Estados de impurezas em semicondutores e nanoesetruturas sob campos externos

!"#$

% & ' (

$ & )

(* +,- . +) )

(* / + 01*

!

" # $ %& ' (

" )* + , +

, " - ).!../,

0 (, + 1 2334$

. 5 " 67 8

! . -

9 , -"

$ ,-$ ' $ #! , 0 "

$ :! ;$ 5$ !

!! ! % $ "

( " )* $ < . <

"

&#" " ,, , :! ;

$ 5$ + "

/ $ # #

$ %< 9 =.

!" # $

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

) !! ! . !/ !" 0

1 !)

03 () 4 5 () / ! /

0 ! 6 / !/ (

7 1 .!! ' 0 " 8

$ 0 59 / 6 0 "/ !/ !

:;::1

2

< $ 0( 59 ! 7 6 0 "/

!" !/ =$ !> 6 0 "/ 1 ! )

0 6 !? & 0> !

30 1 ! . .!! !

(@ ! / ( 7 ) 0

!?

0 059 0(59 0

"/ 0 !/ 03 () / ! /

! " # $% ! "

& ! '()$

* %+ , !% * %

% ! * *!

, -% ++.% , -% / *! %

%+ / %* ++ 0-,

% +% 1- %+! 1

!%2 # + /% % 0

3454346

2

7# -/% 1 *8% *1 9# %0

%+ 1 1: * 1

.+% %. % /

*! 0-, %

1 %+ % /% /% 1

0 0 , % ++.% % 0-,

!"#$"#!"#"%

2

& & ! &'

&(

&(

)

!"#$"#!"#"%

2

) & !

)'

! " #

$ %&

* +

D

0

D

−

,

"

D

−

D

0

D

−

!

" #

D

0

D

−

$% & !'

($% & ) !'

($% & ) '!

"

D

−

#'

) % * +,-. /

* )% ) /'

$ ) 0 ) * /'

$ ) * 0 )

12 ) $3$ ) *

" )2 #

!" #$

% &" '$( )

* " +

,-. . / $ "

( 4) % , $

( )% ) )

( 4) % . ) 6+

* . )

! "

!""#

$ ½

%&' (# %)))

")))*# "))) " *#

! ""+ !

%,-)"-%)".

/ 0 1) 2 $ 2 3

2 2'

2

*4 5 67 ¾

(

!

" # $ % &'

" ! '(')* (+ ) ,

- # $ .& &

- * + +- ,

- + %

/0 1 &.

" - /0 1

( &

" #$

!"

!!#

$%"&

'

()

%*

(+

,

(-(

.

- %

.

23 -

!" # $ %

&! '

!" # $ % &'' ( )'

*+ ","(*+ ( " - " - . /

4 42 5

6 " " # '

$ 7

%' 8( +4+ -'

99 (9 - : &

" *;<,

*;<, = > 2 1

! " #$ "

% &' ( )

* #$

+ #$

#

" #

&' ",

- * * .

/-/ 0

/ 1 *

" 2 - 0,

3 - , 14

% & 5# * " * +

# 6

7# 8%

9 / 14

:;

. . .

℄ $ /+*=> ?@?, : ABC

&/ "

- , > # DB

# DE +

2:2

F F- = 5

n

ǫ

E

n

=

nǫ

=

nhf,

f

h

! "#$% &

6

.

62606957(29)

×

10

−

34

'

·

( )

*

h

≈

4

.

135667516(91)

+

·

(

h

,

. / - . 0 1

)2

%

3 %

h

$ %

"# 1)2

* % 1 4 ,

" 0,

( % 5! 678

% ,

"# 9 " :

( 678 % ;

% < >

( 6 , ( , "

0,1

,

( 68 6? % @*<A< /

, -B :CC.

D

E F, 67 / 6?G *& H 44 / 6?7 " ' 67 / 647

/ @

0 ( I J/

' & 9: K 44? / 6G ,/

3 H 46 / 64?

% 9: K 6G % /

F, % % !

( ;

" * L 67 / 64M ,

% ,/

, % @ " ,: F, ,

" 0, 1

6N 9: K L

2

_×

2

! " # $ " " "

% & '

( " ) *+ " , #

% ,

-. / " 0 $

*+ " )10

%

2 0 0 /3 0 "

4

×

4

-. " %

4 ,,, " 0 "*+

mc

2

m

= 9

.

10938291

×

10

−

31

5 , ,

c

= 299 792 458

6 , 0 + $

+ 0 7.8 % 9 " "

0 0 $ + 0% 2 , " 0

/*+ + 0" /*+ 2 , " &."

&

%

2 $ 0 $ .: ;43

, " $ / $, " 0 0

% # " < = > 5 20 ? . " /3 "

' . @

AB C . . 7 "

1 ' . @

A %

= " $. ' $ + 0 "

*+ " " , + + % 2

+ 0 "

$ " # % 7$ / " "

" " " :" " % 7 *+

. , 1

" " "% = " /3 1

/ , 1 " "*+ " # '

&" % E " : , # " :" '

&" F%

7 "$,+ ;43 "

# " ., . @ 0

H

−

/ "

, % G" " /3 ,/ , + 0 %

G

H

−

/ '0 &" ,

D

−

d

! " # $

%& ' $ (

$ )

* $ +

(

, " $ "$ )

-* ! . ) "

*" $"/ ""

* $ +

* " "

0 ( 1$ 2

$3$ 45 &$ "

6 52.

# 5 7

. 7 5 8.

,- , - $

$

n

,

p

- $ . $ $ / 9

5 :$ " ) 5 "

2 . ' $

$ "

* !$ &

" $; <"=

>; ?

6 . %

# =

6 (

360 000

×

360 000

! "

#"$%&'(&'%&'&

2

) % *

"

"+"

, $ "

- .

/

+

) % 0 1

!

40

# / "

23-12

! /

! 4

-5 % 1

1 ! 1

) % .

5 " -

!"#$%&

'

'(

( )

* +,

++ !- ++

*

.

' + )

( * /0

1234

6

) ) 7 8* 9

"& "& * :

, ")& ) )

, "+ & ) "&

;* $ '' * 9

! - "<:&

) - - 6 ":

x

<

1

! "

# $ # % &

#

'() !% !

* # +&, ,

. ) # /(

&

250

' & / ()

#

& )

!) ( #

! % '

% #

01231201

4 6 7

# ) - !

'

( ) ) % &

& ) 4 # 8' ! '

8

'

) (*

9 : # % !

) ( 0

& ) ) !

& '

) &) % ;

% &

# &

! - ) !

) () (

' ) % #

! "# $

%

&' ( (' '

&' ((( ) '

* +% )

+ "

,

a

∗

-'

Ry

∗

. )

/ ' ( 0( 1* 2 " 1"

.

R

γ

= (

a

∗

_/λ

₎

2

λ

=

/

(

eB

)

3

/ ' ( 4 5 !

m

∗

# !

ǫ

r

# , !

a

∗

#

-' !

Ry

∗

# '!

E

g

# 1*2 " 1" 0(

5

m

∗

_/m0

_ǫ

r

a

∗

!6#

Ry

∗

!7#

E

g

!7#

300

8 1*

0

.

073

12

.

37

9:;<( :09<9 (; 2 "

0

.

067

13

.

13

<=;<= >(;:9 0= 1"

0

.

026

14

.

55

(9: =: :;<9; <=:

&' ((= )

?&@A&@?&@&.

2

' @ B B

$ ' B )

B + B

* + C ( (( " )

' ' D

$ ' CB ) %

'

!

"# " $

%& !

#

! '$(

& # )

# * $ +

& $

$ #

( # , )

# - .

#

$ %+!/ 01

#

%

+ # 2

# % 3

$

& $ #

5 ( & 0 6# #6

→

6

±

# 5 +

#

+

.(

#

%+

z

e

Z

= 0

Z

= 1

Z

= 0

Z

= 1

+

e

!

"

!# $ % &

' (

) (

$ & " *

( " ' *+

, + ( ' *

( *- * (* ""

(

ˆ

H

Ψ(

r, θ, φ

) =

E

Ψ(

r, θ, φ

)

,

. !/

ˆ

H

=

1

2

(

−

i

∇

¯

+

e

A

)

1

m

∗

₍

_r

₎

(

−

i

∇

¯

+

e

A

) +

U

(

r

) +

V

(

r

)

,

. /

r

0

θ

φ

1

A

=

B

×

r/

2

" 1

m

∗

₍

_r

₎

R

U

(

r

) =

⎧

⎪

⎨

⎪

⎩

0

r

≤

R

+

_∞

r > R.

U

(

r

)

c

c

= 1

,

2

, . . . L

U

(

r

)

U

c

!" !"

# $ #

c

= 1

#%

U

(

r

) =

⎧

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎩

U

1

= 0

r

≤

f

2

,

U2

f2

≤

r

≤

f3,

U

c

f

c

≤

r

≤

f

c

+1

,

+

_∞

r > R,

&

f

2

c

= 1

c

= 2

'

f

3

c

= 2

c

= 3

'

R

( )

* (

U

(

r

)

+$,-$,+$,$.

2

/ $!"

0 !"

V

(

r

)

!" 1!"% 2

V

(

r

) =

−

Ze

2

4

πǫ0

ǫ

c

r

+

C

c

.

3

1 !"

V

(

r

)

C

c

) 2

r

=

f

c

!"

C

c

−

1

=

C

c

−

Ze

2

4

πǫ0f

c

1

ǫ

c

−

1

ǫ

c

−

1

,

4

c

ˆ

H

=

₋

F1

m

c

∇

2

−

F2

m

c

i

B

∂

∂φ

+

F3

m

c

B

2

_r

2

_sen

2

₍

_θ

₎

4

−

F4

ǫ

c

2

Z

r

+

C

c

+

U

c

W

c

,

m

c

=

m

∗

_/m0

c

W

c

=

C

c

+

U

c

.

!

B

" " # % & '

F

1

=

2

2

m0

nm

2

≈

38

.

099817461

!

;

(

F

2

=

e

T

2

m0

≈

0

.

057883817

!

;

)*

F

3

=

e

2

_T

2

_nm

2

2

m0

≈

0

.

000087941

!

;

))

F

4

=

e

2

8

πǫ0

nm

≈

719

.

982207470

!

.

)

"+,

C

c

- . /

L

0& 1 2

C

c,L

C

c,L

=

−

2

F4

Z

(1

₋

δ

c,L

)

L

−

1

x

=

c

1

f

x

+1

1

ǫ

x

+1

−

1

ǫ

x

,

)3

δ

c,L

=

⎧

⎨

⎩

0

c

=

L,

1

c

=

L

z

Ψ

m

(

r, θ, φ

) =

e

i

mφ

√

2

π

ψ

m

(

r, θ

)

,

m

ψ

m

(

r, θ

)

H

ˆ

m

ψ

m

(

r, θ

) =

E

m

ψ

m

(

r, θ

)

0

< r < R

ˆ

H

m

=

F1

m

c

⎡

⎢

⎢

⎢

⎣

−

1

r

2

∂

∂r

r

2

∂

∂r

−

_r

₂

_sen(

1

_θ

₎

_∂θ

∂

sen(

θ

)

∂

∂θ

−∇

2

+

m

2

r

2

_sen

2

₍

_θ

₎

⎤

⎥

⎥

⎥

⎦

+

F2

m

c

mB

+

F3

m

c

B

2

_r

2

_sen

2

₍

_θ

₎

4

−

F4

ǫ

c

2

Z

r

+

W

c

.

!

" # $ #%

R

&

Ψ(

R, θ, φ

) = 0

'

θ

φ

('

ψ

m

(

R, θ

) = 0

'

θ

"

H

ˆ

m

'

θ

π

−

θ

) * + &

θ

=

π/

2

,

ψ

m

ψ

m

(

r, π

−

θ

) =

σψ

m

(

r, θ

)

σ

= 1

σ

=

−

1

) &

z

(

σ

= 1

σ

=

−

1

0

- .

'

0

≤

θ

≤

π/

2

" ' * / )

*

) 0 1 & *

2 #.

"

M

c

+ 2

&

N

+ 2

& " / +

s

# 2

s

=

_c

l

=1

M

l

−

1

N

+ (

i

₋

2)

N

+ (

j

₋

1)

,

3

c

+ '

1

,

2

, . . . , L

#

L

! "

i

c

r

i,c

=

f

c

+ (

i

−

1)

h

c

,

# $%&

h

c

=

f

c

+1

−

f

c

M

c+1

'

k

=

₂

_N

π

₊₂

( "

G

i,j,c

=

ψ

m

(

r

i,c

, θ

j

)

) * " +

yu

G

i,j

+1

,c

+ yd

G

i,j

−

1

,c

+ yl

G

i

−

1

,j,c

+ yr

G

i

+1

,j,c

+ yp

G

i,j,c

=

E

m

(

M1, . . . , M

c

, N

)

G

i,j,c

,

# $,&

)

E

m

(

M1, . . . , M

c

, N

)

" -"

E

m

)

yu =

F1

m

c

−

1

k

2

_r

2

i,c

−

cot(

θ

j

)

2

kr

2

i,c

,

# .&

yd =

F1

m

c

−

1

k

2

_r

2

i,c

+

cot(

θ

j

)

2

kr

2

i,c

yl =

F1

m

c

−

1

h

2

c

+

1

h

c

r

i,c

,

yr =

F1

m

c

−

1

h

2

c

−

1

h

c

r

i,c

,

yp =

F1

m

c

2

k

2

_r

2

i,c

+

2

h

2

c

+

m

2

r

2

i,c

sen

2

(

θ

j

)

+

F2

m

c

mB

+

F3

m

c

B

2

4

r

2

i,c

sen

2

(

θ

j

)

−

ZF4

ǫ

c

2

r

i,c

+

W

c

)

.

σ

m

! " # $ " " %

&'" (

r

)$

R

=

f

L

+1

G

M

L

+2

,j,L

= 0

.

* %

z

σ

=

−

1

"

θ

=

π/

2

%

G

i,N

+2

,c

= 0

.

+

*

m

= 0

"

θ

= 0

%

G

i,

1

,c

= 0;

,

*

m

= 0

σ

=

−

1

"

r

= 0

%

G1

,j,

1

= 0

.

-.) $' $" " '

* %

z

σ

= 1

"

θ

=

π/

2

%

∂ψ

∂θ

(

r, π/

2) = 0

.

/

G

i,N

+2

,c

≈

−

G

i,N,c

+ 4

G

i,N

+1

,c

3

.

m

= 0

θ

= 0

∂ψ

∂θ

(

r,

0) = 0

,

G

i,

1

,c

≈

4

G

i,

2

,c

−

G

i,

3

,c

3

.

r

= 0

m

= 0

σ

= 1

!

T

δ

"

T

F1

m1

∇

2

_ψ0

₍

_{r, θ}

₎

_dV

₌

T

F3

m1

B

2

4

r

2

_sen(

_θ

₎

−

F4

_ǫ1

2

_r

Z

−

E

+

W

c

ψ0

(

r, θ

)

dV,

dV

=

r

2

_sen(

_θ

₎

_{dr dθ dφ}

#$! % & '

! ! (

!

r

= 0

)

δ

2

)!

δ

_→

0

+

* ! +, - ! (! . !

F1

m1

π/

2

0

∂ψ

∂r

(0

, θ

) sen(

θ

)

dθ

=

−

ZF4

ǫ1

ψ

(0

,

0)

.

/

0 )

G1

,j,

1

≈

1

η

N

+1

j

=2

(4

G2

,j,

1

−

G3

,j,

1

) sen(

θ

j

) + 2

G2

,N

+2

,

1

−

1

2

G3

,N

+2

,

1,

1

η

= 3

N

+1

j

=2

sen(

θ

j

) +

3

2

−

2

Z h1

m1

F4

k ǫ1

F1

=

3

2

cot

k

2

−

2

Z h1

m1

F4

m

σ

r

=

R

=

f

L

+1

θ

=

π/

2

θ

= 0

r

= 0

0

!" #$" # " #!"

0

% !" &" # " '"

= 0

!" #$" " '"

= 0

% !" &" " '"

( )

L

−

1

* %

) +)

r

*

f2, f3, . . . ,

ou

, f

L

, -)

* - ") .

1

m

c

∂ψ

∂r

(

f

−

c

+1

) =

1

m

c

+1

∂ψ

∂r

(

f

+

c

+1

)

.

#"

* - / 0

G

i,j,c

=

ψ

m

(

r

i,c

, θ

j

)

) - 1) *- .%

∂ψ

∂r

(

f

−

c

+1

)

≈

1

h

c

(3

G

M

c+2

,j,c

−

4

G

M

c+1

,j,c

+

G

M

c

,j,c

)

#'"

∂ψ

∂r

(

f

+

c

+1

)

≈

−

1

h

c

+1

(3

G1

,j,c

+1

−

4

G2

,j,c

+1

+

G1

,j,c

+1

)

.

#2"

3 #'" #2" - #") % -

. * -

G

M

c+2

,j,l

=

G1

,j,c

+1

=

h

c

+1m

c

+1

(

−

G

M

c

,j,c

+ 4

G

M

c+1

,j,c

) +

h

c

m

c

(4

G2

,j,c

+1

−

G3

,j,c

+1

)

3(

h

c

m

c

+

h

c

+1m

c

+1

)

=

a

c

(

−

G

M

c

,j,c

+ 4

G

M

c+1

,j,c

) +

b

c

(4

G2

,j,c

+1

−

G3

,j,c

+1

)

,

4$"

a

c

=

h

c

+1

m

c

+1

3(

h

c

m

c

+

h

c

+1m

c

+1

)

4"

b

c

=

h

c

m

c

3(

h

c

m

c

+

h

c

+1m

c

+1

)

Λ

G

=

E

m

(

M1

, . . . , M

L

, N

)

G,

G

(

M1

+

M2

+

. . .

+

M

L

)

N

G

i,j,c

2

≤

i

≤

M

c

+ 1

!

2

≤

j

≤

N

+ 1

1

≤

c

≤

L

" # $

Λ

$ $ %

Λ

% % ! &% &'

$ % ( )! $% *+% ,

4 000

_×

4 000

! & - '$. &

$ , ' / ! % $

01' 2% % *$ ,

& 3) &4 56 271

1+ 89% $ % "

:;,& 5,

)$<! =) >& ;& =7?! %

:< 2 @$ ! $ , ,

%! !)$, A

61 "! 3! +

:$<! 3 && 6(2B

,

! %, :$< % A$ $ $

%

" $ % & 1' /

!&:<!"

!%,

:?C< ( & %,

:,D$

[

, )! E ! 1'

→

!

1)5

→

10

5

! 2

→

6(

]

<

( ' ) 3 $

-'$.! %, ) 3 6'

.

F# $

M

1

→ ∞

N

→ ∞

! !'@ ! $

M1

N

!!

M1

=

N1

= 100

M1

=

N2

= 200

G@)

E

N

=

E

∞

+

β/N

2

E

∞

= (

N

2

2

E

N

1

−

N

2

1

E

N

2

)

/

(

N

2

2

−

N

1

2

)

E

m

E

N

1

E

N

2

H

ˆ

m

−

H

ˆ

−

m

= 2

mB

E

m

=

E

−

m

+2

mB

ψ

m

(

r, θ

) =

ψ

−

m

(

r, θ

)

m

_≤

0

! " #

$ %&'

|

Ψ

_|

2

dV

=

π

0

+

∞

0

ψ

_m

2

(

r, θ

)

r

2

sen(

θ

)

dr dθ

= 2

I,

$ (('

I

)

I

=

π/

2

0

R

0

ψ

_m

2

(

r, θ

) sen(

θ

)

r

2

dr dθ

$ (&'

≈

k

_L

c

=1

h

c

1

2

M

c+1

i

=2

G

2

_i,N

₊₂

_,c

r

_i,c

2

+

N

+2

j

=2

G

2

_M

_c+2

_,j,c

f

_c

2

₊₁

sen(

θ

j

)

+

N

L

_c

₌₁

M

c

s

=1

h

c

G

2

s

r

2

i,c

sen(

θ

j

)

⎤

⎦

.

$ (&'

* #

2

I

%

#

G

(

L

+ 1 +

L

c

=1

M

c

)

×

(

N

+ 2)

√

2

I

+ , -.

.$

Z

= 0

' $

Z

= 1

' ,

/ (0

! 1 2$' %

,

*

$ ' .

E

0

3 %

E1

s

! -3 $ -' , 4 $' !

Variacional

Diferenças finitas

Bulk

Γ

0

Γ

1

Γ

3

Γ

5

Γ

10

a

0

2

4

6

8

10

0

1

2

3

4

5

6

R

a

Energia

de

ligação

Ry

R

10

R

5

R

3

R

1

R

0.5

b

Variacional

Diferenças finitas

Bulk

0

2

4

6

8

10

1.0

10.0

5.0

2.0

3.0

1.5

7.0

Γ

Energia

de

ligação

Ry

!

"#$#

! % & '

# ( ) * ++

,'!

# " # (

- !# .#/

' 0 #1 ! )

) 2#3 1 0'

& 56'

' % -

7 !/ 8' '

0 #1

" ! 6

%' '

5' # $ # !6

&

"

' $

' (' 7) "

# ( - % !/ 56

Variacional

Diferenças finitas

Γ

0

Γ

1

Γ

3

Γ

5

Γ

10

a

0

2

4

6

8

10

0

5

10

15

R

a

E

0

Ry

R

10

R

5

R

3

R

1

R

0.5

b

Variacional

Diferenças finitas

0

2

4

6

8

10

0.1

0.5

1.0

5.0

10.0

50.0

100.0

Γ

E

0

Ry

!! !! " !! !

!! ! #!$! ! $!!

! !! "!! %!

Variacional

Diferenças finitas

Γ

0

Γ

1

Γ

3

Γ

5

Γ

10

a

0

2

4

6

8

10

0

5

10

15

R

a

E

1

s

Ry

Diferenças finitas

Variacional

b

R

3, 5, 10

R

0.5

R

1

0

2

4

6

8

10

0

5

10

15

20

25

30

35

Γ

E

1

s

Ry

R

3

R

5, 10

0.0

0.5

1.0

1.5

2.0

1.0

0.8

0.6

0.4

0.2

0.0

& ' !! ! (

! ! " !! !

! #! $! ! $! !

!! "! ! %! ) "

! !

! !* !!+ ( +! ! ! !! ! !

!!(!!!!!!,

( # !!

!" ) -"℄ ! !

-!℄!%/!!0

! " # $

% & ' $ ( (

&

& ) &

( ( &) *+

*+ ,

- $

E

0

( " # ( (

& ,

" #$

$ - $ . $

( &

Γ

10

Γ

5

Γ

3

Γ

1

Γ

0

a

0

2

4

6

8

10

0

5

10

15

20

25

30

35

R

a

E

2

p

Ry

Γ

10

Γ

5

Γ

3

Γ

1

Γ

0

b

0

2

4

6

8

10

0

2

4

6

8

10

R

a

E

2

p

Ry

/0 "

+

−

( )

1 ) ( ( #

→

±

$ &( (

2 1

E

2

p

+

−

E

₂

_p

−

= 2

γ

"

E

2

p

E

2

p

R3, 5, 10

R1

R0.5

R

3

R

5

R

10

0

0.25

0.5

1

0

1

2

0

2

4

6

8

10

0

20

40

60

80

Γ

E

2

p

Ry

+

−

+

−

−

!

+

−

" #

a

Γ

10

Γ

5

Γ

3

Γ

1

Γ

0

0

2

4

6

8

10

0

5

10

15

20

25

R

a

1s

2

p

Ry

Γ

0

Γ

1

Γ

3

Γ

5

Γ

10

b

0

2

4

6

8

10

0

1

2

3

4

5

R

a

1s

2

p

Ry

$% &

1

s

→

2

p

+

₁

_s

_→

₂

_p

−

→

+

→

−

→

+

!

→

−

"! # $ %&

R

= 0

.

5

,

1

,

3

,

4

,

10

! '

R

= 3

,

5

,

10

($)

* + #

0

≤

γ

≤

1

! &( $ ($ # +$

R3, 5, 10

R0.5

R1

1s2

p

1s2

p

R

3

5

10

0

0.5

1

0.0

0.5

1.0

1.5

2.0

2.5

0

2

4

6

8

10

0

10

20

30

40

50

Γ

1s

2

p

Ry

, -

→

+

→

−

#

$ %&

2

. /0 ."$0 1.23.21.2.*

2

#( 4-5 6 (

$ #& #& 77 877

" 79 88 : $ ;

( $ $ )

;( #& <6

- ;

=

+

>

!"

#$%&'(")(*+,-.,-+,-,/

2

01!(2 (!34

(( +(& ( 4 ( 3

( %! )(*& $ 5(

( +,-.,-+,-.,

( +,-.,

"6 7 (

!

CdSe

₁

ZnS

₂

CdSe

₃

SiO

₂

₄

CdSe

ZnS

CdSe

SiO

2

1

2

3

4

f

2

f

3

f

4

f

5

c

1

c

2

c

3

c

4

L

4

1!(2 8 !)(*+,

Δ

1

-.,

Δ

2

-+,

Δ

3

-,/

2

Δ

4

&)(

Δ

c

6 (

c

6

L

6 '

0 (

Δ

4

,/

2

& ( "% 6 5 6 (9 ! )( #(3: ( (

$

r

)(

(

f4

+

f5

)

/

2

5 ( & "" % ;(6

(

f

4

+

f

5

)

/

2

4 (

/ * < +,& .,& +, ,/

2

# =# 4 " 2

c

m

c

m

∗

m

e

ǫ

c

!

E

g

"

Δ

E

#$# %&#

%

m

c

=

m

∗

_/m0

_ǫ

c

E

g

(

$

)

Δ

E

(

$

)

' %& ' () * ' + ' ,- *

.) * / / ' ,- *

-0 )1

2

* 0 +

2 ()3.) +**

2 ()3)1

2

*-*

-#

U

(

r

) =

⎧

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎨

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎪

⎩

U1

= 0

,

r

≤

f2

U2

= 900

,

f2

< r

≤

f3

U3

= 0

,

f3

< r

≤

f4

U4

= 3050

,

f4

< r

≤

f5

+

_∞

,

r > f5.

0

45#

f

5

=

R

6 7

f

2

#

f

3

f

4

()3.)# .)3() ()3)1

2

# # 5

8! '*

9 6# # 6

f2

# () .)# 6 # ! :!

# ;<<2$<#5().)#

;

<<<2$ "5 = #

= 8! ''# !> 2

m

= 0

# 6

γ

= 0

F

= 0

1 ; ! #

Δ

3

# () = ?@ )A@

=

5

10

15

20

0

200

400

600

800

1000

3

ML de CdSe

Energia

meV

CdSe

1.7 nm

ZnS

1 ML

CdSe

3

SiO

2

5 nm

Z

0

a

5

10

15

20

0

200

400

600

800

1000

3

ML de CdSe

Energia

meV

CdSe

1.7 nm

ZnS

1 ML

CdSe

3

SiO

2

5 nm

Z

1

b

5

10

15

20

0

200

400

600

800

1000

3

ML de CdSe

Energia

meV

CdSe

1.7 nm

ZnS

4 ML

CdSe

3

SiO

2

5 nm

Z

0

c

5

10

15

20

0

200

400

600

800

1000

3

ML de CdSe

Energia

meV

CdSe

1.7 nm

ZnS

4 ML

CdSe

3

SiO

2

5 nm

Z

1

d

Δ

3

!" # !$ % &

#

Δ

2

= 1

"

Δ

2

= 4

' ( ) % ( *(+ (,+

¼

%- . ( )(

σ

= 1

()(

σ

=

−

1

' /( (%!

N

= 50

4

c

=1

M

c

01

100

(#

2 %- 32 % 2

4 3

1

.

7

2

.

8

$( % /((%! $#().53

(

5

10

15

20

0

200

400

600

800

1000

3

ML de CdSe

Energia

meV

CdSe

2.8 nm

ZnS

1 ML

CdSe

3

SiO

2

5 nm

Z

0

a

5

10

15

20

0

200

400

600

800

1000

3

ML de CdSe

Energia

meV

CdSe

2.8 nm

ZnS

1 ML

CdSe

3

SiO

2

5 nm

Z

1

b

5

10

15

20

0

200

400

600

800

1000

3

ML de CdSe

Energia

meV

CdSe

2.8 nm

ZnS

4 ML

CdSe

3

SiO

2

5 mn

Z

0

c

5

10

15

20

0

200

400

600

800

1000

3

ML de CdSe

Energia

meV

CdSe

2.8 nm

ZnS

4 ML

CdSe

3

SiO

2

5 mn

Z

1

d

Δ

1

= 2

.

8

! "

##$%%&&'%($%%$)

%$ *%%%+$ %",%

m

= 0

Δ

3

= 1

4

5

10

!" #$ &'(

1

.

7

)&*(

4

)&'(

Δ

3

)&+

2

(

5

,- .

# /0

1/ 2,,-/

$#03 4 5

6 / / - .

0 7

Δ

3

10

!" 1- .0 ,

08 019

3 ': ' 0 +

2

' / $ ,

4 $ -

Δ

1

1

.

7

2

.

8

,

; / '

Δ

3

+ -

U

(

r

)

/ & <( - 3 = >8 4

5 3 0$ -

&

3050

?( + / 3

/ +

2

,-

@ > $ $

*

1

!" A

/ ,

+ $ !" * - 0 $

- 6

* -

03

' 1

/ = >8

0

20

40

60

80

100

207

208

209

210

B

T

Energia

meV

CdSe

2.8 nm

ZnS

4 ML

CdSe

1ML

SiO2

5 nm

Z

0

m

0,

Σ

1

m

0,

Σ

1

m1,

Σ

1

m

2,

Σ

1

m

3,

Σ

1

0

20

40

60

80

100

49.5

50.0

50.5

51.0

51.5

52.0

52.5

53.0

B

T

Energia

meV

CdSe

2.8 nm

ZnS

4 ML

CdSe

1ML

SiO

2

5 nm

Z

1

m

0,

Σ

1

m

0,

Σ

1

m1,

Σ

1

m

2,

Σ

1

m

3,

Σ

1

0

20

40

60

80

100

116

118

120

122

124

126

128

130

B

T

Energia

meV

CdSe

2.8 nm

ZnS

4 ML

CdSe

10ML

SiO2

5 nm

Z

0

m

0,

Σ

1

m

0,

Σ

1

m1,

Σ

1

m

2,

Σ

1

m

3,

Σ

1

0

20

40

60

80

100

60

62

64

66

68

70

B

T

Energia

meV

CdSe

2.8 nm

ZnS

4 ML

CdSe

10ML

SiO2

5 nm

Z

1

m

0,

Σ

1

m

0,

Σ

1

m1,

Σ

1

m

2,

Σ

1

m

3,

Σ

1

0

20

40

60

80

100

40

45

50

55

60

B

T

Energia

meV

CdSe

2.8 nm

ZnS

4 ML

CdSe

20ML

SiO2

5 nm

Z

0

m

0,

Σ

1

m

0,

Σ

1

m1,

Σ

1

m

2,

Σ

1

m

3,

Σ

1

0

20

40

60

80

100

0

5

10

15

20

B

T

Energia

meV

CdSe

2.8 nm

ZnS

4 ML

CdSe

20ML

SiO2

5 nm

Z

1

m

0,

Σ

1

m

0,

Σ

1

m1,

Σ

1

m

2,

Σ

1

m

3,

Σ

1

!

Δ

3

= 1

"

10

20

# $% ! $%&

'" " ( ) !

*" + "

)

# #

( (

, - $% $%

m

= 0

m

=

−

1

m

=

−

2

!"# $ ¿¾

% ! &'( &') &'* + ,

+

Δ

3

= 1

10

20

-. / 0 ! &'(

Δ

3

= 1

-.

'11 2 3, ! &') &'*

Δ

3

+ &1 2 4 +

4 +

+ 0 ! &') 5! &'*6 +

7 ))2 5&( 88 )726 9

0

20

40

60

80

100

0

200

400

600

800

1000

1200

B

T

Energia

de

Transiç

ão

meV

CdSe

_{2.8 nm}

ZnS

_{4 ML}

CdSe

_1ML

SiO

₂

_{5 nm}

Z

0

m

0,

Σ

1

m

0,

Σ

1

m

1,

Σ

1

m

1,

Σ

1

m

2,

Σ

1

m2,

Σ1

m

3,

Σ

1

m

3,

Σ

1

0

20

40

60

80

100

0

200

400

600

800

1000

1200

B

T

Energia

de

Transiç

ão

meV

CdSe

_{2.8 nm}

ZnS

_{4 ML}

CdSe

_1ML

SiO

₂

_{5 nm}

Z

1

m

0,

Σ

1

m

0,

Σ

1

m

1,

Σ

1

m

1,

Σ

1

m

2,

Σ

1

m2,

Σ1

m

3,

Σ

1

m

3,

Σ

1

! &'(: ; +

0

20

40

60

80

100

0

100

200

300

400

B

T

Energia

de

Transiç

ão

meV

CdSe

_{2.8 nm}

ZnS

_{4 ML}

CdSe

_10ML

SiO2

_{5 nm}

Z

0

m

0,

Σ

1

m

0,

Σ

1

m

1,

Σ

1

m

1,

Σ

1

m

2,

Σ

1

m2,

Σ1

m

3,

Σ

1

m

3,

Σ

1

0

20

40

60

80

100

0

100

200

300

400

B

T

Energia

de

Transiç

ão

meV

CdSe

_{2.8 nm}

ZnS

_{4 ML}

CdSe

_10ML

SiO2

_{5 nm}

Z

1

m

0,

Σ

1

m

0,

Σ

1

m

1,

Σ

1

m

1,

Σ

1

m

2,

Σ

1

m2,

Σ1

m

3,

Σ

1

m

3,

Σ

1

Δ

3

= 10

0

20

40

60

80

100

0

50

100

150

200

B

T

Energia

de

Transiç

ão

meV

CdSe

2.8 nm

ZnS

4 ML

CdSe

20ML

SiO2

5 nm

Z

0

m

0,

Σ

1

m

0,

Σ

1

m

1,

Σ

1

m

1,

Σ

1

m

2,

Σ

1

m2,

Σ1

m

3,

Σ

1

m

3,

Σ

1

0

20

40

60

80

100

0

50

100

150

200

B

T

Energia

de

Transiç

ão

meV

CdSe

2.8 nm

ZnS

4 ML

CdSe

20ML

SiO2

5 nm

Z

1

m

0,

Σ

1

m

0,

Σ

1

m

1,

Σ

1

m

1,

Σ

1

m

2,

Σ

1

m2,

Σ1

m

3,

Σ

1

m

3,

Σ

1

m

= 0

σ

= 1

!

B

= 80

!

B

= 100

" #$%

m

= 0

σ

= 1

& ' !

B

= 80

&

90

100

( $%

)*

*

**

+ & & , $

! " #

$" % &

!

' ( )

" $ ( !

*

+!

(

( ( ,

→

-±

. " (

( "

" ( / &(

+ " 0123120121'

2

( 45 15

" 6 ( 7 !

7 (

( $

"

0 " (

0123120121'

2

! ( ! " ( 8 01231

0/23/ 9.29

0.

6

.

0

.

4

.

9.29

0.

7

.

0

.

3

.

' )!

$ +

/

+$ "$ !

! " #$ !

%&'(&'%&'&)

2

* #

+,&

% !

# -.

# #

/# 0

/# 01 2# ! 3

#