Nanoindentation de couches minces déposées sur substrat de verre de silice

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Nanoindentation de couches minces déposées sur

substrat de verre de silice

Antoine Perriot

To cite this version:

Antoine Perriot. Nanoindentation de couches minces déposées sur substrat de verre de silice.

Mé-canique [physics.med-ph]. Université Pierre et Marie Curie - Paris VI, 2005. Français. �tel-00112005�

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c k cb  

a

 V K " eKe k dK V eK " eKe "f VK$ " e  "K$  "" hKVK#V k p$ $e$ e$  $ " ff $ VeWK$VV K "#$ " fK$ VK$ "VK eW K m $$$fKV   K" "f VK$ "  e V "K$ c k cb  K V$ " k

c;




    


  

 p mK $  e f"V  " #$ "K#V$ $$$KVf "  $" Ki$f$ "  "$V$K$ "   $" Kf$K"i V " V $ $e " xh$eW  < 9  $"$  " $$"  g

%

k dK VK K$ "  K$f$V "h " $" Kf$KV   e  "$hKV $ eff KeV"$ VKe$ X VK ff K$ eKe

A

 " $Ke " ff  VK $ k o$$ " $ xh$eW   "$hKV  " $" e$ "  f$KmV K" ff

ω = 70, 3

o

k p K " e  "$hKV " $" $"  Ki$f$ "  KV $ eff

a =

p

A/π

 

A

 VK "Ke  VK   eKe k
  
      
c k  pK eWKm $$$fKV " $"  f "Ve "  "$hK"  VK eWKm $$$fKV " $ VK  ff K  eKe  pK i$

h

s

 VK "Ke  Vi$"  VK   eKe  "   K" "f VK$ " $ m" c k9  k vh$ff hKV$ VVK"$ K V eK " eKe "f VK$ " e W WX  K V eK " eKe VK VK$ "K"K V" hK$ " V e$X " $  VK "Ke V$m  VK  VK$ " k dK e $ eKeVK h$  "  " VK fK$ VK$ "e "V eKe k sV$h q WK VKee KV eK" f K $K" WfmXVK VK$ " V$K$ VW WX " Vef f VK$ " " fK$K" $     $$ K  $$ K" $V" m" c k  k n $  eKKe$   K VK fK$  #"V VK$ " K""  V K $K K$$ $hKV$ VW WX " i$ VK$ " W " eKe h$

§

c k:k ;  k + + '% % #&"% $)' ' " pK fW sV$h  q WK  ef   $  "K$ k pK f$X   K$ " e$"  c k cb 

E

∗

₌

S

2βa

c k c :  

β

 " e e$ ee"  V  c "$ ef  VK Ki$f$  V$" k n  "K$ "$ V f"V "$ " fK$K"  K$  VK K$"

*/ '* &.$,(&*.-/ $&$% %,/*$/(% *&&$+$'(/* ,. ./& .% $%)(%,(./ %$0.( %%*2$&+ ,/$0.(



&% %( 0.$1*'(%, (% * .,*%, *. (&$% )(& ( $(%,& //( ,(./&3

 

$ '$%)(%,(./ %(&, -*&*2$&+ ,/$0.(

a

 





 
 cg
                    !     "#$  % & ' ( &)( *+  ,        - ./ 0 1  #/  021

S

  02$2# 3#1   -  

a

       2#4 5      6    26   # -   "#$  %   #   

h

c

  # ## #     $ #  7     #   

h

s

    #    83  #     %   9     3 !    # 

δ

0$ 9!   1: # $ ; 

h

s

= δ − h

c

0<1 =   #-4  

h

s

 # : 2 #   $ 

h

c

= δ − ε

P

S

0>1 ?

ε

  4   # !  #  0

ε = 0.75

   4 

ε =

_π

2

_{(π − 2)}

   @1 A#  # 7#:  # !  #  :   # $#   -  

a

;  ## 

h

c

 5  /

             2  #  ; #    2   : ##      $  4   

h

c

  9: "#$  % $#  #  

H

   # 2  # 7 #  $ 

H =

P

πa

2

0 1 "   7   9  7   $#   ## 2   #  #     ; 7 #   # 7 #    #  7  #  ##   :  9  #      ; # 7 # 7 #     # 7 #  ; # !   7: #   "#$  %    #   #   ##   -   #     #   #!    ! "#" $%& '( )# !* " $'( '  ) +(, (" - #,, (" ., &( (% / $!."( '( / $,,( / " $%& " $  $   #  "#$  %      2 -4:       6  $#0     #  / 2#4 # # #  #  "#$  % ##     $  #   #       !!   -  1 23 456789:; <= >?8;@=> AB C B  # D $ 

§

E: #C F 4 FC # GC  B   B     F   F  7 C #C F-B  GC # H B C GC  B   #C  GC #  B GC GD "#$CF C %FF:

a

C $#   B  #D- B 4C GD   B  B FCC C ./ "F: #C  B 4C GC #C/  C FC  B FC  B F C  G   # F C # B F C #D B   DFC C ; GC F 3 F4   B   " C C FC # B F  7  C #C F-B  GC  B  C  B /$#  F 0>1 0$ B F 9! FC I1 A CC CFFC F G  C  FC B   B  CC GC $#C F G  B G #C FG 

E

∗

0F B  B F B C# ;

a

1 C  F B  GC # G FC

H

0F B  B F B C##C ;

a

2

1 J,K L M N O P Q L M O RS Q T O *+  I  CFC B   C GC #DCFFC F  F #C F-B  GC  B  G C F # FCC GC #C/ U# B F  C #C F-B  GC  B  C

a

r´

eel

: #D # B  GC 0>1   B C     B 4  C GC ./ 5 C F-B  GC  B  C  # B F $#   ! # ;

a

evalu´

´

e

 
          C  GC2C FGC # B GC #DGC B F B GC GC#C9 JIK  C  C  G   B F  C : G  #C    GC  GC  B   B  C : #C FC B F # C FCC  FC F ; I B    B 4C  B /!#!C2#C GDF B !C  #C :#C  B 4C GC #C/  FCC !#!C2#C #C  B ? #C  B 4C GC #C/  DC  !#!C2#C: # C  B 2#C GD$# CF #DFC GC  B  ; # F!C 3#C C !C #DCFCC FG C##C GC #DGC F4 GF!C J,: K 5 C F B 2#4C GC C##C F B C C #C C  C C#  GC # C FC GC # FGC FGC  B  F #  B GC GC # GF!C  C  B F2C GDGC B  C 7 B F  D   C  B  GC C FC $CFC C GC FCCFC  B   C##CC C3# B FC $C  B F B 26C7 GC  B $ B F CC CF GC C FC  B   # B ! G F!CC JE: : <K 1 73 456789:; <; 82 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

              B /G7 B F C  GCC F GC 7 B FC CC$C GFCC GC # 7 B FC FC##C GC #DGCC F 5   B FFC   B  ;  B FCF  B FC  # B F  F # $#C F G F  4FC ! B  F C

ε

 U: B   

ε = m







1 −

2Γ



m

2(m − 1)



√

πΓ



1

2(m − 1)

(m − 1)









01 B ?  C #C C F4FC  C C# F B G G#D6 CCGC #  B F2C GC GF!C #  B F $# CF # FGC F GC  B  F #  B GC GC # GF!C 0  0 11  # F C: #DCC GC CC  B FFC B  C CH 72#C:G # C FC B ? # $F B  GC

ε

C  B FC CFC I < C I 13 6@?<
28?
<; 82 >6?; ; 6;?; <; 46?6 %F#DF B G  B  GD  F4FC

β

G#D  B  01:"#$CF C %FFCFC ;  B FF!CF #C 7  C #C  B C -FG#C 0CF. B $:.CF:1 C  B   G#CC 3-F C 5 C $#C F  D# F B  B C G #  2# B  GF$ #C F  B GC JEK  B  FC GC F$ 3 FGC J,K B ? C##C  B  $# C   B -C GC  # B  F #C 9 C  GC  B 2FC 3  C F C  B  FC ; #D$#  B  GC C F4FC J EI: EK 5 C F F$ 3 B   B F C CFC GCGC GC # $#C F GC

β

$C #C  B CC GC % B  B  G F GC 5 C $F B  G F4FC

β

G #C  GD  GCC F    B F  C #DGCC F CF. B $ C2#C CCG  B FC CFC  IE C I J>KA# D! G B   GC  B FFC B  G B  #D B FGFC GC !FGC F FCC CH C GC$ #C CF GC GC C FC           5 DGC B  F CC:  B #C $C C  B GC  B FFCC GD#-C GC G B C C3FC#C: CFC C FF B  7C GC F B F  C GD   F  7 A CC   B GC F B $C  B   C  B  F G  # D GC GD ## B   F B  C B F B  7F!#C  B F  C GC C #  GFG 0F B  3#C:8C3 B  <  B :  1  C FC F# 5 D# B  # #   B FC GC CC  B GC C3/ F C  #C FCC     B  # FF B    C GC FC$C  C   C GC  F7 C  " C C FC CCG FGCC  F B 2#4C GC #DC F 9C G FC$CC0 B  FC B   #C F # B 2C  CF CC # B F GC #DGC B  GD   2F FC$ C #C F CFF B 

  *&)"#"& (!. , (&

   C # ##C FF C G  B  0C #C F-B  GC # H B C GC  B 1 FCC B B B

 
, 9# 7 # F C: C DC CCG #   B 2#C G4 # B F  C #D B   B G4FC  9#   C  U:  B CFCF C 03 J EEK B  B 2C : C #  #  B GC GD"#$CF C %FF  F  -4C FC$ GD  9# C: C $ B #  B  G  B G #C FG  C F   B F G F!CC: C#  B G #C  $#C FG  A CC $ B #  B  C ## FC F # 9/ ! FC E G #C  GD  $CFFC  B G B # C FC$ GD  9# GC #C GD C C F GC  C# C CC GC  B 4FC " C  G! CF F B  C GC G #C F!CC   U 72#C F B : #C  B G #C FG  G  2F FC$ C  B  C !# ; C#  G 9# 5 C -4C C  B  B FC G B  GC # C 7 B   C D# D! GD  ## B  7  B  B !4C  B   G F G 9#  U F4 7 B FC F B : #C  B G #C FG  G  2F FC$ C C B FC  B   CC 7 B  !# ; C#  G  2F 5 C -4C C  B  B FC C3CC  B C  D#  D! G D   ## B  GC  2F     C !C CFGFC GC F B : #C  B G #C FG  G -4C  !/ CC  B  C $C # F B :CC  C F B  CFC # H B C 9#  7 C  # H B  C  2F        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

a

G  B  FCC C GC$ #C GC B  G 9# C G B 

RST UVWXYZ [V\Y]^__T`\Z ]a_ZYbVZ c dYX_ e]YdZ fV`VdYTd^]` fZgd hdYZ TddY^agVZ c [Z_ fiV`]jX`Z_ [Z

k

__gYTd^]`l`]dTjjZ`dZ`dYZUZ k

Uj Zd UZ_ga_dYTdlmg^ dZ`[Z`d c YV[g^YZUT Y^W^[^dV\]jf]_^dZ [g _n_dXjZ

EI             #C -4C C  B  B FC  B C #C 9# 7 U C FC  C #C F-B  G  B  F B : #   B F2  B  G  2F ; # G7 B F B  G C$C GC #  C #   B FC AB C  #C  2F C #  FGC  C #C 9#: # FGC F  B  B C GC #DCC2#C F B   9: ; F4 7 B F F-B  GC  B : #  B F2  B  G  2F ; # FGC F G -4C GC$C F4 !FGC GC$ C##C G 9#:G B  #D8 CC GC$C !#!C2#C A CC CFF B  C C FC#C7   B   B F: ; C FC  C #DC F G 9# G C: # H B C 9# 7 GC$C GC #  C #  FG C A# FF$C CH 7F CC: # B F C #D B  CFC ;  GCF  FC$CC F4 9:  C #D B  D-  #CC  4 A# GC$C # B F CFC GC  B $ B F C3FFC:; FF GC # H B C GC F B :#C F B F  C G 9#  
$'*) &#" $%& ' !$')( * +#)(%" =  #  B G# B  G  B  B FCC G  2F FC$ G #C H B C 9# 7 C  2F   C  B C  GC F B 2#4C: # GCF B  GC #D$ B #  B  GC  B F2  B  FC#$C G 9# C G  2F   B F GC #DGC B  C F$4#C CH  B #C3C " CFC C !F# ;  B G#CF #C  B G #C  $#C FG  G  2F FC$  B  # 7 B FC GD C # B  GC #!C G -C 

E

_eq

∗

= E

_sub

∗

+ (E

_{f ilm}

∗

_{− E}

_sub

∗

)Φ(a/t)

01

B ?

a

C #C F-B  GC  B :

t

#DC F G 9# C

E

∗

f ilm

0FC

E

∗

sub

1#C  B G #C FG  G 9# 0FC G  2F1 5 C 2  GC GFC  B G4#C C # B F GC F B  B CF C 7 B  B 

Φ

FCG  B C GC #DC3FCC " C  #CF #C  B G4#C F B  B  C F B  !FGC 7##C  #C  B G4#C CF C: #C  B G4#C #- C F B  C #C  B G4#C C/  F C 0 B   B  #CF B   C G  B C #  C GC CC  GC ; GC  B  GC  FC  FCC # C 1 23 6<98; ;:>?5?=; "   C F C 2#CF G C C  ! B FC  B #C  B G4#C F B  B  GC FCGFC  B F

Φ

C 7 B  B  #C CFC GD6 CF !F CC # 7 B FC GC #  B F2C

E

∗

eq

= f (a/t)

 " CF F C 3/ #C  B G4#C C3 B CC#: B F #C C# B   

E

∗

eq

= E

sub

∗

+ (E

f ilm

∗

− E

sub

∗

)e

−αa/t

0,1 C #C  B G4#C GC  B CFCF C 03 JEEK 

1

E

∗

eq

=

1

E

∗

f ilm

+

1

E

∗

sub

−

_E

∗

1

f ilm

!

e

−αt/a

0EI1  #C GC 3 : B  G B C GD  F4FC 6 2#C

α

 FC##C !9 B  - C A C  B G4#C  B  G B  7#C ; #CF J EK  B  C  DCFF B !CF  F #C F

 
E 1 73 6<98; 228 ?=; 2>>56

 A DC  B F CC F B   C GC F$ 3 B   C  B F  B G#CF #- CC #C  B   F   2F FC$  5 C   B  C C 6C  CCG  B #C3C: CF  C F B  CF ; F B GFC #C F B 2#4C GC 7 B  F B C 5 DF B C # #   B  C G F B 2#4C C C##C GC  B C  B ## JE<K   #  C F B C  C F F2$C  F #D CF!C  # C:  B  C   B CF$ #C  GC G7 B F B  B 2C G #C  G -4C  B  B !4C: B C  B ##2 B C  3 # B  GC #!C  $C 

ν

eq

= ν

sub

+ (ν

f ilm

− ν

sub

)



2

π

arctan(t/a) +

t

πa

ln



1 + (t/a)

2

(t/a)

2



0E1 C

µ

eq

= µ

sub

+ (µ

f ilm

− µ

sub

)

×



2

π

arctan(t/a) +

1

2π(1 − ν)



(1 − 2ν)(t/a) ln

1 + (t/a)

2

(t/a)

2

−

t/a

1 − (t/a)

2



0EE1 B ?

ν

eq

C

µ

eq

= E/2(1 + ν

eq

)

 B  FCC$CC #C  B CC GC % B  B  C #C  B G #C GC ##CC  $#C G  2F FC$ :

ν

f ilm

C

µ

f ilm

0FC

ν

sub

C

µ

sub

1 #C  B CC GC % B  B  C  #C  B G # C GC ##C  C G 9# 0F C  G  2F1:

a

#C F-B  GC  B    C 

t

#DC F G 9#  9:GDF4 #C G# GC # # JE<K:

ν

C #C  B CC GC % B  B  G -4C  B  B !4C $ CF F2 B  G  C# F B $C #C  GC G7 B F B   B C  B ## C  F # 72#C 8 CC GC # $#C F FC F

ν

 F 0 EE1 5 D # B  F C   C C 7C F C. C  B ## J EK F B G   ; C##C #C F B 2#4C GC 7 B  #  #C 

ν

f ilm

C   B  !# ;

ν

sub

 C #  B FC: 0 E1 D #  GC F B  GDFC C 0EE1 GC $C 

E

∗

eq

= E

sub

∗

+ (E

f ilm

∗

− E

sub

∗

)

×



2

π

arctan(t/a) +

1

2π(1 − ν

sub

)



(1 − 2ν

sub

)(t/a) ln

1 + (t/a)

2

(t/a)

2

−

t/a

1 − (t/a)

2



0E1 C  GC  F C F #C 9 J E<K C C3FC#C J EK $#GC C  B G4#C  B F GC  B FC GC  B G #C 7FC F ; E 0

0.5 < E

∗

sub

/E

f ilm

∗

< 2

1  C F B C CH #FC   B  #C G # F C C C##C GC  B C JE>K: B ? C C 7 B  #C  C F F2 B    B FC  F #C      GC  B FC   9  G D FCF C  B G B  GDG B  F7C ; #DCF7C 9# 2F  9: C F B 4C F B C C C##C G$C# B C F C C  B ## JK AB GF GD C F  C #C -4C 9# 2F C  FC  B G# F GC FGC F C FC: #   B C C FGC F G B C F

S

sub

= 2aE

sub

∗

C

S

f ilm

= aE

f ilm

∗

πa/t

A# F$C # B

F

 C 

S

_eq

−1

= (f (a)S

f ilm

)

−1

+ (g(a)S

sub

)

−1

0E<1 B ?

f

C

g

: FCCFC  B  # 7 B FC

1 + ka

n

:G B $C !FF  C:  #C 9# C F4  B  B 4GC #C C F B F # C  C #C  2F: B  FCF B $C 2C

S

eq

= S

f ilm



EE             A# 2 B C # B F ; 

1

2aE

eq

=

1

(1 +

2t

πa

)π

a

2

t

E

f ilm

+

1

2a(1 +

2t

πa

)E

sub

0E>1 A C C  B G # B   F C G D   C 3  C #C 9#  B 4GC   B G #C FG   C  GC$ C#  G  2F 13 6<98; ;:?@=:
5?=; " $C GC #C $ B F: #C  B G4#C F B  7 B FC GC 7 B F #C #C ; #CF:    C  B  #C FC CC $#GC  C  F CFC !C GC  B FC GC  B G #C  C F B C #CF$C  B C ;  B CF #C # # #- C   # B   C  B 2#C C ; F B GFC  F CC#C   B   C  B FFC  FC FC #- CC    2 B  C3C#C GC C -C GDF B C C #  B G# B  F B  B C F =  FHCF JE K: F # 2C GCF$ 3 GC
2F. J EK   # C F B C G -C  B GC GC !C: # F B  B C C F FC  B #4C GC  GC  B FC C GC G#CC G #DCC2#C GD   2F FC$  B  # 7 B FC GC  B C GC FC 9C A CC F B C C  #C  B F  #CF   B      F C  F   2F FC$ C  C  FCF #C F B F  C G 9# JEK A CCG CC F B C C2#C  B FF GD2#  F C G4 # B F  C #C F B F

a/t

GC$C  FC F ;  J E,K A DCCC GCF4FC B FC B   C  B ## B  B F $FC G#  C GC CC  GC   # C F B C C2C  F#7 B  B  GC FCC G  2FFC$ :  B  ## B  CFCF ;  B G#CF#C  B  # C  F   2F FC$ GC 7 B  C/  F C 0$ B F FC E1  B  GC C B #:  B  ## B   GCF #C CC GC $F B GC  B FC GC  B G #C C GC  B CC GC % B  B   F # F B C  B  B C G  2F FC$ 0$ B F FC  C <1