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Model of chalcogenide glassy semiconductors based on three-center bonds in a rigid covalent network
Journal of Non-Crystalline Solids 114 (1989) 115-117 North-Holland
115
MODEL OF CHALCOGENIDE GLASSY SEMICONDUCTORS BASED ON THREE-CEN'IER BONDS IN A RIGID COVALENT NETWORK S. A. DEMBOVSKY Institute of General and Inorganic Chemistry, Leninsky Pr. 31, Moscow 117907, USSR A proposed model of mixed covalent and three-center bond network provides an interconnected explanation of many of the characteristic phenomena observed in chalcogenide glasses over a broad temperature range. A detailed discussion of cluster formation, the glass transition and electronic features including the pinning of the Fermi level is given.
nature of the large polaronic shift are discussed below.
1. INTRODUCTION All glasses - including semiconducting ones - have a
5. Similarity between Glassy Semiconductors and a-
large concentration of lone-pair electrons.l,2 It has been
Si:H. This similarity is connected with the possibility of
suggested that in such glasses, configurations known as
the existence of TCB's in both materials. The TCB's are
three-center bonds exist in large concentrations. In Figure
electron-rich in the fLrStcase and electron-deficient4 in the
1 a four-electron three center bond (TCB) which has been
second (a-Si:H).
proposed for selenium3 is shown. In their basic state,
6. Zero-Poin~ ~
.
The soft TCB (one of a
covalent networks as a consequence of the local strain in
distribution of interatomic angles and lengths) leads to the excess energy and excess zero-point entropy (ASo > 0 at T
the rigid covalent bonds due to their random arrangement.
= 0).
these bonds are neutral and diamagnetic. TCB's arise in
The energy of formation2 of a TCB in glassy (g-) Se is
7. Mechanical Pro_nerty Differences. The mechanical
0.14 eV. Thus they exist in relatively high concentrations
properties of glasses such as sound velocity, differ from
(approximately 1%) at temperatures near the glass
those of their crystalline counterparts. This is due to their
transition temperature Tg. The TCB is longer and weaker
dependence on quasielastic constants (e.g. vt,1 = ~/K).
than a covalent bond (CB), with the respective quasielastic constants being in the ratio K(TCB)/K(CB) -~ 10-2.
2. CLUSTER FORMATION
Furthermore, TCB's have various atomic configurations
It has been shown that in a system consisting of rigid
and potentials, including a two-well potential. The TCB
covalent bonds in a continuous random network (CRN)
model can be used as a framework to understand a number of phenomena, including:
and of soft anharmonic TCB's, cluster formation must take place. These clusters are regions of non-crystallineorder
1. Low Temoemture Anomalies. The low temperature
where the relaxation of a CB on a TCB occurs. Thus soft
anomalies are connected with the specific form of the TWP.
TCB's play the role of a "quasinuclcus" of a cluster. The second role of TCB's concerns the formation of
2. Average Temnerature Anomalies. These anomalies
non-breaking (i.e. without dangling bonds) non-phase
such as glass transition and cluster formation are discussed below.
intercluster boundaries and disinclinations. The latter arc
3. High Temnerature Anomalies. These anomalies are
based on the doubled or tripled five- or seven-atom TCB, which can form together with discontinuous disinclination
connected with the fact that the TCB represents a hypervalent bond.2 4. Pinning of the Fermi Level.
In chalcogenide
glasses pinning can be understood in terms of charged diamagnetic TCB's. The mechanism of pinning and the
0022-3093/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
FIGURE 1 A three-centered bond, TCB. Circles are Se atoms, straight lines covalent bonds; and dots represent lone pair orbitals.
S.A. Dembovsky / Model of chalcogenide glassy semiconductors
116
lines (loops, etc.) in a structure. Examples of such paired
level barrier scheme arises similar to that discussed in
and tripled TCB's are shown in Figure 2.
reference 7. In this scheme, the ground state - a rigid CB -
The TCB, being situated on the boundary of a cluster,
relaxes either on the collective TCB at T _>Tg or on the
covers the surface of the cluster and thus this region is "cut
non-collective TCB (single, paired, or tripled ones) at T <
out" of the surrounding CRN. Such a region can be considered as a quasi-polymer containing 103 atoms which
Tg. In such a scheme the value of Tg naturally depends on
can vibrate as a whole. The TCB's on the cluster surface vibrate collectively and jointly with the cluster.
the cooling rate. 4. THE PINNING OF THE FERMI LEVEL
These clusters represent correlated regions of medium-
Ordinarily a TCB, considered as a defect in
range order (10-20/~ according to the low-frequency
comparison to a CB, is neutral and diamagnetic in its
Raman scattering peak), and the distance between them (4-
ground state. This is in contrast to the well-known Stree-
6A) can be associated with the length of the TCB. The
Mott and Kastner-Adler-Fritzsche models where
anomalous peculiarities of the ftrst sharp diffraction peak
diamagnetic defects are charged. Due to their neutrality
(FSDP), namely the increase in the FSDP with
such TCB's with the lowest energy and hence with the
temperature 5 and the shift of the FSDP position with increasing pressure 6, can be connected with the thermal
highest concentration cannot pin the Fermi level, EF. However there can exist TCB's with the same electronic
generation of TCB's and the high compressibility of these
configuration (as shown in Figure 3a) but in a charged
soft bonds. The connection between the freezing of clusters and the
state (as shown in Figure 3b) with a lower concentration of about 1019 cm -3.
glass transition and between cluster formation and the
antibonding orbital non-bonding orbital bonding orbital
suppression of the glass transition temperature is established. Thus clusters can be thought of as non-crystalline regions of the CRN which are relaxationally ordered. A glass can be considered as a polycluster solid with topologically disordered clusters and their conglomerates.
~
f
FIGURE 2 Examples of paired and tripled three-centered bonds, TCB's.
DFIGURE 3 (a) A possible electronic energy configuration for a TCB. (b) Two charge states that could exist in this energy configuration.
Let us consider the charged TCB, e.g. D-, which can play a role of a trap for holes. The capture of a hole leads to the unstable paramagnetic configuration without charge, and the capture of a second hole transfers it into the
3. THE GLASS TRANSITION At T ,; Tg the decomposition of collective vibrations of TCB's covering the cluster boundaries takes place. In this process the TCB's transform into paired (or tripled) TCB's that are more rigid and less mobile. As a result a three-
charged defect. In these processes the binding electrons of the TCB's remain, and only the electrons on non-bonding orbitals are added or removed during the capture. The neutral intermediate paramagnetic TCB provides low but necessary concentration of pinning one-particle
S.A. Dem bovsky / Model of chMcogenide glassy seraicond uctors
117
(one-electron, one-hole) states. The scheme of disposition
Finally, this TCB model perrmts one to predict the
of the TCB levels in the gap would then appear as is
influence of weak external perturbations (e.g. pressures on
shown in figure 4. Because a TCB possesses a soft anharmonic atomic
the order of 1 kilobar, or electric and magnetic fields with
potential, the capture of a carrier is accompanied by a
kT) on the properties of glassy semiconductors in the range T > Tg. Some of these effects, namely the influence
strong rebuilding of the atomic configuration of TCB, which provides large polaron and Stokes Shift. Thus in some respects this model is close to the model 8 of the
an energy that is very low relative to the thermal energy,
of magnetic fields on the viscous flow and crystallization, have been obtained experimentally.
electronic pair autocorrelation REFERENCES 1. S.A. Dembovsky, Izv. Akad. Nauk SSSR. Neorg. Mater. 14 (1978) 803.
I I
2. S.A. Dembovsky and E.A. Chechetkina, J. NonCryst. Solids 64 (1984) 95.
If
3. N.A. Popov, Pis'ma Zh. Eksp. Teor. Fiz. 31 (1980) 437.
,I
F-v
N(E)
to(E)
4. S.A. Dembovsky, Dokl. Akad. Nauk SSSR 298 (1988) 1408. 5. L.E. Busse, Phys. Rev. B 29 (1984) 3639. 6. K. Tanaka, Phil. Mag. Lett. 57 (1988) 183.
FIGURE 4 Density of states and energy level diagram for TCB's.
7. H.W. Leidesker, J. Chem. Phys. 5 (1971) 2028. 8. JM.I. Klinger and V.G. Karpov, Zh. Eksp. Teor. Fiz. 82 (1982) 1687. 9. S.A. Dembovsky and E.A. Chechetldna, Phil. Mag. B 53 (1986) 367. 10. S.A. Dembovsky and E.A. Chechetldna, Izv. Akad. Nauk SSR 50 (1986) 516.
115
MODEL OF CHALCOGENIDE GLASSY SEMICONDUCTORS BASED ON THREE-CEN'IER BONDS IN A RIGID COVALENT NETWORK S. A. DEMBOVSKY Institute of General and Inorganic Chemistry, Leninsky Pr. 31, Moscow 117907, USSR A proposed model of mixed covalent and three-center bond network provides an interconnected explanation of many of the characteristic phenomena observed in chalcogenide glasses over a broad temperature range. A detailed discussion of cluster formation, the glass transition and electronic features including the pinning of the Fermi level is given.
nature of the large polaronic shift are discussed below.
1. INTRODUCTION All glasses - including semiconducting ones - have a
5. Similarity between Glassy Semiconductors and a-
large concentration of lone-pair electrons.l,2 It has been
Si:H. This similarity is connected with the possibility of
suggested that in such glasses, configurations known as
the existence of TCB's in both materials. The TCB's are
three-center bonds exist in large concentrations. In Figure
electron-rich in the fLrStcase and electron-deficient4 in the
1 a four-electron three center bond (TCB) which has been
second (a-Si:H).
proposed for selenium3 is shown. In their basic state,
6. Zero-Poin~ ~
.
The soft TCB (one of a
covalent networks as a consequence of the local strain in
distribution of interatomic angles and lengths) leads to the excess energy and excess zero-point entropy (ASo > 0 at T
the rigid covalent bonds due to their random arrangement.
= 0).
these bonds are neutral and diamagnetic. TCB's arise in
The energy of formation2 of a TCB in glassy (g-) Se is
7. Mechanical Pro_nerty Differences. The mechanical
0.14 eV. Thus they exist in relatively high concentrations
properties of glasses such as sound velocity, differ from
(approximately 1%) at temperatures near the glass
those of their crystalline counterparts. This is due to their
transition temperature Tg. The TCB is longer and weaker
dependence on quasielastic constants (e.g. vt,1 = ~/K).
than a covalent bond (CB), with the respective quasielastic constants being in the ratio K(TCB)/K(CB) -~ 10-2.
2. CLUSTER FORMATION
Furthermore, TCB's have various atomic configurations
It has been shown that in a system consisting of rigid
and potentials, including a two-well potential. The TCB
covalent bonds in a continuous random network (CRN)
model can be used as a framework to understand a number of phenomena, including:
and of soft anharmonic TCB's, cluster formation must take place. These clusters are regions of non-crystallineorder
1. Low Temoemture Anomalies. The low temperature
where the relaxation of a CB on a TCB occurs. Thus soft
anomalies are connected with the specific form of the TWP.
TCB's play the role of a "quasinuclcus" of a cluster. The second role of TCB's concerns the formation of
2. Average Temnerature Anomalies. These anomalies
non-breaking (i.e. without dangling bonds) non-phase
such as glass transition and cluster formation are discussed below.
intercluster boundaries and disinclinations. The latter arc
3. High Temnerature Anomalies. These anomalies are
based on the doubled or tripled five- or seven-atom TCB, which can form together with discontinuous disinclination
connected with the fact that the TCB represents a hypervalent bond.2 4. Pinning of the Fermi Level.
In chalcogenide
glasses pinning can be understood in terms of charged diamagnetic TCB's. The mechanism of pinning and the
0022-3093/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)
FIGURE 1 A three-centered bond, TCB. Circles are Se atoms, straight lines covalent bonds; and dots represent lone pair orbitals.
S.A. Dembovsky / Model of chalcogenide glassy semiconductors
116
lines (loops, etc.) in a structure. Examples of such paired
level barrier scheme arises similar to that discussed in
and tripled TCB's are shown in Figure 2.
reference 7. In this scheme, the ground state - a rigid CB -
The TCB, being situated on the boundary of a cluster,
relaxes either on the collective TCB at T _>Tg or on the
covers the surface of the cluster and thus this region is "cut
non-collective TCB (single, paired, or tripled ones) at T <
out" of the surrounding CRN. Such a region can be considered as a quasi-polymer containing 103 atoms which
Tg. In such a scheme the value of Tg naturally depends on
can vibrate as a whole. The TCB's on the cluster surface vibrate collectively and jointly with the cluster.
the cooling rate. 4. THE PINNING OF THE FERMI LEVEL
These clusters represent correlated regions of medium-
Ordinarily a TCB, considered as a defect in
range order (10-20/~ according to the low-frequency
comparison to a CB, is neutral and diamagnetic in its
Raman scattering peak), and the distance between them (4-
ground state. This is in contrast to the well-known Stree-
6A) can be associated with the length of the TCB. The
Mott and Kastner-Adler-Fritzsche models where
anomalous peculiarities of the ftrst sharp diffraction peak
diamagnetic defects are charged. Due to their neutrality
(FSDP), namely the increase in the FSDP with
such TCB's with the lowest energy and hence with the
temperature 5 and the shift of the FSDP position with increasing pressure 6, can be connected with the thermal
highest concentration cannot pin the Fermi level, EF. However there can exist TCB's with the same electronic
generation of TCB's and the high compressibility of these
configuration (as shown in Figure 3a) but in a charged
soft bonds. The connection between the freezing of clusters and the
state (as shown in Figure 3b) with a lower concentration of about 1019 cm -3.
glass transition and between cluster formation and the
antibonding orbital non-bonding orbital bonding orbital
suppression of the glass transition temperature is established. Thus clusters can be thought of as non-crystalline regions of the CRN which are relaxationally ordered. A glass can be considered as a polycluster solid with topologically disordered clusters and their conglomerates.
~
f
FIGURE 2 Examples of paired and tripled three-centered bonds, TCB's.
DFIGURE 3 (a) A possible electronic energy configuration for a TCB. (b) Two charge states that could exist in this energy configuration.
Let us consider the charged TCB, e.g. D-, which can play a role of a trap for holes. The capture of a hole leads to the unstable paramagnetic configuration without charge, and the capture of a second hole transfers it into the
3. THE GLASS TRANSITION At T ,; Tg the decomposition of collective vibrations of TCB's covering the cluster boundaries takes place. In this process the TCB's transform into paired (or tripled) TCB's that are more rigid and less mobile. As a result a three-
charged defect. In these processes the binding electrons of the TCB's remain, and only the electrons on non-bonding orbitals are added or removed during the capture. The neutral intermediate paramagnetic TCB provides low but necessary concentration of pinning one-particle
S.A. Dem bovsky / Model of chMcogenide glassy seraicond uctors
117
(one-electron, one-hole) states. The scheme of disposition
Finally, this TCB model perrmts one to predict the
of the TCB levels in the gap would then appear as is
influence of weak external perturbations (e.g. pressures on
shown in figure 4. Because a TCB possesses a soft anharmonic atomic
the order of 1 kilobar, or electric and magnetic fields with
potential, the capture of a carrier is accompanied by a
kT) on the properties of glassy semiconductors in the range T > Tg. Some of these effects, namely the influence
strong rebuilding of the atomic configuration of TCB, which provides large polaron and Stokes Shift. Thus in some respects this model is close to the model 8 of the
an energy that is very low relative to the thermal energy,
of magnetic fields on the viscous flow and crystallization, have been obtained experimentally.
electronic pair autocorrelation REFERENCES 1. S.A. Dembovsky, Izv. Akad. Nauk SSSR. Neorg. Mater. 14 (1978) 803.
I I
2. S.A. Dembovsky and E.A. Chechetkina, J. NonCryst. Solids 64 (1984) 95.
If
3. N.A. Popov, Pis'ma Zh. Eksp. Teor. Fiz. 31 (1980) 437.
,I
F-v
N(E)
to(E)
4. S.A. Dembovsky, Dokl. Akad. Nauk SSSR 298 (1988) 1408. 5. L.E. Busse, Phys. Rev. B 29 (1984) 3639. 6. K. Tanaka, Phil. Mag. Lett. 57 (1988) 183.
FIGURE 4 Density of states and energy level diagram for TCB's.
7. H.W. Leidesker, J. Chem. Phys. 5 (1971) 2028. 8. JM.I. Klinger and V.G. Karpov, Zh. Eksp. Teor. Fiz. 82 (1982) 1687. 9. S.A. Dembovsky and E.A. Chechetldna, Phil. Mag. B 53 (1986) 367. 10. S.A. Dembovsky and E.A. Chechetldna, Izv. Akad. Nauk SSR 50 (1986) 516.