• Aucun résultat trouvé

Réalisation et caractérisation de transistors MOS à base de nanofils verticaux en silicium

N/A
N/A
Protected

Academic year: 2021

Partager "Réalisation et caractérisation de transistors MOS à base de nanofils verticaux en silicium"

Copied!
167
0
0

Texte intégral

(1)

HAL Id: tel-01261513

https://tel.archives-ouvertes.fr/tel-01261513v3

Submitted on 13 Oct 2016

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

de nanofils verticaux en silicium

Youssouf Guerfi

To cite this version:

Youssouf Guerfi. Réalisation et caractérisation de transistors MOS à base de nanofils verticaux en silicium. Micro et nanotechnologies/Microélectronique. Université Paul Sabatier - Toulouse III, 2015.

Français. �NNT : 2015TOU30253�. �tel-01261513v3�

(2)

En vue de l’obtention du

DOCTORAT DE L’UNIVERSIT ´E DE TOULOUSE

elivr´e par :l’Universit´e Toulouse 3 Paul Sabatier

Pr´esent´ee et soutenue lejeudi 10 d´ecembre 2015 par : Youssouf GUERFI

ealisation et caract´erisation de transistors MOS `a base de nanofils verticaux en silicium

JURY

Sylvain BOLLAERT Professeur d’Universit´e Rapporteur Laurent PICHON Professeur d’Universit´e Rapporteur Alain CAZARRE Professeur d’Universit´e Pr´esident Bassem SALEM Charg´e de recherche Examinateur

Ecole doctorale et sp´´ ecialit´e : GEET : Micro et Nanosyst`emes Unit´e de Recherche :

Laboratoire d’Analyse et d’Architecture des Syst`emes (UPR 8001) Directeur(s) de Th`ese :

Guilhem LARRIEU et Filadelfo CRISTIANO Rapporteurs :

Sylvain BOLLAERT etLaurent PICHON

(3)
(4)

!"#!"$" ##"! %& '(" ) !#"! *

!#!"!

##+" #!, - (" %! !#"!%"#.!#!"!"

#(#!!##("##!("###/"!"!) ,%"#.!#

, !

#0"1 !#!#0##+" #%! (! #!"("%

!(# !"$" #&" !#/"" !#, #!!#+"

,&,! #(&#(2!#'#!%! (" !!(!#"!

,(!0!!#(" )!#

(5)

* (# ##0#!#"3!,4-567'%

' !"!, !##" "#"$!/"'!!# -#"0 !"!'/"

896

8# (!# %! )! & 4: ,##" '% #! 9" -0! ! #!$" ;!#

8 ( & 3" ! 94<76 ,##" '"% #! # ! -;% =7335 ,##"

'"% #! 3'% ((! ! #! %"1!# 8 ( )!&=##

-38( ) ( ("358>46-, !$" ;!#!!/"'1!"

*!#&1 ,) !!"& (?4464'% ,! ,! # ) 1 ( ! !! '(/" " 1 !# # ( !

!() 5 !!"$" #!"% !" !"#!"$" #""!#"

&#/"#!# "#!!(# "#"!!(/"! 84@-#

# ! "0" "$!#& ( *=!#!A745!"A6" "

!) 0##("### B"0" "! #(" "1

* (!"!'/"58" " #0!!" " #!

(# ! %"1 6!! (8=676 !*>4 #! 875 3"%( -3B64 ! 9#(A== 7--5! 3=7A

8 (&!"###!()"#"3-C8"#!,DE<?5<!

F =7666 8 8585 =55< -E3 0 3 E<AG-<78AB!4-56733-386-0!DAE

<$ 8E<37!!33-=A= (A36!0" 76 * '1("#" #("1/"$'"0

8# (!# %! & # # # "1 %# ! !"! '0 &

0:: 35 8 <AAA6 <( A86 6" 54<E7 ! A$=6-3<!#("1/"!(, ! % #%(" " #"% #

!"#'((" (-A!A$57=388

(6)

(7)

!"#$ ##" %

&

!'

#("'

) *"(")

) + # !)

) + (,#))

)) ##(,#)-

- # !)

((# . #)%

/0, "+ )&

) (( "+ )1

2, . ((# . # " # ("# # !#3333333333333333333333333333333)'

*#####)'

) ### -

- .4#+ ,5678"+ -

# 58 !--

##--

% !####9-&

& : ,## # #(#-'

& 2 ;

(8)

%

&) 2 ,%

1 < + ,=

' 9(>#

#

-

)*## .(#, .# "%-

%

) *# "#+ , %

) + %

)) 6?>##@ .56@8%%

)- .#6@4+ %%

) *,6@%'

) 2##+ &

)% 2"$#&

)& 2" &) )) !#(#(### #, # "&&

)) <, &1

))) #", # "#"&'

))- ."1

)) ( $<1

)) A##, #,1-

)- 2"##"#(#1- )- .?"+ ## .(## "1 )-) #"?#+ $.?1&

)-- $.?"+ ## .(#1'

) .?'

) #'

(9)

&

')

-!(###4#:A# "'&

'1

- *#### ( >B?

. # '1

- !+ #("## #'' -) #"(" # 5<8'' -- " <# ## .:A)

- C, $.?# "-

- # (#

-) *## #$#

-) .##+ ##

-)) *# $#( %

-)- :, $## -

-- <

-- <" (((%

--) A #+ #", #D6@)

--- #" .))

-- *# )-

-- @ E)

--% *##,##)%

- #)1

-

# + ### ! 4 # (#

, .--

-

#+ ##"##-

) #+ #5A8-

(10)

1

- <?#+ "#

## 5A8)

% # -

& .######

1 ."

1 ,

' ,# #&

$'

#

)

##,#

#%

) <#,#&

) #""#&

)) /,"#+ #1

## #(#%

- *, ##%

(##%

(#:#%

(11)
(12)

(13)

$,## ##5#8F #"#9 # ( "##,#+ #2#+ ##G

$ , ,####" . #F#9 #F#

,"F #"H 4 ## # 9#

#F##, #F#"9 #+ $ .+ "#"#2,

$,$>$#9#5(5!88IJF#,

# # # # ("# # (#F # " # 9(# . # # $ # # #" # (( $((

>##"K" !##5K!84--"#

#5L84()F# ")-M4$

#"N"#?### (($((-%"##5L8)&

" # ## H.?H" 4 (( "#

5 !8 $, # ## ""$"

#F ## "## # ( $ " # # # # #F ##

$ ""+ 5$G $ "+ 8F 4 ( # # F 4

$"+ >5+ 8" # ! " # ((# + # ( $"

(" ##( ( . # " # ((F ( . + # ### # ((# (## " # 5 . #8F E

#+ + $ $ ###

$,>" # # # "## 5-/8 # $ # # #"H ## # ###((#" ##((#

#$ ###" #$." #"+ ## "

!,#$ !#) O + ))" I)J # # , ## . # 52L:CF

!FFC #38 O + %P"I-JIJIJI%J)

#+ N #"## ## #("##(#

# ## "" # # # # , " # # !# ( $ # O # + # & "F # # , ##"##+ ##?#+ #+ #F F

(14)

)

## $"" # # ! 4 " E#+ I&J

2 # >#F # ## ! 4 # (#

, .# "F"

"F""4"H $ ( $ # (#($

" E#+ "#((# . #

" " # 4 # , .F ,

$#+ ! # # $ # # #" #F

#(" !##" # # " # : # # # "# $ ## # ((# . # # + # # # ##

"" #(+ (F ((# ."# # $ (#

# .## L ", #, " ( # # # ### !4#(#, .# "

2 # .>"#>"F ##(

##(44##+ 4 (#$! $F#(#, .

# "# # .>"L###

#$ "#+ , + # ,$ , #"

#( # # # # # # # " ( .?

#(# ">#(####>"

# !# #(# #

"#4$"+ + "####

"+ # 4 # # # # # B? 4 ( > L + # , $ ( + $ "+ #, $# # ((# " .

##( # # + F " $" ( $# , ># ( # # ( (F # ((# " .

#+ #,#######

#

(15)

-

+ >" ># # 4 $ # ("#

+ ##4#(#, .# "

(F ## ## #"9 ### ##, .>#

### ,##,# # #, .

(16)

IJ !:KFQ !(!#FRH ! ! 4, (%(4"! 5 ;) )445F)F,F AD-&%DAD-1

I)J FQ!, (#("" # #FR (! A%(#8!)A8! !F)FD%

I-J SH6FKHFKHK F6HTF7H6<FTHTUF!H6 F@

FC6FHSFHFHSK F:9FTFQ-2

%")1*2HV.-2W"H !?UUH###

? ( UHA: #FR ->-!! 4 ("!# 4, ( A)#! , 5((9 #--44I! !F)F)-1D)-'

IJ :9F 2#F # 2BF #F 2 UF A B"F B#?F 2 /# F 7 #F @ F ! CF C#F C,9 F * C,FK6F/6BF 6#F6F6B#F*6 ##F<TF

*T"#F*T,FTF67"F 7F7?F FS F* F BF:F<<BF2<UF<BF<<F*<F<F

<#F<<B,F<F*9"FT(FF,B "F<"F F 7 !F ! !F T K"F SF 7 XF Q2 "

? ( )H !F H #F #(H 11 V.W") *2 #;FR (! A%(#

8!)A8I! !F)F-&D-&-

IJ H6 F CF :#"F T F 2 ?F *#F A :?F F66F22?F 2BFTHT2F2+ F*FA#BF:F

#B?FKF,F/"F##F/BF /KF6/F "B#F FF/F2"F2CF C FYC F6# ;;"FT6F/6?#FTFTFHT TFTT#F7FS7F7F7"F7#UF27 "F!7UF L7UF ;F6H7 FKH6 F2 ,#+ FK FX FK F 9F7?F6:?(FK:FC:F2F<F<,F*

*"F X *F * *#F (F A #F F / #F UF+ FF7F!F6L"F*AFCKF6KF K KF Y KF / KHC"F KF S Y F S SF : XF 7 XFX F7?F F76#F 7#F7#F 9U#BF 6 F : X""F * /,B F T *F ((F < 2F Q6 (" " ! ? U & V.W") "

/*2,#( ";FR(! A%(#8!)A8I

! !F)F-1D-1-

I%J T F T"F 2 KF * F 2 F F 6 XF < 7# F <

9 F#UF27 "F<?F:?F2F*F XF (F ","F Q2F *F / , #

# # ( " ! ? ?FR I -;#" B3- 5();B3->5();JA)#!,5((9 #F)FD)

I&J7/ 9 F:F* #F6C!FC@F:# "F /7UFQHU,( #HH 5C228 ,#HUFR->-!!(! F,)F'F-)D-&F )1

(17)

(18)

(19)

&

#"##$+ ###(( # 1&4,## ,$((##"4 "

" #FG"+ + # # ##, ## 44## ( "#4;1&%F$

# ,$4#, #>#+ 4,

#,4#(+ # #,# ##F#

# + # ( " 4 , 2 ""H4F $N

## 4(# (

$#')%F$,T # (IJF+ ##

4 (( " , 9 ## " ,# $ # ( '-%F .#F,7?#

# # "## 4 #" "# B?F <#F ( + + # # # # # # # (## #

# "" "F,# # "#F,9<:

'% I)J #> " ## " " 4 I-JIJF # ##B?IJI%J# ,#">

#!I&J( 9 #+ $4''G72#>

" !5.?" ((!##8#,# >#

Z4"##( #$(+ "N"+

#" #" I1J ##?#>"H)I'J5(588

"" #(" . ##

(F>#" !4## "F

## 4 + $ 9 $ A? * ( 2"

5*28" !# "

'%)IJIJ"""( 58, "#%

!#,*2

(20)

1

!" # $% & '" ()*+, $%

- ./ $ % 0!!0 1/"

#"## !#( #"##" # '% , C # 5C 8 " 58 ,

# !# ? # # + #F # !# ?

$"(## .$#("'&+ $ ###" #

##,,Z "## $# )- !#

, ["(4 (+ "."&B6;F

#, " :25 : "2?#

" 8,'%$ ,#<#?,+ # (

%")#-#5(588''M# ## ##9 # # # !# "" + # # , # # #?#>"# G

$("# ""#

2 #"F # #### !""$"

# # #,#+ ##>##""0

#"#F#"("#+ #" ##"#

## + "" #(+ ,(( $"#

("# # ###F "" $ # # ! 4

#(#F"+ "N">#

58 58 58

(21)

'

"

"" 2

!#"#"" ### # # + # ((F $ \]F " E ,# $ # $ 2#"""" $+ 4$##, ,#

### #$.?F# .#,#

#+ #### F Z 4 "+

, ,# #" 4 ,# 5 D .? D

" 8F$G"##4(("5()8

!"*3 "

?# #(" F# !##,#

.##+ #("##"$#F#

!? :F# 4$$ ##,#

L !? <F+ #(# ##

$$ #,# < # .#F # ##

#4 ##,### L !#4

##" :"?((# !#4$+ 4 # 4$,#F#4 :"?# # # #

## ##4$+

(22)

""*.2

$$ #

# # # , 4 + < "

!F#"

"

#" 5^#8F"N

!"4 ' "

,_ #$((

`F F A # # F, 5#, ,8 ,

#" I-J+

""*".

< #ACaA

$( .?P#"

#4# ( #"

$#("F

""*"*.

#+ $ #>"

# #,###

# # ( #" # # $(

"##((#"#

,""#

##5,# "5 N" ##"5 b b

((+ # ,"F , $ "F , $#>+ 2+

F - "# ((# .#

H## # #$ :

AF###4 ##$

# #F ## ""

F$G""$ "

###+ 5(588

"#,#+ 5aACaA8F ## #### (

)

# $ "

("

D.?D

^"8#4

885(-8

5

#" F F ,F

#+

4 # (

,# 4

# "9# #

##$

; ,

(23)

#F;

"F#

""*"4. &

2 # AC c A

5 # "#8 # , #+

#("F$

# F##

!"0 3 '

$ %&"

"*6

.# . ">

!F">##

5A/8F (.

588 .>" #

#/(

!"7 3 6

"

58

58

5ACaA8

$#F# + "

### 9 #+ 5(588

F # # $ #

# 4 # ( #"

# #4# (F$#"$,

$ #A/cAF

###5(588

1 $

># ## # # 4 5/8( # $ 5AC8F $# #

#+ #(F d#H4HF

#$AC4A/#5(588

6 $% $'$8'%% $%

58 58

58

5ACaA8

)

###$#

#F # #

# $#

,#

##

% $%

#+ # 5A8

# + # 5(

8

2 $'$89%%

5ACcA8

(24)

))

2#+ ####A/F

/5A/8######F #4 "("

!# #($.#"># . !4

#+ #(F""## A#+ # # :( ###H # $4$.## #/

!

N(""

5?8bKe@5?8ef5?%:6!#

GK# F@f##,"##("

,## , + # # # $+

# ,

;@5?8;bIACHAHg^5?8H)^JY#)h+:Ig^5?8i)^J:6!#*

,A#F^5?8F^F##"Fh#",

# ":# # #"$."

5C H 2."8F G " +

##" "+ #,#5j.85"+ 5j?8#

8F " 5[8 , # < #+ ,## # # # ,fbj[5j#"+ 8$.## , / bK[.k5ACDAH)^DAP)8AD585)h+:85Ai)^8-P)D5)^8-P)Jl :6

!#4

.F#

"*"62&

! $# # ,# (F d#H4H "N" 4 # ## AC ( 4## A5" (,#8F ( ( (( #,F # ## $. # , 0#+ #("+ F# /4 ACbA/bA//F#."""#

(25)

)-

/bK[.57!

).5+AC A8ID.5H+A7!/8J:6!#0

5# ## 8#### "

$ $G# 5"AP8F#"+

#$+ 4$## ###(""$,#

#+ ### # # 5(588.###

b5mmA /

C 8Hb7!+:6!#7

2!b-7 ##4Fb%"AP

(F # # # # 4 + 4 ( ,#F#."$+ # ,

AbAH)^Hh

. :6!#-

"*"*2&

< #ACcAF #+ #

A/#,F + # #"

"" ## ,",#F$#

5(%588$.## /##, /bK[.5ACDADA/

8A/:6!#<

"#ACF ,$ """+ #

##584 # ##

5?b8F,+ # #" 5(%588((#n 4#$ "+ " E $ "

,### # / N."

/bK[.5ACDADA/

8A/:6!#=

# ( # # $## $.?F # 4 i

,7b)h+:P.

(26)

)

2#A/cA/#F /#+ #"#

"4#$# # 4$F !#"# 5(%588F /,

/bK[).5ACDA8):6!#>

!"-3& 6 ? 2 8'"

"4

'%FCF #( #$+ "###

, ## .#IJ"+ "# #"

# \ ] , > (" #

$ " #4" ## !#"""(

&58"##49 #"""

" # "# $ " # # ### # #

"## # # #(#$##B$("

L ">Fn ##F", $ # # #" # ( &58 ." $, $ # #

#" #"n !IJ

58 58 58

(27)

!"<3

"

CZ 4 " #

"8I%JF#("#

((+ ' #%(#I /I1J

# ,#F #$

( ( ( #

## F+ ,

>#" #

<">#

/"# "#5!

!#$"

58 5h2P8 /P 5A

< ####P

"&

58

$%&$% @

F '& 5 ["8 9 #+ $4

"#$ ( -(#F (#F"## Fn

&J

##>#" # "# # ###F # (

" #B + ,, ,# # # ("N"(

#/

"

!.FFKFY98 P7

5:8 7

5A8 PB

PB

8 PB

AP8 PB

P 5A8 PB)

A2 2

58

)

7!

) 5 , "

$ ##

#

"

(

#+ # # "#

#

"

(28)

)%

F#>#" #4 #(

" #,#F4$."F # ## $## $.?

, # # ( (( # ((# ##

" ## # .((## . #5 ((8$#

+ F#">#" #,#(","N"(

$ U# I'J # "+ G # !# #

#+ #$ ##4+ #(""#

oI..5KiK/8)JP-:6!#!

GF# #FKiK/#""# ## F .( #9#

# ># " # # #F " # ,# 9 #+ $ ##)FG ( #, #+ ##((#

. #

"022 B

L ! # # "" "# 4 F #+ # #

#9## 5.F./8# "N" + F##."#

./b)h5A/i^+:iA8:6!#

.b)h5^+:iA /8:6!#*

AA/##,"## H# ##H# #I)J

< !4 F# #

# "+ #,#5j.F #8+ ,

" "+ 5j?F #8 /# #F $." $# # , # ((#

### . #####"# #"$((

. # "> ?#+ "( # # !

(29)

)&

"# " ,# # ,

""#((## ,#

"0"'C&6

< ###(# !#5c["8 ###AC

aAF > , # P#$# ## $#

#+ #ACcAF+ #(" # F

$##" #>

#+ # # # F "# ## #

> # $# # # # # $

##(4 FG "#F;$#

, #$# # "

+ ## $##"#>, F # $9 # # # "N" #+ ACa AI)JI))J ((#""/ U5/85(1588#(""

# F # , # # ##(

( , # F "" # #

#+ #(5(1588

!"= 3 $% ' ? 8' D ! 8 $ % ? 8' E !

$% AF?F $% 6 22'"

# # "+ #+ #$

9 #+ $49# 5.i./p8F50, "+ 5< ! 88

#+ F> , # #" #

(30)

)1

#$#("## #>" # #"9#

## #9## 5#8 #?#

"+ ## ( + (,# ,"

F#."""

/b'h[2A/)

1- :6!#4

G2## (# I)-J

"0"*22 6

+ ( " #B$##"N" ##">#

!F #(( ####+ #"##

!"+ , # #,F9 ##

. ((# . # "" " " # ## F"#((# ,

"0"*"&

#+ " + j?# (F ,## , # # ,","+ F#+ j? , A P"5# # "8F,,4 " #"F9 #+ $4

# 4 ,##&"P##+ j? , . # AP"

"0"*"*'2

+ $,# # 4 # ( #" F .N""

$(H)#$ (j.F,### ## #

# # (5# (#8# ##, (( # # $( j?

" ,### #

(31)

)'

"0"*"4G

$(( ("+ . # ##"#

#$.?4." (( >#

#( #4$(H)+ # ,##

# !I)J

"0"*"0

((5 :8#n4#$ ("+ , 9H("# #+ >

+ " # #H # 5H8 #

"F #" ##5H8,####

F#+ # ## ##### #(" #$((

# 0 4 ,# ## 58 #F G 9 H ("# # #,#F#+ ###

9### ###,#I)J

2("$(($ " "+ # # !4 . F # (, , # # # "## # : L ""# , # # #

# ., .F ##("+

# # , $ ## (" 9

# #>" ?//5//8I)%J

"7/&B22 B 2

"7".

2, " ## !#F#### ##+

###>+ #+ ##########

. (( ## . #F $ ## $ " # , # # # # "" $# :F "#

",##$# #I)&J$ ## #"#

(32)

-

# ### ## Z 4 ( ##, 5# ##8 # + $ (### ## ###F#

#+ #.#! $F## #"?>58 ## ##""#/*2##1F #"##

# # #> 5K8 # # # ( ##, I)1J 2 + O + F # # # # ( ##, ##

## ######F#### #5!8

I)'JF## #58I-J## #B5:8I)1J

"7"*

# $"# $ ( " + F ,## # # # ## 94 ("F9 #+ $4# 4

"# #### # # #O #+ #

"#####")PA# O + 1["4 )")PA# -["I-J

$ ### >#O + '

"F "# $" # ("# # !# "

4 ,# $ " " # # # # I-)J #

## $+ # # H.# "" H.#F # . # ( #F # ># # ## # # $ (F "

((, # # # " 4 ,# # "### ((,# I--J

"((,#."# ,

[((b+q

"r:6!#0 GPq#(+ ## ##+ "r "##((,

@ " # # # " # # # ! F$((#### ## "$( ##?C

$>##I-J ?#"I-J$("#

#F((( ## #I-%J

# # # # !# ? # " #

# # # # H.C.5( '588 $ "

(33)

-

#C "##, # F""# ##### !#

? # # E $ : H## # ##

#+ #5('588I-&JI-1J

!">3 >! $% 9 G$% 1#1"

"7"4B ? 6 & $H (%

6

$ # .? # " 5)8 "" .? # ##(#

!# "F# ##$## #

$ # # #" #F "" Z 4 ## # + # + #

"+ ####(#( #$(F5' A8 + (> $.# # $# + F # + $ (

" , # # ( # # # /# # 4

" #F $## ) , ( & 4 + O + 9 #+ $ O -" ## "I-'JF #

##4)" #O #+ #'%"I-)JF#$

( " ( 4,## # #(( #4 ,#$.?(( F$ " ###+

(#("# "+ + ( ((

" "> . , $## ) IJF

#+ $ "("&" $## "" )4 # ## # + $# # ">" (" IJ # ,#")#+ #, (",6 7 CZ 4 # " .F # ## ( .? , ##

58 58

(34)

-)

?#+ # "N", ,) .## # "#(#F$ ## $.? + ,5 !8+ #(>4$##

+ ## "N"((+ )#$."

!b7

:6!#7

7 h 7# #," $## ", " . 4 (

",h)", )4-'<"#" .# # # ,F$2)-5hb8F6()5hb)%8FX)5hb)8F!)-5hb)8#+ !)5ho 8

$#" .67$####F."# E#

# #F $.?.#("F ", $ !(#

"### "+ + ##"""

##+ # , , "5A8I)J$#

+ $#" .67## ,# # !

" $ "+ ""

?# " " E # # + # F ""

?# " " , $ ! ((F

?# " # $ $ , $(

?# " D ) F $G ##

$ ##" # #" .O + "

"+ $ $6() "" " 7 "+

"4$.?)?# "#,"I-J5(

8

!"!3$%I 607& 6( 6$%

"

58 58

(35)

--

"7"0 $%

$ " ( #+ #("#

.((## . # 4$, $#,#

!# ((+ !F##

$ ( # "## .? .5Y8 #($.?$.?+ (>

" E#+ #+ # "#,"

##F # # $ # YF ! #

" <? / 5</8F # # !#">" ?/5/8<"#,#

+ # # # # F , # ## # # 9#

#H### # #Y5# D# #D# #8F+ #

"###$.? "#( # "F#

"$" E# 5(8

!"3 "

"7"7

$ # # " " # # # + #

" .+ #4(","+ "#"##

((# . #F## "N"#"#

# "$ " " + #( # F+ E

#+ # ( ((FE

#+ # # 4 ,#

( E#(( ,"#+

(36)

-

$( # #$(( #

# " + " /$G $N , , # #E#

" !4 5/C8#BUIJF"

.>" # ## # F # # ((# . #< # #( ###(# !# B 4" #

##5()8G#" ,#"

5#8# + ((##(####

, "" /C ! 5( )588 E #+ # .# # .# .F !4FE#+ # .# #(# 5()588# ."###(###

(( !## 5 !8 #+ # # # > # # #

>" ## # $F # # #," # sH ! 5(

)588tH !5()588F ####4("

# # # # " E #+

# # (

C22 5C228 !5()588F#+

#">" FGE#+ #

"."F ( ( "# ( . # # #

""##((# . #IJ( )5(8# !#

# B

< # # # " + $ " " #F "

"" #((# . ## (/F# ##

,##%"API%JI&JI1J

(37)

-

!"*3?$%'9$%

$ %J$%K$%9//$2%L"

2( " $(( E #+ # ##(# " #

#F <B I%J "# # # # + # #

##(# 4 F s C22 ! - "

"+ "N" ##(4F # $(

# # " + .# 5( -588F # + $""

#+ # #, s C22 ! 5( - 5F 88 E

#+ # ! 4 5C228 + $ # ##

## !##("#F#" !##

9#I'JIJ

!"4362?$%

$%J$ %9//)0-+"

58 58 58

58 58 5(8

(38)

-%

< #"+ E#+ # F

$+ <##"# #("".#

E#+

mjm.imjm?imjm;bHuhb#:6!#-

< !4" #FE#+ #.# #.#?

;F+ "#"#mjPm?mjPm;" "mjPm.

$..F.5(8IJ

!"#3. 6 )07+"

SIJ#,$+ ##F v 5 8 # # # # " + . # $ # "#F # + ## # E I)J< ! 4

" #Fv#$."

vbhh.

. $ hh.

.:6!#<

G#"#F

$( # E#+ #"#((,,

$ " " # + "+ + # ((# . # #

" ."##/##" #"+ $ !##""

( # ((# . # #+ ((, #

# 4v$ "#%(#5Cc%v8IJ ; BI-J# ">

"$#"#####(# !#4#" # .((#

. #### w ( " #+ #$."

(39)

-&

wb)v((

:6!#=

## ##" F#+ #((# . ##F#

##+ , w## 4)& /C !F#+

C22 !F , w4)-## ((#I-JIJ

# !#4" #( ) #$ ##

#" ##+ ( # ##4$ !4

# O + ))"5(8IJ(E#((# . #"#("## !#: #####4 .>"

# !# O + %P " (# #

"9 #(#( !IJI%JI&JI1J

!"7#M1I 6**?M$%$%)4*+"

N # #4" #"("

###(#4# "#((# . #," # # !#! (#F# 9 #+ #E#+ # O # + # # ,#F # ((HH 4 . E

#+ ((# # # # # # = # , + # ## $ #

# ##4 !4 5C22 !8

"-N

#"### !#F###9##

, (.N"" F#+ #$

58 58

(40)

-1

; 4 ; # ( + + # "># # " 2 (F # + # .N"" n ## # "?# $, "+ # # + ##4## #4#" ###;,# ># # "# ( " (( # # " # F "N" , $ # # #F # # 9# # # ># (( 4 # I'J # ! ## 9F + ##

# ", ,">Fd#H4HF####

4 n . # "+ # # # 9# #

#

!"-3N ")0>+"

######9#5T!8##"# .###("

$ " 52!8"#,((+ ##

#"#+ ### 5:i::i8F#+ #T!

#+ #-" . !5:i:i:i8((#("F #2!#("# ( ## 94 #

$(.?D# "F#+ $ T!#("

# "5 (#8$### #$( "+

## ( .# #

( &#(" T!(#

# (" #+ # # ( 4

## 5(&588#+ ##4## F

#("# 5(&588 ( 4"# + # "F#$5(&5889 #+ $4

(41)

-'

5(&588G##,"" ##F$G###4 5##82$,#####4,#F#5A(8

#4 ## 4##

!"<38 N 5$%8O8 $%8D82

$ %8E8B $%? ,8D82EE8 )0>+

< # #+ ####">#?+ # ###(#T!I'JI%JFF#+ # F#""" #"##F# 4(##$."

$ T!$+ '# ,I'J

p%/(&'A//:6!#>

G:/##FK#!## ## ("

# "

"<1& 2

# (# # # (# + # $ + + # ;#

">#"> E ,+ + #">#(

(" (#">#"+ $##

(42)

##""## # "## "$

(# + + # # # G # ((# + + # # #

#

# (###

####(# # ##F""Z4#

/ #F##" #(( #2#I%J

# (" # !# 4 # (#

-"

/" ## # !4#(## "##F

######(#"$F4#,; ,

"<"/ P

,# ? $ # $ #F # # 5"HL8 #5!H/U8">##4(#(#4 # ##+ .>"##4##(##(

"#+ ## #, #"

<"#"#, .# ###(# !4#(#

#F , # , . ( I%)JF # (#

#?## " A H+ D 5A8 # # # $

"" ?# # I%-J # (# "># 4 ) " ##

# ##(## # ## "" .?%"

#"".?### !(## # . ."# (# 5( 1588 / "N" (0F , " # , . I%JFG#(###A## # # , ( H## # (# 5( 1588 N" # $###+ F# #"##,#

##(# !4#(#

$""#P/# B"#$"

# + # #+ # # # # 5( 1588 I%J *"" ! I%%J 5(1588 "# " . "#" # B # # (#F# (#, &"

(43)

"." 1' [2P[" I%&JI%1J " (#

##(# !4#(## # ###"A2>#,

# F# #$2 !### ##G#(#

# ## A/F 9 #+ $4 $ $.? # #

"+ "F?# "#(### #

### # .E#5(1588

!"= 3 ? 2 PB $%

)-*+$%")-0+$ %/P")-7+$%")--+$%")-<+"

#((##+ #4,## #(###"

AF#H## (># . + # A ""0 # #?# # (# # # #

# ###(##"##+ >#I%'J#

# # "# # "## # (# # 4 # ?# #

"+ # "" $2 F F ## "" "#F # #

#+ ## !#

# ##(# ! 4 # (# ; . ## # $

## ##,#F ,""##

* #I&J5('588 9 I&J+ ###$

>#( , #"#4,# "#+ , # + # # # ># # "## 4 .? "+

58 58 58

58 5(8

(44)

)

"4##" 2>##.?F# .(## # #

# ##1"">("## # 5C228

?# "##P/###$ #(##

# # #+ # # # # ### , + # 5%-

"AP&"AP8#+ $ (/5"APA1"APA#,"

#:8L,##4 ####

$P/# BI&)JI&-JF"$"

/ $ " :4 -F& "2P[" # : I&J L

#"##:9";I&JF#(# ###

("##F 5('588

, # $ # ##(# C22 ! 4 # (#

; .## # ## , #"$.?"4

$ 5('588!I&%JKI&&J5('588 4 # ># # "" # I&1J 5( '588

##(? #( 5"8#I&'J

"##+ ## ## 5('5(88

!">3?2$%.)<!+$%)<7+

$ %")<-+$%Q")<<+$%")<=+$2%")<>+"

/# ##(# ! 4 # # . (# ### >"

## C U I1J 5( )588 # + # I1J

58 58 58

58 58 5(8

(45)

-

( # # " # , #" $.? "

F#( # ##$.###

4 "+ # #;6)" #"## ##

#("######## # $.?"

" # (# # # # 9 #+ $4 " "> 5( )588 "$(#, , -F%"2P["F&"2P["F#," :<< #""F"N"

"# #$ 4(#

# # # 4 ( # O + " > # # !## (####P/##F

# F.I1)J5()588

!"*! 39// 9 ? 2 $% 9R ")=!+

")=+$ % I 6!)=*+"

L+ , ##(#; .#

# # #4$ ""(# #PC##

. # #, C "" #( ## 4

#($## " #,C(#(## "

""## #"# #

!U :U C22 ! I1-JI1JI1JI1%JI1&JI11JI1'J G # (#

# # # "> "" - " # # 5( )588 L +

!# # " #" "# # + -/4# + 6@I'J5()588

2( $ " F # # # $""

,(#; ." # #.#PC

##F"" #/ I'J5()588,#

(## &" )"$## F ##

)"E/I')JI'-J+ "+ # #6)(

58 58 58

(46)

$ # # (# 5( )588 ( "# $ "." % "2P[" # : I'J /$ # , .

$""(###I'JI'%J4, # "4,#

"#+ , , # #;%# ,$.?

"("#(#5()588

!"*3$#%G 9 2 2L")=-+6 ")>!+ &,$ %&

2 5A S9 ' " )>0+ L " )>*+

& $% & 2 &

B5)>7+"

)F "(# # #((# ###

!4#(#; .##HU##

58 58 58

58 58

Références

Documents relatifs

Dans chaque cas, on pr´ ecisera les lois

[r]

Universit´ e de Nantes Ann´ ee 2004-2005 D´ epartement de Math´ ematiques Licence de Maths Classiques, module M62.. Liste d’exercices n

Lors de la première année, l'étudiant prépare et passe le CRPE (concours de recrutement des professeurs des écoles), avant d'être nommé professeur stagiaire. Contrairement à

Expliquer pourquoi un seul perceptron n’est pas suffisent pour calculer cette fonction.. Question 3: Etant donn´ ees deux fonctions bool´ ennes f et g sur un ensemble de vari- ables X

On peut par exemple supposer que les cellules d’association ne peuvent d´ ependre que d’au plus d cellules de la r´ etine (perceptron ` a “domaine born´ e”) ou, dans un

Appliquer la m´ ethode de model-checking de LTL bas´ ee sur les automates pour montrer que l’´ etat q 0 de M ne satisfait pas ψ 1.. (On ne demande pas d’utiliser l’algorithme

Notons, par exemple, que certains modules de Brown et Gitler, le module de Carlsson K(1), l’alg` ebre de Carlsson, la cohomologie modulo 2 des espaces d’Eilenberg et MacLane de Z /2 Z