Thermodynamics of second phase conductive filaments

Abstract

We present a theory of second phase conductive filaments in phase transformable systems; applications include threshold switches, phase change memory, and shunting in thin film structures. We show that the average filament parameters can be described thermodynamically. In agreement with the published data, the predicted filament current voltage characteristics exhibit negative differential resistance vanishing at high currents where the current density becomes a bulk material property. Our description is extendible to filament transients and allows for efficient numerical simulation

High-Frequency TaO_{<italic>x</italic>}-Based Compact Oscillators

“…It has been long noted that the peak current in the ON-state of the device dictates the size of the transient filament/nucleus (I ON α r 2 ) [10], [11], [16], [21]. This implies that the higher frequencies require the device to operate such that the filament formed during the oscillations is small.…”

Threshold switching via electric field induced crystallization in phase-change memory devices

“…[7][8][9][10][11][12] However, the fields necessary for such threshold switching by field induced nucleation alone are relatively high, being of the order 300 MVm À1 . This is significantly larger than experimentally measured threshold fields 28 of around 56 MVm À1 (though we note that such experimental measurements are for lateral cells rather than the "mushroom" type cell considered here, and that threshold fields in other types of device such as the recently reported "interfacial" phase-change memory 29 may well be different).…”

“…Mainstream understanding of this switching phenomenon is that it is initiated electronically via the influence of high electric fields on the interband trap states. [5][6][7] However, recent work has suggested that field induced (crystal) nucleation could instead be responsible, [7][8][9][10][11][12] and models for such field-induced nucleation were able to explain several experimental observations on PCM devices, such as the occurrence of relaxation oscillations 8,9 and the relationship between switching voltage (and temperature) and switching delay time. 10 Most models of field-induced nucleation presented to date have concentrated on the role of the electric field in lowering the nucleation barrier and the associated critical nucleus size, an approach extended recently by ourselves to include a fuller kinetic treatment that can identify field ranges where electric field effects might play a significant role in the crystallization of "bulk" samples.…”

Theory of conductive filaments in threshold switches

“…As a newly created filament heats up, it increases its radius from some initially small value until it reaches its steady state value given below [Eq. (12)]. The concomitant temperature increase results in restoring the first terms in Eqs.…”

“…The time dependence of the electric field will rely on the particular circuit being modelled [12] and heat transport will depend on device geometry. In this current work we limit ourselves to the steady state case 0 = / t r ∂ ∂ , which takes place when the free energy is a minimum.…”