Three regions in the IV characteristic of an unspecified chalcogenide PCM device that is representative of the results discussed in the experimental overview. The low-field region is usually described as ohmic, but in some cases of thin samples it is described as . The intermediate region has exponential dependence described as either and/or . Near and below room temperature, two slopes are often observed in the intermediate region. The high field region corresponds to a stronger dependence, possibly .
Sketches of physical processes associated with the one-electron localized states model. Top left: screening in the presence of an applied field due to redistribution of localized electrons to form a dipole. Bottom left: unpaired electrons near the Fermi level (dashed-dotted line) produce a strong ESR signal. Top right: optical absorption of photon energies less then (dashed arrows) and greater than (solid upward arrow) the gap, and photoluminescence (downward arrow) possible at mid-gap energies—solid arrows show what is observed in chalcogenide glasses. Bottom right: hopping conduction via states near the Fermi level. The one-electron localized states model cannot consistently account for the data on chalcogenide glasses.
Sketch of the typical spectroscopic data in chalcogenide glasses: PA, PL, efficiency of photoluminescence excitation (EPLE), PIPL enhancement, and PIPA vs. photon energy . is the optical gap. All the curves except PA are plotted against the left vertical axis.
Energies of localized charge carriers vs. the local lattice deformation . The upward solid arrows represent absorption and the downward solid arrows represent photoluminescence processes; the dashed arrow indicates photoinduced photoabsorption from the nonequilibrium state. E 1 and E 2 represent the equilibrium energies for and localized carriers. is the polaron shift and is assumed to be relatively small.
Left: one-particle energy levels (i.e., energy per particle) corresponding to and electrons in the mobility gap. The levels without electrons represent the bare energy. Solid and dashed lines indicate thermodynamic and optical energy levels, respectively. The dashed electron level close to the valence band edge represents the energy needed to optically ionize the 2e state (solid upward arrow); the solid level close to the midgap represents the energy needed to thermally ionize the same 2e state. The arrows have the same meaning as in Fig. 4 . Right: density of the 2-electron ( ) and 2-hole ( ) states vs. their one-particle energies where negative-U centres near the Fermi level provide its pinning.
Mechanical analogy of the negative-U effect consisting of two elastic springs and two charged balls that can be attached to the springs either separately or together (top row) and its simple model based on the valence bonds representation (bottom row) where two electrons can occupy the states of two broken bonds or one dangling bond. The right column is energetically more favorable when .
Probabilistic distribution of the local spring constants in a glass. The gull-wing singularity at the origin (not particularly important in this context) reflects the instability of very soft potentials with respect to small perturbations. 47
Left: Field induced decrease in activation energy of a coulombic center. Dashed lines show zero field case, tilted red line represents the electric potential of a uniform field. Gray arrow shows vibration of the electron energy due to electron-phonon coupling. Right: Field induced decrease in activation energy of a pair of coulombic centers.
DOS in the mobility gap of a chalcogenide glass. The electric field shifts the mobility edge for holes up by energy (similar effect for electrons is not shown here).
Localized tail states for the electrons below the mobility edge (shown as dashed-dotted line) have linear dimensions decreasing with energy in the mobility gap.
Left: real space representation of space charge (exponential in quasi-Fermi energy) and electric potential where the barrier top plays the role of a virtual cathode. Right: energy space representation with shaded region filled with injected holes.
Temperature dependence of conductivity in a GST based PCM structure.
Left: field emission via hopping through an optimum chain; circles represent localized states. Right: same in the energy space.
Left: Fragment of percolation cluster with mesh size in a material of thickness . Right: equivalent circuit of a filament of the percolation cluster where exponentially different resistors in series are depicted by resistors of different sizes; the first and second maximum resistors are marked for illustration.
Amorphous dome with crystalline inclusions as part of the typical PCM structure including a small area electrode (SAE) and thermal insulator (TI). R is the average distance between crystallites. Arrows represent the current flow utilizing a path of minimum resistance.
Top: a fragment of amorphous matrix with embedded crystallites. Bottom: energy band diagram showing valence band edge in the crystalline and amorphous matrix (with offset ) and the activation energy is an amorphous phase without crystallites. Dotted-dashed line represents the chemical potential. Arrows show the current flow between two crystallites.
Four different fits of the same typical IV curve (presented also in Fig. 1 ) in the reset state of GST based PCM structure corresponding to the expressions discussed in the text: (a) , (b) , (c) , and (d) .
Fitting the data of Fig. 17 in the domain of V, which excludes the steep increase near threshold. The models with and , fit equally well, while that of remains outstanding.
Listing of each conduction mechanism along with the related analytical expression and estimated field range of applicability. The current is given in terms of the electric field , with the pre-exponential . The parameters are defined as follows: is the Boltzmann constant, is temperature, is the elementary charge, is the dielectric constant, is the inter-center distance, is the reduced Planck’s constant, is the effective carrier mass, eV is the characteristic phonon energy, is the characteristic decay of the density of tail states , where is energy, is thickness, (here, is the density of localized states), is the electron localization radius, is the Fermi energy, is a numerical factor, nm is the percolation cluster correlation radius, is the order parameter, is the crystallite radius, is the maximum percolation transport barrier, and eV is the band offset between crystalline and amorphous phases.
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