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Charge carrier statistics of disordered semiconductors with negative-u defects and electrically active impurity atoms
118
Journal of Non-CrystallineSolids114 (1989) 118-120 North-Holland
CHARGE CARRIER STATISTICS OF DISORDERED SF~IGONDUCTORS WITH NEGATIVE-U DEFECTS AND ELECTRICALLY ACTIVE IMPURITY ATOMS K.D.
TSENDIN
A.P.Ieffe Ph~vsical-Technical Institute, Leningrad, 194021, USSR It is shown that the temperature dependences of conductivity of disordered semiconductors: As~Sea doped by Ni and Bi, and a-Si:H doped by E , may be explained by stati~tidal interaction between approximately equal n ~ b e r s of negative-U intrinsic defects and electrically active impurity atoms. I. INTRODUCTION It stands to reason that there is a discrepancy between the results of I-3 and 4 (see Fig.l). In the case of 1"3 the
be explained in the framework of a model which takes into account a statistical interaction of negative-U intrinsic defects (D centers) with electrically active impurity atoms (e.g. donors ).
-2 I
-4
"!
-6 -8
~ ~
1
7 4
'
continued as dashed lines for the hopping conductivity to become striking. In the case of 4 there are only activation dependences of ~ and two slopes may be seen for I% and 7% of Ni. This discrepancy and data of 5'6 me~v
3 .
4 2. MODEL AND EXPLANATIONS The carrier statistics simulated can be described by the following set of equations :
-1( -12 2
3
4
5
6
103/T, K -I
PIGURE I Conductivity of thin films As2Se 3 modified by Ni. Curves with dashed lines are from 1-3, o t h e r s f r o m 4 . I n d i c a t e d near the curves are the concentretions of Ni in at.%. activation conductivity is followed by hopping one and in Fig.1 the activation dependences of conductivity ( ~ ) are
0022-3093/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
nD°/D-=Ncexp (-E 1/kT)
( 1)
n2D+/D -= N2ceXp(-E/kT), E=EI+E 2
(2)
nN+/N°u Ncexp (-Ed/kT)
(3)
n + D" = D + + N +
(4)
N = N + + N ° = const
(5)
D = D + + D- + D ° = const
(6)
where D and N are the concentrations of negative-U intrinsic defects and electrically active impurity atoms, respec-
K.D. Tsendin /Charge carrier statistics of disordered semiconductors
119
tion at the energy E c, n, D ° , D +, D-, N ° , N + are the concentrations of free electrons~ neutral and charged D
E I end E 2 at low temperature. On cooling the activation conductivity with 5E - E/2 can transform into hopping one at the temperature much lower than
centers and donors. E I and E 2 are the first and second ionization energy of D centers, Ed - ionization energy of
that in the case N > D, if the density of tail states g(E/2) is much less than the peak density of impurity states
donors. The energetic diagram of model
g(Ed). On heating one can obtain ~ exp(-E/3kT) from (I)-(6), if the
tively, N c is the effective concentra-
is shown in Fig.2.
--- EF=Ed (N>D) D+ EI .
D-
.
.
.
.
~.F=~.I2(~T~D)
- --
Ev=Eg
FIGURE 2 The energetic diagram of model. The positions of Fermi energy (E~) for N ~ D cases are indicated at=low temperature • The results of 1-3 as one believes correspond to the case N > D when the donors are compensated by the D centers uncompletely so at low temperatures the Ep is located near the energy E d (if Ed< E/2). On cooling the activation depender~ce of o~ with activation energy A E = E d transforms into that determined by a variable-range hopping through the high-density states at E d. The results of 4 are described by an opposite situation, N ~ D. In this case an D - N excess concentration is divided into two equal D + and D" concentrations. Then E F is pinned between
relations Nc> N, E/Ed> 2 + 3[in(l-N/D)] /ln(Nc/N) remain valid. This dependence bears resemblance to ~ott's one 7 but, contrary to 7, in our case the electronic state E d is present on the electrically active impurity atoms. Such a resemblance is due to a complete ionization of impurity atoms dictated by N < D. According to the theoretical results given above, there must be a correlation between the low- and hightemperature values of AE, ym A E H ~ E L T = 2/3 - 0.67. This relation is fulfilled very well for I% Ni (Y-0.67) and 7% Ni (Y-0.63). One can obtain E=O.87 and 0.48 eV for I% and 7% Ni, respectively. At high temperature the difference between the cases N ~ D diminishes and a new conduction regime with c~ exp(-(E + Ed)/3kT) takes place provided that T+(T N end2< E/Ed< 2 + 3]lnl1-N/Dl[ /in(No/N), where T + = (~ - 2 ~ d ) / 3 1 1 n 1 I - N I I ) I I , Tn Ed/In(Nc/N). Such a dependence has been observed experimentally with the thermally sputtered films As2Se3, Bi 5. The values of activation for as-deposited films ( ~E o) in Table 5. After annealing at
doped by energy are shown the tem-
perature 130°C, the values of activation energy, being also shown in Table, decrease to ~ E 1. Suppose that the degree of compensation at the annealing tempe-
120
K.D. Tsendin /Charge carrier statistics of disordered semiconductors
rature decreases so that the value of T + is increased from experimental results ture interval T~< T < how under the action v
T+ O to T~. If the cover the temperaT~, one can see of annealing ~
exp(-(E + Ed)/3kT) changes to o~ exp(-Ed/kT).___ Table demonstrates the
composition E=Eg
EI
As2Se3Bio. I
1.60
0.25
0.60
0.62
Bio.o1
1.68
0.30
0.70
0.66
, Bio.o01
1.70
0.50
0.75
0.73
"
Eo exp.
Eo theor.
sation, because, as seen, with Ni one has N ~ D and with Bi a sufficiently low temperature T +. A more complete account of the theoretical investigation of the model and comparing it with 8"11 is in course of preparation. ACKNOWLEDGEMENTS I would like to thank T.Ph.Mazets and E.A.Smorgonskaya for valuable discussions and O.Yu.Prikhodko for data of Pig.1. REFERENCES I. V.L. Averyanov 6 (1980) 577.
experimental values of aE o and A E I and the theoretical value of A E o determined from the formula AEo=(E+Ed)/3 , where E=Eg and E d- ~E I. There is observed a good agreement between experimentel and theoretical values of AE o for three various concentrations of Bi. The same results can be obtained for a-Si:H doped by Eu 6. A c c o r d i n g t o 6 t h e activation energies of sputtered films are AEo= 0.56 eV and 0.68 eV when substrates are held at the 300°C and 250°C respectively. On heating the substrate to 380°C the activation energy decreases to 5E 1- 0.20 eV. The theoretical value of nEo=(Eg + nEI)/3 = 0.63 eV for Eg= 1.70 eV agrees with experimental ones rather well. 3. CONCLUSION In summary, one can say that the electrical activity of Ni and Bi is well observed in modified and thermally sputtered films As2Se3, respectively, being followed by a strong self-compen-
et al., Pisma ZhTPh
2. B.T. Kolomiets et al., Solar Energy Materials 8 (1982) I. 3. O.Yu. Prikhodko, Ph.D. Thesis, A.F. Ioffe Institute, Leningrad, 1982. 4. R.P. Barclay et al., J.Non-Cryst. Sol. 77-78 (1985) 1269 5. N.P. Kalmykova et al., Phys. Techn. Semicond. 22 (1988) 807. 6. A.R. Regel et 81., Phys. Techn. Semicond. 22 (1988) 161. 7. N.P. mott, Phil. Mag. 34 (1976) 1101. 8. H. Fritzsche, Proceed. of the 7th Intern. Conf. on Amorph. and Liquid Semicond., ed. W.E. Spear (Committee by the Center for Industrial Consultancy and Liaison, University of Edinburgh, 1977) pp. 3-15. 9. T. Uda and E• Yamada, Journ. Phys. Soc. of Jap. 46 (1979) 515. IO.H.J. Hoffmann, Appl. Phys. A27 (1982) 39• 11.P. Nagy, Phil. Mag. B48 (1983) 47.
Journal of Non-CrystallineSolids114 (1989) 118-120 North-Holland
CHARGE CARRIER STATISTICS OF DISORDERED SF~IGONDUCTORS WITH NEGATIVE-U DEFECTS AND ELECTRICALLY ACTIVE IMPURITY ATOMS K.D.
TSENDIN
A.P.Ieffe Ph~vsical-Technical Institute, Leningrad, 194021, USSR It is shown that the temperature dependences of conductivity of disordered semiconductors: As~Sea doped by Ni and Bi, and a-Si:H doped by E , may be explained by stati~tidal interaction between approximately equal n ~ b e r s of negative-U intrinsic defects and electrically active impurity atoms. I. INTRODUCTION It stands to reason that there is a discrepancy between the results of I-3 and 4 (see Fig.l). In the case of 1"3 the
be explained in the framework of a model which takes into account a statistical interaction of negative-U intrinsic defects (D centers) with electrically active impurity atoms (e.g. donors ).
-2 I
-4
"!
-6 -8
~ ~
1
7 4
'
continued as dashed lines for the hopping conductivity to become striking. In the case of 4 there are only activation dependences of ~ and two slopes may be seen for I% and 7% of Ni. This discrepancy and data of 5'6 me~v
3 .
4 2. MODEL AND EXPLANATIONS The carrier statistics simulated can be described by the following set of equations :
-1( -12 2
3
4
5
6
103/T, K -I
PIGURE I Conductivity of thin films As2Se 3 modified by Ni. Curves with dashed lines are from 1-3, o t h e r s f r o m 4 . I n d i c a t e d near the curves are the concentretions of Ni in at.%. activation conductivity is followed by hopping one and in Fig.1 the activation dependences of conductivity ( ~ ) are
0022-3093/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
nD°/D-=Ncexp (-E 1/kT)
( 1)
n2D+/D -= N2ceXp(-E/kT), E=EI+E 2
(2)
nN+/N°u Ncexp (-Ed/kT)
(3)
n + D" = D + + N +
(4)
N = N + + N ° = const
(5)
D = D + + D- + D ° = const
(6)
where D and N are the concentrations of negative-U intrinsic defects and electrically active impurity atoms, respec-
K.D. Tsendin /Charge carrier statistics of disordered semiconductors
119
tion at the energy E c, n, D ° , D +, D-, N ° , N + are the concentrations of free electrons~ neutral and charged D
E I end E 2 at low temperature. On cooling the activation conductivity with 5E - E/2 can transform into hopping one at the temperature much lower than
centers and donors. E I and E 2 are the first and second ionization energy of D centers, Ed - ionization energy of
that in the case N > D, if the density of tail states g(E/2) is much less than the peak density of impurity states
donors. The energetic diagram of model
g(Ed). On heating one can obtain ~ exp(-E/3kT) from (I)-(6), if the
tively, N c is the effective concentra-
is shown in Fig.2.
--- EF=Ed (N>D) D+ EI .
D-
.
.
.
.
~.F=~.I2(~T~D)
- --
Ev=Eg
FIGURE 2 The energetic diagram of model. The positions of Fermi energy (E~) for N ~ D cases are indicated at=low temperature • The results of 1-3 as one believes correspond to the case N > D when the donors are compensated by the D centers uncompletely so at low temperatures the Ep is located near the energy E d (if Ed< E/2). On cooling the activation depender~ce of o~ with activation energy A E = E d transforms into that determined by a variable-range hopping through the high-density states at E d. The results of 4 are described by an opposite situation, N ~ D. In this case an D - N excess concentration is divided into two equal D + and D" concentrations. Then E F is pinned between
relations Nc> N, E/Ed> 2 + 3[in(l-N/D)] /ln(Nc/N) remain valid. This dependence bears resemblance to ~ott's one 7 but, contrary to 7, in our case the electronic state E d is present on the electrically active impurity atoms. Such a resemblance is due to a complete ionization of impurity atoms dictated by N < D. According to the theoretical results given above, there must be a correlation between the low- and hightemperature values of AE, ym A E H ~ E L T = 2/3 - 0.67. This relation is fulfilled very well for I% Ni (Y-0.67) and 7% Ni (Y-0.63). One can obtain E=O.87 and 0.48 eV for I% and 7% Ni, respectively. At high temperature the difference between the cases N ~ D diminishes and a new conduction regime with c~ exp(-(E + Ed)/3kT) takes place provided that T+(T
doped by energy are shown the tem-
perature 130°C, the values of activation energy, being also shown in Table, decrease to ~ E 1. Suppose that the degree of compensation at the annealing tempe-
120
K.D. Tsendin /Charge carrier statistics of disordered semiconductors
rature decreases so that the value of T + is increased from experimental results ture interval T~< T < how under the action v
T+ O to T~. If the cover the temperaT~, one can see of annealing ~
exp(-(E + Ed)/3kT) changes to o~ exp(-Ed/kT).___ Table demonstrates the
composition E=Eg
EI
As2Se3Bio. I
1.60
0.25
0.60
0.62
Bio.o1
1.68
0.30
0.70
0.66
, Bio.o01
1.70
0.50
0.75
0.73
"
Eo exp.
Eo theor.
sation, because, as seen, with Ni one has N ~ D and with Bi a sufficiently low temperature T +. A more complete account of the theoretical investigation of the model and comparing it with 8"11 is in course of preparation. ACKNOWLEDGEMENTS I would like to thank T.Ph.Mazets and E.A.Smorgonskaya for valuable discussions and O.Yu.Prikhodko for data of Pig.1. REFERENCES I. V.L. Averyanov 6 (1980) 577.
experimental values of aE o and A E I and the theoretical value of A E o determined from the formula AEo=(E+Ed)/3 , where E=Eg and E d- ~E I. There is observed a good agreement between experimentel and theoretical values of AE o for three various concentrations of Bi. The same results can be obtained for a-Si:H doped by Eu 6. A c c o r d i n g t o 6 t h e activation energies of sputtered films are AEo= 0.56 eV and 0.68 eV when substrates are held at the 300°C and 250°C respectively. On heating the substrate to 380°C the activation energy decreases to 5E 1- 0.20 eV. The theoretical value of nEo=(Eg + nEI)/3 = 0.63 eV for Eg= 1.70 eV agrees with experimental ones rather well. 3. CONCLUSION In summary, one can say that the electrical activity of Ni and Bi is well observed in modified and thermally sputtered films As2Se3, respectively, being followed by a strong self-compen-
et al., Pisma ZhTPh
2. B.T. Kolomiets et al., Solar Energy Materials 8 (1982) I. 3. O.Yu. Prikhodko, Ph.D. Thesis, A.F. Ioffe Institute, Leningrad, 1982. 4. R.P. Barclay et al., J.Non-Cryst. Sol. 77-78 (1985) 1269 5. N.P. Kalmykova et al., Phys. Techn. Semicond. 22 (1988) 807. 6. A.R. Regel et 81., Phys. Techn. Semicond. 22 (1988) 161. 7. N.P. mott, Phil. Mag. 34 (1976) 1101. 8. H. Fritzsche, Proceed. of the 7th Intern. Conf. on Amorph. and Liquid Semicond., ed. W.E. Spear (Committee by the Center for Industrial Consultancy and Liaison, University of Edinburgh, 1977) pp. 3-15. 9. T. Uda and E• Yamada, Journ. Phys. Soc. of Jap. 46 (1979) 515. IO.H.J. Hoffmann, Appl. Phys. A27 (1982) 39• 11.P. Nagy, Phil. Mag. B48 (1983) 47.