà º\  ¦ ½ ¨ “ ¦, { 9   ü < È Òõ   _

 â ì2 £ § _  q – Ð € ª œ % i † < Æ& h  È Òõ  > à º\  ¦ ½ ¨   H ~ ½ ÓZ O s 



 [7].

III. + s ÇÊ Ý õ m Í À X Ø8 ý

Fig. 3“ É r í ß – o} Œ •`  ¦ \ P  í ß – o ~ ½ ÓZ O õ  e  ¦  Ý ¼  í ß – o ~ ½ Ó Z O

Ü ¼– Ð ] j Œ •ô  Ç Al/AlO x /Al ™ è _  8 £ ¤& ñ   õ \  ¦ — ¸4 S qa A

 

õ ü < q “ §ô  Ç Õ ªa Ë >s  . Õ ªa Ë >\ " f ˜ Ѝ  H  ü < ° ú  s  ¿ º r 

«

Ñ — ¸¿ º ± ú “ É r “ : r • ¸ _ ” > r$ í (I _(280K) /I _(10K) =1.1 ∼ 1.2)`  ¦

 ? / 9, “ : r • ¸ ± ú  f ” \     „  À Ó\  ¦ Ò q t$ í r ~  ´ à º e ” 



 H F K5 Å q ? /_  „   ì  r Ÿ í ×  ¦ # Q[ þ t # Q „  À Ó  Œ • t   H „   + þ

A& h “   ' V , a A „  À Ó_  : £ ¤$ í `  ¦ ˜ Г   . ¿ º r « Ñ_  „  À Ó ß ¼ l

  H  Ø Ôt ë ß – “ : r • ¸ü < “   „  · ú š\  @ /ô  Ç „  À Ó : £ ¤$ í “ É r Ä »



ô  Ç  ⠆ ¾ Ó$ í `  ¦
  · p . Al/AlO ^x í ß – o} Œ • ] j Œ • ~ ½ ÓZ O \ 



 É r Al/AlO x ] X ½ + ˀ  \ " f_  „  0 A © œ# 4  Z  } s  (φ ⁰ ), AlO x

¿

ºa  (d), Ä »„   © œÃ º (ε ^r )\  ¦ — ¸4 S qa A l  0 Aô  Ç õ & ñ “ É r  6 £ § õ

 ° ú   .

Fig. 3. A comparison between the measured (solid line) and calculated (symbols) I-V characteristics. The fitted parameters are (a) Φ 0 =2.2 eV, d=1.0nm, ε r =5.3 ∼ 5.6 (b) Φ 0 =2.3 eV, d=1.15 nm, ε r =5.25 ∼ 5.65, A=

5000nm ² , m ^∗ _Al = m ₀ × 1.16 [9], m ^∗ _AlO

_x

= m ₀ × 0.75 [10].

1) Al/AlO x /Al ] X ½ + ˽ ¨› ¸\ " f ‰ & ³F  · ú ˜ 94 R e ”   H

AlO x _  Ä »„   © œÃ º (ε r ≈ 5)\  ¦ [8,9] s 6   x # Œ image force

´

òõ   © œ@ /& h Ü ¼– Ð  Œ •“ É r 280 K _  ±30 mV % ò % i \ " f „   0

A © œ# 4  Z  } s ü < ¿ ºa \  ¦ Æ ÒØ  ¦ ô  Ç .

2) 0 A õ & ñ \ " f ½ ¨ô  Ç „  0 A © œ# 4  Z  } s ü < ¿ ºa \  ¦ “ ¦& ñ r  v

“ ¦ Z  }“ É r „  · ú š\ " f barrier lowering\   H % ò † ¾ Ó`  ¦ Šҍ  H Ä

»„   © œÃ º\  ¦    or v €  " f, ±0.7 V t _  8 £ ¤& ñ  ) a   õ ü <

q

“ § # Œ „  0 A © œ# 4  Z  } s , ¿ ºa , Ä »„   © œÃ º_  & ñ S X ‰ ô  Ç ° ú כ`  ¦ Æ

ÒØ  ¦ ô  Ç .

3) “ : r • ¸\  % ò † ¾ Ó`  ¦ ~ à ΍  H Ä »„   © œÃ º\  ¦    or &  280 K ˜ Ð



 ± ú “ É r “ : r • ¸\ " f 8 £ ¤& ñ  ) a   õ ü < q “ § # Œ y Œ • “ : r • ¸\  @ / ô

 Ç Ä »„   © œÃ º\  ¦ Æ ÒØ  ¦ ô  Ç . ë ß –€  • Ä »„   © œÃ º\  ¦    or v  8



• ¸ 8 £ ¤& ñ   õ ü < { 9 u  t  · ú §  H  â Ä º  r  % ƒ6 £ § é ß –> \ 

"

f Ò'  œ íl  Ä »„   © œÃ º\  ¦    or v “ ¦ s  3é ß –> _  õ & ñ `  ¦ ì

ø Í4 Ÿ ¤ # Œ „  0 A © œ# 4  Z  } s , ¿ ºa , Ä »„   © œÃ º_  & ñ S X ‰ ô  Ç ° ú כ`  ¦ Æ

ÒØ  ¦ ô  Ç .

Fig. 4  H 8 £ ¤& ñ   õ ü < — ¸4 S qa A   õ \  ¦ q “ § # Œ % 3 “ É r Al ( ¢ ¸  H Nb)/AlO x ] X ½ + ˀ  \ " f_  „  0 A © œ# 4  Z  } s ü < Ä »

„

  © œÃ º\  ¦
  · p  כ s  . — ¸4 S qa A   õ \ " f \ P í ß – o– Ð % 3 

“

É r AlO x ¿ ºa   H ∼1.0 nm\  ¦ % 3 % 3 Ü ¼ 9, e  ¦  Ý ¼  í ß – o\  _

ô  Ç AlO x _   â Ä º  H 1.1 nm (3 œ í), 1.15 nm (10œ í)– Ð
 

z Œ ¤ . TEMÜ ¼– Ð 8 £ ¤& ñ ô  Ç ° ú  “ É r › ¸| \ " f \ P í ß – o– Ð % 3 “ É r AlO x ¿ ºa • ¸ @ /| Ä Ì ∼1 nm ? /ü @s  . ¢ ¸ô  Ç AlO _x Ä »„   © œÃ º



 H Ó ü t| 9  © œÃ º– Ð “ : r • ¸\     5.25 (280 K) ∼ 5.65 (10 K) _

 “ : r • ¸ _ ” > r$ í `  ¦ ˜ Ð% i  . „  0 A © œ# 4  Z  } s  (φ 0 )  H \ P  í ß –



o ~ ½ ÓZ O Ü ¼– Ð $ í  © œô  Ç AlO _x /Al ] X ½ + ˀ  _  „  0 A © œ# 4  Z  } s 

 2.23 eV“    כ \  q K  AlO ^x /Nb ] X ½ + ˀ  \ " f  H 1.0 eV

–

Ð  H s \  ¦ ˜ Ð% i t ë ß –, e  ¦  Ý ¼  í ß – o ~ ½ ÓZ O Ü ¼– Ð $ í  © œô  Ç AlO x /Al ] X ½ + ˀ  _  „  0 A © œ# 4  Z  } s  í ß – o r ç ß –s  3œ í“  

 â

Ä º 2.2 eV, 10œ í“    â Ä º 2.3 eV– Ð \ P  í ß – o ~ ½ ÓZ O õ   _  1

l x{ 9 ô  Ç Z  } s \  ¦
 ? /% 3  . Õ ªo “ ¦ zero-bias\ " f_  Ä »´ ò ô

 Ç þ j@ / „  0 A © œ# 4  Z  } s  (φ ^m )  H Al/AlO x /Al ™ è [ þ t \ " f ] X

½ + ˀ  \ " f ˜ Ð  400 meV y Œ ™™ è % i Ü ¼
 1 l x{ 9 ô  Ç Z  } s \  ¦

 ? /% 3  .

IV. + s Ç Â ] Ø

‘

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c p w Š à U Ø ”  ô

[1] P. Doe and D. Vogler, Solid State Technology 46, 1 (2003).

[2] M. F. Li, Y. T. Hou,Y. Jin and W. H. Lai, J. Appl.

Phys. 91, 264 (2002).

[3] Lingfeng Mao, Changuhua Tan and Mingzhen Xu, Microelectronics Reliability 41, 927 (2001).

[4] Hyunsik Im, Yu. A. Pashkin, T. Yamamoto, O.

Astafiev, Y. Nakamura and J. S. Tsai, Applied Physics Letters 88, 112113 (2006).

[5] J. G. Simmons, J. Appl. Phys. 34, 1793 (1963).

[6] J.G. Simmons, J. Appl. Phys. 35, 2655 (1964).

[7] David K. Ferry, Stephen Marshall Goodnick, Transport in Nanostructures (Cambridge University Press, Cambridge, 1997), p. 97-114.

[8] R. E. Bolz and G. L. Tuve, CRC Handbook of Tables for Applied Engineering Science (CRC Press, Boca Raton FL, 1983).

[9] Panu Koppinen, Temperature Dependence of the Tunneling Conductance of a Metal-insulator-metal Barrier (University of Jyvaskyla Department of Physics, Jyvaskyla, 2001), p.18.

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[11] W. H. Rippard, A. C. Perrella, F. J. Albert and R.

A. Buhrman, Phys. Rev. Lett. 88, 046805 (2002).

Tunnel Leakage Current in Metal-insulator-metal Devices with an Ultra-thin Tunnel Barrier

Hyuntae Jung, Yongmin Kim, Kyooho Jung, Hyunsik Im ^∗ and Woong Jung ^† Department of Semiconductor Science, Dongguk University, Seoul 100-715

Hyungsang Kim ^‡

Department of Physics, Dongguk University, Seoul 100-715 (Received 22 September 2008)

We have studied the transport phenomenon in Al and Nb based metal-insulator-metal tunnel junctions. The deposition of the Al and the Nb thin films was done using angle evaporation through a suspended mask formed in a Ge layer supported by a thermally stable polymer while the tunnel barrier was formed uwing thermal oxidation or plasma oxidation of the bottom Al layer.

After the oxidation, we deposited the Al or the Nb top layer. The measured current-voltage (I-V) characteristics were compared with the modeled ones by using transfer matrix technique. In the modeling, Simmons’ image force correction was taken into account. We extracted basic junction parameters, such as the barrier height and width. The measured and the modeled I-V curves were in good agreement.

PACS numbers: 68.55.L, 73.40, 85.30.M

Keywords: Tunneling, Transmission coefficient, Transfer matrix

∗

E-mail: [email protected]

†

E-mail: [email protected]

‡

E-mail: [email protected]