1073 K shows that the Ta dimer structures tend to merge into the Ta tetramer, which
further confirms that the formation of Ta clusters is energetically preferable in the
O-deficiency state of a-Ta 2 O 5 . This could be probably attributed to the simple
equilibrium solid-phase diagram for the Ta-O system: there are only two stable
phases below 1273 K: the single-metal-valence compound Ta 2 O 5 and Ta metal [42].
Subsequently, in order to understand the structural evolution of Ta-O systems
during operation, various a-TaO x (x ¼ 2.85, 2.67, 2.50, 2.25, 2, 1.5, 1 and 0.75)
structures were examined [7]. The values of Ta-O/Ta-Ta bond lengths and Ta(O)/O
(Ta) coordination numbers (CNs) as the function of O contents are shown in
Fig. 14a,b, respectively. Note that Ta(O) CN denotes the number of O atoms
surrounding a Ta atom. From the figure, we can see that: (1) with the increase of x
values, the Ta-O bond length gradually decreases; (2) the Ta(O) CN values increase
with the increase of x values until it keeps almost a constant value (corresponding to
TaO 6 ) in the region of x > 2.50. All the above features agree well with experimental
data [43], supporting the reliability of our simulation results. In addition, other
features of the structural evolution can also be seen: (3) the O(Ta) CN increases
with the increase of V O concentrations; (4) there is the close relationship between the
O(Ta) CN and Ta-O bond length, and between the Ta(O) CN and Ta-Ta bond length;
(5) considerable amount of Ta-Ta metallic bonds are formed in the case of
O-deficient a-TaO x , which could dramatically enhance the electronic conductivity
of a-TaO x and corresponds to LRS of the a-TaO x based device [5, 28].
To understand the correlation between electronic properties of a-TaO x and O
contents, the calculated DOS of all the considered a-TaO x (x ¼ 2.85, 2.67, 2.50, 2.25,
2, 1.5, 1 and 0.75) are shown in Fig. 15. This figure reveals that: (1) in the case of
a-TaO x with x > 2.50, the defect states near the Fermi level mainly consist of the
O-O bonds [43]; (2) a-TaO 2.5 is an insulator with a big band gap; (3) in the case of
a-TaO x with x < 2.50, the Fermi level shift towards the conduction band due to the
formation of Ta-Ta bonds, and the intensity of defect states around the Fermi level
becomes stronger with the decrease of O content concentration.
As revealed in the previous experiment [28], the chemical compositions of Ta-O
system for HRS and LRS in a-TaO x based device correspond to the values x > 2 and
x < 1, respectively. Accordingly, we chose the a-TaO 2.25 and a-TaO 0.75 to represent
of the HRS and LRS, respectively, and studied their structures and electronic
properties in detail (Fig. 16). In the case of a-TaO 2.25 , several Ta clusters can be
found which are apart from each other, and the corresponding local density of states
(LDOS) around the Fermi level (Fig. 16a) shows that the electrons are localized on
these Ta clusters. Accordingly, no connected conduction path is formed. It is noted
that the isolated Ta-rich regions were observed in the experiment in the HRS of
a-TaO x based device [4]. On the other hand, in a-TaO 0.75 (Fig. 16b), a considerable
amount of Ta-Ta bonds can be found which are connected with each other. The
corresponding LDOS (Fig. 16b) reveals that electrons are delocalized on these Ta-Ta
bonds, which results in the formation of conduction path. The results agree well with
experiments showing the formation of a connected Ta-rich region in LRS of such
device [4, 28]. In addition, the volume of a-TaO 2.25 structure is about twice of
a-TaO 0.75 , which agree with the experimental finding that the thickness of a-TaO x
Atomistic Simulations for Understanding Microscopic Mechanism of. . .
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further confirms that the formation of Ta clusters is energetically preferable in the
O-deficiency state of a-Ta 2 O 5 . This could be probably attributed to the simple
equilibrium solid-phase diagram for the Ta-O system: there are only two stable
phases below 1273 K: the single-metal-valence compound Ta 2 O 5 and Ta metal [42].
Subsequently, in order to understand the structural evolution of Ta-O systems
during operation, various a-TaO x (x ¼ 2.85, 2.67, 2.50, 2.25, 2, 1.5, 1 and 0.75)
structures were examined [7]. The values of Ta-O/Ta-Ta bond lengths and Ta(O)/O
(Ta) coordination numbers (CNs) as the function of O contents are shown in
Fig. 14a,b, respectively. Note that Ta(O) CN denotes the number of O atoms
surrounding a Ta atom. From the figure, we can see that: (1) with the increase of x
values, the Ta-O bond length gradually decreases; (2) the Ta(O) CN values increase
with the increase of x values until it keeps almost a constant value (corresponding to
TaO 6 ) in the region of x > 2.50. All the above features agree well with experimental
data [43], supporting the reliability of our simulation results. In addition, other
features of the structural evolution can also be seen: (3) the O(Ta) CN increases
with the increase of V O concentrations; (4) there is the close relationship between the
O(Ta) CN and Ta-O bond length, and between the Ta(O) CN and Ta-Ta bond length;
(5) considerable amount of Ta-Ta metallic bonds are formed in the case of
O-deficient a-TaO x , which could dramatically enhance the electronic conductivity
of a-TaO x and corresponds to LRS of the a-TaO x based device [5, 28].
To understand the correlation between electronic properties of a-TaO x and O
contents, the calculated DOS of all the considered a-TaO x (x ¼ 2.85, 2.67, 2.50, 2.25,
2, 1.5, 1 and 0.75) are shown in Fig. 15. This figure reveals that: (1) in the case of
a-TaO x with x > 2.50, the defect states near the Fermi level mainly consist of the
O-O bonds [43]; (2) a-TaO 2.5 is an insulator with a big band gap; (3) in the case of
a-TaO x with x < 2.50, the Fermi level shift towards the conduction band due to the
formation of Ta-Ta bonds, and the intensity of defect states around the Fermi level
becomes stronger with the decrease of O content concentration.
As revealed in the previous experiment [28], the chemical compositions of Ta-O
system for HRS and LRS in a-TaO x based device correspond to the values x > 2 and
x < 1, respectively. Accordingly, we chose the a-TaO 2.25 and a-TaO 0.75 to represent
of the HRS and LRS, respectively, and studied their structures and electronic
properties in detail (Fig. 16). In the case of a-TaO 2.25 , several Ta clusters can be
found which are apart from each other, and the corresponding local density of states
(LDOS) around the Fermi level (Fig. 16a) shows that the electrons are localized on
these Ta clusters. Accordingly, no connected conduction path is formed. It is noted
that the isolated Ta-rich regions were observed in the experiment in the HRS of
a-TaO x based device [4]. On the other hand, in a-TaO 0.75 (Fig. 16b), a considerable
amount of Ta-Ta bonds can be found which are connected with each other. The
corresponding LDOS (Fig. 16b) reveals that electrons are delocalized on these Ta-Ta
bonds, which results in the formation of conduction path. The results agree well with
experiments showing the formation of a connected Ta-rich region in LRS of such
device [4, 28]. In addition, the volume of a-TaO 2.25 structure is about twice of
a-TaO 0.75 , which agree with the experimental finding that the thickness of a-TaO x
Atomistic Simulations for Understanding Microscopic Mechanism of. . .
113