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Dynamics of electronic excitations relaxation in hydrophilic colloidal CdS quantum dots in gelatin with involvement of localized states
Author’s Accepted Manuscript Dynamics of electronic excitations relaxation in hydrophilic colloidal CdS quantum dots in gelatin with involvement of localized states M.S. Smirnov, O.V. Buganov, E.V. ShabunyaKlyachkovskaya, S.A. Tikhomirov, O.V. Ovchinnikov, A.G. Vitukhnovsky, A.S. Perepelitsa, A.S. Matsukovich, A.V. Katsaba
PII: DOI: Reference:
www.elsevier.com/locate/physe
S1386-9477(16)30292-2 http://dx.doi.org/10.1016/j.physe.2016.07.004 PHYSE12507
To appear in: Physica E: Low-dimensional Systems and Nanostructures Received date: 25 April 2016 Revised date: 27 June 2016 Accepted date: 7 July 2016 Cite this article as: M.S. Smirnov, O.V. Buganov, E.V. ShabunyaKlyachkovskaya, S.A. Tikhomirov, O.V. Ovchinnikov, A.G. Vitukhnovsky, A.S. Perepelitsa, A.S. Matsukovich and A.V. Katsaba, Dynamics of electronic excitations relaxation in hydrophilic colloidal CdS quantum dots in gelatin with involvement of localized states, Physica E: Low-dimensional Systems and Nanostructures, http://dx.doi.org/10.1016/j.physe.2016.07.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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) & .6/ & & ! & ( # ! ) ! ! & & @<$@ . # % $/ ) & .dn /dt ≈ 0/ J 9 ) ! & ! & # ! # " & Gαγ . I = αn γ = .*/ # 1 & & α[γ + γ ] + γ ) ! # & $*@$:@ & 68@*6@ 1 # " & ) ! # ! ! ( .6/ & !! & γ 6 & , ! & ! ) ! I = βn γ = βn γ . .+/ βγ + γ ! . J 9 / ! ! ! γ & γ & ! & ! J & '& 3" # ) ! # & ! & ! ! ( # % E & & ! E ) γ (T · exp(−ΔE /kT ) J , & A # %! & ( .*/ ) = γ (0) ( & .+/ . */ 3
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nonrad
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DAP
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1 N (t) = N (0)exp − + nk t , .$+/ τ J & & ! 3" n
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t −ΔD ∝ N (0) − − < n > , .$:/ τ ΔD %! & ! & & ! & # # exp[< n >] # A
:
0.58 0.352 0.398 0.486 1.03
0.042 0.062 0.017 0.028 0.0275
0.55 0.7 0.67 0.62 0.36
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< n >n − 1 e + nk t = exp − n! τ n=1
t = N (0)exp − − < n > [1 − exp(−kt)] . τ
− ΔD ∝
2800 3670 5080 2590 3280
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6 "# 2
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PII: DOI: Reference:
www.elsevier.com/locate/physe
S1386-9477(16)30292-2 http://dx.doi.org/10.1016/j.physe.2016.07.004 PHYSE12507
To appear in: Physica E: Low-dimensional Systems and Nanostructures Received date: 25 April 2016 Revised date: 27 June 2016 Accepted date: 7 July 2016 Cite this article as: M.S. Smirnov, O.V. Buganov, E.V. ShabunyaKlyachkovskaya, S.A. Tikhomirov, O.V. Ovchinnikov, A.G. Vitukhnovsky, A.S. Perepelitsa, A.S. Matsukovich and A.V. Katsaba, Dynamics of electronic excitations relaxation in hydrophilic colloidal CdS quantum dots in gelatin with involvement of localized states, Physica E: Low-dimensional Systems and Nanostructures, http://dx.doi.org/10.1016/j.physe.2016.07.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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180 3.8 ± 0.1 2.83 ± 0.01 1.74 ± 0.01
600 4.5 ± 0.1 2.74 ± 0.01 1.68 ± 0.01
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3.1 3.3 3.5 3.8 4.5
a1 0.021 0.0345 0.072 0.0158 0.0136
τ1 4500 10000 4000 4500 5500
τ2 100 100 92 95 92
a2 0.0120 0.0130 0.0250 0.0097 0.0210
τ3 3.5 4.0 4.0 4.0 4.5
a3 0.0090 0.0100 0.0080 0.0045 0.0110
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) & .6/ & & ! & ( # ! ) ! ! & & @<$@ . # % $/ ) & .dn /dt ≈ 0/ J 9 ) ! & ! & # ! # " & Gαγ . I = αn γ = .*/ # 1 & & α[γ + γ ] + γ ) ! # & $*@$:@ & 68@*6@ 1 # " & ) ! # ! ! ( .6/ & !! & γ 6 & , ! & ! ) ! I = βn γ = βn γ . .+/ βγ + γ ! . J 9 / ! ! ! γ & γ & ! & ! J & '& 3" # ) ! # & ! & ! ! ( # % E & & ! E ) γ (T · exp(−ΔE /kT ) J , & A # %! & ( .*/ ) = γ (0) ( & .+/ . */ 3
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!
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E2 0.084 0.081 0.086 0.083 0.082
5
0.180 0.168 0.125 0.180 0.150
2
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2
⎧ n˙ 1 = G − n1 α(γ1 + γ1 ) − n1 (γ2 + γ3 + γ5 )+ ⎪ ⎪ ⎪ ⎪ ⎪ +n2 γ2 + n3 γ3 + n5 γ5 ⎪ ⎪ ⎪ ⎨n˙ = n γ − n γ 2 1 2 2 2 ⎪ n ˙ = n γ + n 3 1 1 3 (γ3 β + γ3 ) ⎪ ⎪ ⎪ ⎪ ⎪ n˙ 5 = n1 γ5 − n5 γ5 ⎪ ⎪ ⎩ α = 1 − β.
.,/
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! ( &
.8/ !! &K ) & ) & & I # ! 6 # ! ! 6*@ n γ − n γ = Δ(I + I +I ), .9/ I & I %! & I .+/ I ) %! & # '& 3" ! G = Iexc + Inonrad + IDAP
2 2
exc
1 2
exc
nonrad
nonrad
DAP
DAP
DAP
Iexc = αn1 γ1 = = αγ1 n3
γ3 β + γ3 αγ1 αγ1 γ3 , = I + DAP γ3 γ3 γ3 γ3 β
Inonrad = =
γ3 β + αγ1 n3 γ3
.9/ n2 γ2
αn1 γ1
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= IDAP
αγ1 αγ1 γ3 . + γ3 γ3 γ3 β
e
.
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=
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5
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.$$/
)
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9+5 & ) ) & & 48$78+ F ) & # # & ! '& 3" 4$9 $: 6$ 6+ 6<5 ) & # $ $ % & &
γ2 dt .
& & # & ! '& 3" # & 4,67 ,85 1 && & # % '& 3" & & ! 1
& # # % ! # ) & & ! & 46$ 6< 8, 885
9
e
3/2
3/2
# %! & ( .$9/ ) + # A # ! % & & <@L =) ΔD ∝ N (0)/exp[< n >] ! & # # # 3" ) & ! & 1/exp[< n >] ! # 3" ) & ! # & $ % & & !! # $ & # " & & - & & J & & 3" & # % .J $/ +@ & # " & ! # & # ! @*8 . +/ ) 2 # % & # - # # " ) ! # 3" ) & & 2 # " # ! # ! ) & & '& 3" 4$: 6$5
& & # & & & ) & # !
) &# & & & 4$: 6$5 % & ! & J& %! & & ! ./ ! - & & # & ! ) ) #& 0 ( ./ % # $ ! # % ! - & $ # # - & & & 3" & & .3" )
) & - & / N !! & 49,5 & - & # & 4+: 985 # ! ! k ) # n ! n · k dN 1 + nk N , .$*/ =− dt τ ) N ! A& $ 3" n ! τ # # 3" # !
1 N (t) = N (0)exp − + nk t , .$+/ τ J & & ! 3" n
3/2
n
rad
n
n
n
−ΔD ∝
+ J ! # %! & ( .$9/ τ ! < n > k ! 1/exp(< n >) &
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n=1
3.1 3.3 3.5 3.8 4.5
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∞
N (0)
.$9/ J t ∼ 0 # ! # ΔD & ! # ! ! # ! ) # ! 3" J 3" ) & ! ( .$9/ !A &
t −ΔD ∝ N (0) − − < n > , .$:/ τ ΔD %! & ! & & ! & # # exp[< n >] # A
:
0.58 0.352 0.398 0.486 1.03
0.042 0.062 0.017 0.028 0.0275
0.55 0.7 0.67 0.62 0.36
) & & & & $ &# & )& & # ! ) #& 1 4997:@5 ) !! & ! & I # 3" & E) ! K & % # ! 3" 4995 1 ) & # ! '& 3" ) ) ) ! & & ! - & 46<5 1 %!
# ! # ,@@9@@ # @, ! 1 ) # ! # % & # ! ) & ) ! # ! ! & ,@@9@@ & ! # - & & % ) ! # # 46$ 6<5 E) & & # # &# & & # ! '& 3" & ! !& - & # # '& 3" & ! # ) - & # '& e
< n >n −
t = N (0)exp − − < n > [1 − exp(−kt)] . τ
− ΔD ∝
2800 3670 5080 2590 3280
3" & # &K - ) 0 & !! ! # ) # # !!! & ! ) ) ! & 0 ( ! & & & # % % & & # 4$,7$: 6$ 66
6< *@ 8, 885 % ! # & ! # ! & # # ! & & & E) # ! ) ( # !
) .@ 8 1 , G ! > + '(% (+3(+( % " / @ ! "# % '( ''(&+ ? 2 H << # " / @ "# 2
+) '((+ ')3? 4 2 H << # /$5 $ - - " / @ ! "# '+ '((& (&)4( & " / @ < )) '( *3 + . / # -8 2 H "# ? '((( <33)+* <33%' '( . / ! "# () '((( ?'*?'3 ' " / @ "# ))? '(% +' '' << # 2 H /$5 $ - " / @* "# < 2
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+? '((? (%4)(& '4 0 "= < )' '((+ '((% '& -! > 2 $G < H "# < %3 ++? ?3)4 '+ " 1# " / @ ! "# 3) '( (+)4(? 3( !. $ - - < G# / < 8 # " / @ ! "# 4 '(3 ))' 3 1 ! 5 H . / "# 2
&' '((3 '4+3*'4+% 3' G C
6 > 2
% '((% '3?(*'3?) 33 C 8 !6 6 < / </ "# 2
33( '((( '34*')' 3) " - C " 1 < 5 = 5J . ! "#K
( ++& '((4*'(+ 3% 0, < # , =# -= 02 # , / # C "# " , ! "# ) '(( '')4&*'')&? 3? 0 0 . 0 - 1 0 # + '(% 4))*4%3 34 . / " 5 5 / = "# < %3 ++? )?3*)?4 3& 2 1 $* # ! "# (' ++& %?%'*%?%& 3+ . / " 5 * 5 / = / *
'( ++? 3+%*)() )( 5 1 - # . / 5 / = "# ?' ++? 3*( ) . / ! H = -8 2 H "# < ?( +++ <'44*<'&( )' 2 1 $* # ! "# (3 +++ (44% )3 / @ C# @= *
# > 2@ # < . "> )4 '(3 3'&*33' )) / @ @= # C# > 2@ / @ < . * ! "# 3 '(3 &)3(? )% -. ; 0 0 > 2 # 0 1 " 0 *
# % '(3 ?%*?%+ )? !! < ) '((4 )% )4 0 0 1 , / . # @= ! > < ? '() ''&? )& 0 0 1 *
# @= " ! 2 %? '() ''*'&
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) ) !! & # FJ F !I $, ,6@+@9: QQ & FJJF J$,F @89 ! " "# $ %& '() ')*'+ ' , # - . / -/ 0 !$1" 2
%) ++ ))'*))% ++ 3 - . / -/ 0 , # & ++' ''4*'3( ) 5* 6 7*8 - ,*9 8 :* ,* , * !*# 6 "# $ )+ '(3 *) % 0;< = > 3%3 ++ 434*4)( ? 5 " / ! "# 2
) '(3 3+&3*3++ 4 > : @ " = / A 0 B @ "# $ 4) '(% 4)*&? & ! < =*C = -D@ C !E 2 < ! C "# 2
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<
)+ > / 0 0 1 "# $ ?& '(% %+*?3 %( ,* , /* / */ 2 ,- ", , ! "# +' '((' ?'*?) % C 8 B ! ('*(3 '((3 33&*3)3 %' > # 1- 5 < 5 2$ ! # +( +&? 33+3 %3 5E@ $# F 5 8 "# 2
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6 "# 2
4% +++ '+4'*'+4) ?( C <@ C
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