¾Ì ¦ R× D¶  ¥ ö n Ú Œ ˜ my ¢= k Ga x In 1−x P y Sb z As 1−y−z /GaSb8 ý  ¹ Å X ì Ä — ¤V R Ë

~

¾Ì ¦ R× D¶  ¥ ö n Ú Œ ˜ my ¢= k Ga ^x In 1−x P y Sb z As 1−y−z /GaSb8 ý  ¹ Å X ì Ä — ¤V R Ë



™ »¦ P 

 â

l @ /† < Ɠ § s õ @ /† < Æ „   Ó ü t o † < Æõ , à º" é ¶ 443-760

(2010¸   1 Z 4 20{ 9  ~ à Î6 £ §, 2010¸   4 Z 4 21{ 9  à º& ñ ‘ : r ~ à Î6 £ §, 2010¸   5 Z 4 12{ 9  > F  S X ‰& ñ )

GaSb l ó ø Í\      & ñ ½ + Ër †   š ¸" é ¶  o½ + ËÓ ü t ì ø ͕ ¸^ ‰ Ga

x

In

1−x

P

y

Sb

z

As

1−y−z

_     & ñ ½ + ˛ ¸| õ  \  - t

  ½ ™× ¼Ì “ s1 p x „   & h  : £ ¤$ í `  ¦ # 3 6   x& h x 9 ] X   ½ + Ë ~ ½ ÓZ O `  ¦ s 6   x # Œ ½ ¨ % i  . > í ß –   õ    © œ@ / 3 ∼ 5 µm (7 £ ¤,  ½ ™× ¼Ì “ ss  0.41 eV ∼ 0.25 eV)“   ×  æ& h ü @‚  % ò % i _   ½ ™× ¼Ì “ s“ É r ŠҖ Ð 0.1 < Sb < 0.2 \ " f + þ A$ í

÷

&% 3  . Sb\  ¦ 0.09  Ò'  0.21 t  0.02 m ”  7 £ x r &  > í ß –ô  Ç   õ , Sb  7 £ x  ½ + É Ã º2 Ÿ ¤ GaSb \     & ñ

½

+ Ë r ~  ´ à º e ”   H x ü < y_  # 3 0 A V , # Qt  9,  ½ ™× ¼Ì “ sõ  „   {  þ j@ /° ú כ• ¸ 7 £ x † < Ê`  ¦ · ú ˜ à º e ” % 3  . ¢ ¸ ô

 Ç ×  æ& h ü @‚  % ò % i _  Ga

x

In

1−x

P

y

Sb

z

As

1−y−z

ü < GaSb l ó ø Í  s _  ] X ½ + ˀ  \ " f  H ] j1+ þ Aì ø ͕ ¸^ ‰ H † d

` 

¦ · ú ˜ à º e ” % 3  . þ j   H   & ñ $ í  © œ  ) a W 1> h_  Ò  re  ¦ Ga

x

In

1−x

P

y

Sb

z

As

1−y−z

/GaSb \  @ /ô  Ç  ½ ™× ¼Ì “ s z  ´+ « >

u

ü < q “ §K  ‘ : r   õ  ¸ ú ˜ { 9 u  % i  .

Ù þ

˜d ” # Q: š ¸" é ¶  o½ + ËÓ ü t ì ø ͕ ¸^ ‰,Ga(x)In(1-x)P(y)Sb(z)As(1-y-z),MIR(midinfrared),   & ñ ½ + ˛ ¸| ,UTB(universal tight binding), ½ ™× ¼Ì “ s

Electronic Properties of the Pentanaly Alloy Ga _x In _1−x P _y Sb _z As _1−y−z Lattice-matched to GaSb

Kyu Rhee Shim ^∗

Department of Electro-physics, Kyonggi University, Suwon 443-760 (Received 20 January, 2010 : revised 21 April, 2010 : accepted 12 May, 2010)

The electronic band gaps and the lattice-matching conditions for the pentanary alloy Ga

x

In

1−x

P

y

Sb

z

As

1−y−z

lattice-matched to GaSb in the mid-infrared (MIR) spectral region were calculated by using the universal tight binding method. The calculation suggested that the alloy Ga

x

In

1−x

P

y

Sb

z

As

1−y−z

/GaSb in 0.1 ≤ Sb ≤ 0.2 was suitable for the MIR spectral region from 3 to 5 µm (i.e., band gaps of 0.41 eV ∼ 0.25 eV). With increasing z from 0.09 to 0.21, the lattice- matching x and y regions became broader, and the band gap and the valence band maximum (VBM) also increased. This implies that the interface the between Ga

x

In

1−x

P

y

Sb

z

As

1−y−z

and the GaSb is a type-I semiconductor. Our theoretical band gaps were compared with experimental band gap data for four samples of Ga

x

In

1−x

P

y

Sb

z

As

1−y−z

/GaSb.

PACS numbers: 71.22.+i, 71.20 Nr

Keywords: Pentanary alloy Ga(x)InA(1-x)P(y)Sb(z)As(1-y-z), Midinfrared, Lattice matching condition, Universal tight binding method, Band gap

∗

E-mail: kshim@kyonggi.ac.kr

-505-

I. " e  ] Ø

III-V  " é ¶  o½ + ËÓ ü t ì ø ͕ ¸^ ‰  H $ í ì  r q \      ½ ™× ¼Ì “ s,   



 © œÃ º,  â > €  \ " f_   ½ ™× ¼& ñ § > = © œI 1 p x`  ¦ › ¸] X ½ + É Ã º e ” 

#

Q, „   x 9  F  g † < Æ& h  “ ¦î ß –¾ ¡ § \   € ª œ >  6 £ x6   x ÷ &“ ¦ e ”  .



Œ

™" é ¶  o½ + ËÓ ü t ì ø ͕ ¸^ ‰  H ô  Çt _  $ í ì  r q \  _ K  „   & h  :

£ ¤$ í `  ¦ › ¸] X  >  ÷ &t ë ß –,  " é ¶ x 9  š ¸" é ¶  o½ + ËÓ ü t ì ø ͕ ¸^ ‰  H

¿

ºt  s  © œ_  $ í ì  r q \  ¦ y Œ •y Œ • 1 l qw n & h Ü ¼– Ð › ¸] X ½ + É Ã º e ” 

#

Q, 7 á §  8 î ß –& ñ & h s “ ¦  € ª œô  Ç Û ¼& 7 ˜à Ô! 3  % ò % i _  ì ø ͕ ¸^ ‰

\

 ¦ ½ ¨‰ & ³½ + É Ã º e ”  . Õ ª! 3 \ • ¸ Ô  ¦ ½ ¨ “ ¦ ™ D ¥ ½ + Ë0 l x • ¸\   

 É

r Á º| 9 " f ´ òõ ü < ™ D ¥  o$ í Ì “ s(miscibility gap)1 p x   & ñ $ í  © œ _

 # Q 9¹ ¡ § Ü ¼– Ð z  ´+ « > ¢ ¸  H s  : rƒ  ½ ¨ ] jô  Ç÷ &# Q M ® o  . þ j



 H LPE(liquid phase epitaxy)
 MOVPE(metal organic vapour phase epitaxy)1 p x \ x „ à Ìr    & ñ $ í  © œ l Õ ü t s  µ 1 Ï

² ú

˜ H † d \      .š ¸" é ¶  o½ + ËÓ ü t \  @ /ô  Ç ƒ  ½ ¨  Ö ¸ µ 1 Ïy  s À Ò

#

Qt “ ¦ e ”   [1,2].



 © œ@ / 3-5 µm “   ×  æ& h ü @‚  (midinfrared : MIR)% ò

%

i _  F  g ~ ½ ÓØ  ¦ l 
  Ž Ø  ¦ l   H @ /l š ¸% i Û ¼ 8 £ ¤& ñ s 
 Á º‚   F 

g: Ÿ x’  1 p x \  s 6   x| ¨ c à º e ” # Q, MIR % ò % i  ì ø ͕ ¸^ ‰ > hµ 1 Ïs  þ j



 H ´ ú §“ É r › ' a d ” `  ¦ % 3 “ ¦ e ”   [3,4]. Ä »} © œô  Ç MIR % ò % i  ì ø ͕ ¸

^

‰– Ð" f š ¸" é ¶  o½ + ËÓ ü t ì ø ͕ ¸^ ‰ Ga x In _1−x P _y Sb _z As _1−y−z 

· ú

˜ 94 R e ”  . 1999 ¸   % ƒ6 £ § Ü ¼– Ð # 3 6   x& h x 9 ] X   ½ + Ë~ ½ Ó Z O

(universal tight binding method : UTB) [5] ü <  © œ  

ñ„  > h† < Êà º(correlated function expansion :CFE)~ ½ ÓZ O  [6] \  _ K  Ga x In _1−x P _y Sb _z As _1−y−z \  @ /ô  Ç s  : r& h “  

ƒ

 ½ ¨ à º' Ÿ ÷ &% 3  . # Œl " f Ga ^x In 1−x P y Sb z As 1−y−z _  l

ó ø Í 7 á x À Ó (InAs, InP, GaSb) \    É r    & ñ ½ + ˛ ¸

|

õ  $ í ì  r q \    É r Å Òכ ¹ \  -t  Ì “ sõ   © œI x 9 • ¸1 p x

„

  & h  : £ ¤$ í \  @ /ô  Ç s  : r& h  > í ß –   õ  µ 1 ϳ ð÷ &% 3 



[5-6]. Õ ª s Ê ê 2002¸   InAs l ó ø Í\     & ñ ½ + Ër †   Ga _0.92 In _0.08 P _0.05 As _0.08 Sb _0.87 _    & ñ $ í  © œs  LPE ~ ½ ÓZ O  Ü

¼– Ð % ƒ6 £ § $ í / B N # Œ 77 K \ " f_   ½ ™× ¼Ì “ ss  695 meVs  9 300 K \ " f_   ½ ™× ¼Ì “ s 640 meV Ü ¼– Ð ˜ Г ¦  ) a   e ” 



 [7]. ¢ ¸ô  Ç 2007 ¸   LPE ~ ½ ÓZ O Ü ¼– Ð GaSb l ó ø Í0 A\  Ga 0.02 In 0.98 P 0.02 As 0.84 Sb 0.14 _    & ñ $ í  © œs  $ í / B N €  " f [3], / B I s # Q ° ú  “ É r ~ ½ ÓZ O Ü ¼– Ð MIR % ò % i _  W 1> h   & ñ [ þ t;

Ga _0.03 In _0.97 P _0.06 As _0.81 Sb _0.13 , Ga _0.04 In _0.96 P _0.04 As _0.83 Sb 0.13 , Ga 0.07 In 0.93 P 0.03 As 0.82 Sb 0.15 , Ga 0.03 In 0.97 P 0.17

As 0.64 Sb 0.19 `  ¦ $ í  © œ # Œ PL(photoluminescence)\  _  ô

 Ç  ½ ™× ¼Ì “ s   õ \  ¦ µ 1 ϳ ð % i   [8]. ¢ ¸ô  Ç Ga _x In _1−x P _y Sb z As 1−y−z _    & ñ `  ¦ $ í  © œr ~  ´ M : l ó ø ÍÜ ¼– Ð" f GaSb

\

 ¦  6   x   H  כ s  InAs\  ¦  6   x   H  כ ˜ Ð  l ó ø Í Â Òd ” 

`

 ¦ ×  ¦ s   H X < ´ òõ & h s    H  כ `  ¦ · ú ˜ Í Ç x  [8].

‘

: r  7 Hë  H \ " f  H þ j   H   & ñ $ í  © œs  $ í / B N& h Ü ¼– Ð s À Ò# Q t 

“

¦ e ”   H GaSb \      & ñ ½ + Ër †   MIR % ò % i _  š ¸" é ¶  o½ + ËÓ ü t ì

ø ͕ ¸^ ‰ Ga x In _1−x P _y Sb _z As _1−y−z /GaSb \  @ /ô  Ç „   & h  : £ ¤

$ í

`  ¦ UTB ~ ½ ÓZ O `  ¦ s 6   x # Œ · ú ˜ ‘ : r  .

II. T  Â ] Ø

III-V 7 á ¤  " é ¶  o½ + ËÓ ü t ì ø ͕ ¸^ ‰_  „   & h   © œI \  ¦ > í ß – 



 H X < e ” # Q UTB ~ ½ ÓZ O “ É r q “ §& h  ç ß –é ß – “ ¦ & ñ S X ‰ >  ½ ¨½ + É Ã

º e ”   H ~ ½ ÓZ O Ü ¼– Ð · ú ˜ 94 R e ”   [9]. UTB\ " f  " é ¶  o½ + Ë Ó

ü

t ì ø ͕ ¸^ ‰  H — ¸› ¸  & ñ (pseudo-crystal)Ü ¼– Ð 2 [/ å L ) a   [5].

#

Œl " f š ¸" é ¶  o½ + ËÓ ü t ì ø ͕ ¸^ ‰ Ga x In _1−x P _y Sb _z As _1−y−z _  K  x 9

ž Ðm î ß –“ É r # Œ$ Á > h_  s " é ¶  o½ + ËÓ ü t ì ø ͕ ¸^ ‰ GaP, GaSb, GaAs, InP, InSb, InAs [ þ t _  Ä »´ òK x 9 ž Ðm î ß –(effective Hamiltonian)`  ¦ ×  æ¨ î ç  H ô  Ç ° ú כÜ ¼– Ð
  · p .

H ˆ Ga

x

In

1−x

P

y

Sb

z

As

1−y−z

= xy ˆ H GaP

+ xz ˆ H GaSb + x(1 − y − z) ˆ H GaAs

+ (1 − x)y ˆ H _InP + (1 − x)z ˆ H _InSb + (1 − x)(1 − y − z) ˆ H InAs (1) GaSb _  Ä »´ òK x 9 ž Ðm î ß – ( ˆ H _GaSb )“ É r GaSb _  | 9 " fK x 9 ž Ð m

î ß –(ordered Hamiltonian) ( ˆ H _GaAs ⁰ ) õ  Á º| 9 " fK x 9 ž Ðm  î

ß –(disordered Hamiltonian) (∆ ˆ H GaSb ) _  ½ + ËÜ ¼– Ð
 ? / t

 9,   É r s " é ¶  o½ + ËÓ ü t \  @ /K " f• ¸  ð ø Ít s  .

H ˆ _GaSb = ˆ H _GaSb ⁰ + ∆ ˆ H _GaSb H ˆ GaP = ˆ H _GaP ⁰ + ∆ ˆ H GaP

H ˆ _GaAs = ˆ H _GaAs ⁰ + ∆ ˆ H _GaAs H ˆ InP = ˆ H _InP ⁰ + ∆ ˆ H InP

H ˆ InSb = ˆ H _InSb ⁰ + ∆ ˆ H InSb

H ˆ InAs = ˆ H _InAs ⁰ + ∆ ˆ H InAs . (2)

#

Œl " f GaSb _  | 9 " fK x 9 ž Ðm î ß – ˆ H _GaSb ⁰   H ¢ - a„    

&

ñ é # Qo  © œI _  K x 9 ž Ðm î ß –s  9, Á º| 9 " f K x 9 ž Ðm î ß –

∆ ˆ H GaSb   H GaSb _  s “ : r u  ¨ 8 Š \  _ ô  Ç q ‚  + þ A´ òõ \  ¦ Ä »

•

¸   H € ª œÜ ¼– Ð" f ∆ ˆ H GaSb:In , ∆ ˆ H GaSb:P , ∆ ˆ H GaSb:As [ þ t _

 u  ¨ 8 Š$ í ì  r q  Y  L _  ½ + ËÜ ¼– Ð
 ? /”   .   É r s " é ¶  o½ + Ë Ó

ü

t \  @ /K " f• ¸  ð ø Ít – Ð & h 6   x ÷ &# Q,

∆ ˆ H GaP = (1 − x)∆ ˆ H GaP :In + z∆ ˆ H GaP :Sb

+(1 − y − z)∆ ˆ H _{GaP :As}

∆ ˆ H GaSb = (1 − x)∆ ˆ H GaSb:In + y∆ ˆ H GaSb:P

+(1 − y − z)∆ ˆ H _GaSb:As

∆ ˆ H GaAs = (1 − x)∆ ˆ H GaAs:In + y∆ ˆ H GaAs:P

+z∆ ˆ H GaAs:Sb

∆ ˆ H InP = x∆ ˆ H InP :Ga + z∆ ˆ H InP :Sb

+(1 − y − z)∆ ˆ H InP :As

∆ ˆ H _InSb = x∆ ˆ H _InSb:Ga + y∆ ˆ H _InSb:P +(1 − y − z)∆ ˆ H InSb:As

∆ ˆ H _InAs = x∆ ˆ H _InAs:Ga + y∆ ˆ H _InAs:P

+z∆ ˆ H InAs:Sb . (3)

(3)d ” `  ¦ (2)d ” õ  (1)d ” \  @ /{ 9  # Œ & ñ o  €  , š ¸" é ¶  o½ + ËÓ ü t Ga x In 1−x P y Sb z As 1−y−z _  8 ú x K x 9 ž Ðm î ß –“ É r  6 £ § õ  ° ú   s

 ³ ð‰ & ³ ) a  .

H Ga

_x

In

_1−x

P

_y

Sb

_z

As

_1−y−z

= xyH _GaP ⁰ + xzH _GaSb ⁰ + x(1 − y − z)H _GaAs ⁰ +(1 − x)yH _InP ⁰ + (1 − x)zH _InSb ⁰

+(1 − x)(1 − y − z)H _InAs ⁰ + xyzV GaP Sb

+xy(1 − y − z)V _{GaP As} + xz(1 − y − z)V _GaSbAs +(1 − x)yzV InP Sb + (1 − x)y(1 − y − z)V InP As

+(1 − x)z(1 − y − z)V InSbAs + x(1 − x)yV GaP In

+x(1 − x)zV _GaSbIn + x(1 − x)(1 − y − z)V _GaInAs (4)

#

Œl " f V ^{GaP Sb}   H GaP:Sb ü < GaSb:P_  8 ú x Á º| 9 " f \ 



-t – Ð" f ∆ ˆ H GaP :Sb ü < ∆ ˆ H GaSb:P _  ½ + Ë`  ¦
 ? / 9 (7 £ ¤, V GaP Sb = ∆ ˆ H GaP :Sb + ∆ ˆ H GaSb:P ), s   H ¿ º s " é ¶  o½ + ËÓ ü t _

 | 9 " fK x 9 ž Ðm î ß –_   ˆ H _GaP ⁰ − ˆ H _GaSb ⁰ – Ð é  H  .

x 9

] X   ½ + Ë(tight binding :TB)~ ½ ÓZ O \ " f j   P : Ú Ô Z …s  Û

¼_  ν   P : s “ : r _    & ñ “ ¦Ä » © œI  † < Êà º Ψ n (~ k, ~ r)  H Bloch

&

ñ o \  ¦ ë ß –7 á ¤ r v   H þ jü @y Œ • " é ¶  C • ¸ † < Êà º[ þ t φ ^ν _αj (~ r) _  ‚   + þ

A  ½ + ËÜ ¼– Ð
 ? /”   .  ƒ   o½ + ËÓ ü t ½ ¨› ¸\  ¦ ° ú   H III-V ì

ø ͕ ¸^ ‰  H sp ³ s Ú Ôo × ¼– Ð   ½ + Ë © œI \  ¦ s À Ò# Q € ª œs “ : r õ

 6 £ § s “ : r \  y Œ • 4> hm ”  (α = s, p x , p y , p z ) 8 ú x 8 > h_  þ jü @ y

Œ

• " é ¶  C • ¸† < Êà º K x 9 ž Ðm î ß –_  l $ † < Êà º  ) a  . y Œ • K

x 9 ž Ðm î ß – ' Ÿ § > =כ ¹™ è  H

H _mn =< Ψ _m |H|Ψ _n > (5)

–

Ð" f, 8 × 8 K x 9 ž Ðm î ß – ' Ÿ § > =d ” `  ¦ % 3 > ÷ & 9 s \  ¦ : Ÿ x K  4 > h_  „   { ü < 4> h_  „  • ¸{  8 ú x 8 > h_  \  -t  “ ¦Ä »

° ú

כ`  ¦ % 3 >   ) a  . s M :, K x 9 ž Ðm î ß –_  " é ¶  C • ¸† < Êà º\  @ / ô

 Ç & h ì  r“ É r TB B > h  à º– Ð ¿ º  H X <, ' Í   P :  î  r " é ¶  

\

 @ /ô  Ç  © œ  ñ Œ •6   x`  ¦ “ ¦ 9 €   9> h, ¿ º  P :  î  r " é ¶



 t  “ ¦ 9 €   23> h_  TB B > h  à º € 9 כ ¹ >   ) a



. (5)d ” `  ¦ (4)d ” \  @ /{ 9  >  ÷ &€  , š ¸" é ¶  o½ + ËÓ ü t ì ø ͕ ¸^ ‰ Ga x In 1−x P y Sb z As 1−y−z _  \  -t  “ ¦Ä »° ú כ“ É r s " é ¶  o½ + Ë Ó

ü

t ì ø ͕ ¸^ ‰[ þ t _  TB B > h  à ºü < ™ D ¥ ½ + Ëq _  † ½ ÓÜ ¼– Ð
 ? /

”

    H  כ `  ¦ · ú ˜ à º e ”  .

Ga x In 1−x P y Sb z As 1−y−z \  ¦ # Q‹ "  l ó ø Í0 A\  $ í  © œr v 


\

        & ñ ½ + ˛ ¸| s  ² ú ˜ t >   ) a  . s   H s p  µ 1 Ï

³

ð  ) a   e ”   [5].

x = 1

(−0.175 + 0.009z) − 0.008y

×(d ^o _substrate + 0.082y − 0.182z − 2.623) (6)

Fig. 1. Allowed composition relationships for lat- tice matching of the substrate GaSb to the alloy Ga _x In _1−x P _y Sb _z As _1−y−z with respect to z (= 0.2, 0.4, 0.6, 0.8)

#

Œl " f GaSb\  ¦ l ó ø ÍÜ ¼– Ð × þ ˜ % i `  ¦ M :, d ^o substrate = d GaSb = 2.639˚ A s Ù ¼– Ð Ga ^x In 1−x P y Sb z As 1−y−z \  ¦ GaSb \      & ñ ½ + Ë r ~  ´ à º e ”   H › ¸| “ É r

x = 0.082y − 0.182z + 0.016

−0.175 + 0.009z − 0.008y . (7) s

  ) a  .

Ga x In 1−x P y Sb z As 1−y−z _  \  -t   © œI \  ¦ ½ ¨ l  0 A K

  6   x ) a s " é ¶  o½ + ËÓ ü t GaP, GaSb, GaAs, InP, InSb, InAs _  TB B > h   à ºx 9    ½ + ËU  ´s   H ‚ à Г ¦ë  H‰  ³ [3]_   כ `  ¦



6   x  9, Table 1\ 
ü < e ”  . s  TB B > h  à º[ þ t“ É r s 

"

é

¶  o½ + ËÓ ü t ì ø ͕ ¸^ ‰_  „   {  þ j@ /° ú כ(valence band max- imum : VBM) s  0s  ÷ &>  €  " f, z  ´“ : r \ " f_  Å Òכ ¹@ /g A

&

h _  z  ´+ « >& h  \  -t  Ì “ s[ þ t õ  ´ ú ð  r  כ s  . € ª œs “ : r õ  6 £ § s 

“

: r _  $ í ì  r q   H 0 s  © œõ  1s   s # Q  Ù ¼– Ð, 0 ≤ x ≤ 1 s

 9 0 ≤ y + z ≤ 1 _  › ¸| `  ¦ (7)d ” \  & h 6   xÙ þ ¡`  ¦ M :, Ga x In 1−x P y Sb z As 1−y−z _  GaSb\      & ñ ½ + Ë % ò % i “ É r Sb _

 $ í ì  r q (7 £ ¤, z) \     Ga ü < P _  $ í ì  r q  (7 £ ¤, x ü < y)% ò

%

i s  ² ú ˜ t  9, s \     \  -t  Ì “ s_  % ò % i s  ² ú ˜  ”  



.

III. 4  ˜ m+ s ÇÊ Ý õ m Í À X Ø8 ý

š

¸" é ¶  o½ + ËÓ ü t ì ø ͕ ¸^ ‰ Ga x In _1−x P _y Sb _z As _1−y−z \  ¦ GaSb l

ó ø Í0 A\  $ í  © œr ~  ´M :,    & ñ ½ + Ë › ¸$ í q “   x, y, z_  › ' a >  d ”

“ É r (7)d ” \  _ K  ½ ¨½ + É Ã º e ” Ü ¼ 9 s   H Fig. 1 \ 
 
 e ”

 . Figure 1“ É r z\  ¦ 7 £ x † < Ê\     ² ú ˜ t   H x ü < y_ 

 

 & ñ ½ + ˛ ¸| `  ¦ Õ ª 2 ;  כ s  .

Ga _x In _1−x P _y Sb _z As _1−y−z /GaSb _  „   & h  : £ ¤$ í `  ¦ ½ ¨  l

 0 A # Œ, · ú ¡\ " f ½ ¨ô  Ç    & ñ ½ + Ë › ¸| \     UTB

~

½ ÓZ O Ü ¼– Ð Å Òכ ¹@ /g A& h (Γ, L, X)\  @ /ô  Ç \  -t ° ú כ[ þ t`  ¦ ½ ¨

Table 1. TB parameters and bond lengths of GaP, GaSb, GaAs, InP, InSb, and InAs.

TB

parameters and GaP GaSb GaAs InP InSb InAs

bond lengths

P

1

-6.285 -6.093 -6.724 -6.294 -6.724 -7.179

P

2

-2.789 -3.886 -3.978 -3.429 -3.978 -4.487

P

3

1.094 0.810 0.641 1.843 0.641 1.660

P

4

2.382 2.348 2.874 2.609 2.874 2.336

P

5

-7.750 -6.218 -6.900 -6.220 -6.900 -6.400

P

6

5.260 5.100 5.300 4.700 5.300 5.400

P

7

4.950 4.110 4.250 4.380 4.250 4.000

P

8

2.440 1.600 2.000 2.280 2.000 2.000

P

9

5.560 5.500 5.5 5.300 5.500 5.460

P

10

-1.138 -0.920 -0.339 -0.720 -0.339 -0.824

P

11

-1.186 -2.012 -1.756 -1.338 -1.756 -1.202

P

12

0.760 0.760 0.60 0.520 0.600 0.550

P

13

1.330 1.330 0.960 0.910 0.960 0.880

P

14

0.854 0.599 0.444 0.384 0.444 0.227

P

15

1.189 1.008 1.121 0.739 1.121 0.983

P

16

0.024 0.042 0.045 0.087 0.045 0.056

P

17

0.083 0.060 0.096 0.102 0.096 0.086

P

18

-0.167 -0.163 -0.047 -0.032 -0.047 -0.092

P

19

-0.181 -0.224 -0.065 -0.034 -0.065 -0.126

P

20

1.180 0.750 0.780 0.90 0.780 0.840

P

21

-0.080 -0.240 -0.08 -0.006 -0.080 -0.080

P

22

0.0 0.0 0.0 0.0 0.0 0.0

P

23

0.0 0.0 0.0 0.0 0.0 0.0

d

⁰

(˚ A) 2.358 2.639 2.448 2.541 2.805 2.623

Table 2. Principal energy band gap ranges for the alloy Ga x In 1−x P y Sb z As 1−y−z lattice matched to GaSb.

z (Sb) of E(Γ) E(L) E(X)

Ga

x

In

1−x

P

y

Sb

z

As

1−y−z

(eV) (eV) (eV)

0.1 0.265 1.346 2.199

0.2 0.265 - 0.305 1.332 - 1.385 2.013 - 2.152

0.3 0.245 -0.513 1.255 - 1.425 1.925 - 1.965

0.4 0.289 - 0.901 1.224 - 1.586 1.854 - 1.954

0.5 0.359 - 0.878 1.208 - 1.521 1.801 - 1.863

0.6 0.447 - 0.863 1.201 - 1.476 1.756 - 1.829

0.7 0.542 - 0.849 1.200 - 1.432 1.727 - 1.800

0.8 0.638 - 0.835 1,201 - 1.376 1.723 - 1.772

0.9 0.727 - 0.818 1.200 - 1.298 1.724 - 1.745

1.0 0.801 1193 1.720

½

+ É Ã º e ”  . — ¸Ž  H @ /g A& h \  @ /K  4> h_  „    { ü <

4 > h_  „  • ¸ {  > í ß –÷ &# Q t   H X <, Å Òכ ¹  ½ ™× ¼Ì “ s E(Γ), E(L), E(X)“ É r „  • ¸{  þ j™ è° ú כ(conduction band minimum : CBM) \ " f „   {  þ j@ /° ú כ(valence band maximum : VBM)`  ¦  É ™ ° ú כÜ ¼– Ð ½ ¨½ + É Ã º e ”  . Table 2\ " f  H

Ga x In 1−x P y Sb z As 1−y−z /GaSb _  Å Òכ ¹ @ /g A& h \ " f_   ½ ™

×

¼Ì “ s    o Sb (7 £ ¤, z) 7 £ x \     # Qb  G>       H t 
 

? /% 3  .

Table 2 \ " f ˜ Ѝ  H  ü < ° ú  s , Ga x In 1−x P y

Sb z As 1−y−z /GaSb “ É r „   % ò % i \    5 g E(Γ) E(L)

Table 3. Lattice matching ranges and the corresponding VBM and band gaps for the MIR Ga x In 1−x P y

Sb z As 1−y−z /GaSb.

z x range Ga

x

In

1−x

P

y

Sb

z

As

1−y−z

VBM E

o

y range /GaSb (eV) (eV)

0.09 0 ≤ x ≤ 0.0023 Ga

0.002

In

0.998

Sb

0.09

As

0.91

0.043 0.271

0 ≤ y ≤ 0.0049 InP

0.049

Sb

0.09

As

0.91

0.042 0.271

0.11 0 ≤ x ≤ 0.023 Ga

0.023

In

0.977

Sb

0.11

As

0.89

0.051 0.260

0 ≤ y ≤ 0.047 InP

0.047

Sb

0.11

As

0.843

0.044 0.268

0.13 0 ≤ x ≤ 0.044 Ga

0.044

In

0.956

Sb

0.13

As

0.87

0.059 0.251

0 ≤ y ≤ 0.093 InP

0.093

Sb

0.13

As

0.777

0.048 0.274

0.15 0 ≤ x ≤ 0.065 Ga

0.065

In

0.935

Sb

0.15

As

0.85

0.067 0.243

0 ≤ y ≤ 0.138 InP

0.138

Sb

0.15

As

0.712

0.054 0.286

0.17 0 ≤ x ≤ 0.081 Ga

0.081

In

0.919

Sb

0.17

As

0.83

0.073 0.235

0 ≤ y ≤ 0.182 InP

0.182

Sb

0.17

As

0.648

0.062 0.306

0.19 0 ≤ x ≤ 0.107 Ga

0.107

In

0.893

Sb

0.19

As

0.81

0.080 0.233

0 ≤ y ≤ 0.227 InP

0.227

Sb

0.19

As

0.583

0.072 0.333

0.21 0 ≤ x ≤ 0.128 Ga

0.128

In

0.872

Sb

0.21

As

0.79

0.085 0.232

0 ≤ y ≤ 0.271 InP

0.271

Sb

0.21

As

0.519

0.084 0.368

Table 4. Comparison of our estimate with the experimental band gaps (300 K) [8] for the MIR Ga x In 1−x P y Sb z As 1−y−z /GaSb.

x y z E

o

(µm) E

o

(µm)

exp. ours

0.03 0.06 0.13 4.05 4.56

0.04 0.06 0.13 4.10 4.49

0.07 0.03 0.15 4.05 4.75

0.03 0.17 0.19 3.38 4.09

s


 E(X)˜ Ð   s `›    Œ •“ É r f ” ] X   ½ ™× ¼Ì “ s (direct gap)Ü ¼– Ð

 
 f ” ] X   ½ ™× ¼Ì “ s (E _o ) s   ) a  . ¢ ¸ô  Ç Sb 7 £ x † < Ê\ 



   ½ ™× ¼Ì “ s ° ú כs  & t   H  כ `  ¦ · ú ˜ à º e ”  .

MIR % ò % i  ì ø ͕ ¸^ ‰  H  ½ ™× ¼Ì “ s   © œ@ / 3 - 5 µm “   ì ø ͕ ¸

^

‰ (7 £ ¤, E o  0.41 eV ∼ 0.25 eV) \  ¦ { 9 ( Ž >   ) a  . Table 2 \ " f
 è ß –  ü < ° ú  s  GaSb \     & ñ ½ + ˝ ) a š ¸" é ¶  o½ + Ë Ó

ü

t ì ø ͕ ¸^ ‰ Ga x In _1−x P _y Sb _z As _1−y−z /GaSb ×  æ \ " f Sb  0.1{ 9  M : E ^o   H 0.265 eV s  9, Sb 0.2{ 9  M :  H 0.265 eV

≤ E _o ≤ 0.305 eV s Ù ¼– Ð, Sb 0.1 õ  0.2 % ò % i \ " f MIR ì

ø ͕ ¸^ ‰ H † d`  ¦ · ú ˜ à º e ”  .

MIR % ò % i _  Ga ^x In 1−x P y Sb z As 1−y−z /GaSb \  @ /ô  Ç

&

ñ x 9 ô  Ç „   & h  : £ ¤$ í `  ¦ · ú ˜  ˜ Ðl  0 AK , Sb\  ¦ 0.09 Â Ò '

 0.21  t  0.02 m ”  7 £ x r &  xü < y_     & ñ ½ + ˛ ¸| 

% ò

% i õ  VBM, Õ ªo “ ¦  ½ ™× ¼Ì “ s    o\  ¦ Table 3 \ 
 ? /

%

3  . Table 3 \ " f ˜ Ѝ  H  ü < ° ú  s  Sb 7 £ x ½ + Éà º2 Ÿ ¤ GaSb \     & ñ ½ + Ë r ~  ´ à º e ”   H x ü < y_  # 3 0 A V , # Qt  9, GaSb \ " f 0s % 3 ~   VBM ï  r 0 A z 7 £ x ½ + Éà º2 Ÿ ¤

VBM \  -t  ï  r 0 A  © œ@ /& h Ü ¼– Ð 7 £ x † < Ê`  ¦ · ú ˜ à º e ” % 3 



. l ó ø ͓   GaSb _  VBM   H 0 eV s “ ¦ ì Á œ× ¼Ì “ s(E _o )“ É r 0.801 eV \  q K , s  l ó ø Í\     & ñ ½ + Ër †   MIR % ò % i 

š

¸" é ¶  o½ + ËÓ ü t ì ø ͕ ¸^ ‰ GaInPSbAs/GaSb_  VBM   H 0 ˜ Ð



 ß ¼“ ¦  ½ ™× ¼Ì “ s“ É r 0.801 eV ˜ Ð   Œ •“ É r 0.41 eV ∼ 0.25 eV ° ú כ`  ¦ % 3 >   ) a  . s   H GaSb ü < MIR š ¸" é ¶  o½ + ËÓ ü t ì ø ͕ ¸

^

‰ Ga ^x In 1−x P y Sb z As 1−y−z _   â > €  \ " f ] j1+ þ Aì ø ͕ ¸^ ‰ (type I semiconductor)  H † d`  ¦ · ú ˜ à º e ” % 3  . s   H  



É r z  ´+ « >  7 Hë  H \ " f• ¸ Ga ^x In 1−x P y Sb z As 1−y−z /GaSb  ]

j1+ þ Aì ø ͕ ¸^ ‰ H † d`  ¦ µ 1 ߘ 2 ³   e ”   [3].

þ

j   H LPE ~ ½ ÓZ O \  _ K    & ñ $ í  © œr †   4 > h_  Ga x In 1−x P y Sb z As 1−y−z /GaSb Ò  re  ¦ \  @ /ô  Ç  ½ ™× ¼Ì “ s z 

´+ « >° ú כ(300K) [3]`  ¦ ‘ : r  7 Hë  H \ " f ½ ¨ô  Ç s  : r ° ú כõ  Table 4 \ " f q “ § % i  . Table 4 \ " f ˜ Ѝ  H  ü < ° ú  s  z  ´+ « >u  ü

< s  : r u   s \   H €  •ç ß –_  s  e ” 6 £ §`  ¦ · ú ˜ à º e ”  .

s

  H z  ´+ « >& h Ü ¼– Ð ½ ¨ô  Ç     & ñ ½ + Ëq (x,y,z) s  : r& h Ü ¼

–

Ð ½ ¨ô  Ç    & ñ ½ + Ëq  ((7)d ” )ü < s  e ” % 3 Ü ¼ 9, z  ´+ « >› ¸

|

(“ : r • ¸
     © œÃ º)1 p x Ü ¼– РÒ'  Ò q tU  ´ à º e ”   H š ¸  “ ¦ ì

 r$ 3  ) a  .

IV. + s Ç Â ] Ø

(i) š ¸" é ¶  o½ + ËÓ ü t Ga x In _1−x P _y Sb _z As _1−y−z /GaSb _  „  

% ò

% i \    • 2 ; Å Òכ ¹  ½ ™× ¼Ì “ s(E(Γ), E(L), E(X))`  ¦ UTB ~ ½ Ó Z O

Ü ¼– Ð > í ß –ô  Ç   õ  ; 0.265 eV ≤ E(Γ) ≤ 0.901 eV, 1.193

eV ≤ E(L) ≤ 1.586 eV, 1.720 eV ≤ E(X) ≤ 2.199 eV Ü ¼

–

Ð E(Γ) E(L)s 
 E(X) ˜ Ð   s `›    Œ •“ É r f ” ] X   ½ ™× ¼Ì “ s

`

 ¦
 ? /% 3  . (Table 1)

(ii) Ga _x In _1−x P _y Sb _z As _1−y−z /GaSb  H Sb  0.1 õ  0.2



s \ " f 0.265 eV ≤ E ^o ≤ 0.305 eV “   MIR % ò % i  ì ø ͕ ¸

^

‰ H † d`  ¦ · ú ˜ à º e ” % 3  . (Table 2)

(iii) MIR % ò % i  ì ø ͕ ¸^ ‰ GaInPSbAs_  VBM   H l ó ø ͓   GaSb \  q K  7 £ x   9,  ½ ™× ¼Ì “ s“ É r GaSb \  q K  y Œ ™™ è† < ÊÜ ¼

–

Ð, GaSb ü < MIR % ò % i ì ø ͕ ¸^ ‰ Ga x In 1−x P y Sb z As 1−y−z



s _  ] X ½ + ˀ  \ " f ] j1+ þ Aì ø ͕ ¸^ ‰ (type I semiconduc- tor)  H † d`  ¦ · ú ˜ à º e ” % 3  . (Table 3)

(iv) UTB \  _ ô  Ç s  : r& h  > í ß – x 9  ì  r$ 3 [ þ t s  z  ´+ « >    õ

[ þ t õ  q “ §& h  ¸ ú ˜ { 9 u  % i  . (Table 4)

P

c p 8 ý ò k >

‘

: r ƒ  ½ ¨  H 2007¸  • ¸  â l @ /† < Ɠ § “ §? /ƒ  ½ ¨q  t " é ¶ \  _  K

 à º' Ÿ ÷ &% 3  .

Y

c p w Š à U Ø ”  ô

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