Proof Copy

1 2 3

. , . , .

4

5 ,

6

. , 56, 46001 ,

7

8 ( 03.10.20154; online 24.12.2015)

9 10

, -

11 ,

12 13 -

- . -

14

, -

15 35 %.

1617

: , ,

18

, , , .

1920

PACS numbers: 73.21.Ac, 73.40.Gk, 73.63.Hs 21

2223 1.

24 ( ) [1,

25 2] ( ) [3, 4] -

26

-

27

( ). -

28

29 -

30 31

. ,

32 33 -

34 ,

[5-7].

35

,

36

-

37 38 ,

,

39

, -

40

41 -

42 . -

43

[8], -

44

-

45 46 ,

[9, 10].

47 48 49

-

50 51 ,

[11, 12] -

52

.

53

, -

54

55 ,

56

, -

57

. -

58

, ,

59 60 -

. ,

61 62

,

63 64 .

65 ,

66 ,

67 68

- -

69 .

70

In Ga As1 _{x x} – In Al As_{1 x x} –

71 72 73

74 ,

75

35 % . -

76

77 .

78

-

79 80

. , ,

81

82 , -

83

,

84

, .

85

, ,

86

, -

87 88

,

89 90 ,

91 .

92 93

2. .

94 95 -

-

96 97 9899

100

, Oz

101

. 1).

102

-

103 104 105 .

106 :

107

Proof Copy

3 2

0 2 1 2 1 2 2 1

0 0

( ) ( _p ) ( _p) ( _p) ( _p )

p p

m z m z z z z m z z z z (1)

1 2

34

. 1 – 5

67

2

2 2 1

0

( ) ( ( _p) ( _p ) ,

p

U z U z z z z (2)

8 9

( )z – , z ₁ 0, z₆ , m₀

10

m1 –

11

.

12

, -

13

E

14

n0 15

.

16 17 ,

( , )z t ,

18

:

1920

0

( , )z t ( ( ) ( , )) ( , ),

i H z H z t z t

t (3)

21

22

2 0

( ) 1 ( )

2 ( )

H z U z

z m z z , (4)

23

24 ,

2526

1 1 2 2

1 2

5 5

( , ) ( ) ( )

( ) ( ) ( )

i t i t i t i t

H z t e e e e e

z z z z z z

27 (5)

28 ,

29

, -

30

1 2 -

31

1 2.

32

33 , -

34 -

35

, (3) -

36

:

3738

0 0 1

0 1 0 1 2

0 1 2

( )

0 1

( ) ( )

1 2

( )

2

( , ) ( ) ( )

( ) ( )

( ) ,

i t i t

i t i t

i t

z t z e z e

z e z e

z e

39 (6)

40

0 E/ .

41

(6)

42 (3), -

43

, e ^{i t1} e ^{i(1 2)t} -

44 45 :

46

0( ) 0( ) 0,

H z E z (7)

47

0 1 1

1 5 5 0

( )) ( ) ( )

( ) ( ) ( ) ( ) 0,

H z E z

z z z z z z z (8)

48

0 1 2 2

5 5 1

( ) ( ( )) ( )

( ) ( ) ( ) ( ) 0,

H z E z

z z z z z z z (9)

49

50

1 1, 2 2.

51

(7)-(9)

52

0( )z ₁( )z -

53

2( )z .

54

(7),

55

0( )z :

56 57

( 0 ) ( 0)

0 0

(6 )

0 5

( )

0 1

(0) (6)

0 0 0 5

5 ( )

0 1

1

(0) (0)

0 0

( )

(6)0 5

5 ( ) ( )

1 0

( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

( ) ( )

( )

[ ^{p p}

p

p p

p

ik z ik z

ik z z

ik z z p p

z z z z z z

z z z z z

A e B e z

A e z z

A e

58

( )0 ( 1) ( )

0^{p ikp z zp} ] ( _p1) ( _p) ,

B e z z z z (10)

59 60 61

(0) (2) (4) (6) 1

0 0 0 0 2 0 ,

k k k k m E

62

(1) (3) (5) 1

0 0 0 2 (1 )

k k k m E U (11)

63 64

(10) ₀( )z -

65 66

/ /

0( , )k z 0( , )k z dz (k k) (12)

67 68 -

-

69 7071

5 2

0 0 5

( ) 1^z ( )

W z z dz

z , (13)

72

– -

73

(E_n) ( _n) -

74

[13].

75

(8-9)

76

:

7778

( )z ( )z ( ),z 1, 2 (14)

79 80

Proof Copy

( ) ( )

(0 ) (6 )

1 1

5

(0) (6) 5 ( )

5 1

1

5 ( ) ( )

( )

(0) (6) ( ) ( )

5 1

1

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) [ ^{p p p p} ] ( ) ( )

p

p p

p

ik z z ik z z

ik z ik z z p p

p p

p

z z z z z z z z z z z

B e z A e z z A e B e z z z z ,

(15)

1

2

(0) (2) (4) (6) 1 (1) (3) (5) 1

1 1 1 1 0 1 1 1 1 1 1

(0) (2) (4) (6) 1 (1) (3) (5) 1

2 2 2 2 0 1 2 2 2 2 1 1 2

2 ( ); 2 (( ) ),

2 ( ( )); 2 (( ) ( )),

k k k k m E k k k m E U

k k k k m E k k k m E U (16)

3

4

5 ( ) (6)

1 1 1 1 5

1 ( )

5 1 ( ) 2 1 0 1 (6)

0 2 1 0 5

1 1 5 5 1 1

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

p

p p

p

p p

p p

p p

z z z z z z z z z

d z

U z U U

z z z z z z z z

z m z dz

(17)

5

6 - (8),

78

5 ( ) (6)

2 2 1 2 5

1

2 ( )

2 2

5 1 2 1 2 0 ( ) 1 2 1 2 0

2 2 0 2 2 2

1 1 1 2 5 1 2 5 5 1 1 2

2 1 2

5 1 1 2

( ) ( ) ( ) ( ) ( ) ( )

4 ( ) (3 ) ( )

( ) ( ) ( )

( )

p

p p

p

p p

p p

p

z z z z z z z z z

E d z

U U z U U

z z

z dz

m z mz

U U m z

2 2 ( ) 2 ( )

0 2 ( ) 2 1

1 1

2 2

2 5 5 2

(6) (6)

1 2 2

0 1 5

1 1 2 2

( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( )

p p

p p p

p

d z U z U d z

z z z z z

z dz

dz m z

U U z U z z z

9 (18)

10

(9), U₁ e z_{1 5},

11

2 2 5

U e z .

12 13

(0) (0) (6) ( ) ( ) (0) (6) ( ) ( )

0 , 0 , 0 , 0^p, 0^p, 1, 1, 1^p, 1^p,

A B A A B B A A B

14

( ) ( )

2, 2 ( 0 5)

p p

A B p B⁽⁰⁾₂,A⁽⁶⁾₂, -

15

( , )z t

16 17

t:

18 19

( ) ( 1)

( ) ( 1)

1

( , ) ( , );

1 ( , ) 1 ( , ) ,

p p

p p

p p

p p

p z z p z z

z t z t

d z t d z t

m dz m dz

(19)

20

21 (12) -

22

0( )z

23

1( )z ₂( )z ,

24

( , )z t .

25 26

1( )z ₂( )z -

27 28

:

2930

1(2) 1(2)

1(2) 0 1(2) 1(2)

( ) ( )

( ) ( ) ,

2 _p

d z d z

j ie n z z

m dz dz (20)

31

32 33

.

34

-

35

-

36 37 :

38

( ) (1) (2)

1 2 1 1 2

( , ) ( ) ( , ),

II (21)

39 40 4142

(1) (1) (1)

1 1 1

( ) ( ) ( ), (22)

43 44

2 2 2

(1) 1 5 0 (6) (6) (6) (6) 1

1 2 1 1 1 1 01 01

0 1 1

( ) ,

2 2

e z n U

k A k A P P

m U (23)

45

46

2 2 2

(1) 1 5 0 (0) (0) (0) (0)

1 2 1 1 1 1

0 1

( ) ,

2 e z n

k B k B

m U (24)

47

(21):

4849

(2) (2) (2)

1 2 1 2 1 2

( , ) ( , ) ( , ), (25)

50 51

2 2 2

(2) 1 2 5 0 (6) (6) (6) (6) 2 1 2

1 2 2 2 2 2 2 12 12 02 02

2 1 1 2

0 2

2 (6) (6)2 (6) (6)2 2

2 1 2

1 1 1 1 01 01

2 1 2 1 2

( )

( , )

2 2 ( )

2 ( ) ;

e z n k A k A U P P U U P P

m U

U k A k A U U P P

52 (26)

Proof Copy

2 2 2

(2) 1 2 5 0 (0) (0) (0) (0)

1 2 2 2 2 2 2

0 2

( )

( , ) e z n k B k B .

m U (27)

1

2 (26) :

34

(6) 6 (6) (6) (6) (6)

01 ( 0 1) 0 1 0 1 ;

P k k A A A A (28)

5 6

(6) 6 (6) (6) (6) (6)

02 ( 0 2) 0 2 0 2 ;

P k k A A A A (29)

7 8

6 6 (6) (6) (6) (6)

12 ( 1 2) 1 2 1 2 .

P k k A A A A (30)

9 10

(21)-(27)

11 12 ,

( ( )) ( ( ))

13 14 -

.

15

, ,

16 , -

17

1 2 -

18

,

19 20 .

21

3.

2223

[13],

24

25 , , -

26 -

27

( )

28 29 ,

. , -

30

[5, 7] [14] -

31 32 33 .

In Ga As1 _{x x} 34

– In Al As_{1 x x} – -

35 36 :

16 3

0 10 cm

n ; m₀ 0,046 ;m_e m₁ 0,089 ;m_e

37

516 meV U

38

1 2 3 1,5 nm)

39

( _{1 2} 1,5nm; ₃ 4,5nm) 1 4,5 nm;

40

1 3 1,5 nm)

41

1 2 5,4 nm b b

42

(E E E₁, ₂, ₃)

43

( ₁, ₂, ₃) -

44 45 -

b1 46

1 2

b b .

47

. 2, a, b, c, d, e, f.

48

-

49

(E_n) b₁, . 2, a, b, c ,

50 51 .

52 53

54

.

55

( _n)

56 57

. 2, d, e, f), , b₁

58 59 -

60 ,

.

61

-

62

-

63

64 - -

65

, -

66

. ,

67 68

(U₁ e z_{1 5 1};U₂ e z_{2 5 2}) U1 69

U2 (U₁ 10³ ₁; U₂ 10³ ₂ ).

70

, -

71 72 -

73 74

, 1 1 1, 2 1 2

n n En En n n En En ,

75

-

76 77 .

78 , -

79

,

80

, -

81 82 -

83 .

84 -

,

85 86 ,

87

1 12 1 12

88

2 23,

89

-

90

( ) (1) ( )

( ^II ) ^II -

91

b1 -

92

. 3, a, b, c, d, e, f.

93

. 3, d ,

94

b1 95

,

96

3,3 nm b1 5,2 nm. . 3, a, -

97

, -

98

-

99 100

. , . 3, a ,

101 ,

102 , -

103

b1 -

104

( ) ( )

12,23II 12,23II , -

105 106 107 .

Proof Copy

1 . 2 – (En) ( n) b1 - 2

34

5 . 3 – , -

6

, ^{(1) ( )II} ₀ 1S/cm, -

7

b1 8

910 . 3, e , -

11

b1 , -

12

2,7 nm b1 5,4 nm 6,0 nm b₁ 8,0 nm.

13

. 3, b, -

14

15 ,

16

( _12,23^{( )II} _12,23^{( )II} ), -

17

18 -

19

. -

20 21

( _12,23^{( )II} _12,23^{( )II} ). ,

22

-

23

, .

24 . 3, f ,

25

b

26

Proof Copy

,

1

5,8 nm b1 7,9 nm. . 3, c -

2

, -

3 -

4 , . ,

5

35% -

6

.

7 8

4.

109

11 12 13

, - -

14

. ,

15

,

16 17 18

.

19

, , -

20

-

21 22 -

35 %. ,

23

-

24

.

25 26 27

28 29 30

31 . , . , .

32

33 , . , 56, 46001

34

,

35 36 37 -

, , -

38 39 -

- -

40

. ,

41

35 %.

4243

: , , -

44 , , ,

45

. 46

47 48

Contribution of Two-photon Detector Electronic Transitions in the Formation of Dynamic

49

Conductivity of Three-barrier Resonant Tunneling Structures

50

51 I.V. Boyko, M.R. Petryk, H.B. Tsupryk

52 53

Ternopil National Technical University, 56, Ruska Str., 46001 Ternopil, Ukraine

54 55

In approximations of the effective mass and rectangular potential wells and potentials for the electron, 56

by using solutions of the complete Schrödinger equation, was developed the theory of active dynamic con- 57 ductivity of three barrier resonant tunnel structure in a weak electromagnetic field, taking into account 58

the contribution of detector one- and two-photon electronic transitions with different frequencies. It is 59 shown that the value of the contribution of two-photon transitions in the formation of the total amount of 60

active dynamic conductivity in detector transitions is not less 35 %.

61 6263

Keywords: Resonance tunnelling structure, Quantum cascade detector, Active dynamic conductivity, 64 Resonance energies, Resonance width, Two-photon electronic transitions.

65 66 67 6869

1. . Bonzon, I.C. Chelmus, K. Ohtani, M. Geiser, M. Beck, 70 J. Faist,Appl. Phys. Lett. 104, 161102 (2009).

71

2. J.M. Wolf, A. Bismuto, M. Beck, J. Faist,Opt. Express 22, 72

2111 (2014).

73 3. A. Buffaz, M. Carras, L. Doyennette, A. Nedelcu, 74 X. Marcadet, V. Berger, Appl. Phys. Lett. 96, 172101 75

(2010).

76 4. D. Hofstetter, F.R. Giorgetta, E. Baumann, Q. Yang, 77 C. Manz, K. Kohler,Appl. Phys. Lett. 93, 221106 (2008).

78

5. M.V. Tkach, Ju.O. Seti, I.V. Boyko, O.M. Voitsekhivska, 79

Condens. Matt. Phys. 16, 33701 (2013).

80 6. M. Tkach, Ju. Seti, I. Boyko, O. Voitsekhivska, Romanian 81

Report. Phys. 65, 1443 (2013).

82 7. M.V. Tkach, Ju.O. Seti, V.O. Matijek I.V. Boyko,J. Phys.

83

Studies 16, 4701 (2012).

84

8. E. Saczuk, J.Z. Kaminski, phys. status solidi b 240, 603 85 (2003).

86 9. N.V. Tkach, Yu.A. Seti,JETP Lett. 95, 271 (2012).

87

10. N.V. Tkach, Ju.A. Seti,Semiconductors 48, 590 (2014).

88 11. A.B. Pashkovskii,JETP Lett. 89, 30 (2009).

89 12. A.B. Pashkovskii,Semiconductors 45, 743 (2009).

90

13. N.V. Tkach, Yu.A. Seti,Low Temp. Phys. 35, 556 (2009).

91

14. N.V. Tkach, Ju.A. Seti,Semiconductors 45, 376 (2011).

92

93

Proof Copy