Diode Bolometer䈱․ᕈ
䋺Characteristic of Diode Bolometer
䋱䇭ℂᗐDiode(Ideal Diode)
䋱䇭ℂᗐDiode䋨Ideal Diode)
䇭 䊶䌉䋭䌖․ᕈ䈫଀
䇭䇭䊶ᓸಽଥᢙ
䇭䇭䊶ㄭૃᑼ
䇭䇭䊶േ૞ὐ
䇭䇭䊶ᶖ⾌㔚ജ
䇭䇭䊶䌎୘⋥೉․ᕈ
䇭䇭䊶䌎୘ਗ೉․ᕈ
䊶䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ
䋲䇭⃻ታDiode(Real or Actual Diode)
䋳䇭Bolometer䈱ᕈ⢻Ყセ
䋴䇭Heat Model of Uncooled FPA IR Detector
䇭䇭(FPA IR䋺Focal Plane Array Infra Red)
䋨ᩣ䋩ർᎹ⛔วᛛⴚ⎇ⓥᚲ
[KUTELA Corporation]
Copyright (c) KUTELA Corporation 2009. All Rights Reserved
䋱䇭ℂᗐDiode䋨Ideal Diode)
䇭 䊶䌉䋭䌖․ᕈ䈫଀
䇭䇭䊶ᓸಽଥᢙ
䇭䇭䊶ㄭૃᑼ
䇭䇭䊶േ૞ὐ
䇭䇭䊶ᶖ⾌㔚ജ
䇭䇭䊶䌎୘⋥೉․ᕈ
䇭䇭䊶䌎୘ਗ೉․ᕈ
䊶䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ
2000A1890
1
2
i
䌉䋭䌖․ᕈ䈫଀
䋱䇭ℂᗐDiode(Ideal Diode)
䌉䋭䌖․ᕈ䈫଀
䌔䋫㰱䌔䋾䋰
i
䌔
䌖
䊶䌉䋭䌖․ᕈ䈫଀
䊶ᓸಽଥᢙ
䊶ㄭૃᑼ
䊶േ૞ὐ
䊶ᶖ⾌㔚ജ
䊶䌎୘⋥೉․ᕈ
䊶䌎୘ਗ೉․ᕈ
䊶䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ
䌖
䌔
䌔䋫㰱䌔䋾䋰
ExactExpession
㘻๺㔚ᵹ䋨Saturation Current䋩
i[ A] = i0 S [ A m2 ]S[ m 2 ]exp(−
iS ≡ i0 [ A]exp( −
qVG 
qV
qV



)  exp( ) − 1 = iS [ A]  exp( ) − 1 where V ≤ VG
kT 
kT
kT



qVG
) where i0 = i0 S S
kT
kT
i
ln( + 1)
V=
q
iS
i0䈲ធว㕙Ⓧ䋨䌓䋩䈮Ყ଀
i0S䋽䋱䋰䌞䋶䌾䋱䋰䌞䋱䋰[A/m^2]
Si,Ge╬䈱᧚ᢱ䇮CarrierỚᐲ䇮ਇ⚐‛䇮
⵾ㅧᛛⴚ╬䈪᳿䉁䉎䇯
q = 1.6 ×10−19 [C ], k = 1.38 ×10−23[ J ],
K
VG ( Si) = 1.12[V ], VG (Ge) = 0.66[V ],VG (GaAs) = 1.42[V ] at 300 K
3
䌉䋭䌖․ᕈ䈫଀
電圧正大領域：V kT
qV
⇔
1
q
kT
28mV at 330K
kT
≈ 26mV at 300K
q
q
1 1
1.12
0.66
[ ] where 300 K , exp(−
) ≈ 2 ×10−19 , exp(−
) ≈ 9.5 ×10−12
=
0.026
0.026
kT 0.026 V
䌉䋭䌖․ᕈ䈫଀
4
電圧ゼロ領域：V ≈ 0 ⇔ V ≤ 2.6mV
㸠10^-9
23mV at 270K
I 0 S = 107 [ A / m2 ]
η = 2 : Ideality Factor
I 0 S = 107 [ A / m 2 ]
S = 10−6 [m 2 ]
VG = 1.12[V ] : Si
VG = 1.12[V ]: Si
Green䋺300K
I 0 = 10[ A]
Blue䋺270K
I S ≈ 4 ×10−9 [ A] at 300 K
I 0 = 10[ A]
Red䋺330K
S = 10−6 [m2 ]
Red䋺330K
㔚ᵹ䋨䌁䋩
㔚ᵹ䋨䌁䋩
η = 2 : Ideality Factor
Green䋺300K
Blue䋺270K
I S ≈ 4 × 10 −9 [ A] at 300 K
Diode䈱᷷ᐲ䈏㜞䈇䈾䈬
᷷ᐲ਄᣹䈮ᢅᗵ
㔚࿶䋨䌖䋩
5
㔚࿶䋨䌖䋩
6
1
䌉䋭䌖․ᕈ䈫଀
電圧負大領域：V −
kT
qV
⇔
−1
q
kT
−
kT -23mV at 270K
≈
q -26mV at 300K
-28mV at 330K
㸠10^-8
Blue䋺270K
Green䋺300K
I 0 S = 107 [ A / m 2 ]
η = 2 : Ideality Factor
S = 10−6 [ m 2 ]
VG = 1.12[V ]: Si
㔚ᵹ䋨䌁䋩
䋱䇭ℂᗐDiode(Ideal Diode)
Red䋺330K
ᓸಽଥᢙ
Diode䈱᷷ᐲ䈏㜞䈇䈾䈬
᷷ᐲ਄᣹䈮ᢅᗵ
I 0 = 10[ A]
I S ≈ 4 ×10−9 [ A] at 300 K
䊶䌉䋭䌖․ᕈ䈫଀
䊶ᓸಽଥᢙ
䊶ㄭૃᑼ
䊶േ૞ὐ
䊶ᶖ⾌㔚ജ
䊶䌎୘⋥೉․ᕈ
䊶䌎୘ਗ೉․ᕈ
䊶䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ
7
㔚࿶䋨䌖䋩
8
ᓸಽଥᢙ
ExactSolution
1 V = 0 ⇒ i = 0
qV
qV  iS q 
qV
∂i i q 
 ≥ 0 where V ≥ 0
2 = S
VG (exp( ) − 1) − V exp( )  =
 (VG − V ) exp( ) − VG 
kT
kT  T kT 
kT
∂T T kT 
 ≤ 0 where V ≤ 0
q
qV
q
qV
∂i
exp( ) =
(i + iS ) ≥ 0 where iS ≡ i0 exp(− G )
= iS
kT
kT
kT
kT
∂V
∂i
1
qV 
diS iS qVG
∂V
T
∂
)  , =
−(VG − V ) + VG exp(−
= −
=
∂i T 
kT 
dT T kT
∂T
∂V
1 kT 
∂V
∂i −1 kT
qV
kT
q(VG − V )
kT 1
qV 
3 R ≡
exp(−
)=
exp(
)=
)
=( ) =
=
1 − exp(−
∂i
∂V
iS q
kT
i0 q
kT
q (i + iS ) i q 
kT 
1 dR
1  q(VG − V ) 
dR
k q(VG − V )
q(VG − V )
) =− (
− 1) exp(
⇒ = 1 −

kT
dT V = const
i0 q
kT
kT
R dT V = const T 

䋱䇭ℂᗐDiode(Ideal Diode)
ㄭૃᑼ
qV



dR
1k
qV
qV 
1 dR
1
kT
) exp(−
)  =
⇒ = 1−

1 − (1 +
dT i = const i q 
kT
kT 
R dT i = const T  exp( qV ) − 1 


kT


䊶䌉䋭䌖․ᕈ䈫଀
䊶ᓸಽଥᢙ
䊶ㄭૃᑼ
䊶േ૞ὐ
䊶ᶖ⾌㔚ജ
䊶䌎୘⋥೉․ᕈ
䊶䌎୘ਗ೉․ᕈ
䊶䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ
q = 1.6 ×10 −19 [C ], k = 1.38 ×10−23 [ J ],
K
300 K
VG ( Si) = 1.12[V ], VG (Ge) = 0.66[V ], VG (GaAs ) = 1.42[V ] at 1 1
q
=
[ ] where 300 K
kT 0.026 V
ㄭૃᑼ䋱
i = i0 exp(−
電圧正大領域：V kT
qV
⇔
1 ⇔ V 26mV (300K ) ⇔ V ≥ 0.26V (300K )
q
kT
qVG 
qV
qV
qV

)  exp( ) − 1 ≈ iS exp( ) where V ≤ VG , iS ≡ i0 exp(− G )
kT 
kT
kT
kT

∂i iS q 
qV

=
 (VG − V ) exp( ) − VG 
∂T T kT 
kT

i q 
qV  T ∂i q(VG − V )
i
≈ S
≈
= − ln( ) ≥ 0
 (VG − V ) exp( )  ⇒
T kT 
kT 
i ∂T
kT
i0
∂i
q
qV
kT
qV
= iS
exp( ) , R =
exp(−
)
∂V
kT
kT
iS q
kT
qV
k
i
T ∂V
V −V
1
∂V 1 

) − 1)  ≈ − (VG − V ) ≈ ln( ) ⇒
=  V + VG (exp(−
≈− G
kT
T
q i0
V ∂T
V
∂T T 

T dR
1 dR
1  q(VG − V ) 
 q(VG − V ) 
= 1 −
⇒ ≈ 1 −
 ≤0
R dT V =const T 
kT
R dT V = const 
kT


qV


Bias㔚ജᱜᏫㆶലᨐ䋨᷷ᐲ਄᣹㸢ૐᛶ᛫䋩
 1
T dR
1 dR
1
kT
= 1 −
⇒ ≈1≥ 0
 ≈ R dT i =const T  exp( qV ) − 1  T
R dT i = const


kT


Bias㔚ജ⽶Ꮻㆶലᨐ䋨᷷ᐲ਄᣹㸢㜞ᛶ᛫䋩
V
10
9
kT
qV
qV
qV
⇔
1 , i ≈ iS exp( ) where V ≤ VG , iS ≡ i0 exp(− G )
q
kT
kT
kT
∂i iS q 
qV  T ∂i q (VG − V )
∂i
q
qV
∂V
T ∂V
V −V
1
≈
≈
≥ 0 ≈− G
, = iS
exp( ) , ≈ − (VG − V ) ⇒
 (VG − V ) exp( )  ⇒
∂T T kT 
∂V
∂T
kT 
i ∂T
kT
kT
kT
T
V ∂T
V11
ㄭૃᑼ䋲
電圧零近傍：V ≤ 0.1×
kT
⇔ V ≤ 2.6mV (300K )
q
(exp( x ) ≈ 1 + x where x 1)
qVG 
qV
qV
qV
qV



)  exp( ) − 1 ≈ iS 1 + ( ) − 1 = iS
where iS ≡ i0 exp( − G )
kT 
kT
kT
kT
kT



∂i iS q 
qV
qV
 iS q 

) − VG 
=
 (VG − V ) exp( ) − VG  ≈
 (VG − V )(1 +
kT
kT
∂T T kT 
 T kT 

i q 
qV  iS qV  qVG  iS qV  qVG  T ∂i  qVG 
VG  ≈
− 1 ≈
≈
≈ S


⇒

 −V +
T kT 
kT
i ∂T  kT 
 T kT  kT 
 T kT  kT
q
qV
q
qV
q
∂i
exp( ) ≈ iS
(1 +
) ≈ iS
= iS
kT
kT
kT
kT
kT
∂V
qV
V qV
V qV
T ∂V
qV
∂V 1 

) − 1)  ≈ − ( G − 1) ≈ − ( G ) ⇒
=  V + VG (exp(−
≈ −( G ) ≤ 0
kT
T kT
T kT
V ∂T
kT
∂T T 

i = i0 exp(−
T dR
qV
1 dR
1  q(VG − V ) 
1 qVG
⇒ ≈− G ≤0
= 1 −
≈−
R dT V = const
kT
R dT V = const T 
kT
T kT

qV


Bias㔚ജᱜᏫㆶലᨐ䋨᷷ᐲ਄᣹㸢ૐᛶ᛫䋩

T dR
1 dR
1
kT
= 1 −
⇒ ≈0
 ≈ 0 R dT i =const T  exp( qV ) − 1 
R dT i =const


kT


qV
qV
where iS ≡ i0 exp(− G )
kT
kT
∂i iS qV  qVG  T ∂i  qVG 
∂i
q
∂V
V qV
T ∂V
qV
, ≈ iS
, ≈ − ( G ) ⇒
≈
≈
≈ −( G ) ≤ 0

⇒
 12
∂T T kT  kT 
i ∂T  kT 
∂V
kT
∂T
T kT
V ∂T
kT
, i ≈ iS
V ≈ 0 2
ㄭૃᑼ䋳
電圧負大領域：V −
kT
qV
⇔
−1 ⇔ V −26 mV (300 K ) ⇔ V ≤ −0.26V (300 K )
q
kT
qVG 
qV
qV

)  exp( ) − 1 ≈ −iS where iS ≡ i0 exp(− G )
kT 
kT
kT

∂i iS q 
qV
iS qVG
 iS q
=
≤0
( −VG ) = −
 (VG − V ) exp( ) − VG  ≈
∂T T kT 
kT
T kT
 T kT
T ∂i qVG
⇒
≈
≥0
i ∂T
kT
∂i
q
qV
= iS
exp( ) ≈ 0 （Ｉ−Ｖ特性で水平）
∂V
kT
kT
∂V 1 
qV
qV  T ∂V VG
qV
 1
=  V + VG (exp(−
) ⇒
exp(−
)
≈
) − 1)  ≈  VG exp(−
∂T T 
kT
kT  V ∂T V
kT
 T
䋱䇭ℂᗐDiode(Ideal Diode)
i = i0 exp(−
േ૞ὐ
㕖Ᏹ䈮ᄢ䋺ਇ቟ቯ
1 dR
1  q(VG − V ) 
1  q(VG − V ) 
T dR
 q(VG − V ) 
1−
=
⇒ ≈ −
 ≈ −T 
 ≤0
R dT V =const T 
kT
kT
R dT V =const
kT





qV


Bias㔚ജᱜᏫㆶലᨐ䋨᷷ᐲ਄᣹㸢ૐᛶ᛫䋩
 1 qV
T dR
qV
1 dR
1
kT
≥0
= 1 −
⇒ ≈
≈
R dT i = const T  exp( qV ) − 1  T kT
R dT i = const kT


ਇ቟ቯ
kT


䊶䌉䋭䌖․ᕈ䈫଀
䊶ᓸಽଥᢙ
䊶ㄭૃᑼ
䊶േ૞ὐ
䊶ᶖ⾌㔚ജ
䊶䌎୘⋥೉․ᕈ
䊶䌎୘ਗ೉․ᕈ
䊶䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ
kT
qV
qV
, i ≈ −iS where iS ≡ i0 exp( − G )
⇔
−1 q
kT
kT
∂i
iS qVG
T ∂i qVG
∂i
q
qV
T ∂V VG
qV
, = iS
exp( ) ≈ 0 , exp( −
)
≈−
≤ 0 ⇒
≈
≥ 0 ≈
∂T
T kT
i ∂T
kT
∂V
kT
kT
V ∂T V
kT 13
V −
േ૞ὐ䋨V㻍0䋩
േ૞ὐ䋨৻⥸䋩
+
䌖1
i
+
V1/r
i
r
14
䌖1
䌔
䌖x
V1
iX = iS
ix
䌖
qVX
kT
dVX
V
=− X
dT
T
䌖
䌔
⽶⩄⋥✢
䌖x
qV


i X = iS  exp( X ) − 1
kT


V1 = riX + V X ⇒ iX =
r䋺ᄢ
V1 VX
−
r
r
VX qVG q (riS )
T kT kT
qVG
−1
diX iX kT
=
dT T q(riS ) + 1
kT
i qVG
≈ X
T kT
qV
q (ri )
Since G 1 S 1
kT
kT
䌖x
Diodeᦛ✢
⽶⩄⋥✢
V1 = ri X + V X
⽶⩄⋥✢䈫䉻䉟䉥䊷䊄ᦛ✢䈱੤ὐ䈏േ૞ὐ䇭㸢䇭৻⥸⊛䈮䈲⸃ᨆ⸃䈲᳞䉁䉌䈭䈇
15
qVG
−1
kT
kT
+1
q(riS )
≈−
ix
r䋺ዊ
㔚ᵹ䋨䌁䋩
Diodeᦛ✢
V1
q(riS )
+1
kT
1
V
iX = 1
r kT + 1
q (riS )
VX =
ix
r
16
㔚࿶䋨䌖䋩
ᶖ⾌㔚ജ䋨ၮᧄᑼ䋩
ᶖ⾌㔚ജP(W)䈲㔚ᵹ䈮㔚࿶䉕䈎䈔䉏䈳⦟䈇
䋱䇭ℂᗐDiode(Ideal Diode)
ᶖ⾌㔚ജ
ExactExpession
䊶䌉䋭䌖․ᕈ䈫଀
䊶ᓸಽଥᢙ
䊶ㄭૃᑼ
䊶േ૞ὐ
䊶ᶖ⾌㔚ജ
䊶䌎୘⋥೉․ᕈ
䊶䌎୘ਗ೉․ᕈ
䊶䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ
P[W ] = V [V ]i[ A] = V × i0 S [ A m 2 ]S[ m 2 ]exp(−
qV


= V × iS [ A]  exp( ) − 1 where V ≤ VG
kT


qV
iS ≡ i0 [ A]exp(− G ) where i0 = i0 S S
kT
i0S䋽䋱䋰䌞䋶䌾䋱䋰䌞䋱䋰[A/m^2]
kT
i
Si,Ge╬䈱᧚ᢱ䇮CarrierỚᐲ䇮ਇ⚐‛䇮
ln( + 1)
V =
⵾ㅧᛛⴚ╬䈪᳿䉁䉎䇯
q
iS
ExactExpession
P = Vi0 S S exp( −
17
qVG 
qV

)  exp( ) − 1
kT 
kT

RealDiode
qVG 
qV

) exp( ) − 1
kT 
kT


q(VG − V − VP ) 
)
P = Vi0 S S  exp(−
η kT


18
3
ᶖ⾌㔚ജ䋨䉫䊤䊐䋩䋺㗅Bias
i
ᶖ⾌㔚ജ䋨䉫䊤䊐䋩䋺ㅒBias
䌔䋫㰱䌔䋾䋰
i
ቯ㔚࿶㚟േDiode䈪ᾲᐔⴧ䈱ᤨ䋺
䇭䇭ᄖ⊛䈭ᾲ䉣䊈䊦䉩䉕ട䈋䉎䈫䇮Diode᷷ᐲ䈏਄᣹䈚䇮
䌔
䈖䈱㕙Ⓧ䈏᷷ᐲ䌔䋫㰱䌔
䈪䈱ᶖ⾌㔚ജ
ቯ㔚࿶㚟േDiode䈪ᾲᐔⴧ䈱ᤨ䋺
䇭䇭ᄖ⊛䈭ᾲ䉣䊈䊦䉩䉕ട䈋䉎䈫䇮Diode᷷ᐲ䈏਄᣹䈚䇮
䈖䈱㕙Ⓧ䈏᷷ᐲT
䈪䈱ᶖ⾌㔚ജ
䇭䇭 Diode䈪䈱ᶖ⾌㔚ജ䈏Ⴧട䈚䇮䈘䉌䈮᷷ᐲ䈏਄᣹䈜䉎䇯
䌔䋫㰱䌔䋾䋰
䌔
䇭䇭 Diode䈪䈱ᶖ⾌㔚ജ䈏Ⴧട䈚䇮䈘䉌䈮᷷ᐲ䈏਄᣹䈜䉎䇯
ቯ㔚࿶Bias
Bias㔚ജᱜᏫㆶലᨐ
Bias㔚ജᱜᏫㆶലᨐ
䈖䈱㕙Ⓧ䈏᷷ᐲT䈪䈱ᶖ⾌㔚ജ
䌖
䌔
i
䌔䋫㰱䌔䋾䋰
䌔䋫㰱䌔䋾䋰
䌔
䈖䈱㕙Ⓧ䈏᷷ᐲ䌔䋫㰱䌔
䈪䈱ᶖ⾌㔚ജ
䌖
䌔
ቯ㔚࿶Bias
䌔䋫㰱䌔䋾䋰
ቯ㔚ᵹ㚟േDiode䈪ᾲᐔⴧ䈱ᤨ䋺
䇭䇭ᄖ⊛䈭ᾲ䉣䊈䊦䉩䉕ട䈋䉎䈫䇮Diode᷷ᐲ䈏਄᣹䈜䉎䈏䇮
䈖䈱㕙Ⓧ䈏᷷ᐲ䌔䋫㰱䌔
䈪䈱ᶖ⾌㔚ജ
䌔䋫㰱䌔䋾䋰
䌔
䇭䇭Diode䈪䈱ᶖ⾌㔚ജ䈏ᷫዋ䈚䇮᷷ᐲ䈲⷗ដ䈾䈬਄᣹䈚䈭䈇䇯
ቯ㔚ᵹBias
i
ቯ㔚ᵹ㚟േDiode䈪ᾲᐔⴧ䈱ᤨ䋺㕖Ᏹ䈮ਇ቟ቯ
Bias㔚ജ⽶Ꮻㆶലᨐ
䈖䈱㕙Ⓧ䈏᷷ᐲT䈪䈱ᶖ⾌㔚ജ
䌖
䌔
䌖
䌔
䌔䋫㰱䌔䋾䋰
ቯ㔚ᵹBias
䌔䋫㰱䌔䋾䋰
䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䋨Diode᷷ᐲ䉶䊮䉰䋩
Bias㔚ജᱜᏫㆶലᨐ䋨᷷ᐲ਄᣹㸢ૐᛶ᛫䋩䋺ቯ㔚࿶Bias䈱ᤨ䇮Bais㔚ജ䈏Ⴧട䈚᷷ᐲᄌൻ䈮ᢅᗵ䈮䈭䉎䇯
19
Bias㔚ജ⽶Ꮻㆶലᨐ䋨᷷ᐲ਄᣹㸢㜞ᛶ᛫䋩䋺ቯ㔚ᵹBias䈱ᤨ䇮Bais㔚ജ䈏ᷫዋ䈚᷷ᐲᄌൻ䈮㊰ᗵ䈮䈭䉎䇯
䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䋨Diode᷷ᐲ䉶䊮䉰䋩
Bias㔚ജᱜᏫㆶലᨐ䋨᷷ᐲ਄᣹㸢ૐᛶ᛫䋩䋺ቯ㔚࿶Bias䈱ᤨ䇮Bias㔚ജ䈏Ⴧട䈚᷷ᐲᄌൻ䈮ᢅᗵ䈮䈭䉎䇯
20
Bias㔚ജ⽶Ꮻㆶലᨐ䋨᷷ᐲ਄᣹㸢㜞ᛶ᛫䋩䋺ቯ㔚ᵹBias䈱ᤨ䇮Bias㔚ജ䈏ᷫዋ䈚᷷ᐲᄌൻ䈮㊰ᗵ䈮䈭䉎䇯
ᶖ⾌㔚ജ䋨ᓸಽଥᢙㄭૃᑼ䋩䋺㔚࿶৻ቯ
䇭䇭䇭䇭䇭ో䈩ᱜ୯㸢Bias㔚ജᱜᏫㆶലᨐ
ᶖ⾌㔚ജ䋨ᓸಽଥᢙ䋩
dP ∂V
∂i
i
qV
i q 
qV


=
i +V
= V + VG (exp(−
) − 1)  + V S
 (VG − V ) exp( ) − VG 
dT ∂T
∂T T 
kT
T kT 
kT


qV 
qV
qV
qV



i0 S = 106 ∼ 108 [ A m 2 ]
i = i0 S S exp(− G )  exp( ) − 1 = iS  exp( ) − 1 where; iS ≡ i0 S S exp(− G ), kT 
kT
kT
kT



dP ∂V
qV
i q 
qV
∂i i 


i +V
=
=  V + VG (exp(−
) − 1)  + V S
 (VG − V ) exp( ) − VG 
dT ∂T
kT
T kT 
kT
∂T T 


qV 
qV
qV
qV



i0 S = 106 ∼ 108 [ A m 2 ]
i = i0 S S exp(− G )  exp( ) − 1 = iS  exp( ) − 1 where; iS ≡ i0 S S exp(− G ), kT 
kT
kT
kT



電圧正大領域：V ExactExpession
1 dP
V iS q 
qV
qV
qVG
 Vi0 S q 

=
)
 (VG − V ) exp( ) − VG  =
 (VG − V ) exp( ) − VG  exp( −
S dT V = CONST S T kT 
kT
kT
kT
 T kT 

Vi0 S q 
q(VG − V )
qVG 
=
(VG − V ) exp(−
) − VG exp(−
)
T kT 
kT
kT 
=
ᶖ⾌㔚ജ䋨ᓸಽଥᢙㄭૃᑼ䋩䋺㔚ᵹ৻ቯ
䇭䇭䇭䇭ో䈩⽶୯㸢Bias㔚ജ⽶Ꮻㆶലᨐ
P S = Vi0S exp(−
=
kT
qV
⇔
1 ⇔ V 26mV (300K ) ⇔ V ≥ 0.26V (300 K )
q
kT
1 dP
S dT
=
I =CONST
I = CONST
1 dP
S dT
=−
I =CONST
1 (VG − V ) P
T
V
S
i ∂V
V qV
qV  qV 
∂V
V qV
≈ − ( G )i0 S exp(− G ) 
≈− ( G)
 ≤ 0, where,
S ∂T
T kT
kT  kT 
∂T
T kT
電圧負大領域：V −
1 dP
S dT
kT
⇔ V ≤ 2.6mV (300K )
q
kT
qV
⇔
−1 ⇔ V −26mV (300 K ) ⇔ V ≤ −0.26V (300 K )
q
kT
kT
qV
⇔
−1 ⇔ V −26mV (300 K ) ⇔ V ≤ −0.26V (300 K )
q
kT
1 dP
V ∂i
Vi qV
qV
∂i
i qV
=
≈ − 0 S G exp(− G ) ≥ 0(∵V ≤ 0), where
≈− S G ≤0
S dT V =CONST S ∂T
T kT
kT
∂T
T kT
䌎୘⋥೉․ᕈ
i (V − V )
1
i ∂V
q(VG − V )
∂V
exp(−
) ≤ 0, where
≈ − 0S G
≈ − (VG − V )
S ∂T
T
kT
T
∂T
電圧零近傍：V ≤ 0.1×
V ∂i
V i0 S q V q V G
∂i
i qV  q VG 
≈
≥ 0, w h ere
≈ S
S ∂T
T kT kT
T k T  k T 
∂T
22
䋱䇭ℂᗐDiode(Ideal Diode)
dP ∂V
qV
i q 
qV
∂i i 


i +V
=
=  V + VG (exp(−
) − 1)  + V S
 (VG − V ) exp( ) − VG 
dT ∂T
kT
T kT 
kT
∂T T 


qVG 
qV
qV
qVG



i0 S = 106 ∼ 108 [ A m 2 ]
i = i0 S S exp(−
)  exp( ) − 1 = iS  exp( ) − 1 where; iS ≡ i0 S S exp(−
), kT 
kT
kT
kT



I =CONST
=
V =CONST
1 dP
1 q(VG − V ) P
≈
S dT V =CONST T
kT
S
kT
⇔ V ≤ 2.6mV (300K )
q
qVG 
qV

)  exp( ) − 1
kT 
kT

ExactExpession
電圧正大領域：V 電圧零近傍：V ≤ 0.1×
電圧負大領域：V −
21
kT
qV
⇔
1 ⇔ V 26mV (300K ) ⇔ V ≥ 0.26V (300 K )
q
kT
1 dP
V ∂i Vi0 S q(VG − V )
q(VG − V )
∂i i0 S S q 
q(VG − V ) 
=
≈
≈
exp(−
) ≥ 0, where
)
 (VG − V ) exp(−
∂T
S dT V =CONST S ∂T
T
kT
kT
T kT 
kT

1 dP
S dT
1 i
qV 
)
 −(VG − V ) + VG exp( −
ST
kT 
I =CONST
qV  
q(VG − V )
qV 
i0 S 
)  exp(−
) − exp(− G ) 
=
 −(VG − V ) + VG exp(−
T 
kT  
kT
kT 
1 dP
S dT
qVG 
qV

)  exp( ) − 1
kT 
kT

ExactExpession
ExactExpession
1 dP
S dT
P S = Vi0S exp(−
䊶䌉䋭䌖․ᕈ䈫଀
䊶ᓸಽଥᢙ
䊶ㄭૃᑼ
䊶േ૞ὐ
䊶ᶖ⾌㔚ജ
䊶䌎୘⋥೉․ᕈ
䊶䌎୘ਗ೉․ᕈ
䊶䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ
㕖Ᏹ䈮ਇ቟ቯ
i ∂V
i V
q(VG + V )
∂V 1 
qV 
=
≈ − 0 S G exp( −
) ≤ 0, where
≈  VG exp( −
)
S ∂T
T
kT
∂T T 
kT 
23
24
4
䌎୘⋥೉․ᕈ䋨䌉䋭䌖․ᕈ䋩
i
䋱୘
i
䌖S
䌎୘⋥೉․ᕈ䋨ᓸಽଥᢙ䋩
䋲୘
V䋺৻୘䈱䉻䉟䉥䊷䊄䈮䈎䈎䉎㔚࿶
VS䋺ో㔚࿶
VS
を代入
n
䋱୘
ExactExpession
m
2
1 VS = 0 ⇒ i = 0
䌖S
䋲୘
i[ A] = i0 S [ A
㘻๺㔚ᵹ䋨Saturation Current䋩
]S[m 2 ]exp(−
qVG 
q VS
q VS



)  exp(
) − 1 = iS [ A]  exp(
) − 1 where VS ≤ nVG kT 
kT n
kT n



qV
iS ≡ i0 [ A]exp( − G ) where i0 = i0 S S （i0 , iSは１個のdiodeの値）
kT
i0S䋽䋱䋰䌞䋶䌾䋱䋰䌞䋱䋰[A/m^2]
VS kT
i
Si,Ge╬䈱᧚ᢱ䇮CarrierỚᐲ䇮ਇ⚐‛䇮
i0䈲ធว㕙Ⓧ䋨䌓䋩䈮Ყ଀
ln( + 1)
=
⵾ㅧᛛⴚ╬䈪᳿䉁䉎䇯
n
q
iS
q = 1.6 ×10 −19 [C ], k = 1.38 ×10−23[ J ],
K
VG ( Si ) = 1.12[V ],VG (Ge) = 0.66[V ],VG (GaAs ) = 1.42[V ] at 300 K
１個のDiodeの式のV の所に
nkT
q VS
q VS
qV
⇔
, i ≈ iS exp(
) where VS ≤ VG , iS ≡ i0 exp(− G )
1 q
kT n
kT n
kT
V
q(VG − S )
∂i iS q 
∂i
VS
q VS  T ∂i
q
q VS
n ≥ 0 ≈
V
−
⇒
≈
=
i
(
)
exp(
)
,
exp(
) S
 G

∂T T kT 
n
kT n 
i ∂T
kT
∂VS
nkT
kT n
∂VS
n
V 
T ∂VS
≈ −  VG − S  ⇒
≈−
∂T
T
n  VS ∂T
VG −
VS
n
26
䋱䇭ℂᗐDiode(Ideal Diode)
VS
n
䌎୘ਗ೉․ᕈ
q VS
qV
where iS ≡ i0 exp( − G )
kT n
kT
∂i iS q VS  qVG  T ∂i  qVG 
∂i
q
≈
⇒
≈
, ≈ iS
∂T T kT n  kT 
i ∂T  kT 
∂VS
nkT
∂ VS
VS qVG
T ∂VS
qVG
≈− (
≈ −(
)⇒
)≤0
∂T
T kT
VS ∂T
kT
VS ≈ 0 , i ≈ iS
㔚࿶㔖ㄭற
q = 1.6 ×10−19 [C ], k = 1.38 ×10−23 [ J ],
K
VG ( Si ) = 1.12[V ], VG (Ge) = 0.66[V ],VG (GaAs) = 1.42[V ] at 300 K
VS
を代入
n
VS V ≤ 2.6mV (300K )
∂i
∂V
n V
q VS

) − 1) 
S = − ∂T =  S + VG (exp(−
∂i
T n
kT n
∂T

∂VS
25
䌎୘⋥೉․ᕈ䋨ᓸಽଥᢙㄭૃᑼ䋩
V ≥ 0.26V (300 K )
∂i i q 
q VS
V
q VS  iS q 
VS
q VS
 ≥ 0 where VS ≥ 0
2 = S
) − 1) − ( S ) exp(
) =
) − VG 
VG (exp(
 (VG − ) exp(
∂T T kT 
kT n
n
kT n  T kT 
n
kT n
 ≤ 0 where VS ≤ 0
∂i
q
q VS
q
qVG
= iS
)
exp(
)=
(i + iS ) ≥ 0 where iS ≡ i0 exp(−
∂VS
nkT
kT n
nkT
kT
q
1 1
=
[ ] where 300 K
kT 0.026 V
q
1 1
=
[ ] where 300 K
kT 0.026 V
㔚࿶ᱜᄢ㗔ၞ
VS
を代入
n
ExactSolution(VS = nV )
䌖
１個のDiodeの式のV の所に
１個のDiodeの式のV の所に
䊶䌉䋭䌖․ᕈ䈫଀
䊶ᓸಽଥᢙ
䊶ㄭૃᑼ
䊶േ૞ὐ
䊶ᶖ⾌㔚ജ
䊶䌎୘⋥೉․ᕈ
䊶䌎୘ਗ೉․ᕈ
䊶䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ
nkT
q VS
qV
⇔
−1 , i ≈ −iS where iS ≡ i0 exp(− G )
q
kT n
kT
∂i
iS qVG
T ∂i qVG
∂i
q
q VS
≈−
≤ 0 ⇒
≈
≥ 0 , = iS
exp(
) ≈ 0 T kT
i ∂T
kT
nkT
kT n
∂T
∂VS
VS −
㔚࿶⽶ᄢ㗔ၞ
V ≤ −0.26V (300K )
T ∂VS nVG
q VS
≈
exp(−
)
VS ∂T
VS
kT n
27
䌎୘ਗ೉․ᕈ䋨䌉䋭䌖․ᕈ䋩
iP
䋲୘
䋱୘
28
䌎୘ਗ೉․ᕈ䋨ᓸಽଥᢙ䋩
iP
１ 個 の Diodeの 式の iの所 に
i
䌖
iP
を代 入
n
ExactSolution
i䋺৻୘䈱䉻䉟䉥䊷䊄䈮ᵹ䉏䉎㔚ᵹ
iP䋺ో㔚ᵹ
１ 個 の Diodeの 式の iの所 に
1 V = 0 ⇒ iP = 0
䋲୘
ExactExpession
㘻๺㔚ᵹ䋨Saturation Current䋩
iP [ A] = ni0 S [ A m 2 ]S[ m2 ]exp( −
iS ≡ i0 [ A]exp( −
V=
qVG 
qV
qV



)  exp( ) − 1 = niS [ A]  exp( ) − 1 where V ≤ VG kT 
kT
kT



qVG
) where i0 = i0 S S （i0 , iS ,Sは１個のdiodeの値）
kT
kT
i
ln( P + 1)
q
niS
−19
䌖
䋱୘
iP
を代 入
n
i0䈲ធว㕙Ⓧ䋨䌓䋩䈮Ყ଀
i0S䋽䋱䋰䌞䋶䌾䋱䋰䌞䋱䋰[A/m^2]
Si,Ge╬䈱᧚ᢱ䇮CarrierỚᐲ䇮ਇ⚐‛䇮
⵾ㅧᛛⴚ╬䈪᳿䉁䉎䇯
−23
q = 1.6 ×10 [C ], k = 1.38 × 10 [ J
],
K
VG ( Si) = 1.12[V ],VG (Ge) = 0.66[V ],VG (GaAs) = 1.42[V ] at 300 K
q
1 1
=
[ ] where Si and 300 K
kT 0.026 V
∂i
i q 
qV
qV 
iS q 
qV
 ≥ 0 where V ≥ 0
2 P = n S
 VG (exp( ) − 1) − V exp( )  = n
 (VG − V )exp( ) − VG  ≤ 0 where V ≤ 0
T kT 
kT
kT 
T kT 
kT
∂T

q
qV
q iP
qV
∂i
exp( ) = n
( + iS ) ≥ 0 where iS ≡ i0 exp(− G )
P = niS
kT
kT
kT n
kT
∂V
∂iP
1
qV
∂V

) − 1) 
= − ∂T = V + VG (exp(−
∂iP T 
kT
∂T

∂V
q = 1.6 × 10−19 [C ], k = 1.38 ×10−23[ J
],
K
300 K
VG (Si ) = 1.12[V ], VG (Ge) = 0.66[V ],VG (GaAs ) = 1.42[V ] at 1 1
q
=
[ ] where Si and 300 K
kT 0.026 V
29
30
5
䌎୘ਗ೉․ᕈ䋨ᓸಽଥᢙㄭૃᑼ䋩
V
㔚࿶ᱜᄢ㗔ၞ
V ≥ 0.26V (300 K )
１ 個 の Diodeの 式の iの所 に
iP
を代 入
n
䋱䇭ℂᗐDiode(Ideal Diode)
qV
kT
qV
qV
⇔
1 , iP ≈ niS exp( ) where V ≤ VG , iS ≡ i0 exp( − G )
q
kT
kT
kT
∂iP
i q 
qV  T ∂iP q(VG − V )
∂i
q
qV
≈n S
≈
≥ 0 , P = niS
exp( )
 (VG − V ) exp( )  ⇒
∂T
∂V
T kT 
kT  iP ∂T
kT
kT
kT
∂V
T ∂V
V −V
1
≈ − (VG − V ) ⇒
≈− G
∂T
T
V ∂T
V
䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ
䇭䇭䇭䇭䇭䇭䋨Diode䉕᷷ᐲ䉶䊮䉰䈫䈚䈩↪䈇䉎ᤨ䋩
qV
qV
where iS ≡ i0 exp( − G )
kT
kT
∂i
qV  qVG  T ∂iP  qVG 
q
≈
, P ≈ niS

⇒
 ∂V
kT  kT  iP ∂T  kT 
kT
qV
T ∂V
qV
≈ −( G ) ≤ 0
( G)⇒
kT
V ∂T
kT
V ≈ 0 , iP ≈ niS
㔚࿶㔖ㄭற
V ≤ 2.6mV (300K )
∂iP
i
≈n S
∂T
T
∂V
V
≈−
∂T
T
䊶䌉䋭䌖․ᕈ䈫଀
䊶ᓸಽଥᢙ
䊶ㄭૃᑼ
䊶േ૞ὐ
䊶ᶖ⾌㔚ജ
䊶䌎୘⋥೉․ᕈ
䊶䌎୘ਗ೉․ᕈ
䊶䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ
kT
qV
qV
⇔
−1 , iP ≈ −niS where iS ≡ i0 exp( − G )
q
kT
kT
∂iP
i qVG
T ∂iP qVG
∂i
q
qV
≈ −n S
≤ 0 ⇒
≈
≥ 0 , P = niS
exp( ) ≈ 0
∂T
T kT
iP ∂T
kT
∂V
kT
kT
V −
㔚࿶⽶ᄢ㗔ၞ
V ≤ −0.26V (300K )
T ∂V VG
qV
≈
exp( −
)
V ∂T V
kT
31
䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ䋨䉫䊤䊐䋩
䇭䇭䇭䋨Diode䉕᷷ᐲ䉶䊮䉰䈫䈚䈩↪䈇䉎ᤨ䋩
i
䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ䋨ᑼ䋺⋥೉䋩
䊶㗅ቯ㔚࿶Bais䈪䈲ᗵᐲ䈲䋱୘䈫ห䈛
䊶⋥೉䈱ലᨐή䈚
䊶Bias㔚ജᱜᏫㆶലᨐ
䋱୘
i
32
䊶㗅ቯ㔚ᵹBias䈪䈲⋥೉䈱ᗧ๧᦭䉍
䊶䋱୘䈱䌮୚ᗵᐲ਄᣹
䊶Bias㔚ജ⽶Ꮻㆶലᨐ
䌖S
䋲୘
䊶ㅒቯ㔚࿶Bias䈪䈲ਗ೉䈱ᗧ๧᦭䉍 iP
䊶䋱୘䈱䌮୚ᗵᐲ਄᣹
䊶Bias㔚ജᱜᏫㆶലᨐ
ᵈ䋩White Noise䈱ૐᷫኻ╷ᔅⷐ
䋲୘
nkT
T ∂i
⇒ ≈
q
i ∂T
q(VG −
kT
VS
V
)
VG − S
T ∂VS
n n
≈−
, VS
VS ∂T
n
ቯ㔚ᵹBias
iP
㔚࿶⽶ᄢ㗔ၞ VS −
䌖
䌖
䋱୘
䋲୘
ㅒቯ㔚ᵹBias䈲㕖Ᏹ䈮ਇ቟ቯ䇯
䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ䋨ᑼ䋺ਗ೉䋩
ਗ೉
䇭䇭䇭䋨Diode䉕᷷ᐲ䉶䊮䉰䈫䈚䈩↪䈇䉎ᤨ䋩
ቯ㔚࿶Bias
㔚࿶ᱜᄢ㗔ၞ
ਗ೉䈱ᗧ๧䈭䈚
T ∂iP  qVG 
T ∂V
qV
≈
≈ −( G )
, iP ∂T  kT 
V ∂T
kT
㔚࿶㔖ㄭற V ≈ 0 ⇒ 33
iP = ni
PFCV
∂iP n q(VG − V )
≈
i
∂T T
kT
kT
T ∂i
q(VG − V )
T ∂V
V −V
V
, ⇒ P ≈
≈− G
q
iP ∂T
kT
V ∂T
V
⊒ᾲᄢ䋨No Good䋩
nkT
T ∂i qVG
T ∂VS nVG
q VS
⇒ ≈
≈
, exp(−
) No Good
q
i ∂T
kT
VS ∂T
VS
kT n
ቯ㔚࿶Bias
㕖Ᏹ䈮ᄢ䈐䈭୯㸢ਇ቟ቯ
SFCC䋺Series Forward Constant Current ; OFCV䋺One Diode Forward Constant Voltage
SSCC䋺Series Small Constant Current ; PRCV䋺Parallel Reverse Constant Voltage
PFCV䋺Parallel Forward Constant Voltage
34
䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ䋨䉁䈫䉄䋩
䇭䇭䇭䇭䋨Diode䉕᷷ᐲ䉶䊮䉰䈫䈚䈩↪䈇䉎ᤨ䋩
䋱䇭㗅ᣇะቯ㔚࿶Bias䈪䈲䇮䌎୘⋥೉䈲䋱୘䈱䉻䉟䉥䊷䊄䈫ห䈛ᗵᐲ䇯Bias㔚ജᱜᏫㆶലᨐ䇯䋺OFCV
䋲䇭㗅ᣇะቯ㔚࿶Bias䈪䈲䇮䌎୘ਗ೉䈲ᗵᐲ䌎୚䇯Bias㔚ജᱜᏫㆶലᨐ䇯䋺PFCV
䋳䇭㗅ᣇะቯ㔚ᵹBias䈪䈲䇮䌎୘⋥೉䈲ᗵᐲ䌎୚䇮Bias㔚ജ⽶Ꮻㆶലᨐ䇯䋺SFCC
䋴䇭ㅒᣇะቯ㔚࿶Bias䈪䈲䇮䌎୘ਗ೉䈲ᗵᐲ䌎୚䇮Bias㔚ജᱜᏫㆶലᨐ䇯䋺PRCV
䇭䇭䇭䈚䈎䈚䈭䈏䉌䇮White Noise䈱ૐᷫኻ╷ᔅⷐ䇯
One Diode䋫㗅ቯ㔚࿶Bias
䋨䌏 䌆 䌃 䌖䋩
⿒ᨒ䋺ቯ㔚࿶Bias䈱ᤨ
䇭䇭䇭䊶ਗ೉䈱ലᨐ᦭䉍䋨䌮୚䋩
䇭䇭䇭䊶Bias㔚ജᱜᏫㆶലᨐ䇭
kT
T ∂i
qV
T ∂V VG
qV
⇒ P ≈ G ≈
, exp(−
)
㔚࿶⽶ᄢ㗔ၞ V −
q
iP ∂T
kT
V ∂T V
kT
∂VS
n qV
≈ − ( G )V
∂T
T kT
⋥೉䈱ᗧ๧䈭䈚
⋥೉䈱ᗧ๧䈭䈚
Bias䋺Good 㗔ၞ
SSCC
T ∂i  qVG 
T ∂VS
qV
⇒ ≈
≈ −( G )
, 㔚࿶㔖ㄭற VS ≈ 0  i ∂T  kT 
VS ∂T
kT
䋱୘
SFCC
∂VS
n
≈ − (VG − V )
∂T
T
⋥೉䈱ᗧ๧䈭䈚
ቯ㔚࿶Bias
Bias䋺Good 㗔ၞ
䋱୘
㔚࿶ᱜᄢ㗔ၞ VS VS = nV
㕍ᨒ䋺ቯ㔚ᵹBias䈱ᤨ
䇭䇭䇭䇭䊶⋥೉䈱ലᨐ᦭䉍䋨䌮୚䋩
䇭䇭䇭䇭䊶Bias㔚ജ⽶Ꮻㆶലᨐ䇭
OFCV
T ∂i q(VG − V )
≈
i ∂T
kT
⿒ᨒ䋺ቯ㔚࿶Bias䈱ᤨ
䇭䇭䇭䊶⋥೉䈱ലᨐ䈭䈚䋨䋱୚䋩
䇭䇭䇭䊶Bias㔚ജᱜᏫㆶലᨐ䇭
䋲୘
䌖S
⋥೉
䇭䇭䇭䇭䋨Diode䉕᷷ᐲ䉶䊮䉰䈫䈚䈩↪䈇䉎ᤨ䋩
ਗ೉Diode䋨䌎୘䋩䋫ㅒቯ㔚࿶Bias
䋨䌐 䌒 䌃 䌖䋩
iP
䋲୘
ਗ೉Diode䋨䌎୘䋩䋫㗅ቯ㔚࿶Bias
䋨䌐 䌆 䌃 䌖䋩
䋱୘
PRCV
∂iP n  qVG 
≈
i
∂T T  kT 
䌖
䋱୘
㕖Ᏹ䈮ᄢ䈐䈭୯㸢ਇ቟ቯ
SFCC䋺Series Forward Constant Current ; OFCV䋺One Diode Forward Constant Voltage
SSCC䋺Series Small Constant Current ; PRCV䋺Parallel Reverse Constant Voltage
PFCV䋺Parallel Forward Constant Voltage
⋥೉Diode䋨䌎୘䋩䋫㗅ቯ㔚ᵹBias
䋨䌓 䌆 䌃 䌃䋩
䋲୘
35
SFCC䋺Series Forward Constant Current
OFCV䋺One Diode Forward Constant Voltage
SSCC䋺Series Small Constant Current
PRCV䋺Parallel Reverse Constant Voltage
PFCV䋺Parallel Forward Constant Voltage
Bias䋺Good 㗔ၞ
਄⸥䋴Case䉕ቯ㊂⊛䈮ᬌ⸛ᔅⷐ
36
6
⃻ታDiode․ᕈ
i iS ≅ exp(qV kT )
䋲䇭⃻ታDiode(Real or Actual Diode)
10
䋱䇭ℂᗐDiode䋨Ideal Diode)
䇭 䊶䌉䋭䌖․ᕈ䈫଀
䇭䇭䊶ᓸಽଥᢙ
䇭䇭䊶ㄭૃᑼ
䇭䇭䊶േ૞ὐ
䇭䇭䊶ᶖ⾌㔚ജ
䇭䇭䊶䌎୘⋥೉․ᕈ
䇭䇭䊶䌎୘ਗ೉․ᕈ
䊶䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ
䋲䇭⃻ታDiode(Real or Actual Diode)
䋳䇭Bolometer䈱ᕈ⢻Ყセ
䋴䇭Heat Model of Uncooled FPA IR Detector
(FPA IR䋺Focal Plane Array Infra Red)
i iS ≅ exp( qV 2kT + 5.4)
㱓=1
(Real or Actual Diode)
= exp( q(V + 0.28) 2kT )
7
㱓=2
i iS ≅ exp(qV 2kT )
㔚ᵹᲧ䋨i/iS䋩䈲ℂᗐ․ᕈ䉋䉍
䋲䌾䋳ᩴᄢ䈐䈇
ㅒᣇะ㔚ᵹ䈲ℂᗐ㘻๺㔚ᵹ䉋䉍
䋲䌾䋳ᩴᄢ䈐䈇
1
q V kT
0.26V
0.52V
0.78V
at 300K
37
38
Ref)㔚ሶ‛ᕈṶ⠌䇮ችᎹᶑ䇮Ꮏቇ࿑ᦠ䋨ᩣ䋩䇮䌰䋲䋲䋲
⃻ታDiode․ᕈ䋨䋱䋩
i
䌔䋫㰱䌔䋾䋰
(Real or Actual Diode)
䌔
䌖
䌔
䌔䋫㰱䌔䋾䋰
ExactExpession
V=
η kT
q
ln(
qVG
η kT
i
+ 1)
iS
⃻ታDiode․ᕈ䋨䋲䋩
i0䈲ធว㕙Ⓧ䋨䌓䋩䈮Ყ଀
䌔䋫㰱䌔䋾䋰
䌔
䌖
䌔
䌔䋫㰱䌔䋾䋰



qVG 
qV
qV
) exp(
) − 1 = iS [ A]  exp(
) − 1 where V ≤ VG
η kT 
η kT
η kT



) where i0 = i0 S S
i
(Real or Actual Diode)
䊶㱓䋺Diode Ideality Factor
䇭䇭䇭䋨ℂᗐ䉻䉟䉥䊷䊄࿃ሶ䋩
䇭䇭㱓=1䋺ℂᗐ䉻䉟䉥䊷䊄
䇭䇭㱓=1䌾2䋺Si,Ge
䇭䇭㱓=4䋺ᄥ㓁㔚ᳰ䋨Siએᄖ䋩
䊶k䈱ᚲ䈮㱓k䉕ઍ౉䈜䉏䈳⦟䈇
䊶Recombination Current by Defect,
Surface Current Effect ,
Tunneling Current╬䋨⵾ㅧᛛⴚ䋩䈮䉋䉎
䊶㱓䈱ઍ䉒䉍䈮n䉅ᘠ↪⊛૶↪
Empirical Expression
㘻๺㔚ᵹ䋨Saturation Current䋩
i[ A] = i0 S [ A m 2 ]S[m 2 ]exp( −
iS ≡ i0 [ A]exp(−
䊶㱓䋺Diode Ideality Factor
䇭䇭䇭䋨ℂᗐ䉻䉟䉥䊷䊄࿃ሶ䋩
䇭䇭㱓=1䋺ℂᗐ䉻䉟䉥䊷䊄
䇭䇭㱓=1䌾2䋺Si,Ge
䇭䇭㱓=4䋺ᄥ㓁㔚ᳰ䋨Siએᄖ䋩
䊶k䈱ᚲ䈮㱓k䉕ઍ౉䈜䉏䈳⦟䈇
䊶Recombination Current by Defect,
Surface Current Effect ,
Tunneling Current╬䋨⵾ㅧᛛⴚ䋩䈮䉋䉎
䊶㱓䈱ઍ䉒䉍䈮n䉅ᘠ↪⊛૶↪
i = i0 S S exp( −
qVG 
q(V + VP ) 

q(VG − V − VP ) 
)  = i0 S S  exp(−
)
η kT



) exp(
η kT 
η kT

q(V + VP ) 
qV
qV
= iS  exp(
)  where 10 ≤
≤ 25 ；iS ≡ i0 S S exp(− G )
η kT
η kT
kT


η kT
i
ln( ) − VP
V=
VP ≈ 0.2 ∼ 0.3V
q
iS
i0S䋽䋱䋰䌞䋶䌾䋱䋰䌞䋱䋰[A/m^2]
Si,Ge╬䈱᧚ᢱ䇮CarrierỚᐲ䇮ਇ⚐‛䇮
⵾ㅧᛛⴚ╬䈪᳿䉁䉎䇯
䋨ℂᗐ㘻๺㔚ᵹ䉋䉍䋲䌾䋳ᩴᄢ䈐䈒䈜䉏䈳⦟䈇䋩
V → V + VP
q = 1.6 ×10−19 [C ], k = 1.38 ×10−23[ J ],
K
VG ( Si) = 1.12[V ], VG (Ge) = 0.66[V ],VG (GaAs) = 1.42[V ] at 300 K
q = 1.6 ×10−19 [C ], k = 1.38 ×10−23[ J ],
K
VG ( Si) = 1.12[V ], VG (Ge) = 0.66[V ],VG (GaAs) = 1.42[V ] at 300 K
q
1 1
1.12
0.66
[ ] where 300 K , exp(−
) ≈ 2 ×10−19 , exp(−
) ≈ 9.5 ×10−12 39
=
kT 0.026 V
0.026
0.026
q
1 1
1.12
0.66
[ ] where 300 K , exp(−
) ≈ 2 ×10−19 , exp(−
) ≈ 9.5 ×10−12 40
=
0.026
0.026
kT 0.026 V
Bolometer䈱ᕈ⢻Ყセ䋨Thermistor䈫⊕㊄ᛶ᛫᷹᷷૕䋩
䋳䇭Bolometer䈱ᕈ⢻Ყセ
Thermistor Bolometer䋨Bias㔚ജᱜᏫㆶലᨐ䋩
dR
dP
≤0⇔
≥ 0：Bias電力正帰還効果
dT
dT


R (Ω )
1
1
)  , B = 2000 ∼ 6000 K
= exp  B ( K ) ⋅ (
−
R0 ( Ω )
T ( K ) T0 ( K ) 

B ∆T
∆R
∆T B ∆T
, 2 1 ≅ −
⋅
W here ∆ R = R − R 0 , ∆ T = T − T0 and R0
T0 T0
T0
T0
䋱䇭ℂᗐDiode䋨Ideal Diode)
䇭 䊶䌉䋭䌖․ᕈ䈫଀
䇭䇭䊶ᓸಽଥᢙ
䇭䇭䊶ㄭૃᑼ
䇭䇭䊶േ૞ὐ
䇭䇭䊶ᶖ⾌㔚ജ
䇭䇭䊶䌎୘⋥೉․ᕈ
䇭䇭䊶䌎୘ਗ೉․ᕈ
䊶䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ
䋲䇭⃻ታDiode(Real or Actual Diode)
䋳䇭Bolometer䈱ᕈ⢻Ყセ
䋴䇭Heat Model of Uncooled FPA IR Detector
(FPA IR䋺Focal Plane Array Infra Red)
⇒
T0 ∆ R
B
≅ −
≈ − 12 W hereB = 3500 K , T 0 = 300 K
R 0 ∆T
T0
⽶䈱୯䈪⛘ኻ୯䈏ᄢ䈐䈇䈾䈬㜞ᗵᐲ䋨䌂୯䋨䋽᧚ᢱ䋩䈮䉋䉍᳿䉁䉎䋩
dR
dP
⊕㊄ᛶ᛫᷹᷷૕䋨Bias㔚ജ⽶Ꮻㆶലᨐ䋩 dT ≥ 0 ⇔ dT ≤ 0：Bias電力負帰還効果
∆R
R0
⇒
41
=α(
1
∆T
) ⋅ ∆T ( K ) = α T0
K
T0
T0 ∆ R
≈ α T0 = 1.1 where α ≅ 3850 ×10−6 (1/ K ), T0 = 300 K
R0 ∆T
䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䋨Diode᷷ᐲ䉶䊮䉰䋩
Bias㔚ജᱜᏫㆶലᨐ䋨᷷ᐲ਄᣹㸢ૐᛶ᛫䋩䋺ቯ㔚࿶Bias䈱ᤨ䇮Bias㔚ജ䈏Ⴧട䈚᷷ᐲᄌൻ䈮ᢅᗵ䈮䈭䉎䇯
42
Bias㔚ജ⽶Ꮻㆶലᨐ䋨᷷ᐲ਄᣹㸢㜞ᛶ᛫䋩䋺ቯ㔚ᵹBias䈱ᤨ䇮Bias㔚ജ䈏ᷫዋ䈚᷷ᐲᄌൻ䈮㊰ᗵ䈮䈭䉎䇯
7
Bolometer 䈱ᕈ⢻Ყセ䋨Si-Diode䈱Bias䈮䉋䉎:at300K䋩
T dR
R dT
䋴䇭Heat Model of Uncooled FPA IR Detector
FCV : Forward Constant Voltage
FCC : Forward Constant Current
T dR
 q (VG − V ) 
≈ −
− 1 ≈ −32 atV = 0.26V
R dT V =const
kT


(V = 0.7V ⇒ −15)
≈ 1 atV = 0.26V
i = const
䋱䇭ℂᗐDiode䋨Ideal Diode)
䇭 䊶䌉䋭䌖․ᕈ䈫଀
䇭䇭䊶ᓸಽଥᢙ
䇭䇭䊶ㄭૃᑼ
䇭䇭䊶േ૞ὐ
䇭䇭䊶ᶖ⾌㔚ജ
䇭䇭䊶䌎୘⋥೉․ᕈ
䇭䇭䊶䌎୘ਗ೉․ᕈ
䊶䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ
䋲䇭⃻ታDiode(Real or Actual Diode)
䋳䇭Bolometer䈱ᕈ⢻Ყセ
䋴䇭Heat Model of Uncooled FPA IR Detector
(FPA IR䋺Focal Plane Array Infra Red)
⽶䈱୯䈲Bias㔚ജᱜᏫㆶലᨐ
RCV : Reverse Constant Voltage
SCC : Small Constant Current
T dR
R dT
T dR
 q (VG − V ) 
≈ −
 ≈ −53 atV = −0.26V
R dT V = const
kT


৻⷗ᗵᐲ⦟䈘䈠䈉䈪䈅䉎䈏㸢No
Good
(V = −10V ⇒ −430)
≈ 0 at V ≤ 2.6mV
i = const
⚿⺰䋺Diode䈲Thermistor Bolometer䉋䉍䉅㜞ᗵᐲ䇯
䈚䈎䉅䇮Bias㔚࿶䈮䉋䉍ᗵᐲ䈲ᄌൻ䈜䉎䇯
䌆䌃䌖䋨㗅ᣇะቯ㔚࿶䋩䈫䌒䌃䌖䋨ㅒᣇะቯ㔚࿶䋩Bias䈏㜞ᗵᐲ䈫䈭䉎
44
43
Heat Model of Uncooled FPA IR Detector(Model):Bias Current
Coffee Break䋺First Order Solution of Bias Current for Real Diode
k L [W mK ]

q(VG − V )  dP
1 q(VG − V )
),
=
S L [m2 ]∆TB [ K ] = PB [W ] where PB = Vi0 S S E  exp(−
P
η kT
lL [m]

 dT V =CONST T η kT
ೋᦼ᧦ઙ䉕᳞䉄䉎䇯ో♽䈏᷷ᐲT0䈱ᤨ䇮Bias㔚ᵹ䉕ᵹ䈚䇮Element䈱᷷ᐲ䈏TE䈪ᾲᐔⴧ䈮䈭䈦䈢䇯
0=
+ ka [0]Φ[W ] ：背景赤外線の吸収
Vacuum
k L [W mK ]
S L [m2 ]∆TB [ K ] ：足からの熱伝導
lL [m]
W
−α G [
]S [m 2 ]∆TB [ K ] ：残留ガスの熱伝達
m2 K E
−4εσ T 3[W 2 ]S E [m2 ]∆TB [ K ] ：放射伝達
mK
+ PB [W ] ：Bias電力
−
Legs
IR
Light
Heat Sink
And
Read Out
Integrated
Circuit
Φ=0
Window
Example
148[W mK ]
2 × 5[ µ m 2 ]∆TB [ K ] ≈ 50[µW ]
30[ µ m]
⇒ ∆TB ≈ 1K
q (VG − V ) 

PB ≈ Vi0 S S E  exp(−
)
kT


1 q(VG − V )
kL
SL −
PB (TO , V ))∆TB = PB (TO , V )
lL
TO η kTO
148
1 (1.12 − 0.75)
2 × 5µ m 2 −
55µW )∆TB = 55µW
30µ m
300 2 × 0.026
IR
Light
HC [ J
∆Φ
Window
Single Element Detector
−
148
1 (1.12 − 0.8)
2 × 5µ m 2 −
150 µW )∆TB = 150µW
30 µ m
300 2 × 0.026
(4.9 ×10−5 − 3.1×10−6 )∆TB = 150 µW ⇒ ∆TB = 3.3K
1.12 − 0.75
1.12 − 0.8
) = 1.53mW
) = 550µW PB = 0.8 × 109 × (30 × 30µ m 2 ) exp(−
2 × 0.026
2 × 0.026
148
1 (1.12 − 0.8)
148
1 (1.12 − 0.75)
2 × 5µ m 2 −
1.53mW )∆TB = 1.53mW
2 × 5µ m 2 −
550µW )∆TB = 550µW (
30µ m
300 2 × 0.026
30µ m
300 2 × 0.026
(4.9 × 10−5 − 1.3 × 10−5 )∆TB = 550µW ⇒ ∆TB = 15K
(4.9 × 10−5 − 3.1×10−5 )∆TB = 1.53mW ⇒ ∆TB = 85K
46
ᾲᐔⴧᤨ䈎䉌ᤨ㑆dt 㑆䈮䇮⿒ᄖశ㰱㱂䈏⚛ሶ䈮౉኿䈚䇮න⚛ሶ᷷ᐲ䈏㰱䌔਄᣹䈜䉎
Legs
k L [W mK ]
S L [m2 ]∆TΦ [ K ]dt[sec] ：足からの熱伝導
l L [ m]
]S [m 2 ]∆TΦ [ K ]dt[sec] ：残留ガスの熱伝達
m2 K E
3 W
−4εσ T [
]S [m2 ]∆TΦ [ K ]dt[sec] ：放射伝達
m2 K E
dPB W
+
[
]∆TΦ [ K ]dt[sec] ：Bias電力(正、負)帰還効果
K
dT
㈩⟎䌁
IR
Light
∆Φ
Heat Sink
And
Read Out
Integrated
Circuit
Window
Single Element Detector
㈩⟎䌂
㕙Ⓧ䋺SE
H C [ J ]∆T [ K ] =：センサに蓄えられるエネルギ
K
+ ka [0]∆Φ[W ]dt[sec] ：赤外線の吸収
Vacuum
]∆TΦ [ K ] =：センサに蓄えられるエネルギ
−α G [W
න⚛ሶ
(Top View)
−
නጀ
ዊ䈘䈭Diode䉕⋥䇮ਗ೉䈮ਗ䈼䉎䋨SE=䌎䊶SD䋩䇭
k L [W mK ]
SL [m 2 ]∆T [ K ]dt[sec] ：足からの熱伝導
lL [m]
−α G [W
m2 K
]S [m 2 ]∆T [ K ]dt[sec] ：放射伝達
m2 K E
+ PB [W ]dt[sec] ：Bias電力
dP
+ B [W ]∆T [ K ]dt[sec] ：Bias電力(正、負)帰還効果
K
dT
Where ∆T = ∆TB + ∆TΦ
㈩⟎䌁
㕍䋺න⚛ሶ㕙Ⓧ
⿒䋺Diodeធว㕙Ⓧ
]S E [m2 ]∆T [ K ]dt[sec] ：残留ガスの熱伝達
−4εσ T 3[W
㈩⟎䌂
න⚛ሶ
(Top View)
㕙Ⓧ䋺SE
㕙Ⓧ䋺SD
න⚛ሶ
(Side View)
(
1.12 − 0.8
) = 150 µW
2 × 0.026
Heat Model of Uncooled FPA IR Detector(Model)䋺General
K
+ ka [0]∆Φ[W ]dt[sec] ：赤外線の吸収
Heat Sink
And
Read Out
Integrated
Circuit
PB = 0.8 × 108 × (30 × 30 µ m 2 ) exp(−
PB = 0.75 × 109 × (30 × 30µ m 2 ) exp(−
(
ᾲᐔⴧᤨ䈎䉌ᤨ㑆dt 㑆䈮䇮⿒ᄖశ㰱㱂䈏⚛ሶ䈮౉኿䈚䇮න⚛ሶ᷷ᐲ䈏㰱䌔਄᣹䈜䉎
Legs
Bias㔚ജ䈏ᄢ䈐䈒䈭䉎䈫ᕆỗ䈮
⚛ሶ᷷ᐲ䈲਄᣹䈜䉎䇯
䋨Bias㔚ജᱜᏫㆶലᨐ䈱䈢䉄䋩
45
Heat Model of Uncooled FPA IR Detector(Model)䋺Infra Red
Vacuum
1.12 − 0.75
) = 55µW
2 × 0.026
(4.9 × 10−5 − 1.3 ×10−6 )∆TB = 55µW ⇒ ∆TB = 1.15K
㔖ᰴㄭૃ
⿷䈎䉌䈱ᾲવዉ䈱䉂䈏ല䈒ᤨ
(
(
ᾲᐔⴧ䈱ᤨ䋺㱂=0䈫䈚䈩⦟䈇
k L [W mK ]
S L [m 2 ]∆TB [ K ] ≈ PB [W ]
lL [m]
kL
dP
SL ∆TB = PB (TO + ∆TB , V ) ≈ PB (TO , V ) + B ∆TB
lL
dT
PB = 0.75 ×108 × (30 × 30µ m2 ) exp(−
where ∆TB = TE − TO
Single Element Detector
Given V , TO ⇒ ∆TB
㕍䋺න⚛ሶ㕙Ⓧ
⿒䋺Diodeធว㕙Ⓧ
㕙Ⓧ䋺SD
න⚛ሶ
(Side View)
䌎ጀ
ᄢ䈐䈘SE䈱Diode䉕⋥䇮ਗ೉䈮㊀䈰䉎䋨SE=SD䋩䇭
47
නጀ
ዊ䈘䈭Diode䉕⋥䇮ਗ೉䈮ਗ䈼䉎䋨SE=䌎䊶SD䋩䇭
䌎ጀ
ᄢ䈐䈘SE䈱Diode䉕⋥䇮ਗ೉䈮㊀䈰䉎䋨SE=SD䋩䇭
48
8
Heat Model of Uncooled FPA IR Detector(Model)䋺General Equation
H C (∆TB + ∆TΦ ) = ka ∆Φdt −
− 4εσ T 3 S E (∆TB + ∆TΦ )dt + PB dt +
HC (
Heat Model of Uncooled FPA IR Detector(Equation)
kL
S L (∆TB + ∆TΦ )dt − α G S E (∆TB + ∆TΦ )dt
lL
d (∆TB ) d (∆TΦ )
+
) + GC (∆TB + ∆TΦ ) = ka ∆Φ + PB
dt
dt
d (∆TB )
d (∆TΦ )
+ GC ∆TB = PB , H C
+ GC ∆TΦ = ka ∆Φ
HC
dt
dt
1 dPB
kL SL
G
) and GC′ [W m2 K ] ≡ C
+ α G + 4εσ T 3 −
where GC [W K ] ≡ SE (
lL SE
S E dT
SE
k ∆Φ
P
, ∆TΦMAX [ K ] = a
∆TBMAX [ K ] = B GC
GC
HC (
dPB
( ∆TB + ∆TΦ ) dt
dT
d (∆TB ) d (∆TΦ )
k
dP
+
) + ( L S L + α G SE + 4εσ T 3 S E − B )(∆TB + ∆TΦ )
dt
dt
lL
dT
d (∆TB ) d (∆TΦ )
+
) + GC ∆TB + GC ∆TΦ = ka ∆Φ + PB
dt
dt
k
dP
where GC ≡ L S L + α G S E + 4εσ T 3 SE − B
lL
dT
= HC (
τ [sec] =
Where ∆Φ = 0 ⇒ ∆TΦ = 0
d (∆TB )
HC (
) + GC ∆TB = PB
dt
Bias㔚ജ䈣䈔䈱ᤨ
dPB/dT䋾0䋨Bias㔚ജᱜᏫㆶലᨐ䋩㸢GC䈲ዊ㸢ᦨ㜞᷷ᐲ਄᣹䇮ᤨቯᢙ㐳
Where ∆Φ ≠ 0
d (∆TΦ )
HC (
) + GC ∆TΦ = ka (∆Φ )
dt
dPB/dT䋼0 䋨Bias㔚ജ⽶Ꮻㆶലᨐ䋩 㸢GC䈲ᄢ㸢ᦨ㜞᷷ᐲૐਅ䇮ᤨቯᢙ⍴
⿒ᄖାภ౉኿䈱ᤨ
GC[W/K]䋺Thermal䇭Conductance
HC[J/K]䋺Heat Capacity
ో᷷ᐲᄌൻ䈲෺ᣇട▚䈚䈢᷷ᐲᄌൻ
ฦ㗄䈱⷗Ⓧ䋨OFCV䈫SFCC䈱Ყセ䋩
䊶SD䋼SE䋺No Good
䊶SD=SE 䋺Good
OFCV : One − Diode
q(VG − VO )
1 dP S D VO i0 S q (VG − VO )
exp( −
)
≈
S E dT S E T
kT
kT
㈩⟎䌂
䈫䈜䉎
䊶SD䋼SE䋺No Good
䊶SD=SE 䋺Good
⃻ታ⊛
OFCV : One − Diode
q(VG − VO )
1 dP VO i0 S q(VG − VO )
exp( −
)
≈
η kT
η kT
S E dT
T
PRCV
q(VG − VO )
)
(V − V )V
qV
kT
= G O O exp( O ) 1
qV
nVG (−VP )
kT
nVG (−VP ) exp(− G )
kT
OFCV ≥ SFCC
SFCC䋺Series Forward Constant Current ; OFCV䋺One Diode Forward Constant Voltage
SSCC䋺Series Small Constant Current ; PRCV䋺Parallel Reverse Constant Voltage
PFCV䋺Parallel Forward Constant Voltage
ฦ㗄䈱⷗Ⓧ䋨OFCV䈫PFCV䈱Ყセ䋩
exp(
䋱୘䈱䉻䉟䉥䊷䊄䈫N୘ਗ೉䉻䉟䉥䊷䊄䈱
Biasᶖ⾌㔚ജ䈏ห䈛䈫䈜䉎
OFCV : One − Diode
q(VG − VO )
1 dP S D VO i0 S q (VG − VO )
≈
exp( −
)
S E dT S E T
kT
kT
㈩⟎䌂
䈫䈜䉎
OFCV : One − Diode
q(VG − VO )
1 dP VO i0 S q(VG − VO )
≈
exp( −
)
η kT
η kT
S E dT
T
q(VG − VO′ )
S V ′i q (VG − VO′ )
1 dP
≈ n D O 0S
exp(−
)
S E dT
SE T
kT
kT
⇓
OFCV ≈ PFCV
q(VO − VO′ )
nV ′
) ≈ O ⇒ VO ≈ VO′
kT
VO
53
OFCV䈱ᣇ䈏㜞ᕈ⢻
52
] × SE [m2 ] where EIR = 0.025[W 2 ]
m2
m
τ λ = 0.5, ∆TO = 0.1K
at F = 1, GC′[W
HC [ J
SFCC䋺Series Forward Constant Current ; OFCV䋺One Diode Forward Constant Voltage
SSCC䋺Series Small Constant Current ; PRCV䋺Parallel Reverse Constant Voltage
PFCV䋺Parallel Forward Constant Voltage
䊶OFCV䈱ᣇ䈏㜞ᕈ⢻䇯
䇭䋨୯䈲ᄢ䇮䈎䈧ᱜ୯䋩
䊶Diode䋱୘䈱ቯ㔚࿶Bias䈱ᣇ䈏
䇭䋱䋰୘⋥೉䈱ቯ㔚ᵹBias䉋䉍䉅㜞ᗵᐲ䇯
∆Φ[W ] ≈ EIR [W
m2 K
∆TΦMAX =
OFCV䈫PFCV䈲ᱴ䈬ห䈛ᕈ⢻䇯
䈚䈎䈚䈭䈏䉌䇮
PFCV䈱Nጀᓸ⚦ടᎿ䈲࿎㔍䇯
䊶㈩⟎䌁䈱ᤨ䈲䋱୘䈱䉻䉟䉥䊷䊄䈫ห䈛䇯
䊶㈩⟎䌂䈲䌮୚䈮䈭䉎䇯
䊶୯䈲⽶୯䋺Bias㔚ജ⽶Ꮻㆶലᨐ䇯
䇭ᵈ䋩V0䈲䋱୘䈱䉻䉟䉥䊷䊄䈮䈎䈎䉎㔚࿶
ฦ㗄䈱⷗Ⓧ䋨䋱䋩
䊶㈩⟎䌁䈱ᤨ䈲䋱୘䈱䉻䉟䉥䊷䊄䈫ห䈛䇯
䊶㈩⟎䌂䈲䌮୚䈮䈭䉎䇯
䇭ᵈ䋩V0㵭䈲ਗ೉䉻䉟䉥䊷䊄䈮䈎䈎䉎㔚࿶
䊶OFCV䈫PFCV䈲ᱴ䈬ห䈛䇯
䊶PFCV䈲ᓸ⚦ടᎿ࿎㔍䇯
⃻ታ⊛
OFCV : One − Diode
q(VG − VO )
1 dP VO i0 S q(VG − VO )
exp( −
)
≈
η kT
η kT
S E dT
T
SFCC䋺Series Forward Constant Current ; OFCV䋺One Diode Forward Constant Voltage
SSCC䋺Series Small Constant Current ; PRCV䋺Parallel Reverse Constant Voltage
PFCV䋺Parallel Forward Constant Voltage
51
⃻ታ⊛
PFCV
OFCV
V (V − V )
q(V − V ′ )
(V − V )
= O G O exp( O O ) ≈ G O ≈ 1
PFCV nV ′ (V − V ′ )
kT
(VG − VO′ )
O
G
O
i (V − V )
1 dP
q(VG − VO )
)
≈ − n 0 S G O exp(−
SE dT
T
kT
⇓
OFCV䈱ᣇ䈏㜞ᕈ⢻
㈩⟎䌂
䈫䈜䉎
SFCC
OFCV 1 qVO
=
≈ 1 ∼ 2.7 at n = 10
SFCC n kT
(VG − VO )VO exp(−
⇓
OFCV : One − Diode
q(VG − VO )
1 dP S D VO i0 S q (VG − VO )
exp( −
)
≈
S E dT S E T
kT
kT
䊶㈩⟎䌁䈱ᤨ䈲䋱୘䈱䉻䉟䉥䊷䊄䈫ห䈛
䊶㈩⟎䌂䈲䌮୚䈮䈭䉎
䇭ᵈ䋩VP䋼0㸢Ꮐㄝ䈲ᱜ䈱୯
1 dP nS D (−VP )i0 S  qVG 
qVG
)
≈

 exp(−
SE dT
SE
T
kT
 kT 
OFCV PRCV
50
49
ฦ㗄䈱⷗Ⓧ䋨OFCV䈫PRCV䈱Ყセ䋩
OFCV
=
PRCV
G
HC
or f [ Hz ] = C
HC
GC
]=
GC [W K ] kL S L
1 dPB
=
+ (α G + 4εσ T 3 ) −
S E [m 2 ]
lL SE
S E dT
ka ∆Φ ka EIR
ka EIR
=
=
k L SL
1 dPB
GC
GC′
+ (α G + 4εσ T 3 ) −
lL S E
S E dT
] = S E [m2 ]lD [m]ρ D [kg
]C [ J
]
m3 PD kgK
kL
dPB
3
S L + (α G + 4εσ T )S E −
G
GC′
l
dT
f [ Hz ] = C = L
=
HC
S E lD ρ D CPD
lD ρ DCPD
K
54
9
ฦ㗄䈱⷗Ⓧ䋨䋲䋩䋺OFCV䈪ᬌ⸛
ฦ㗄䈱⷗Ⓧ䋨䋳䋩
W
G
k S
1 dPB k L S L 1 dPB
GC′[ 2 ] ≡ C = L L + (α G + 4εσ T 3 ) −
≈
−
m K
S E lL S E
S E dT lL S E S E dT
W
k k P R
αG [ 2 ] ≈ S V
where MeanFreePath ≥ lGAP
mK
3 T W
5
3
5
6
( He, Xe：
) 2( H 2 , N 2 , CO 2, H 2O, SF6 ) 、 kV： ( He, Xe：
) ( H 2 , N 2 , CO 2)： ( H 2O, SF6 )
k：
S
2
2
2
2
ήⷞน
=
4εσ T ≈ 6.12[W m K ] where T = 300 K , ε = 1
3
2
ρ DSi = 2.33 ×103 [kg m3 ], C PDSi = 714[ J kgK ], k LSi = 148[W mK ]
J
H
J
H C′[ 2 ] ≡ C = lD ρ DCPD = lD [ µ m] × 1.66 ≈ 5 ∼ 10[ 2 ]
mK
SE
mK
ρ DSi CPDSi = 1.66 ×106 [ J m3 K ]
∆TΦMAX [ K ] =
OFCV : One − Diode
1 dPB VBi0 S q (VG − VB )
q (VG − VB )
1 q(VG − VB ) PB
≈
exp(−
)≈
η kT
η kT
S E dT
T
T η kT
SE
1 dPB 1 q (VG − VB ) PB
≈
S E dT T
η kT
SE
q(VG − VB )
) : i0 S = 106 ∼ 1010 [ A m 2 ]
η kT
f [ Hz ] =
55
ᗵᐲ਄᣹䈜䉎
GC GC′
=
HC H ′
C
56
ήᰴరൻ
ฦ㗄䈱⷗Ⓧ䋨䋴䋩
GC ′ =
䊶⿷䈎䉌䈱ᾲવዉ䈮䉋䉍ㅏ䈕䉎ᾲ
䊶㕖Ᏹ䈮ᄢ䋺㻍䋱䋰䌞䋴[W/m^2K]
1 dPB
を正で大きくし、GC ′を小さくする
SE dT
C
q(VG − VB )
PB [W ] ≈ VB i0 S S D exp( −
：
) i0 S = 106 ∼ 1010 [ A m2 ]
η kT
iB [ A] ≈ i0 S S D exp( −
ka [0]EIR [W m 2 ]
G ′ [W m 2 K ]
k L S L 1 q (VG − VB ) PB
−
lL S E T η kT
SE
1 kL
1 q(VG − VB )
( SL −
PB )
η kT
S E lL
T
∆TΦMAX =
1
148
1 (1.12 − 0.8)
(
2 × 5µ m 2 −
0.5mW )
30 × 30µ m 2 30µ m
300 2 × 0.026
1
−5
−5
4
2
=
(4.9 ×10 − 1×10 ) = 4.4 ×10 [W m K ]
9 ×10−10
=
ka × 0.025
= 5.7 × 10−7 K
G′
C
H C′ = lD [ µ m] × 1.66 = 3.3[ J m 2 K ]
f = GC ′ H C ′ = 13kHz
1 kL
1 q(VG − VB )
k × 0.025
( SL −
PB )
∆TΦMAX = a
= 6.25 × 10−6 K
S E lL
T η kT
GC ′
1
148
1 (1.12 − 0.8)
=
(
2 × 5µ m 2 −
× 1mW )
H C′ = lD [ µ m] ×1.66 = 3.3[ J m 2 K ]
50 × 50 µ m 2 50µ m
300 2 × 0.026
1
−5
−5
3
2
=
(3
×
10
−
2
×
10
)
=
4
×
10
[
W
m
K
]
f = GC ′ H C′ = 1.2kHz
2.5 ×10−9
GC′ =
W
k S 
l 1 q(VG − VB ) 
GC′[ 2 ] ≈ L L 1 − L
PB 
mK
lL S E  k L S L T η kT

l L [ m]
1 q(VG − VB )
gC [0] =
PB [W ]
k L [W mK ]S L [m2 ] T [ K ] η kT
gC =
gC =
30µ m
1 (1.12 − 0.8)
1mW = 0.42
148 × 2 × 5µ m2 300 2 × 0.026
30 µ m
1 (1.12 − 0.8)
30 µW = 0.012
148 × 2 × 5µ m 2 300 2 × 0.026
57
䌎୘⋥೉䇮ਗ೉෸䈶Biasὐ䈱Ყセ䋨0.26Vએ਄䈪䈱⹦⚦Ყセ䋩
䋱䇭㗅ᣇะቯ㔚࿶Bias䈪䈲䇮䌎୘⋥೉䈲䋱୘䈱䉻䉟䉥䊷䊄䈫ห䈛ᗵᐲ䇯Bias㔚ജᱜᏫㆶലᨐ䇯䋺OFCV
䋲䇭㗅ᣇะቯ㔚࿶Bias䈪䈲䇮䌎୘ਗ೉䈲ᗵᐲ䌎୚䇯Bias㔚ജᱜᏫㆶലᨐ䇯䋺PFCV
䋳䇭㗅ᣇะቯ㔚ᵹBias䈪䈲䇮䌎୘ਗ೉䈲䋱୘䈱䉻䉟䉥䊷䊄䈫ห䈛ᗵᐲ䇯Bias㔚ജ⽶Ꮻㆶലᨐ䇯䋺OFCC
䋴䇭㗅ᣇะቯ㔚ᵹBias䈪䈲䇮䌎୘⋥೉䈲ᗵᐲ䌎୚䇯Bias㔚ജ⽶Ꮻㆶലᨐ䇯䋺SFCC
㗅ᣇะቯ㔚࿶Bias
䊶䋱୘䋽䌎⋥೉
䊶䌎ਗ೉
i
䌖S
1 dP
S dT
iP
䌖
=−
I = CONST
1 (VG − V ) P
T
V
S
iP
䋲୘
1 dP
1 q (VG − V ) P
=
S dT V =CONST T
kT
S
䋱୘
iS q 
qV 
 (VG − V ) exp( )  ∆T q(V − V ) ∆T
∆i 1 ∂i
T kT 
kT 
G
=
∆T =
=
qV 

i
i ∂T
kT
T
iS  exp( ) 
kT 

ka EIR
1 q(VG − V ) ka EIR 1 q(VG − V )
=
≈
T
kT
T η kT  k L S L 1 q(VG − V ) P 
GC′
−


 lL S E T η kT SE 
V䋺䋱୘䈱Diode䈮䈎䈎䉎㔚࿶
P䋺䋱୘䈱Diode䈱ᶖ⾌㔚ജ
∆i
1 (1.12 − 0.26)
0.025
=
≈ 2.5 × 10−8
i 300 2 × 0.026  148 10µ m 2
1 (1.12 − 0.26) 0.16µW 
−

2
2 
 30µ m 900µ m 300 2 × 0.026 900µ m 
0.055
5.5E4
5.5E4
䌖
䋱୘
䋲୘
OFCV䋨One Diode Forward Constant Voltage䋩 ᤨ䈱㔚ᵹᄌൻ䈱⷗Ⓧ
9.8
∆i
1 (1.12 − 0.65)
0.025
≈
≈ 2.3 ×10−8
i 300 2 × 0.026  148 10µ m 2
1 (1.12 − 0.65) 0.7mW 
−

2
2 
0.03
 30µ m 900µ m 300 2 × 0.026 900µ m 
㗅ᣇะቯ㔚ᵹBias
䊶䋱୘䋽䌎ਗ೉
䊶䌎⋥೉
OFCV䋺One Diode Forward Constant Voltage
PFCV䋺Parallel Forward Constant Voltage
OFCC䋺One Diode Forward Constant Current
SFCC䋺Series Forward Constant Current
58
2.3E4
∂i iS q 
qV 
qV 
ka ∆Φ

=
 (VG − V ) exp( )  , i = iS  exp( )  , ∆TΦMAX =
∂T T kT 
kT 
kT 
GC

0.26Vએ਄
EIR = 0.025[W
ᵈ䋩PFCV䈲OFCV䈪䊋䉟䉝䉴㔚࿶䉕਄᣹䈘䈞䈢䈱䈫ห䈛ലᨐ
59
∆TΦMAX [ K ] =
m2
] at F = 1, τ λ = 0.5, ∆TO = 0.1K
2
k a [0]EIR [W m ]
G ′[W m2 K ]
C
1 dP
1 q(VG − V ) P
=
S dT V =CONST T
kT
S
W
k S
1 dP k L SL 1 q(VG − V ) P
GC′[ 2 ] ≈ L L −
=
−
m K
lL S E S E dT lL S E T η kT SE
60
10
PFCV䋨Parallel Forward Constant Voltage䋩ᤨ䈱㔚ᵹᄌൻ䈱⷗Ⓧ
∆iP 1 ∂iP
1 q (VG − V ) ∆T q(VG − V ) ∆T
=
∆T =
iP
=
iP
iP ∂T
iP
kT
T
kT
T
=
V䋺䋱୘䈱Diode䈮䈎䈎䉎㔚࿶
P䋺䋱୘䈱Diode䈱ᶖ⾌㔚ജ
1 q(VG − V ) ka EIR 1 q(VG − V )
ka EIR
≈
T
kT
T η kT  k L S L 1 q(VG − V ) nP 
GC′
−

l
S
T
η kT S E 
 L E
∆iP
1 (1.12 − 0.26)
0.025
=
≈ 2.5 ×10−8
iP
300 2 × 0.026 
1 (1.12 − 0.26) 2 × 0.16µW 
4
5.5
×
10
−

0.055
300 2 × 0.026
900 µ m 2 

20
190
∆TΦMAX [ K ] =
1900
] at F = 1, τ λ = 0.5, ∆TO = 0.1K
2
k a [0]EIR [W m ]
G ′[W m 2 K ]
GC ′[
C
V䋺䋱୘䈱Diode䈮䈎䈎䉎㔚࿶
P䋺䋱୘䈱Diode䈱ᶖ⾌㔚ജ
∆V
1 1.12 − 0.65
0.025
=−
≈ −1×10−9
V
300
0.65 
1 (1.12 − 0.65) 0.7mW 
4
×
+
5.5
10


-0.0024
300
0.65
900µ m2 

4.7E4
m2
V − V ∆T
∆V 1 ∂V
=
∆T = − G
V
V ∂T
V
T
1 VG − V ka EIR
1 VG − V
ka EIR
=−
≈−
T V
T V  kL S L 1 (VG − V ) P 
GC′
+


V
SE 
 lL S E T
∆V
1 1.12 − 0.26
0.025
=−
≈ −5 × 10−9
V
300
0.26 
1 (1.12 − 0.26 ) 0.16 µW 
4
 5.5 × 10 +
2 
-0.011
300
0.26
900µ m 

∆iP
1 (1.12 − 0.65)
0.025
=
≈ 9.3 × 10−8
iP
300 2 × 0.026 
1 (1.12 − 0.65) 2 × 0.7 mW 
4
5.5
×
10
−

2 
0.03
300
2
0.026
900
m
µ
×


EIR = 0.025[W
OFCC䋨One Diode Forward Constant Current䋩ᤨ䈱㔚࿶ᄌൻ䈱⷗Ⓧ
∂V
1
≈ − (VG − V )
∂T
T
W
k S
1 dP k L S L 1 q(VG − V ) nP
]= L L −
=
−
m2K
lL S E S E dT lL S E T η kT
SE
n q (VG − V ) P
∂iP 1 q(VG − V )
qV 
k ∆Φ 1 dP

=
=
iP , iP = niS  exp( )  , ∆TΦMAX = a
S dT V =CONST T
kT
S
∂T T
kT
kT 
GC

61
1 dP
S dT
=−
I =CONST
W
k S
1 dP
k S
1 (VG − V ) P
V
S62
E
1 (VG − V ) P GC ′[
]≈ L L −
= L L+
m2 K
lL S E S E dT lL S E T
T
V
S
SFCC䋨Series Forward Constant Current䋩ᤨ䈱㔚࿶ᄌൻ䈱⷗Ⓧ
∆VS
1 ∂VS
V − V ∆T
V − V ∆T
=
∆T ≈ − n G
=− G
VS
VS ∂T
nV T
V
T
=−
V䋺䋱୘䈱Diode䈮䈎䈎䉎㔚࿶
P䋺䋱୘䈱Diode䈱ᶖ⾌㔚ജ
1 VG − V ka EIR
1 VG − V
ka EIR
≈−
T V
T V  kL S L 1 (VG − V ) nP 
GC′
+


V
SE 
 lL S E T
i = i0 S S exp(−
qVG 
qV
i = 1010 × 30 × 30µ m2 exp(−
∆VS
1 1.12 − 0.26
0.025
=−
≈ −5 ×10−9
300
0.26
VS

1 (1.12 − 0.26 ) 2 × 0.16 µW 
4
 5.5 ×10 +

2
300
0.26
900 µ m 
-0.011

⇒ P = 0.16µW
∆VS
1 1.12 − 0.65
0.025
=−
≈ −1× 10−9
300
0.65 
VS
1 (1.12 − 0.65) 2 × 0.7 mW 
4
 5.5 ×10 +
2 
-0.0024
300
0.65
900 µ m 

⇒ P = 0.7mW
i = 1010 × 30 × 30µ m2 exp(−
4

) exp(
) − 1
η kT 
η kT

1.12 
0.26

)  exp(
) − 1 = 4nA (148 − 1) = 0.6 µ A
2 × 0.026 
2 × 0.026

1.12 
0.65

)  exp(
) − 1 = 4nA ( 2.7 × 105 − 1) = 1mA
2 × 0.026 
2 × 0.026

3.7E3
∂ VS
n
≈ − (VG − V )
∂T
T
EIR = 0.025[W
m2
1 dP
S dT
=−
I = CONST
1 (VG − V ) nP
T
V
S
] at F = 1, τ λ = 0.5, ∆TO = 0.1K
k [0]EIR [W m2 ]
∆TΦMAX [ K ] = a
G ′[W m2 K ]
C
P = Vi0S S exp( −
qVG 
qV

)  exp( ) − 1
kT 
kT

1 dP k L S L 1 (VG − V ) nP
W
k S
GC′[ 2 ] ≈ L L −
=
+
63
mK
lL SE S E dT lL SE T
V
SE
64
Heat Model of Uncooled FPA IR Detector
䇭䇭䇭䇭䇭䇭䇭䇭䇭䇭䋨䉁䈫䉄䋩
䊶න⚛ሶో㕙䉕䋱୘䈱䉻䉟䉥䊷䊄䈱ធว㕙Ⓧ䈫ห䈛䈫䈜䉎䇯
䊶Bias䉕㗅ᣇะቯ㔚࿶䈫䈜䉎䇯
䊶䈠䈱Bias㔚࿶䉕಴᧪䉎㒢䉍㜞䈒⸳ቯ䈚䇮
䇭Bias㔚ജᱜᏫㆶലᨐ䉕㜞䉄䉎䋨ᔕ╵ᤨ㑆䈮䈲૛⵨䈏᦭䉎䋩䇯
ෳ⠨⾗ᢱ
䇭䋨Ᏹ䈮Bias㔚ᵹ䉕ో⚛ሶ䈮ᵹ䈚⛯䈔䉎䈫䇮FPA䈱᷷ᐲ䈏਄᣹䈜䉎䈢䉄䇮
䇭䇭Dynamical Biasing䈫䈚䇮৻ㇱ䈱ᢙⴕ䈮Bias㔚ᵹ䉕ᵹ䈚Scan䈜䉎䇯䋩
SFCC䋺Series Forward Constant Current
OFCV䋺One Diode Forward Constant Voltage
OFCC䋺One Diode Forward Constant Current
SSCC䋺Series Small Constant Current
PRCV䋺Parallel Reverse Constant Voltage
PFCV䋺Parallel Forward Constant Voltage
䊶䌇C䈏ዊ䈘䈒䈭䉍ᗵᐲ䈏ะ਄䈜䉎䇯
65
66
11
END
67
12

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