- Email: [email protected]
Impurity effects in amorphous germanium and silicon
25—428. Solid State Communications, Vol.30, pp.4 Pergamon Press Ltd. 1979. Printed in Great Britain.
-
IMPURITY EFFECTS IN AMORPHOUS GERMANIUM AND SILICON* Jos~Alzamir and M.M.Collver Instituto de Fisica “Gleb Wataghin”, Universidade Estadual de Campinas Caixa Postal 1170, 13100 Campinas, Sao Paulo, Brasil (Received 2’4 October 1978 by R.C.C.Leite; in revised form 7 February 1979) A systematic study of the hopping conductivity of amorphous germanium — transition metal (Cr, Co, Fe) films reveals an exponential decrease of the hopping parameter, T 0, as a function of the transition metal concentration. A similar, but often unnoticed, behavior is found in the literature. A linear decrease in the energy gap as a function of concentration is postulated as an explanation.
In this Communication we report the first systematic study of deep level impurities (Cr, Co, Fe) on the hopping conductivity of amorphous germanium. From conductivity measurements and the hopping conductivity relation oo~, exp {_(T0/T)hf~) we find an exponential decrease of the hopping parameter, T0, as a function of concentration. Further, the rate of decrease of T0 correlates with the relative position of the levels produced by these impurities in crystalline germanium. It is also our purpose here to demonstrate that the exponential decrease with concentration is a common characteristic found not only in the results presented here but also in the literature, though it has often gone unnoted. Since this appears to be a general phenomenon we expect a common explanation despite the various types of levels each impurity produces and thus propose a simple model in which the mobility gap decreases linearly with concentration, Past studies of hopping conductivity of amorphous elemental semiconductors doped with deep level impurities (1—10) have revealed a strong variation in T0, while small changes in occur for large concentrations of shallow level impurities (2,3,7). The hopping 3/kNf, is the length of a parameter, T0, wherecC’ is given (11, 12)decay by localized T0=16 cz wavefunction at the Fermi level, Ef, and Nf is the localized density of states at
i~npurities. This is not surprising in view of the variation in the data among different researchers for the same alloy system. Despite this the data does reveal that T0 decreases exponentially with concentration for most of the amorphous alloys and an argument can be made that it is true for the remainder (13). To observe any systematic effects as a function of the impurity, it is thus necessary to prepare all samples of each alloy system, as well as the different systems, under identical conditions. Consequently we have employed two source evaporation (electron beam) in order to prepare the complete set of alloys simultaneously, and in the case of Ge—Cr and Ge—Fe, the films were prepared consecutively during the same pumpdown cycle. The evaporation rate of each element was monitored and controlled by ionization gauge type rate monitors and was typically 100 Vsec for germanium and 4 Vsec for the impurity element as measured vertically above each source at the substrate position. The films were evaporated Onto a row of alumina substrates maintained at 295 K in a background pressure of iO~ torr. Composition was determined from electron microprobe analysis in which the data were treated as bulk (~3microns) and the absence of athickness measurements because of the film backscattering signal from the substrate. Values of T 0 were obtained from four point probe resistance measurements from 300 K to as low a temperature as possible (down to 4 k) consistent with the limiting resistance of 1010 ohms. The measured resistance exhibited a considerable deviation from a constant activation energy behavior. A log—normal plot of the resistance vs. Th/1 yielded straight lines over more than three orders of magnitude of resistance (depending upon the impurity concentration) except for those samples with concentrations > 6 at %. In these latter cases the resistance behavior fit reasonably well to an exp (T0/T)h/ behavior, however, the deviation from a constant activation energy resistance, exp (L~E/kT), was not as marked in comparison with the lower concentration samples.
Ef. These results have been interpreted as reflecting the ability of deep levels to produce localized states at Ef(2,3). However, no variation in the behavior of T0 as a function of the deep level impurity has been recognized at present. An examination of the literature data reveals that there is little to suggest such systematic behavior in terms of T0, at fixed concentration, for different
Supported in part by Conselho Nacional de Desenvolvinento Cientifico e Tecnol~gico (CNPq), Financiadora de Estudos e Projetos (FINEP) and Coordenaç~o do Aperfeiçoamento de Pessoal de Nivel Superior (CAPES) *
425
IMPURITY EFFECTS IN AMORPHOUS CERM~IUM AND SILICON
426
I
‘
I
I
108
I
Vol. 30, No. 7
I
I
• Ge-Fe • Ge - Co
iOl
I
I
I
I Ge—Fe • Ge—Bi
• Ge- Cr
A Ge
-
—
Cr (x 0.1
-
20 I0~
•
I—0
Ge:crkO.I
H -
-
06
-
U
N
N
~-
IO~ ..._..._L I 0 2 4 6 IMPURITY CONCENTRATION (at. Figure 1
—
I 8 0/)
IO~ I I I I I 0 2 4 6 8 IMPURITY CONCENTRATION (at.
%)
The hopping parameter, T
0, as a function of impurity composition for amorphous Ge transition metal (Fe,Co,Cr) alloys, demonstrating the exponential decrease of T0 with increasing transition metal composition.
In Figure 1 the values of 1~are shown as a function of composition for each impurity. The prominent observations to be made from the results in Fig. 1 are (i) the exponential decrease of T0 with concentration for each alloy system and (ii) the relative order of the gradients, G=dlnT0/dx, according to G(Cr)>G(Co)>G(Fe). In addition we note a deviation from an exponential dependence for Ge—Cr at the higher concentrations; similar deviations are observed for Fe and Co at higher concentrations (> 8 at.%) than shown here, We now turn our attention to the literature data to examine the concentration dependence of T0, where an exponential dependence on concentration (T0exp(—bx)) is found to be a common result in the low concentration range, though it has gone unnoticed, except as noted in ref. 10 for metastable crystalline Si—Co and Si—Ni films, but not explained. Values of T for amorphous germanium alloys are shown in °Fig. 2. These were taken directly from the literature for Ge—Cr (1,5) and were extracted from published resistivity data for Ge—Bi (4) and Ge—Fe(6). Fig. 3 shows the data for disordered crystalline Si—Ni and Si—Co alloys (10) and amorphous Si—Au (9). Deviations from the exponential behavior are observed at higher concentrations in some cases. Since the deviation is in the direction of larger To,
Figure 2
—
The hopping parameter, T0, taken from published data for the amorphous Ge based alloys Ge—Cr(l), Ge—Cr(5), Ge—Bi(4) and Ge—Fe(6), exhibits an exponential decrease with impurity concentration in the low concentration range.
precipitation of impurities is suggested, which would diminish Nf (increase T0). Other possibilities will be discussed later. The exponential behavior for such a wide variety of impurities suggests a common explanation. We propose the following model to explain the exponential dependence of T0 on concentration, x, and the relative order of the gradients, G, produced by the impurities. The salient features are a linearly decreasing mobility gap as a function of concentration, and an impurity band, located at E0(x). Since deep levels are regarded as being associated with electron states of both the conduction and valence band, we write for simplicity that the level varies proportionately with the energy gap, rather than being strongly associated with one band or the other. Thus we let the gap be given by E g (x)=E g(0)(l—yx),
(1)
where x is the atom fraction of the impurity and y serves as an impurity dependent parameter representing the effectiveness of the impurity in decreasing the gap. For simplicity we assume E fixed at midgap (3,14), such that EfE~(x)/2, and a Gaussian
IMPURITY EFFECTS IN AMORPFIOUS GERMANIUM AND SILICON
Vol. 30, No. 7
108
I
I
I
l61~~a .a~
T 0~
kBnx ~
exp
427
2E2(O) ((1/2_f) 2a~
2E2(O) x
}
1 )
(3)
I07
exp~— (l/2—f)
106
value The for factor the constant (1/2—f)2exponential introduces factor a larger in T relative 0, but provides order of anG as explanation a functionforofthe the impurity concentration, as explained below. Though the values of the impurity energy levels may be different in a—Ge, we assume that the relative order of levels produced by these impurities in crystalline Ge (16) is
• U -
•
preserved in amorphous Ge, i.e.,
• -
-
• Si-Co
•
• Si-Ni U Si-Au I
—
f(Cr)
0 2 4 6 iMPURITY CONCENTRATION (at. O/~)
Figure 3
i
Hopping parameter, T0, taken from published data for amorphous Si—Au (9) and metastable Si—Co(1O) and Si—Ni(lO) films as a function of impurity metal concentration.
energy gap change is proportional to the transition metal atom range concentration over This the entire concentration of interest. would not be true in the case where T 0 remains unchanged up to a certain inpurity concentration, x0, which in general would depend on the impurity. Up to the concentration x0, the impurities are regarded as occupying ineffective sites (see ref. 2 and 3). In such a case Eq. 1 would be replaced by E =E~0Il—Y(X—x0)~,whichis applicable only for x~x0. While this expression would not alter the conclusions obtained from the model with
for the impurity band, centered at E0(x)f Eg(x), where f is the ratio of the energy of the isolated impurity in the amorphous semiconductor to the energy gap, Eo/Eg(O). Thus the density of states at Ef from the impurity band is given by: ______
~
exp
(
________________ tF (x) — E (~))2 0
2a~
}
,
(2)
1
3) of where atoms in n the is host the number semiconductor. density (cm Substituting Ef(x) and E 0(x) we have: 2 E~(O) (l—’ x)2 ~ I (1/2—f) exp~— i ~ 2a~ 1
i
The total density of states is N~+N1, where NGe is the number of states present at Ef due to amorphous Ge. Though this quantity (_l018 states/ev—atom) has been found to decrease in the presence of impurities (15), we may leave it as independent of x. We then evaluate T0 in the concentration regime where Nj>>NGe (x>.0I) and x
respect to the relative values of the gradient G, it could possibly aide in the understanding of the relative order of the values of T0 as a function of the impurity species at a fixed concentration. However since a constant T0 behavior is not observed over the concentration range in the data, a modified variation in ojhere. that Eq. 1 Including serves no auseful purpose increases with increasin~concentration of the form (17), exp (—ac /3), does not alter the conclusions here. Some variation in T0 due to changes in a is also expected. From the relation a—1~ijIh,we estimate a change in T0 by a factor of 3 if the gap is reduced by range of concentrations considered here the one—half its about original value, which expected at 10 at.%(3). Thus might in the be variation in Nf due to a decreasing gap is sufficient to account for the major variation in T 0. There is experimental that of x. supports a decreasing gap asevidence a function Vass et al (18) report a weak quadratic variation of the optical gap in amorphous Ge—Bi films, which fits a linear relation quite well in the range of x (<0.06) of interest here. They do not, however, correlate this behavior with their resistivity A decreasing found in the data data (4). of Zavetova et al gap (19)is also for
428
IMPURITY EFFECTS IN AMORPhOUS GERMANIUM AND SILICON
Au, Ag, Ga, Sb and P for dopant concentrations > 1 at % in amorphous Ge. Nath et al (20) find a decreasing gap for Fe in a—Ge, however, for Al and Cu impurities the gap first increases.
Vol.
30, No. 7
strongly favored, resulting in a conductivity that is not sensitive to the shape of the density of states. The deviation of T 0 from an exponential dependence at the higher concentrations may reflect a deviation of Eg(x) from linearity, a concentration dependenE band width, 0(x), or Ef entering the region of the Gaussian band where the density of states does not vary rapidly. However one must at this time maintain a strong inclination toward precipitation (few atom clusters) as an explanation. It is noted that the model presented here does not contradict other models for N(E) in the gap of pure amorphous germanium, i.e., whether there is an acceptor band or a minimum near mid—gap (14).
Tunneling studies (3) have also exhibited a smaller gap with the presence of deep level impurities, We note that the density of states model contradicts the assumptions of the Mott model, namely, a constant density of states. This depends, of course, on where the Fermi level lies in relation to the impurity band. We have assumed in the derivation of N(Ef), that it is in the impurity or valence and conduction band tails. Pollak (21) has shown that a constant density of states at Ef is not necessary as states very close to Ef are more
REFERENCES
1. DAVER,H., MASSENET,O, CH.AXRAVERTY,B.K., Sol. St. Commun. 11, 131 (1972) 2. HAUSER,J.J., Sol.St. Commun. 13, 1451 (1973) 3. HAUSER,J.J., Phys.Rev. B.9, 2544 (1974) 4. VASS,R.W., MEININGER,M.A., ANDERSON,R.M., J.Appl. Phys. 45, 843 (1974)
85,
5. Edited CLANK, by A.H., COHEN,M.M., LANYON,P.D.Amorphous and Liquid Semiconductors, v.2, p.ll J.Stuke and W.Brenig (1974) 6. h4ASSENET,O., DAVER,H., GENESTE,J., J.de Physique 35, C4, 279 (1974) 7. BARTHWAL,S.K., NATh,P., CHOPRA,K.L., Sol.St.Commun. 16, 723 (1975) 8. AR.AKI,M., OSAKI,H., Sol.St. Commun. 18, 1603 (1976) 9. KISHII4OTO,N., MORIGAXI,K., SHIMIZU,A., HIRAKI,A., Sol.St.Commun. 20, 31 (1976) 10. COLLVER,M.M., Sol. St.Commun. 23, 333 (1977) 11. MOTT,N.F., Phil.Mag. 19, 835 (1969) 12. AMBEGAOKAR,V., HALPERIN,B.I., LANGER,J.S., Phys.Rev. B 4, 2619 (1974) 13. These exceptions occur in sputtered films (see ref. 2 and 3) and evaporated Ge—In films (ref. 8) in which T 0 initially remains unchanged up to some concentration, followed by a rapid (exponential?) decrease. In the low concentration range the impurities are postulated as occupying sites in the defect network of the amorphous structure and are therefore ineffective in producing states at Ef (see ref. 3). 1,4, MOlT, N.Y., DAVIS,E.A., Electronic Processes in Non—Crystalline Materials, Clarendon Press Oxford (1971) 15. HUMEDA,M, JINNO,Y., WATANABE,I., SHIMIZU,T., SSC 23, 833 (1977) 16. SZE,S.M., Physics of Semiconductor Devices, p.30. J.W.Wiley and Sons, Inc., New York (1969) 17. MOTT,N.F., Phil. Mag. 22, 7 (1970) 18. VASS,R.W., ANDERSON,R.M., J.Appl. Phys. 45, 855 (1974) 19. ZAVETOVA,M., KOC,S., ZEMEK,J., in: Recent Advances in Science and Technology of Materials, Ed.A.Bishay, vol. 1, Plenum Press, New York 1974 (p.285) 20. NATH,P., PANDYA,O.K., CHOPPA,K.L., Phys. Stat.Sol. 34, 405 (1976) 21. POLLAK,M., Phys.Rev.Lett (1973)
-
IMPURITY EFFECTS IN AMORPHOUS GERMANIUM AND SILICON* Jos~Alzamir and M.M.Collver Instituto de Fisica “Gleb Wataghin”, Universidade Estadual de Campinas Caixa Postal 1170, 13100 Campinas, Sao Paulo, Brasil (Received 2’4 October 1978 by R.C.C.Leite; in revised form 7 February 1979) A systematic study of the hopping conductivity of amorphous germanium — transition metal (Cr, Co, Fe) films reveals an exponential decrease of the hopping parameter, T 0, as a function of the transition metal concentration. A similar, but often unnoticed, behavior is found in the literature. A linear decrease in the energy gap as a function of concentration is postulated as an explanation.
In this Communication we report the first systematic study of deep level impurities (Cr, Co, Fe) on the hopping conductivity of amorphous germanium. From conductivity measurements and the hopping conductivity relation oo~, exp {_(T0/T)hf~) we find an exponential decrease of the hopping parameter, T0, as a function of concentration. Further, the rate of decrease of T0 correlates with the relative position of the levels produced by these impurities in crystalline germanium. It is also our purpose here to demonstrate that the exponential decrease with concentration is a common characteristic found not only in the results presented here but also in the literature, though it has often gone unnoted. Since this appears to be a general phenomenon we expect a common explanation despite the various types of levels each impurity produces and thus propose a simple model in which the mobility gap decreases linearly with concentration, Past studies of hopping conductivity of amorphous elemental semiconductors doped with deep level impurities (1—10) have revealed a strong variation in T0, while small changes in occur for large concentrations of shallow level impurities (2,3,7). The hopping 3/kNf, is the length of a parameter, T0, wherecC’ is given (11, 12)decay by localized T0=16 cz wavefunction at the Fermi level, Ef, and Nf is the localized density of states at
i~npurities. This is not surprising in view of the variation in the data among different researchers for the same alloy system. Despite this the data does reveal that T0 decreases exponentially with concentration for most of the amorphous alloys and an argument can be made that it is true for the remainder (13). To observe any systematic effects as a function of the impurity, it is thus necessary to prepare all samples of each alloy system, as well as the different systems, under identical conditions. Consequently we have employed two source evaporation (electron beam) in order to prepare the complete set of alloys simultaneously, and in the case of Ge—Cr and Ge—Fe, the films were prepared consecutively during the same pumpdown cycle. The evaporation rate of each element was monitored and controlled by ionization gauge type rate monitors and was typically 100 Vsec for germanium and 4 Vsec for the impurity element as measured vertically above each source at the substrate position. The films were evaporated Onto a row of alumina substrates maintained at 295 K in a background pressure of iO~ torr. Composition was determined from electron microprobe analysis in which the data were treated as bulk (~3microns) and the absence of athickness measurements because of the film backscattering signal from the substrate. Values of T 0 were obtained from four point probe resistance measurements from 300 K to as low a temperature as possible (down to 4 k) consistent with the limiting resistance of 1010 ohms. The measured resistance exhibited a considerable deviation from a constant activation energy behavior. A log—normal plot of the resistance vs. Th/1 yielded straight lines over more than three orders of magnitude of resistance (depending upon the impurity concentration) except for those samples with concentrations > 6 at %. In these latter cases the resistance behavior fit reasonably well to an exp (T0/T)h/ behavior, however, the deviation from a constant activation energy resistance, exp (L~E/kT), was not as marked in comparison with the lower concentration samples.
Ef. These results have been interpreted as reflecting the ability of deep levels to produce localized states at Ef(2,3). However, no variation in the behavior of T0 as a function of the deep level impurity has been recognized at present. An examination of the literature data reveals that there is little to suggest such systematic behavior in terms of T0, at fixed concentration, for different
Supported in part by Conselho Nacional de Desenvolvinento Cientifico e Tecnol~gico (CNPq), Financiadora de Estudos e Projetos (FINEP) and Coordenaç~o do Aperfeiçoamento de Pessoal de Nivel Superior (CAPES) *
425
IMPURITY EFFECTS IN AMORPHOUS CERM~IUM AND SILICON
426
I
‘
I
I
108
I
Vol. 30, No. 7
I
I
• Ge-Fe • Ge - Co
iOl
I
I
I
I Ge—Fe • Ge—Bi
• Ge- Cr
A Ge
-
—
Cr (x 0.1
-
20 I0~
•
I—0
Ge:crkO.I
H -
-
06
-
U
N
N
~-
IO~ ..._..._L I 0 2 4 6 IMPURITY CONCENTRATION (at. Figure 1
—
I 8 0/)
IO~ I I I I I 0 2 4 6 8 IMPURITY CONCENTRATION (at.
%)
The hopping parameter, T
0, as a function of impurity composition for amorphous Ge transition metal (Fe,Co,Cr) alloys, demonstrating the exponential decrease of T0 with increasing transition metal composition.
In Figure 1 the values of 1~are shown as a function of composition for each impurity. The prominent observations to be made from the results in Fig. 1 are (i) the exponential decrease of T0 with concentration for each alloy system and (ii) the relative order of the gradients, G=dlnT0/dx, according to G(Cr)>G(Co)>G(Fe). In addition we note a deviation from an exponential dependence for Ge—Cr at the higher concentrations; similar deviations are observed for Fe and Co at higher concentrations (> 8 at.%) than shown here, We now turn our attention to the literature data to examine the concentration dependence of T0, where an exponential dependence on concentration (T0exp(—bx)) is found to be a common result in the low concentration range, though it has gone unnoticed, except as noted in ref. 10 for metastable crystalline Si—Co and Si—Ni films, but not explained. Values of T for amorphous germanium alloys are shown in °Fig. 2. These were taken directly from the literature for Ge—Cr (1,5) and were extracted from published resistivity data for Ge—Bi (4) and Ge—Fe(6). Fig. 3 shows the data for disordered crystalline Si—Ni and Si—Co alloys (10) and amorphous Si—Au (9). Deviations from the exponential behavior are observed at higher concentrations in some cases. Since the deviation is in the direction of larger To,
Figure 2
—
The hopping parameter, T0, taken from published data for the amorphous Ge based alloys Ge—Cr(l), Ge—Cr(5), Ge—Bi(4) and Ge—Fe(6), exhibits an exponential decrease with impurity concentration in the low concentration range.
precipitation of impurities is suggested, which would diminish Nf (increase T0). Other possibilities will be discussed later. The exponential behavior for such a wide variety of impurities suggests a common explanation. We propose the following model to explain the exponential dependence of T0 on concentration, x, and the relative order of the gradients, G, produced by the impurities. The salient features are a linearly decreasing mobility gap as a function of concentration, and an impurity band, located at E0(x). Since deep levels are regarded as being associated with electron states of both the conduction and valence band, we write for simplicity that the level varies proportionately with the energy gap, rather than being strongly associated with one band or the other. Thus we let the gap be given by E g (x)=E g(0)(l—yx),
(1)
where x is the atom fraction of the impurity and y serves as an impurity dependent parameter representing the effectiveness of the impurity in decreasing the gap. For simplicity we assume E fixed at midgap (3,14), such that EfE~(x)/2, and a Gaussian
IMPURITY EFFECTS IN AMORPFIOUS GERMANIUM AND SILICON
Vol. 30, No. 7
108
I
I
I
l61~~a .a~
T 0~
kBnx ~
exp
427
2E2(O) ((1/2_f) 2a~
2E2(O) x
}
1 )
(3)
I07
exp~— (l/2—f)
106
value The for factor the constant (1/2—f)2exponential introduces factor a larger in T relative 0, but provides order of anG as explanation a functionforofthe the impurity concentration, as explained below. Though the values of the impurity energy levels may be different in a—Ge, we assume that the relative order of levels produced by these impurities in crystalline Ge (16) is
• U -
•
preserved in amorphous Ge, i.e.,
• -
-
• Si-Co
•
• Si-Ni U Si-Au I
—
f(Cr)
0 2 4 6 iMPURITY CONCENTRATION (at. O/~)
Figure 3
i
Hopping parameter, T0, taken from published data for amorphous Si—Au (9) and metastable Si—Co(1O) and Si—Ni(lO) films as a function of impurity metal concentration.
energy gap change is proportional to the transition metal atom range concentration over This the entire concentration of interest. would not be true in the case where T 0 remains unchanged up to a certain inpurity concentration, x0, which in general would depend on the impurity. Up to the concentration x0, the impurities are regarded as occupying ineffective sites (see ref. 2 and 3). In such a case Eq. 1 would be replaced by E =E~0Il—Y(X—x0)~,whichis applicable only for x~x0. While this expression would not alter the conclusions obtained from the model with
for the impurity band, centered at E0(x)f Eg(x), where f is the ratio of the energy of the isolated impurity in the amorphous semiconductor to the energy gap, Eo/Eg(O). Thus the density of states at Ef from the impurity band is given by: ______
~
exp
(
________________ tF (x) — E (~))2 0
2a~
}
,
(2)
1
3) of where atoms in n the is host the number semiconductor. density (cm Substituting Ef(x) and E 0(x) we have: 2 E~(O) (l—’ x)2 ~ I (1/2—f) exp~— i ~ 2a~ 1
i
The total density of states is N~+N1, where NGe is the number of states present at Ef due to amorphous Ge. Though this quantity (_l018 states/ev—atom) has been found to decrease in the presence of impurities (15), we may leave it as independent of x. We then evaluate T0 in the concentration regime where Nj>>NGe (x>.0I) and x
respect to the relative values of the gradient G, it could possibly aide in the understanding of the relative order of the values of T0 as a function of the impurity species at a fixed concentration. However since a constant T0 behavior is not observed over the concentration range in the data, a modified variation in ojhere. that Eq. 1 Including serves no auseful purpose increases with increasin~concentration of the form (17), exp (—ac /3), does not alter the conclusions here. Some variation in T0 due to changes in a is also expected. From the relation a—1~ijIh,we estimate a change in T0 by a factor of 3 if the gap is reduced by range of concentrations considered here the one—half its about original value, which expected at 10 at.%(3). Thus might in the be variation in Nf due to a decreasing gap is sufficient to account for the major variation in T 0. There is experimental that of x. supports a decreasing gap asevidence a function Vass et al (18) report a weak quadratic variation of the optical gap in amorphous Ge—Bi films, which fits a linear relation quite well in the range of x (<0.06) of interest here. They do not, however, correlate this behavior with their resistivity A decreasing found in the data data (4). of Zavetova et al gap (19)is also for
428
IMPURITY EFFECTS IN AMORPhOUS GERMANIUM AND SILICON
Au, Ag, Ga, Sb and P for dopant concentrations > 1 at % in amorphous Ge. Nath et al (20) find a decreasing gap for Fe in a—Ge, however, for Al and Cu impurities the gap first increases.
Vol.
30, No. 7
strongly favored, resulting in a conductivity that is not sensitive to the shape of the density of states. The deviation of T 0 from an exponential dependence at the higher concentrations may reflect a deviation of Eg(x) from linearity, a concentration dependenE band width, 0(x), or Ef entering the region of the Gaussian band where the density of states does not vary rapidly. However one must at this time maintain a strong inclination toward precipitation (few atom clusters) as an explanation. It is noted that the model presented here does not contradict other models for N(E) in the gap of pure amorphous germanium, i.e., whether there is an acceptor band or a minimum near mid—gap (14).
Tunneling studies (3) have also exhibited a smaller gap with the presence of deep level impurities, We note that the density of states model contradicts the assumptions of the Mott model, namely, a constant density of states. This depends, of course, on where the Fermi level lies in relation to the impurity band. We have assumed in the derivation of N(Ef), that it is in the impurity or valence and conduction band tails. Pollak (21) has shown that a constant density of states at Ef is not necessary as states very close to Ef are more
REFERENCES
1. DAVER,H., MASSENET,O, CH.AXRAVERTY,B.K., Sol. St. Commun. 11, 131 (1972) 2. HAUSER,J.J., Sol.St. Commun. 13, 1451 (1973) 3. HAUSER,J.J., Phys.Rev. B.9, 2544 (1974) 4. VASS,R.W., MEININGER,M.A., ANDERSON,R.M., J.Appl. Phys. 45, 843 (1974)
85,
5. Edited CLANK, by A.H., COHEN,M.M., LANYON,P.D.Amorphous and Liquid Semiconductors, v.2, p.ll J.Stuke and W.Brenig (1974) 6. h4ASSENET,O., DAVER,H., GENESTE,J., J.de Physique 35, C4, 279 (1974) 7. BARTHWAL,S.K., NATh,P., CHOPRA,K.L., Sol.St.Commun. 16, 723 (1975) 8. AR.AKI,M., OSAKI,H., Sol.St. Commun. 18, 1603 (1976) 9. KISHII4OTO,N., MORIGAXI,K., SHIMIZU,A., HIRAKI,A., Sol.St.Commun. 20, 31 (1976) 10. COLLVER,M.M., Sol. St.Commun. 23, 333 (1977) 11. MOTT,N.F., Phil.Mag. 19, 835 (1969) 12. AMBEGAOKAR,V., HALPERIN,B.I., LANGER,J.S., Phys.Rev. B 4, 2619 (1974) 13. These exceptions occur in sputtered films (see ref. 2 and 3) and evaporated Ge—In films (ref. 8) in which T 0 initially remains unchanged up to some concentration, followed by a rapid (exponential?) decrease. In the low concentration range the impurities are postulated as occupying sites in the defect network of the amorphous structure and are therefore ineffective in producing states at Ef (see ref. 3). 1,4, MOlT, N.Y., DAVIS,E.A., Electronic Processes in Non—Crystalline Materials, Clarendon Press Oxford (1971) 15. HUMEDA,M, JINNO,Y., WATANABE,I., SHIMIZU,T., SSC 23, 833 (1977) 16. SZE,S.M., Physics of Semiconductor Devices, p.30. J.W.Wiley and Sons, Inc., New York (1969) 17. MOTT,N.F., Phil. Mag. 22, 7 (1970) 18. VASS,R.W., ANDERSON,R.M., J.Appl. Phys. 45, 855 (1974) 19. ZAVETOVA,M., KOC,S., ZEMEK,J., in: Recent Advances in Science and Technology of Materials, Ed.A.Bishay, vol. 1, Plenum Press, New York 1974 (p.285) 20. NATH,P., PANDYA,O.K., CHOPPA,K.L., Phys. Stat.Sol. 34, 405 (1976) 21. POLLAK,M., Phys.Rev.Lett (1973)