Electronic structure of defect semiconductors A3B6

Institute of Radiation Problems

Institute of Radiation Problems

Azerbaijan National Academy of

Azerbaijan National Academy of

Sciences

Sciences

ELECTRONIC STRUCTURE OF DEFECT SEMICONDUCTORS А

3

_В

6

Madatov R.S., Mehrabova M.A

.

Firudin Aghayev str. 9, Phone: (+994 12) 4383224

•

TheThe electronic structure of electronic structure of local local defects – vacancies as well as their compensated states in semiconductors defects – vacancies as well as their compensated states in semiconductors АА

3

3ВВ66 are are determineddetermined on the basis of the theory of Green function and bond orbital model. Energy levels in forbidden on the basis of the theory of Green function and bond orbital model. Energy levels in forbidden

zone, change of electronic density in semiconductors GaS, GaSe, InSe with anion and cation vacancy and compensate

zone, change of electronic density in semiconductors GaS, GaSe, InSe with anion and cation vacancy and compensate

of these vacancies are calculated. It is established, that

of these vacancies are calculated. It is established, that in order toin order to compensate compensate a vacancy in a lattıce, compe a vacancy in a lattıce, compennsatıngsatıng atom should have the

atom should have the follofollowwıngıng propertpropertiies:es:

•

-- same tetrahedral coordination same tetrahedral coordination

•

- smaller - smaller atom radius atom radius

•

- same atomıc- same atomıc number number

•

Then tThen the local levels formed at compensation of vacancy completely disappear. Using this mechanism it is possible to he local levels formed at compensation of vacancy completely disappear. Using this mechanism it is possible to restore parameters of crystal and also to improve its characteristics.

restore parameters of crystal and also to improve its characteristics.

INTRODUCTIONINTRODUCTION

•

Obtaining radiation-resistant materials with good electric and optical characteristics is an actual problem of Obtaining radiation-resistant materials with good electric and optical characteristics is an actual problem of modern physics. It is connected with development of nuclear power, flights in space, ecology and etc. Materials in

modern physics. It is connected with development of nuclear power, flights in space, ecology and etc. Materials in

these conditions under the strongest influence of various

these conditions under the strongest influence of various radiations change radiations change theirtheir physical properties physical properties, therefore , therefore radiati

radiation on defects form. Restoration of defects form. Restoration of the the properties of such materials properties of such materials requires requires studying of naturestudying of nature,, properties of properties of defects, and reasons of their formations.

defects, and reasons of their formations.

The purpose of suggested work consisted to theoretical investigation of electronic structure of semiconductors The purpose of suggested work consisted to theoretical investigation of electronic structure of semiconductors А

А33ВВ66having defects and determine the mechanism of restoration of their properties. In suggested work energy levels having defects and determine the mechanism of restoration of their properties. In suggested work energy levels

of local defects-vacancy and their compensated conditions in semiconductors GaS, GaSe, InSe were calculated by

of local defects-vacancy and their compensated conditions in semiconductors GaS, GaSe, InSe were calculated by

Green's function and bond orbital methods.

Green's function and bond orbital methods.

ElectronicElectronic structure of layered semiconductors structure of layered semiconductors А3В6 А3В6 has been investigated by various methods. Influence of an has been investigated by various methods. Influence of an ionizing radiation on semiconductors such as GaSe, InSe has been experimentally investigated. The nature and

ionizing radiation on semiconductors such as GaSe, InSe has been experimentally investigated. The nature and

structure of the energy levels of radiation including defects localized in a forbidden zone are not studied enough,

structure of the energy levels of radiation including defects localized in a forbidden zone are not studied enough,

representations about mechanisms of influence of defects on properties are not generated. In our works it has

representations about mechanisms of influence of defects on properties are not generated. In our works it has

theoretically been researched electronic structure of semiconductors GaSe having vacancy by bond orbital and Linear

theoretically been researched electronic structure of semiconductors GaSe having vacancy by bond orbital and Linear

Combination of Atomic O

1 BOND ORBITALS MODEL

1 BOND ORBITALS MODEL

2

1

1

i

a



( s i  >± 2

1

_i i

c

a



(

2

1

c_i (

3

p_yi > -p xi > ) + pzi > ) ) (1) _oi = _{( b} i si > ± pzi > ) 2

1

1

i

a



₁

2 i i

c

a



_i = _{( s}i  ± ( c i pxi > + pzi > ) ) 2

1

1

i

a



₁

2 i i

c

a



2

1

₃i = ( si  ± ₍ c i ( -

3

pyi > -pxi > ) + pzi > ) )

)

2

(

2

2

_

i

c

)

2

(

)

1(

2

2 2





i i

c

c

a_i = , bi = ₍₂₎ 2 1 1 i b  3i =

 

_         



0 ) ( ,

(

)

l R k i r r k i j i l i j

e

e

k

H

  





)

(

i _l i

r

r

R

b

H



b

_j

(



-r



r

j

)

d



r

( 4)  





b

H

b

d

r

B

_{1 1 1}

_B

_



_b

_H



_b

_d



_r

2 2 2  





b

H

b

d

r

B

_{3 1 2}  





b

H

b

d

r

B

_{a 2 3}

B

_c





b

₂

H



b

₃

d



r

  





)

(

i _l i

r

r

R

b

(3)

)

(

exp

1

0 ,k _l l i i

_N

i

k

R

r

    











Н

₁₁

=В

₁

, Н

₁₂

= Н

₁₃

=Н

₁₄

=Н

₁₅

=Н

₁₆

=Н

₁₇

=Н

₂₁

=Н

₃₁

=Н

₄₁

=Н

₅₁

=Н

₆₁

=Н

₇₁

=В

₃

,

Н

₂₂

=Н

₃₃

=Н

₄₄

=Н

₅₅

=Н

₆₆

=Н

₇₇

=В

₂

, Н

₂₃

=Н

₅₆

=В

_с

+В

_а

е

ip

_,

Н

₂₄

=Н

₅₇

=В

_с

+В

_а

е

i(p+q)

Н

₃₂

=Н

₆₅

=В

_с

+В

_а

е

-ip

_{, Н}

34

=Н

67

=В

с

+В

а

е

iq

.

Н

₄₂

=Н

₇₅

=В

_с

+В

_а

е

-i(p+q)

_,

Н

₄₃

=Н

₇₆

=В

_с

+В

_а

е

-iq

_.

Table 1 Parameters of semiconductors

Semicond

uctor

ε

g

, eV

d

ac

, A

º

_d

cc

, A

º

θ

ε

sc

,eV

ε

pc

,eV

ε

sa

,eV

ε

pa

,eV

c

c

c

a

GaSe

2

2.42

2.58

118.2

-11.37

-4.90

-20.32

9.53

1.88

1.88

GaS

2.5

2.30

2.52

117.7

-11.37

-4.90

-20.8

-10.27

1.88

1.88

2. THE GREEN FUNCTION METHOD

( I – V G

₀

(E) )  = 0 (9)

(7)

(Н

_о

+ V) = E  (6)

=(E I - H

_o

)

-1

V  ,  = G

0

(Е) V 

G

₀

(E) = (E I- Ho )-1 (8)

Det 1 - V G

₀

(E)  = 0 (10)

[1 – (G

₂₂

– G

₂₃

)

]

2

_{[1 – G}

11

 - G

22

 - 2G

23

 - 3G

122

 + G

11

G

12

 + 2G

11

G

23

] = 0 (11)



=

B

₁/-

B

₁

_{and }

₌

B

₂ - /

B

₂

(12)

2

1

1

c

b



1

2

1

c

b



- 1

B

₌ ( 2 c

b



sc+



pcz)+ ( 2 c

b

V

ss -2

b

c

V

sp

V

pp) (13) 2

B

= (



2c +



2a)/2 - [(



2c-



2a )2/4 + V22]1/2; (14) i 2



=(1+

a

_i 2₎-1 _[



_{si +}

a

_i2₍₁₊

c

_i 2₎-1 ₍

c

_i 2



_{pix +}



_{piz)] (15)} pcz



=



_{pc - 0.40}

m

2



₍ 2 2

3

ac

d

n

l

+ ₂ cc

d

l

) ; (16) paz



₌



_pa

-2

3

0.40

m

2



2 2 ac

d

n

; pix



₌



_pi -

2

3

0.40

m

2



2 2 ac

d

l

;

2

)

1

(

2

2 2





i i

c

c

2

2

2

_

i

c

i

a

_{= ;} i

b

= ; (17)  ss

V

(

d

) = -1.32

m

2



2

d

l

;

m

2



2

d

l

m

2



2

d

l

 sp

V

(

d

) = 1.42 ;

V

pp(

d

) = 2.22 ; (18)

1) Vacancy of anion’s atom.



_sa/

= 0, 

pa /

= 0

 = 0

1 – (G22 – G23)  = 0 (19)

1 – (G22 + 2 G23)  = 0

β=0.2

InSe - anion vacancy

GaSe- anion vacancy

GaS- anion vacancy

2) Anion replacement

GaSе (N) – anion replacement

GaS (Se) - anion replacement



_sc/

= 0, 

pc /

= 0

3) Vacancy of cation’s atom.

GaSe- cation vacancy

GaS- cation vacancy

4) Cation replacement

GaSе (Tl) – cation replacement.

GaS (Tl) – cation replacement

GaS-change of density of states from anion and cation vacancies in an interval from Е =-15 up to Е =-5 eV; Е=0 corresponds to top of a valence zone, dashed lines-anion vacancy, continuous lines-cation vacancy

Change of density of states

 n =



1

dE

E

d



(

)



(

_E

) = -

arctg

(

Im

G

0

Re

G

0

)

GaS-change of density of states from anion and cation replacements in an interval from Е =-15 up to Е =-5 eV; Е=0 corresponds to top of valence zone

GaSе-change of density of states from anion and cation vacancies in an interval from Е =-15 up to Е =-5 eV; Е=0 corresponds to the top of a valence zone a) anion vacancy, b) cation vacancy

Table 2. Energy levels of vacancies and their replacements in semiconductors А

3

_В

6

Semi

condu

c

tor

Е

_а1

_{, eV}

_Е

с2

, eV

Replacement

of

anion

Replacement

of cation

ε

_eV

g

,

forbid

zone

valenc

zone

zone

of

cond.

forbid.

zone

valence

zone

GaSe

0.36;

0.46↑

0.45

2.86;

0.56

0.76;

0.56

0.05;

0.35

N: 0.06; 0.35;

0.55;

0.75

v.z.

Tl: 0

2

GaS

0.1;

0.5↑

0.1↓

0.3;

0.7

2.2

0.2;

0.4;

0.6

0.5;

0.8

Se: 0.1; 0.3 –

v.z.

Tl: 0

Ge:0.4;0.6;

0.9;1.0 –

v.z.

Cd: 0.4; 0.6; 2.3;

2.5--f.z.

0.1; 0.3; 0.6;

0.7- v.z.

2.5

InSe

0.3;

0.4↑

0.2;

2.

6;

2.9;

3.03;

0.7;

3.17;

1.17

0.2;

0.5; 0.6

0.3; 0.7

N:

0.826;

0.326;

0.926

–

v.z.

Ga: 0.325 –v.z.

1.1

Table 3. Density of states of semiconductors А

3

_В

6

_.

Semi

conduc

tor

Density

of states

Е

_а1

_{, эВ}

Е

_с2

_{, эВ}

Anion

replacement

(Se)

Cation

replacement

(Tl)

forbid.

zone

valenc

zone

forbid.

zone

valenc

zone

forbid

zone

valenc

zone

forbid.

zone

valenc

zone

GaS

resonant

0.5,

0.2

0.7

0.5

0.6

0.6,

0.2

0.76, 0.86

1.36, 2.16

anti

resonant

0.4

0.6

0.6,

0.3

0.6

0.96, 1.16,

1.46, 2.16

GaSe

_resonant

0.66

0.15,

0.04

0.36,

0.86

2.44

0.36,

0.66,

2

2.34

0.56

2

anti

resonant

0.66

0.05

0.76,

0.56

2.34

0.46

2.14

0.56

2

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