CAP 1-4.pdf

© A. Calomarde, Edicions Virtuals

Transparencia 1-1

$&DORPDUGH 'HSDUWDPHQWG¶(QJLQ\HULD(OHFWUzQLFD 8QLYHUVLWDW3ROLWqFQLFDGH&DWDOXQ\D

)tVLFDGHOHVWDGRVyOLGR &RQGXFFLyQ

(OHFWUyQLFD

(OHFWUyQLFD

&DUDFWHUtVWLFDVGHORV6HPLFRQGXFWRUHV • 6HPLFRQGXFWRULQWUtQVHFR60&SXUR6L*H*D$V – %DQGDGHYDOHQFLDHOHFWURQHV

• &DUDFWHUtVWLFDVD. – &DGDiWRPRHVWiURGHDGRGHHOHFWURQHVH – /RVHGHODEDQGDGHYDOHQFLDHVWiQFRPSDUWLGRVFRQORViWRPRV YHFLQRV – &DGDSDUGHHFRPSDUWLGRVIRUPDQXQHQODFHFRYDOHQWH – 7RGRVORVHHVWiQHQODEDQGDGHYDOHQFLD%9 +4

+4

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+4

(VTXHPDELGLPHQVLRQDO 60&D.


Transparencia 1-2

(OHFWUyQLFD

*HQHUDFLyQGHSDUHVHOHFWUyQKXHFR +4

+4

+4

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e-

h+ +4

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7!.

• $7!.HOHVDOWDDODEDQGDGHFRQGXFFLyQ • /DFRQGXFFLyQVHSURGXFLUiSRU – HHQODEDQGDGHFRQGXFFLyQ – KHQODEDQGDGHYDOHQFLD

w Nº de electrones en la BC = Nº de huecos en la BV © A. Calomarde, Edicions Virtuals

Transparencia 1-3

(OHFWUyQLFD

0RYLPLHQWRGHOKXHFR +4

+4

+4

+4

+4

+4

+4

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h+ +4

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• 3XHGHFRQVLGHUDUVHHOPRYLPLHQWRGHOKGHELGRD ODWUDQVIHUHQFLDGHODLRQL]DFLyQDRWURiWRPRD FDXVDGHOVDOWRGHOH


Transparencia 1-4

(OHFWUyQLFD

60&H[WUtQVHFRV • 60&LQWUtQVHFR60&FULVWDOLQRVLQLPSXUH]DV • 60&H[WUtQVHFR60&FULVWDOLQRHQHOTXHVHKDQ LQWURGXFLGRLPSXUH]DVGHXQDIRUPDFRQWURODGD

,PSXUH]DVJUXSR,,,60&WLSR3 %$O,Q*D 0D\RUQ~PHURGHKXHFRV³OLEUHV´


,PSXUH]DVJUXSR960&WLSR1 3$V6E 0D\RUQ~PHURGHHOHFWURQHVHQ%&

Transparencia 1-5

(OHFWUyQLFD

60&H[WUtQVHFRV Tipo N

QHOHFWURQHVOLEUHV

Tipo P

+4

+4

+4

+4

+4

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+5

+4

+4

+3

+4

+4

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+4

+4

,RQL]DFLyQLPSXUH]DV5RWXUD

QHOHFWURQHVOLEUHV

+4 5RWXUDHQODFHVFRYDOHQWHV

HQODFHVFRYDOHQWHV QKXHFRVOLEUHV

5RWXUDHQODFHVFRYDOHQWHV

QKXHFRVOLEUHV

,RQL]DFLyQLPSXUH]DV5RWXUD HQODFHVFRYDOHQWHV

QHOHFWURQHVOLEUHV!QKXHFRVOLEUHV

QHOHFWURQHVOLEUHVQKXHFRVOLEUHV


Transparencia 1-6

(OHFWUyQLFD

5HODFLyQHQWUHFRQFHQWUDFLRQHV HQHTXLOLEULRGHORVSRUWDGRUHV • /H\GHDFFLyQGHPDVDV » Q FRQFHQWUDFLyQGHHOHFWURQHVOLEUHVQHOHFWURQHVYROXPHQ » S FRQFHQWUDFLyQGHKXHFRVOLEUHVQKXHFRVYROXPHQ – $XQDWHPSHUDWXUDGDGDODJHQHUDFLyQGHSRUWDGRUHV\OD UHFRPELQDFLyQVHSURGXFLUiQDODPLVPDYHORFLGDG » /DVFRQFHQWUDFLRQHVQ\SVHPDQWHQGUiQFRQVWDQWHVHQHOWLHPSR – (QXQVHPLFRQGXFWRULQWULQVHFRWHQGUHPRV n = p = ni GRQGHQLHVODFRQFHQWUDFLyQGHH\KHQXQPDWHULDOLQWUtQVHFR 3XHGHGHPRVWUDUVHTXH

QL2 (7 ) = $ ⋅ 7 3 ⋅ H © A. Calomarde, Edicions Virtuals

− ( JR

.7

Transparencia 1-7

(OHFWUyQLFD – 3DUDHO*H\HO6L

QL2 (7 ) = 3,1 ⋅1032 ⋅ 7 3 ⋅ H −9100 / 7 FP −6 *H QL2 (7 ) = 1,5 ⋅1033 ⋅ 7 3 ⋅ H −14000 / 7 FP −6 6L

– 3XHGHGHPRVWUDUVHTXHSDUDFXDOTXLHUVHPLFRQGXFWRUVH FXPSOHODUHODFLyQ

Q ⋅ S = Q 2 (7 ) L

– TXHHVOD/(<'($&&,Ï1'(0$6$6


Transparencia 1-8

(OHFWUyQLFD

/H\GHQHXWUDOLGDGGHFDUJD • 1RVLQGLFDTXHODFDUJDQHWDHQXQFULVWDOHVQXOD – $VtVLVXSRQHPRV { ND&RQFHQWUDFLyQGHGRQDGRUHV(Donadores/volumen). { NA&RQFHQWUDFLyQGHDFHSWDGRUHV(Aceptadores/volumen). { n\pFRQFHQWUDFLyQGHe-\h+. – 7HQHPRVTXH Total carga positiva = total carga negativa.

1' + S = 1 $ + Q


Transparencia 1-9

(OHFWUyQLFD

• $VtWHQHPRV – 6LND >> NAHQWRQFHVn >> p60&WLSRQ

Q2 Q ≈ 1 ' S ≈ L 1' 6LNA >> NDHQWRQFHVp >> n60&WLSRS

S ≈ 1 $ Q ≈

QL2 1$


Transparencia 1-10

(OHFWUyQLFD

&RQGXFWLYLGDGHQ60& V

E A

L

– 6yOLGRHQHOTXHH[LVWHQHOLEUHVREHGHFHQDXQFDPSRHOpFWULFR – /RVHOLEUHVVHPXHYHQFRQXQDYHORFLGDGPHGLDSURSRUFLRQDODOFDPSR (OpFWULFR

YGULIWα (

/ODPDUHPRVµPRYLOLGDGHQcm2/V·s DODFRQVWDQWHGHSURSRUFLRQDOLGDG

YGULIW = µ ( © A. Calomarde, Edicions Virtuals

Transparencia 1-11

(OHFWUyQLFD – /DFRUULHQWHHVPRYLPLHQWRGHFDUJDVSRUXQLGDGGHWLHPSR

,≡

&DQWLGDG GHFDUJD T (Q ⋅ YROXPHQ ) T (Q ⋅ $ ⋅ / ) = = = T ⋅ Q ⋅ $ ⋅ YGULIW W W W

-=

, 9 = T ⋅ Q ⋅ YGULIW = T ⋅ Q ⋅ µ H ⋅ ( = T ⋅ Q ⋅ µ H ⋅ $ /

/DGHQVLGDGGHFRUULHQWHHVSURSRUFLRQDOD /DGHQVLGDGGHFDUJD /DPRYLOLGDGGHORVSRUWDGRUHV

6LUHODFLRQDPRVHOUHVXOWDGRDQWHULRUFRQODOH\GH2KP, 95

5=
/ $

1 / T ⋅ Q ⋅ µH $

WHQHPRVTXH

ρ=

1 1 ≡ T ⋅ Q ⋅ µH σ


Transparencia 1-12

(OHFWUyQLFD – 3DUDREWHQHUODFRQGXFWLYLGDGHQXQVHPLFRQGXFWRUWHQGUHPRV TXHWHQHUHQFXHQWDODFRQGXFWLYLGDGGHKXHFRV\HOHFWURQHV » σH= conductividad del electrón. » σK= conductividad del hueco. – $VLPLVPRSDUDODPRYLOLGDG » µH= movilidad del electrón. » µK= movilidad del hueco. – 3RUORTXHSRGUHPRVHVFULELUSDUDXQVHPLFRQGXFWRU

- = (σ H + σ K )( - = T (Qµ H + µ K )(

– $VtODFRQGXFWLYLGDGHQXQVHPLFRQGXFWRUVHUi

σ = T(Qµ H + µ K )

– 3DUDORV60&PiVXWLOL]DGRV

 µ = 2,1 ⋅109 7 − 2, 5 6LOLFLR  H 9 −2, 7 µ H = 2,3 ⋅10 7

µ = 4,9 ⋅10 7 7 −1, 66 *HUPDQLR H 9 − 2 , 33  µ H = 1,05 ⋅10 7 © A. Calomarde, Edicions Virtuals

para 160º . < 7 < 400º . para 150º . < 7 < 400º . para 100º . < 7 < 300º . para 125º . < 7 < 300º . Transparencia 1-13

(OHFWUyQLFD

'HQVLGDGGH&RUULHQWHWRWDOHQXQ60& • ([LVWHQPHFDQLVPRVGHFRUULHQWHHQXQ60& – $ 'HQVLGDGGHFRUULHQWHGHGLIXVLyQ n

Corriente de difusión

x

δQ δ[ = T ⋅ gradQ ⋅ 'Q

- GLI α − - GLI ,Q

- GLI , S = − T ⋅ gradS ⋅ ' S – 'RQGHDn\DpVRQORVFRHILFLHQWHVGHGLIXVLyQGHORV HOHFWURQHV\KXHFRV © A. Calomarde, Edicions Virtuals

Transparencia 1-14

(OHFWUyQLFD – % 'HQVLGDGGHFRUULHQWHGHDUUDVWUH

- GULIW = T(Qµ H + Sµ K )(
- 727$/ = - GULIW + - GLI

- 727$/ = T (Qµ H + Sµ K )( + T (grad Q ⋅ 'Q − grad S ⋅ ' S )
δS   δQ - 727$/ = T (Qµ H + Sµ K )( + T 'Q − ' S  δ[   δ[


Transparencia 1-15

(OHFWUyQLFD

5HODFLyQGH(LQVWHLQ • 6HFXPSOHTXH 'Q = µ Q97

' S = µ S97 – 'RQGH

.7 (tensión termodinámica) T K = 1,38 ⋅10 -23 -RXO ⋅ VHJ (constante de Boltzman)

97 =

q = 1,6 ⋅10-19 & (carga del electrón) © A. Calomarde, Edicions Virtuals

Transparencia 1-16

(OHFWUyQLFD

(FXDFLyQGH%ROW]PDQSDUDSRUWDGRUHV • 3HUPLWHUHODFLRQDUFRQFHQWUDFLyQGHSRUWDGRUHV\ SRWHQFLDOHV – 3DUWLPRVGHXQ60&VLQH[FLWDFLyQH[WHULRU\FRQXQD FRQFHQWUDFLyQGHSRUWDGRUHV n

x1

x2

/DFRUULHQWHWRWDOGHHOHFWURQHVHQHO60&HVFHURSRUORTXH

Tµ Q Q( + T © A. Calomarde, Edicions Virtuals

δQ ' =0 δ[ Q Transparencia 1-17

(OHFWUyQLFD –(VGHFLU

Tµ Q Q( = − T

δQ ' δ[ Q

– 7HQLHQGRHQFXHQWDODUHODFLyQGH(LQVWHLQ

( = −97

1 δQ Q δ[

4XHHVSUHFLVDPHQWHHOFDPSRHOpFWULFRTXHVHRSRQHDODGLIXVLyQ GHHOHFWURQHV\PDQWLHQHn(x)FRQVWDQWHHQHOWLHPSRHQFDGDSXQWR 3RUODOH\GH*DXVVSDUDXQDGLPHQVLyQ

−

δ9 1 δQ = −97 δ[ Q δ[

2SHUDQGR

δ9 = 97

δQ Q


Transparencia 1-18

(OHFWUyQLFD – (VGHFLUHQWUHORVSXQWRVx1\x2ODGLIHUHQFLDGHSRWHQFLDOVHUi

∫

2

1

∂9 = 97 ∫

2

1

∂Q Q

6L9\9VRQORVSRWHQFLDOHVGH[\[HQWRQFHV

92 − 91 = 97 ln

Q2 Q1

2PiVKDELWXDOPHQWH

Q1 = Q2 ⋅ H

91 −92 97

S2 = S1 ⋅ H © A. Calomarde, Edicions Virtuals

91 −92 97 Transparencia 1-19

(OHFWUyQLFD

5HVXPHQ – 3ULQFLSDOHVVHPLFRQGXFWRUHV6L*H*D$V – &RUULHQWHVJHQHUDGDVSRUHOHFWURQHV\KXHFRV – 7UHVWLSRVGHVHPLFRQGXFWRUHV » 6HPLFRQGXFWRULQWUtQVHFRn = p = ni » 6HPLFRQGXFWRUH[WUtQVHFRWLSRQn >> p » 6HPLFRQGXFWRUH[WUtQVHFRWLSRSp >> n – 5HODFLyQHQWUHSRUWDGRUHV

Q ⋅ S = QL2 (7 )

1' + S = 1$ + Q –&RUULHQWHVHQXQ60& »3RUDUUDVWUHSURYRFDGDSRUHOFDPSRHOpFWULFR »3RUGLIXVLyQSURYRFDGDSRUODGLIHUHQFLDGHFRQFHQWUDFLRQHV


Transparencia 1-20


Transparencia 2-1


8QLyQ31

(OHFWUyQLFD

(OHFWUyQLFD

8QLyQ31VLQSRODUL]DU 1'1$ =RQD3

=RQD1

&RQFHQWUDFLyQGH LPSXUH]DV

[

QQ

SS QS

&RQFHQWUDFLyQGH SRUWDGRUHVDQWHV GHODXQLyQ

SQ [

KXHFRVPD\RULWDULRV HOHFWURQHVPLQRULWDULRV

HOHFWURQHVPD\RULWDULRV KXHFRVPLQRULWDULRV


Transparencia 2-2

(OHFWUyQLFD V R L U D W L U R X \ I D L ' P H G Q y L V

Q

[

H G H U W V D U U $

[

[

V R L U D W L U R Q L P

[

Q

Q

S

2

9

[

ρ

H

ω

Q

ω

Q

$

1 T

[ (

0

(

'

[ 9

1 T

S

S

S

ω

S

ω

S

ω

K

ω

ω

Q

ω

Q

S

S

Q

H G O L I U H 3

R G D S R '


H G G D G L V

D W H Q D Q J H U D ' F

R S P D &

R F L U W F p O

(

O D L F Q H W

R 3

Transparencia 2-3

(OHFWUyQLFD

'HQVLGDGGHFDUJD –3XHGHDGPLWLUVHTXHODVFDUJDVHQOD]RQD1VRQ ρ(x) = q [ND(x) - nn(x)] –

Transparencia 2-4

(OHFWUyQLFD

&DPSR(OpFWULFR – 3DUDREWHQHUORVHDSOLFDUiODOH\GH*DXVVHQXQDGLPHQVLyQ

( ( [) = 1 ∫ ρ ( [)G[ ε

– 2EWHQLHQGRSDUDOD]RQD1\]RQD3 Zona P ⇒ (3 ( [ ) = −

T1 $

Zona N ⇒ (1 ( [) = −

ε

([ + ω 3 )

T1 ' (ω − [ ) 1 ε

– &RLQFLGLHQGRVXYDORUPi[LPRHQ[

(0 = − T1 $ ω 3 = − T1 ' ω 1 ε

ε

–
T 1 $1' ω ε 1 $ + 1' Transparencia 2-5

(OHFWUyQLFD

3RWHQFLDOGHFRQWDFWR – $WHQLHQGRDODHFXDFLyQGH%ROW]PDQQ TXHQRVGDODGLIHUHQFLDGHSRWHQFLDOHQ XQ60&HQIXQFLyQGHODVFRQFHQWUDFLRQHV GHSRUWDGRUHV 92 − 91 = −97 ln

Q

S1 S2

[

[

–3XHGHDSOLFDUVHHQODXQLyQ31SDUDREWHQHUHOSRWHQFLDO

91 − 93 = −97 ln

S SQ0 = 9 ln S 0 S S 0 7 SQ0

–$SOLFDQGROD/H\GHDFFLyQGHPDVDV

S Q = Q2 QR

QR

S =

L

QR

Q2 Q L

QR


Transparencia 2-6

(OHFWUyQLFD –
S Q 91 − 93 = 97 ln S 02 Q 0 QL –
1 $1' QL2

– 3XHGHREWHQHUVHWDPELpQHOSRWHQFLDODSDUWLUGHOFDPSR HOpFWULFR

93 ( [) = T1 $ ( [ + ω 3 )2 ε

91 ( [) = T1 ' [ω 1 (ω 3 + ω 1 ) − (ω 1 − [ )2 ] ε

92 = T1 $ω 3 ω = T1 'ω 1 ω 2ε


2ε

Transparencia 2-7

[

(OHFWUyQLFD

$QFKRGHOD]RQDGHFDUJDHVSDFLDO – 3DUDREWHQHUHODQFKRGHOD]FHVHSXHGHREVHUYDUTXH

92 = 1 (− (0 )ω 2

–
90 = T 1 $ 1 ' ω 2 2ε 1 $ + 1 ' –
ω=

1 $ + 1' 9 T 1 $1' 0

2ε


Transparencia 2-8

(OHFWUyQLFD

&DUDFWHUtVWLFD7HQVLyQ&RUULHQWH • 3DUDODREWHQFLyQGHODFDUDFWHUtVWLFD9,VXSRQGUHPRV – (QOD]FHQRH[LVWHQLJHQHUDFLyQQLUHFRPELQDFLyQ – ,Q\HFFLyQGHSRUWDGRUHVGpELOVyORYDUtDQODVFRQFHQWUDFLRQHVGH PLQRULWDULRV – 7RGRHOSRWHQFLDOH[WHUQRDSOLFDGRDSDUHFHHQOD]FH\QRHQODV ³]RQDVQHXWUDV´

• 'RVWLSRVGHSRODUL]DFLRQHV – 'LUHFWD ÍVP > VN – ,QYHUVDÍVN > VP


Transparencia 2-9

(OHFWUyQLFD

3

9 )

1

S S 1 $

QQ

H

K

SQ[

QS[

Q S

1'

[S

SQ

[Q

– ([LVWHXQDLQ\HFFLyQGHSRUWDGRUHVPLQRULWDULRVHQ-xp\xn /RV PD\RULWDULRVQRVHYHUiQPRGLILFDGRVHQGpELOLQ\HFFLyQ – 'HELGRDHVWDLQ\HFFLyQGHSRUWDGRUHVDSDUHFHXQJUDGLHQWHGH SRUWDGRUHVPLQRULWDULRV

∂Q S ( [ ) ∂[

≠0


Transparencia 2-10

(OHFWUyQLFD –
∂S ( [) ∂Q( [)   - GLII = - GLI , S + - GLI , Q = T − '3 + '1 ∂[ ∂[   – 3DUDFRQRFHUHOJUDGLHQWHXWLOL]DUHPRVOD³(FXDFLyQGH &RQWLQXLGDG´SDUWLFXODUL]DGD

∂SQ ( [, W ) ∂ 2 S ( [ , W ) SQ ( [ ) − SQ 0 = '3 − ∂W ∂[ 2 τ3 – 'RQGHτHVHOWLHPSRGHYLGDPHGLRGHORVSRUWDGRUHV –
'3

∂ S ( [ , W ) SQ ( [ ) − SQ 0 − =0 ∂[ 2 τ3 2

– /DVFRQGLFLRQHVGHFRQWRUQRVRQ

Q2 a) Para [ → ∞ SQ ( [) = SQ 0 = L 1' b) Para [ = x n ; SQ ( [Q )


Transparencia 2-11

(OHFWUyQLFD » 3DUDREWHQHUODFRQGLFLyQXWLOL]DPRVODHFXDFLyQGH %ROW]PDQQ

En equilibrio : S 92 = 97 ln S 0 SQ 0 92

S S 0 = SQ 0H 97 Fuera de equilibrio :

92 −9 )

S S 0 = SQ ( [)H 97

» $OWHQHUGpELOLQ\HFFLyQHQDPERVFDVRVpp0 FRLQFLGLUi

SQ 0H

90 97

= SQ ( [ )H

90 −9 ) 97

9)

SQ ( [Q ) = SQ 0H 97

⇒£££(VWDPRVLQ\HFWDQGR SRUWDGRUHVGHIRUPD H[SRQHQFLDOFRQOD


VF

Transparencia 2-12

(OHFWUyQLFD – &RQODVGRVFRQGLFLRQHVUHVROYHPRVODHFGLIHUHQFLDO

 9)  − ( [ − [Q ) SQ ( [ ) = SQ 0 + SQ  H 97 − 1H /3     – 6LHQGRODORQJLWXGGHGLIXVLyQGHORVKXHFRV /3 = '3τ 3 – $KRUDSRGHPRVFRQRFHUODFRUULHQWHGHGLIXVLyQGHORVKXHFRV

- GLI , S ( [Q ) = −T'3 ∂S( [) ∂[ [ = [

= Q

T'3 SQ0  H99 /3 

)

7

 − 1  

– $QiORJDPHQWHSDUDORVHOHFWURQHV

- GLI , Q ([ S ) = T'1 ∂Q( [) ∂[ [ = [


= S

T'1 Q S0  99 H /1 

)

7

 − 1  

Transparencia 2-13

(OHFWUyQLFD – 6LUHFRUGDPRVTXHQRKD\QLUHFRPELQDFLyQQLJHQHUDFLyQHQOD ]FHWHQGUHPRVTXHODFRUULHQWHHVFRQVWDQWHHQHOOD\DVt WHQGUHPRV -

-

7

- 7

- -

1', ))

7

-

3', ))

-

1', ) )

3' ,))

[ 1

[ 3

[

[

3

[

1


Transparencia 2-14

(OHFWUyQLFD – $VtODVXPDGHORVGRVWpUPLQRVPHGDUiODFRUULHQWHWRWDO

9)   T'1 Q S 0 T'3 SQ 0  97 + ,7 = $- 7 = $ H − 1   /3   /1   IS ,

,6 9


Transparencia 2-15

(OHFWUyQLFD

0RGHORGLQiPLFRGHO'LRGR • 6H KD REWHQLGR OD FDUDFWHUtVWLFD I-V EDMR FRQGLFLRQHV HVWiWLFDV SHUR EDMR FRQGLFLRQHV GLQiPLFDV DSDUHFHQ WUHV HIHFWRVQRFRQVLGHUDGRVKDVWDDKRUD • D &DSDFLGDGGHWUDQVLFLyQCJ – 3URYRFDGDSRUODYDULDFLyQGH]FHDOYDULDUODWHQVLyQHQODXQLyQ

ρ[

[


Transparencia 2-16

(OHFWUyQLFD – /DYDULDFLyQGHFDUJDFXDQGRVHDSOLFDXQDWHQVLyQ9-VHUi

T (9 ) = 4 Y

-

-

(0) + 4- (9- )

– 7HQLHQGRHQ – 3RODUL]DFLyQGLUHFWDqV(VJ) > 0, VJ > 0 – 3RODUL]DFLyQLQYHUVDqV(VJ) < 0, VJ < 0 – 3RUORTXHODFDUJDPyYLODOPDFHQDGDHQODV]RQDVQHXWUDV DXPHQWDUiDODXPHQWDUODWHQVLyQ9-\ODFDSDFLGDGGH WUDQVLFLyQVHUi

&- = GT9 (9- ) G9– &RPRQJ(0) = cteWHQGUHPRVTXH &- = −


G4- (9- ) G9-

Transparencia 2-17

(OHFWUyQLFD – 3DUDHOORODFDUJDWRWDOHQHOODGR1GHOD]FHFRQXQDWHQVLyQ 9-VHUi

4- = $T1 'ω 1 = $T1 ' $T

1$ ω= 1 $ + 1'

 1 $ 1 '  2ε  1 1  (92 − 9 ) +   1 $ + 1 '  T  1 $ 1 '  

1

2

–
&- = $

1

2

ε 2ε  1 1   (92 − 9 ) + T  1 $ 1 ' 


Transparencia 2-18

(OHFWUyQLFD –
&- = $

ε ω

•E &DSDFLGDGGHGLIXVLyQ – 'HELGDDODYDULDFLyQGHODVFRQFHQWUDFLRQHVGHSRUWDGRUHVHQ ODV]RQDVQHXWUDVDOSRODUL]DUODXQLyQ QS

[


Transparencia 2-19

(OHFWUyQLFD – 3XHGHGHPRVWUDUVHTXHHVWDFDSDFLGDGVLJXHXQDOH\GHOWLSR 9

&' = .H97 – /DFXDODXPHQWDWDPELpQFRQODWHQVLyQDSOLFDGDSHURDXQ ULWPRVXSHULRUVLHQGRpVWD~OWLPDSUHGRPLQDQWHHQ SRODUL]DFLyQGLUHFWD\HQSRODUL]DFLyQLQYHUVDODFDSDFLGDGGH WUDQVLFLyQ

&' &-

9 © A. Calomarde, Edicions Virtuals

Transparencia 2-20

(OHFWUyQLFD

• F 5HVLVWHQFLDGLQiPLFD – &RQVLGHUDUHPRVODUHVLVWHQFLDGLQiPLFDFRPR

UG =

G9 G, 4

,

,&

4

UG =

9&

9

1 G9 = WDQψ G, 4

Ψ


Transparencia 2-21

(OHFWUyQLFD – $VtHOYDORUGHODUHVLVWHQFLDGLQiPLFDSXHGHGHGXFLUVHDSDUWLU GHODH[SUHVLyQGHODFRUULHQWHHQODXQLyQ 9

1 G, , = = 6 H97 UG G9 4 97 – 3RUORTXH

UG

97

=

,6H

9 97

97

= ,

+ ,6H

9 97

≈

97

si 9 >> 97

,


Transparencia 2-22

(OHFWUyQLFD

0HFDQLVPRVGHUXSWXUD • $ODXPHQWDUODWHQVLyQLQYHUVDGHSRODUL]DFLyQ OOHJDXQSXQWRHQHOFXDOODFRUULHQWHDXPHQWDXQ HOHYDGRLQFUHPHQWRGHELGRDGRVPHFDQLVPRV , GLIHUHQWHV – (IHFWR]HQHU – (IHFWRDYDODQFKD

9= 9


Transparencia 2-23

(OHFWUyQLFD – 5XSWXUD]HQHU » 3UHGRPLQDHQGLRGRVFRQWHQVLyQGHUXSWXUDEDMD » 3URGXFLGRHQXQLRQHVGRQGHORVGRSDGRVVRQHOHYDGRVORV FXDOHVSURGXFHQXQHOHYDGRFDPSRHOpFWULFRTXHHVFDSD] GHDUUDQFDUHOHFWURQHVGHORVHQODFHVFRYDOHQWHVHQOD]FH » 6HGHPXHVWUDTXHVHSURGXFHSDUDWHQVLRQHVTXHFXPSOHQ VZ ≤ 4Ego/q – 5XSWXUDDYDODQFKD » 3UHGRPLQDHQGLRGRVFRQWHQVLyQGHUXSWXUDDOWD » 3URGXFLGRSRUODDFHOHUDFLyQGHORVHHQOD]FHGHELGRD ODSUHVHQFLDGHOFDPSRHOpFWULFR/DHQHUJtDFLQpWLFDTXH DGTXLHUHQODHPSOHDQSDUDLRQL]DUSRULPSDFWRiWRPRVGHOD ]FHJHQHUDQGRQXHYRVSRUWDGRUHVTXHVHDFHOHUDQDVX YH]GDQGROXJDUDXQHIHFWRPXOWLSOLFDWLYR » 6HGHPXHVWUDTXHVHSURGXFHSDUDWHQVLRQHVTXHFXPSOHQ VZ ≥ 6Ego/q

Ego= Energía del gap


Transparencia 2-24

(OHFWUyQLFD

&RQFOXVLRQHV • 8QLyQ31'LVSRVLWLYRIRUPDGRSRUXQH[WUHPRSRU 60&WLSR1\HQHORWUR60&WLSR3 • $SDUHFHQHQODXQLyQPHFDQLVPRVGH – – – –

'LIXVLyQGHPD\RULWDULRV 'HQVLGDGGHFDUJDQRQXOD &DPSRHOpFWULFRTXHSURYRFDDUUDVWUHGHPLQRULWDULRV 3RWHQFLDOGHFRQWDFWR

• 6XFDUDFWHUtVWLFD,9HV ,'

 9'  = , 6  H 97 − 1    

– &RQXQDIXHUWHGHSHQGHQFLDGHODFRUULHQWHFRQODWHPSHUDWXUD © A. Calomarde, Edicions Virtuals

Transparencia 2-25

(OHFWUyQLFD

• (QUpJLPHQGLQiPLFRDSDUHFHQWUHVHIHFWRV – &DSDFLGDGGHWUDQVLFLyQ – &DSDFLGDGGHGLIXVLyQ – 5HVLVWHQFLDGLQiPLFD

• &RQWHQVLRQHVLQYHUVDVHOHYDGDVDSDUHFHHO HIHFWR]HQHURDYDODQFKD • $SDUWLUGHDKRUDOHGHQRPLQDUHPRV',2'2\VX UHSUHVHQWDFLyQHVTXHPiWLFDVHUi


]RQD3

]RQD1

È12'2

&È72'2

Transparencia 2-26


Transparencia 3-1


7UDQVLVWRU%LSRODU

(OHFWUyQLFD

(OHFWUyQLFD

,QWURGXFFLyQ • 'LVSRVLWLYREDVDGRHQGRVXQLRQHV31 – WLSRV Unión Emisora Emisor

Unión Emisora

Unión Colectora

P

N

Emisor

P

Unión Colectora

N

Base

P

N

Colector

Base

BJT PNP

BJT NPN Colector

Colector Base

Base

Emisor

Emisor © A. Calomarde, Edicions Virtuals

Transparencia 3-2

(OHFWUyQLFD

3RODUL]DFLRQHV • ([LVWLUiQWLSRVGHSRODUL]DFLyQ 3RODUL]DFLyQ 6DWXUDFLyQ $FWLYD $FWLYDLQYHUVD &RUWH

8QLyQHPLVRUD 'LUHFWD 'LUHFWD ,QYHUVD ,QYHUVD

8QLyQ&ROHFWRUD 'LUHFWD ,QYHUVD 'LUHFWD ,QYHUVD

• 7HQVLRQHV\FRUULHQWHVHQSRODUL]DFLyQDFWLYD VBC

VCB IC

IB

VEB


IC IB

IE

VEC VBE

IE

VCE

Transparencia 3-3

(OHFWUyQLFD

3RODUL]DFLyQHQDFWLYD • (OHPLVRUVXHOHHVWDUDOWDPHQWH GRSDGR\ODEDVHVXHOHVHUHVWUHFKD

p+

n++

n

» 2EWHQHPRVXQDLQ\HFFLyQGHSRUWDGRUHV HQHOFROHFWRUSURYHQLHQWHVGHOHPLVRU GHELGRDODJUDQGLIXVLyQGHSRUWDGRUHV PLQRULWDULRVHQODEDVH e

-

0 ωE

ωB


ωC

Transparencia 3-4

(OHFWUyQLFD

&RUULHQWHVHQHO%-7 Emisor

Base

Colector

IEP

ICP

IE

IC IEP-ICP IEN

IBB

ICN

IB

r r r r r

IEP&RUULHQWHGHKXHFRVHQHOHPLVRU IEN&RUULHQWHGHHOHFWURQHVHQHOHPLVRU ICP&RUULHQWHGHKXHFRVHQHOFROHFWRU ICN&RUULHQWHGHHOHFWURQHVHQHOFROHFWRU IBB+XHFRVUHFRPELQDGRVHQODEDVH IE =IEP + IEN IC =ICP + ICN IBB =IEP - ICP


Transparencia 3-5

(OHFWUyQLFD

'HQVLGDGGHSRUWDGRUHVPLQRULWDULRV • %DVH – $SDUWLUGHODFRUULHQWHGHGLIXVLyQ GHPLQRULWDULRV 2 '3  δ S2 Q  − SQ − SQ0 = 0 τS  δ[  –/DFXDOWHQGUiXQDVROXFLyQGHOWLSR SQ ( [ ) = SQ 0 + F1H

[

/S

+ F2 H

−[

B

E

ω

0

-XE

C

XC

ωB

/S

–4XHFRQODVVLJXLHQWHVFRQGLFLRQHVGHFRQWRUQR 9  S (0 ) = S H (% 97 Q0  Q  SQ (ω ) = 0 –6HREWLHQH 9(%

SQ ( [ ) =  SQ 0H 

97

   [  ω − [     VLQK    VLQK /   /3    3  + SQ 0 1 − − 1     ω  ω    VLQK /    VLQK /    3   3   


Transparencia 3-6

(OHFWUyQLFD

'HQVLGDGGHSRUWDGRUHVPLQRULWDULRV – 3XHGHQGLIHUHQFLDUVHGRVFDVRV ω  / >>&RPSRUWDPLHQWRH[SRQHQFLDO 3 ω  <<&RPSRUWDPLHQWRUHFWLOtQHR  /3 (QHOFDVRGHFRPSRUWDPLHQWRUHFWLOtQHR

9 (% [  [   9   = SQ2H 7 1 −   ω  ω – 4XHHVHOFDVRPiVKDELWXDOHQHO%-7

Q ( [ ) = SQ (0)1 −

S

• (PLVRU

(

)

[ [( Q( ( [ = − [( ) = Q(2H (% 97  9 (% /1( 9  Q( ( [ ) = Q(2 + Q(2 H 7 − 1 H  Q( ( [ → ∞ ) = Q(2 9


+

Transparencia 3-7

(OHFWUyQLFD

'HQVLGDGGHSRUWDGRUHVPLQRULWDULRV – &ROHFWRU

Q ( [ = [ ) = Q H ( &2  & Q& ( [ → ∞ ) = Q&2

− 9&%

97

[ [ −/ & ≈ 0 1& Q& ( [ ) = Q&2 − Q&2H  −

– $SDUWLUGHODVFRQFHQWUDFLRQHVGHPLQRULWDULRVVHSRGUiQ REWHQHUODVFRUULHQWHVGHOWUDQVLVWRUELSRODU


Transparencia 3-8

(OHFWUyQLFD

([SUHVLRQHVGHODVFRUULHQWHVHQHO%-7 Emisor

Base

Colector

IEP

ICP

IE

IC IEP-ICP IEN

IBB

ICN

IB

w IEP  ∂S , (3 = $− T'3 Q ∂[  , (3

 = [ =0 

     ω   9(% 97 SQ 0 1  = $T'3 − 1 + coth    H   ω  /S  /3   cosh     /3   


Transparencia 3-9

(OHFWUyQLFD

([SUHVLRQHVGHODVFRUULHQWHVHQHO%-7 – 7HQLHQGRHQFXHQWDTXH 6L

1 ω << 1 \VDELHQGRTXHFRWK\ = ≈ SDUD \ << /3 WDQ\ \

– 7HQHPRVTXH

, (3 = T$'3 , (3 =

QL2 1 /3  9(% 97 − 1 + 1 H   1 % /3 ω 

T$'3 QL2  9(% 97 T$'3 QL2 − 1 + H  1 %ω  1 %ω


Transparencia 3-10

(OHFWUyQLFD


Base

Colector

IEP

ICP

IE

IC IEP-ICP IEN

IBB

ICN

IB

w ICP   ∂S , &3 = $T'3 Q = [ ∂  [ =ω  S , &3 = $T'3 Q0 /S


 9(% 97  ω  1 − 1 + cosh   H   ω    /3  VLQK   /3 

Transparencia 3-11

(OHFWUyQLFD

([SUHVLRQHVGHODVFRUULHQWHVHQHO%-7 – 7HQLHQGRHQFXHQWDTXHVLω/LP

, &3 =

T$'3 QL2  9(% 97  T$'3 QL2 − 1 + H  1 %ω  1 %ω

– 3XHGHREVHUYDUVHTXHHVSUiFWLFDPHQWHHOYDORUGHIEP


Transparencia 3-12

(OHFWUyQLFD


Base

Colector

IEP

ICP

IE

IC IEP-ICP IEN

ICN

IBB

IB

w IEN

(

T$'1( Q(2 H , (1 = − $T'1( ∂Q( ( [) = ∂ [ /1( = − [ [   



9(%

97

)

−1

(

w ICN T$'1& Q&2 , (1 = $T'1& ∂Q& ( [) = [ /1(& ∂ = − [ [  &  




Transparencia 3-13

(OHFWUyQLFD


Base

Colector

IEP

IE

ICP IC IEP-ICP IEN

IBB

ICN

IB

w IE

(

, ( = , (3 + , (1 = D11 H

• 'RQGH

9(%

97

)

− 1 + D12

  '3 SQ 0 ω  ' Q   ' Q2 ' Q  coth  + 1( ( 0  ≅ T$ 3 L + 1( ( 0  D11 = T$ /1 0  /1 0   /3   1 %ω  /3         ' Q2  1  D = T$ '3 SQ 0 ≅ T$ 3 L   12   1 %ω   /3 VLQK ω     /    3   


Transparencia 3-14

(OHFWUyQLFD


Base

Colector

IEP

ICP

IE

IC

I EP-ICP IEN

ICN

IBB

IB

w IC

• 'RQGH

(

9 (%

, & = , &3 + , &1 = D21 H

97

)

− 1 + D22

       '3 QL2  1  D11 = T$ '3 SQ 0   ≅ T$   1 %ω   /3 VLQK ω        /3      '3 SQ 0 ω  ' Q   ' Q2 ' Q  coth   + 1& & 0  ≅ T$ 3 L + 1& & 0  D12 = T$ /1&  /1&   /3   1 %ω  /3 


Transparencia 3-15

(OHFWUyQLFD


Base

Colector

IEP

ICP

IE

IC IEP-ICP IEN

ICN

IBB

IB w IB

(

9 (%

, % ≡ , ( − , & = D11 H

(

= (D11 − D21 ) H

9(%

97

97

)

(

− 1 + D12 − D21 H

)

9(%

97

)

− 1 − D22 =

− 1 + (D12 − D22 )


Transparencia 3-16

(OHFWUyQLFD

(ILFLHQFLDGHLQ\HFFLyQ • &RUUHVSRQGHDODUHODFLyQHQWUHFRUULHQWHGH HPLVRU\SRUWDGRUHVLQ\HFWDGRVHQODEDVH γ=

γ=

, (3 , (3 + , (1

, (3 , (3 + , (1

T$'3 QL2  9(% 97 T$'3 QL2 − 1 + H  1%Z  1 %ω ≅ 2 9 (% T$'3 QL2  9(% 97 T$' Q T$' 3 L + 1( Q(2  H 97 − 1 − 1 + H      1 %ω  1 %ω /1(

T$'3 QL2 '3 QL2 1 1 %ω ≅ = = 2 T$'3 QL T$'1( Q(2 1 ω' Q 1 ω' Q '3 QL2 + % 1( (2 1 + % 21( (2 + 1 %ω /1( /1( '3 QL /1(

γ≅


1 1 % ω '1( 1+ 1 ( /1( '3 Transparencia 3-17

(OHFWUyQLFD

• 9HPRVTXHSDUDREWHQHUXQDHILFLHQFLDGH LQ\HFFLyQDOWDHVQHFHVDULR – ωEDMDDQFKRGHODEDVH r NE >> NB » 9DORUHVWtSLFRVVRQ { NE≅FP { NB≅FP { NC≅FP – (VWDVGRVFRQGLFLRQHVVHHQXPHUDURQDOSULQFLSLR\VHKDQ HVFRJLGRFRPRSDUiPHWURVSDUDODVLPSOLILFDFLyQGHDOJXQDV H[SUHVLRQHV


Transparencia 3-18

(OHFWUyQLFD

)DFWRUGHWUDQVSRUWH • 5HODFLyQHQWUHODFRUULHQWHTXHOOHJDDOFROHFWRU\ ODTXHVDOHGHOHPLVRU α7 =

ω  , &3 ω2 sec K  ≅ 1 − 2 , (3 /3  /3 

– 3DUDREWHQHUXQIDFWRUGHWUDQVSRUWHDOWRHOWUDQVLVWRUGHEHUi WHQHUXQDωSHTXHxD


Transparencia 3-19

(OHFWUyQLFD

*DQDQFLDGHO%-7 • /DJDQDQFLDGHO%-7YHQGUiGDGDSRUODUHODFLyQ GHODFRUULHQWHWRWDOGHOHPLVRUTXHOOHJDDO FROHFWRU α=

, &3 , (3 , &3 = ,( , ( , (3

 ω2  1 − 2   /   3  = γα 7 ≅ 1 % ω '1( 1+ 1 ( /1( '3

– 9DORUTXHVXHOHVHUPX\SUy[LPRDSHURPHQRUTXH%DMR HVWDVFRQGLFLRQHVVHGHILQHHOSDUiPHWURβFRPRODJDQDQFLD GHOWUDQVLVWRUHQWUHODEDVH\HOFROHFWRU ,& ,(

= α 2 + , &%2  α2 ,& = = ,& + , %  1 − α2


,%

+

, &%2

1 − α2

Transparencia 3-20

(OHFWUyQLFD

– 6LGHILQLPRV

β=

α0 1 − α0

, &(2 =

, &%2 α0

– 7HQGUHPRVODVVLJXLHQWHVUHODFLRQHVEiVLFDVHQWUHFRUULHQWHV HQHOWUDQVLVWRUHQSRODUL]DFLyQDFWLYD ,& ,( ,&

= α 0 + , &%2 = ,& + , %

= β, % + , &(2

– /DVFXDOHVQRVLQGLFDQTXHHO%-7HVXQGLVSRVLWLYR FRQWURODGRSRUFRUULHQWH


Transparencia 3-21

(OHFWUyQLFD

'LIHUHQWHVPRGRVGHRSHUDFLyQ npe

Directa

VBE pn npc

pn npe

npc

ACTIVA

SATURACIÓN

Inversa

Directa

npe

pn

npe Inversa

npc

pn CORTE

npc

ACTIVA INVERSA


Transparencia 3-22

(OHFWUyQLFD

0RGHORGH(EHUV0ROO • 8QDIRUPDJHQpULFDGHREWHQHUHOIXQFLRQDPLHQWR HQORVFXDWURPRGRVGHIXQFLRQDPLHQWRHV LQWHQWDUHVFULELUXQDH[SUHVLyQJHQHUDOGHOWLSR 9

9

&% (% , ( = , )2  H 97 − 1 − α 5 , 52  H 97 − 1     9

9

&% (% , & = α ) , )2  H 97 − 1 − , 52  H 97 − 1    

– 4XHSRUVLPLOLWXGFRQORVUHVXOWDGRVREWHQLGRVSDUDODV FRUULHQWHVGHOWUDQVLVWRUSXHGHQGHGXFLUVHORVSDUiPHWURVGH ODVHFXDFLRQHVGH(EHUV0ROO


Transparencia 3-23

VBC

(OHFWUyQLFD

&DUDFWHUtVWLFD,9 – 6LUHSUHVHQWDPRVODVHFXDFLRQHVDQWHULRUHVSDUDXQWUDQVLVWRU131REWHQHPRV

IB

IC

RUPTURA

SATURACIÓN IB2 IB1 IB0

βIB2 βIB1 βIB0

IB2>IB1>IB0

ACTIVA

VBE

ACTIVA INVERSA

CORTE

VCE

££6LPLODUDXQD XQLyQ31HQGLUHFWD


Transparencia 3-24

(OHFWUyQLFD

&RQFOXVLRQHV • WLSRVGHWUDQVLVWRUELSRODU

NPN

PNP

Colector

Colector Base

Base

Emisor

Emisor

– &XDWURWLSRVGHIXQFLRQDPLHQWR » $FWLYD » &RUWH » 6DWXUDFLyQ » $FWLYDLQYHUVD – (QDFWLYD ,& ,(

= α 0 + , &%2 = ,& + , %

= β, % © A. Calomarde, Edicions Virtuals ,&

+ , &(2 Transparencia 3-25


Transparencia 4-1


7UDQVLVWRU026

(OHFWUyQLFD

(OHFWUyQLFD

,QWURGXFFLyQ • (VWiIRUPDGRSRUXQDHVWUXFWXUDGH0HWDOÏ[LGR 6HPLFRQGXFWRU026 • 6LQGXGDDOJXQDHVHOGLVSRVLWLYRPiVXWLOL]DGRHQ HOHFWUyQLFDDFWXDOPHQWH • /DJUDQYHQWDMDTXHSUHVHQWDUHVSHFWRDO%-7HV VXJUDQFDSDFLGDGGHLQWHJUDFLyQ • 3DUDVXHVWXGLRHOXGLUHPRVODWHRUtDGHEDQGDV\ XVDUHPRVHOSRWHQFLDOGHFRQWDFWR\HOSULPHU SDVRVHUiFRQRFHUODHVWUXFWXUD026SDUD GHVSXpVHVWXGLDUHOWUDQVLVWRU026


Transparencia 4-2

(OHFWUyQLFD

3RWHQFLDOGHFRQWDFWR • 'RVPDWHULDOHVGHGLVWLQWDFRQFHQWUDFLyQGH SRUWDGRUHVDOSRQHUORVHQFRQWDFWRJHQHUDQHO OODPDGRSRWHQFLDOGHFRQWDFWR Fe Cu – (OHJLPRVXQPDWHULDOGHUHIHUHQFLDHO YDFtR\SRGUHPRVGHILQLUHOSRWHQFLDOGH FRQWDFWRGHOPDWHULDOUHVSHFWRGHOYDFtR Φ 0 1,9$&,2 = Φ 0 1 − Φ9$&,2 = Φ 0 1

Vo

– 6LFRQHFWiUDPRVHQVHULHYDULRVPDWHULDOHVWHQGUtDPRV

M1

M2

M3

M4

ΦM1,M2 ΦM2,M3 ΦM3,M4 Φ 0 1, 0Q = Φ 0 1, 0 2 + Φ 0 2, 0 3 +

MN- 1 MN

K

ΦMn-1,Mn

Φ 0Q −1, 0Q = = (Φ 0 1 − Φ 0 2 ) + (Φ 0 2 − Φ 0 3 ) + + (Φ 0Q −1 − Φ 0Q ) = = Φ 0 1 − Φ 0Q


K

Transparencia 4-3

(OHFWUyQLFD

7HQVLyQGHEDQGDSODQD Estructura M.O.S.

– $SDUHFHUiXQSRWHQFLDOHQWUH ODSXHUWD\HOVXEVWUDWRTXHVHUi

Metal Óxido (SiO2)

Puerta

EXON

 SRWHQFLDO    = Φ *$7( −Φ %8/. ≡ Φ 06 ∑ JDWH  GHFRQWDFWR

Si (P ó N) Sustrato

– 6LΦMS≠ DSDUHFHUiQFDUJDV DDPERVODGRVGHOy[LGRVLPLODUDODFDSDFLWDQFLDCV = Q – (VWDVFDUJDVGHVDSDUHFHUiQVLDSOLFDPRVXQDWHQVLyQH[WHUQDVGB TXHVHD H[DFWDPHQWHLJXDODΦMSSHURGHVLJQRFRQWUDULR

9*% = Φ 06 – (VWRQRHVWRWDOPHQWHFLHUWRGHELGRDTXHH[LVWHQFDUJDVSURYHQLHQWHVGH – LPSXUH]DVHQODLQWHUIDFHy[LGR60&\HQHOy[LGR


Transparencia 4-4

(OHFWUyQLFD – (VWDVFDUJDV4 SURYRFDUiQTXHODWHQVLyQSDUDKDFHU GHVDSDUHFHUWRGDVODVFDUJDVVHDDKRUD 4 9*% = Φ 06 + Φ 2; = Φ 06 − 0 &0

4XHSRUGHILQLFLyQHVOD7(16,Ï1'(%$1'$3/$1$ 9)% = Φ 06 −

40 &0

9DORUHVWtSLFRV Q0/C0 = - 0.45v

ΦMS

ΦM(Al) = 4.1 v ΦM(Poli N++) = 4.15 v; ΦM(Poli P++) = 5.25 v ΦS= 4.71 VT ln N/ni ≅0.29 v VFB SMC P(NA=1015) SMC N(ND=1015)


Al -1.35 -0.77

Poli N++ -1.3 -0.72

-Q0/C0

Poli P++ -0.2 +0.38

Transparencia 4-5

(OHFWUyQLFD

%DODQFHGHSRWHQFLDO\FDUJDSDUD XQDWHQVLyQH[WHUQD V GB

w VGB =ΦMS +ΦOX +ΦS – &XDQGRKD\DXQDYDULDFLyQGH9

HVWDVHUi

*%

DEVRUELGDSRUΦOX \RΦS SRU\DTXHΦMS HVFRQVWDQWH

QG Q0 z.c.e.

» ∆VGB =∆ΦOX +∆ΦS

ΦOX ΦS

QSC

w Q’G + Q’0 + Q’SC = 03DUDQHXWUDOLGDG – 6LKD\XQLQFUHPHQWRGHFDUJDHQHO³JDWH´VHUi – DEVRUELGRSRUQSC\DTXHQ0HVFRQVWDQWH » ∆Q’G +∆Q’SC =


Transparencia 4-6

(OHFWUyQLFD

(IHFWRGHVGB\VFBHQODVXSHUILFLH GHOVHPLFRQGXFWRU

• &RQVLGHUDUHPRVVXEVWUDWRWLSRP\JDWHGHAl (VFB =v) w VGB < VFB ⇒$&808/$&,Ï1 – /DFDUJDDGLFLRQDOHQ³JDWH´HVQHJDWLYDSRUORTXHDWUDHDODVXSHUILFLHGHO 60&FDUJDSRVLWLYDGHO6L\H[LVWHXQD³DFXPXODFLyQ´GHKXHFRV

− ΦS < 0 r Q’SC > 0

w VGB = - v = VFB⇒&RQGLFLyQGH%$1'$3/$1$ − ΦS = 0 r Q’G = - Q’0⇒Q’SC = 0

w VGB > VFB = -⇒'(3/(;,Ï1 – /DFDUJDHQ³JDWH´HVSRVLWLYDSRUORTXHDWUDHDODVXSHUILFLHGHO60&FDUJD QHJDWLYDGHO6L\H[LVWHXQD³GHSOH[LyQ´R]FHHQODVXSHUILFLHGHO60&

− ΦS > 0 , Q’SC < 0 © A. Calomarde, Edicions Virtuals

Transparencia 4-7

(OHFWUyQLFD

w VGB >> VFB⇒,19(56,Ï1 – /DFDUJDHQ³JDWH´HVSRVLWLYD\HOHYDGDSRUORTXHDWUDHDOD VXSHUILFLHGHO60&XQDHOHYDGDFDUJDQHJDWLYDHQODVXSHUILFLH GHWDOPDQHUDTXHqNAHVLQVXILFLHQWHSDUDFRPSHQVDUODFDUJD HQHOJDWH\DSDUHFHXQDEDQGDGHHHQODVXSHUILFLHGHO60& TXHDODXPHQWDUVGBKDUiTXHSUHGRPLQHQORVe-VREUHORVh+

− ΦS > 0 , Q’SC < 0

Balance de cargas para diferentes tensiones de V GB y SMC tipo P O

M

S

M

O

S

O

M

S

QG

h+

O

M

S

QG

QG

qNa

Acumulación QG < 0

Banda Plana VGB = VFB

Deplexión VGB > VFB

Inversión VGB >> VFB

VG B © A. Calomarde, Edicions Virtuals

Transparencia 4-8

(OHFWUyQLFD

&DUJDOLEUHLQYHUWLGD – /DFDUJDOLEUHLQYHUWLGDFRUUHVSRQGHDODFDUJDHQODVXSHUILFLH GHOVHPLFRQGXFWRUFXDQGRHO026HVWiHQLQYHUVLyQ – 6HJ~QODUHODFLyQGH%ROW]PDQ

Qsup = QEXON H

Φ6

97

– &RPR

S% Q% = QL2 \ S% ≅ 1 $ ⇒Q% ≅

QL2 1$

– 7HQHPRVTXH

Qsup =

QL2 Φ 6 97 H 1$


Transparencia 4-9

(OHFWUyQLFD – /DH[SUHVLyQGHOSRWHQFLDOGHFRQWDFWRGHO60&3HV Φ3 1$ 1 Φ ⇒ $ = H 97 3 = 97 ln QL QL

– 6XVWLWX\HQGR HQ REWHQHPRV Qsup = QL H

(Φ 6 − Φ 3 ) 9

ns(log)

7

–
Qsup = 1 $H

(Φ 6 − 2Φ 3 ) 9

7

– 'HELGRDTXHSHTXHxDVYDULDFLRQHV GHΦ6SURYRFDQJUDQGHVDXPHQWRV GHnsHQIXHUWHLQYHUVLyQ FRQVLGHUDUHPRVΦS= cte = 2ΦP

ΦP

ΦS

2ΦP

n=p=ni Acumulación Débil Fuerte Inversión Deplexión


Transparencia 4-10

(OHFWUyQLFD

7UDQVLVWRU026 – (O WUDQVLVWRU 026 VH REWLHQH DxDGLHQGR HQ ORV H[WUHPRV GH OD FDSD GH LQYHUVLyQ GRV FRQWDFWRV TXH IRUPDQ HO VXUWLGRU \ GUHQDGRU – $SOLFDQGR XQD WHQVLyQ HQWUH HVWRV GRV FRQWDFWRV FLUFXODUi FRUULHQWH D WUDYpV GH OD FDSDGHLQYHUVLyQ – &RPRHOQ~PHURGHSRUWDGRUHVGLVSRQLEOHV SDUDODFRQGXFFLyQHQODFDSDGHLQYHUVLyQ GHSHQGH GHO SRWHQFLDO GH SXHUWD pVWD SXHGH VHU XWLOL]DGD SDUD PRGXODU XQD WHQVLyQ – 3DUDXQIXQFLRQDPLHQWRQRUPDOODVXQLRQHV SQ IRUPDGDV SRU IXHQWHVXEVWUDWR \ GUHQDGRUVXEVWUDWRGHEHQHVWDUHQ LQYHUVD SRUORTXHSDUDXQ026GHFDQDO11026 { VSB > 0 { VDB > 0 © A. Calomarde, Edicions Virtuals

Puerta

Fuente n+

Drenador n+

canal N

p

Substrato

3026

*

' %

1026 *

6

' % 6

Transparencia 4-11

(OHFWUyQLFD

&DUDFWHUtVWLFD,9 – 6XSRQGUHPRV6XUWLGRUFRPRUHIHUHQFLD w w w

VB = VBS VG = VGS VD = VDS VG x

n+ y

QN (canal)

VD n+

y

QB (z.c.e.)

p VB

– ([LVWHQWUHVWLSRVGHFDUJD { QN&DUJDHQHOFDQDOIRUPDGDSRUHOHFWURQHV { QB&DUJDHQOD]RQDGHFDUJDHVSDFLDO { QP&DUJDHQHOVXEVWUDWRQHXWUD © A. Calomarde, Edicions Virtuals

Transparencia 4-12

(OHFWUyQLFD

&DUDFWHUtVWLFDI-V – (QODGLUHFFLyQ\KDEUiXQDYDULDFLyQGHSRWHQFLDOHVHQWUH\ 9' { y = 0 V(0) = 0 + VB ω { y = L V(L) = VD + VB – 2EWHQGUHPRVODUHVLVWHQFLDHQXQ x0 dyGHOFDQDO

, ' ≡ , '6 =

G9 G9 G\ = G5 G\ G5

– &RPR G5 =

ρ ( [)G\ ω[0

– 7HQHPRV G5 = © A. Calomarde, Edicions Virtuals

dy

1 G\ TQ( [) µ 1 ( [ ) ω[0 Transparencia 4-13

(OHFWUyQLFD – 3RUORWDQWR

G\ = TQ( [) µ ( [)ω[ 1 0 G5 – 6LFRQVLGHUDPRVXQYDORUPHGLRSDUDODPRYLOLGDG\TXHODFDUJD WRWDOVHUiQP = q p(x) x0

G\ = µ ω4 ( \ ) G5 1 1 – 3RUORTXH

, ' = µ 1ω41 ( \ )

G9 G\

–
9 % +9 '

0

9%

∫ , ' G\ =

∫ µ 1ω41 ( \ )G9

,' = µ1

9 +9

ω % ' 41 ( \ )G9 / 9∫%


Transparencia 4-14

(OHFWUyQLFD – (O YDORU GH QN(y) HQ UHDOLGDG HV QN[V(y)] VH SXHGH REWHQHU SODQWHDQGR ODV HFXDFLRQHV GH 0D[ZHOO FRQVLGHUDQGR HO YHFWRU GHVSOD]DPLHQWRFRQVWDQWHDOFDPELDUGHPHGLRHQHOLQWHUIDFH r

r

'1 = '2 r r (1ε = (2ε 2;

6,

–
r 9 + 9% − (Φ 6 + Φ 06 ) (1 = * W2; r 42; + 4Q + 4E (2 = − ε 6, – 6XVWLWX\HQGR 9* + 9% − (Φ 6 + Φ 06 )


ε 2; 4 + 4Q + 4E ε 6, = − 2; ε 6, W2;

Transparencia 4-15

(OHFWUyQLFD –
42; + 4Q + 4E &2;

 (QHOVXUWLGRU\ = ⇒ Φ 6 = 2Φ ) + 9% – (OYDORUGHΦSHQIXHUWHLQYHUVLyQHV   (QHOGUHQDGRU\ = / ⇒ Φ 6 = 2Φ ) + 9 ( \ )

–
4% =

2Tε 0ε 6, 1 ' (2Φ ) + 9 ( \ ) )

– 6XVWLWX\HQGR

9* − Φ 06 + 9% = −

2Tε 0ε 6, 1 ' 42; 41 − + &2; &2; &2;

(2Φ ) + 9 ( \ ) )

– 6LWHQHPRVHQFXHQWDTXHVFB =ΦMS - QOX/COX\TXHDOFRFLHQWH

γ=

2Tε 0ε 6, 1 ' &2;


Transparencia 4-16

(OHFWUyQLFD –
, ' = µ&2; ω [9* − 9)% − 2Φ ) ]9' − 9' − 2 γ [(9% + 9' + 2Φ ) )3 2 − (9% − 2Φ ) )3 2 ] / 2 3  2

– 2WDPELpQ ,'

2  2 9 = β [9* − 9)% − 2Φ ) ]9' − ' − γ 2 3 

[( % + 9

9'

+ 2Φ ) )

32

− (9% − 2Φ ) )

32

] 

6LHQGR

β = µ&2;


ω

/

Transparencia 4-17

(OHFWUyQLFD

7HQVLyQ8PEUDO

– /DWHQVLyQXPEUDOHVODWHQVLyQGHSXHUWD VGTXHKDFHTXHODFRUULHQWHID VHDFHUR – 'H OD H[SUHVLyQ DQWHULRU VH UHDOL]D XQ GHVDUUROOR HQ VHULHV GH 7D\ORU SDUD VD⇒SDUDHOWpUPLQR(VB + 2ΦF+VD)3/2REWHQLpQGRVH ,'

≅ β {[9* − 9)% − 2Φ ) ]9' − γ (

9%

− 2Φ ) )9' }

3RUORWDQWR

97 = 9)% + 2Φ ) + γ 9% + 2Φ ) –
97 0 = 9)% + 2Φ ) + γ 2Φ ) – <

9 = 90 + { 7

7

6LHPSUH

<0

γ [ 9 + 2Φ − 2Φ ] 1444 424444 3 %

> 0 WLHQHPLVPRVLJQR  < 0

)

)

SDUDFDQDO 1VXEVWUDWR 3 SDUDFDQDO 3VXEVWUDW R 1


Transparencia 4-18

(OHFWUyQLFD

&DUDFWHUtVWLFDV\PRGHORGHO026 Características MOS canal N IDS

IDS

V DS(sat ) =VGS- VT

saturación

VD S c te

zona lineal

V’’GS >VGS V’GS >VGS VGS >VT >0

VT0

V’T


VGS

VDS

Transparencia 4-19

(OHFWUyQLFD

([SUHVLRQHVI-VVLPSOLILFDGDV – 3XHGHQ REWHQHUVH H[SUHVLRQHV PiV VHQFLOODV SDUD HO FiOFXOR µD PDQR¶ GH ODV H[SUHVLRQHVI-VWHQLHQGRHQFXHQWDODWHQVLyQVTO\REWHQLHQGRXQDUHODFLRQI-V SDUDFDGDXQDGHODV]RQDVGHIXQFLRQDPLHQWR IDS – 3DUDOD]RQDOLQHDO β VGS3 >V GS2 2 ,' = 2(9*6 − 97 0 )9'6 − 9'6 2

[

]

– 4XHHVYiOLGDSDUDWHQVLRQHV VDS < VGS - VT0 – 9DORUTXHFRUUHVSRQGHDODWHQVLyQ GUHQDGRUVXUWLGRUSDUDODFXDOHO WUDQVLVWRUHVWiHQVDWXUDFLyQ – $VtSDUDHOUpJLPHQGHVDWXUDFLyQ , ' , VDW

= , ' (9'6 = 9'6 , VDW ) =

VGS2 >VGS 1

VGS1 VDS =V GS-VTO

β (9*6 − 97 0 )2 2

VDS

.1 = β

– (QDOJXQRVOLEURVVHXWLOL]DKnR(Kp)HQOXJDUGHβ

2


=

µ&2; ω 2/

Transparencia 4-20

(OHFWUyQLFD

2WURVWLSRVGH026 NMOS de acumulación(enrequecimiento) NMOS de deplexión(empobrecimiento). Puerta

Fuente

Drenador

n+

Puerta

Fuente

n+

n+

p

Drenador n+

Canal N

p

Substrato

PMOS

NMOS D

L'

B Y+ '6

G

+

-

Y6* +

S

D

+

B

G

-

S

D

D

L'

+

Y' 6

G

+

Y*6 -


G

-

D

L'

Y 6* +

S

+

B

G

Y6'

D

D

Y6'

G

-

Y* 6 - S

+

-

PMOS

-

+

S

Y6* +

S

L'

L'

B Y+ '6

Y6'

Y *6 -

VGS =0

Substrato NMOS

L'

+

Y'6

G

+

Y *6 -

S

Y 6* +

+

-

Y6'

G

-

S

L'

D

L'

Transparencia 4-21

CAP 1-4.pdf

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