Theoretical Model of the Anodic Oxidation Growth Kinetics of Si at Constant Voltage

Abstract

An analytical model for the growth kinetics of the anodic oxidation of Si is developed, in which oxidant anions are drifted across the as-grown SiO2 by the electric field from an applied constant voltage. Literature evidence for an anionic transport mechanism is reviewed. The theoretical model derived for the film growth rate is consistent with an empirical relation due to Jain et al., r(t) = at 1/2 + ro, where r(t) represents the oxide thickness as a function of time, and a and ro are constants (3). The net anion mobility was calculated using the model and earlier experimental results. Electronic current density, the major total current component, is shown to be nonohmic and space charge limited. Equations are derived, each as a function of time, for the total current density, the electronic current density, and the ionic efficiency during anodic oxidation. These theoretical predictions are in good agreement with the available experimental data.At present, the technique most commonly used for fabrication of SiO2 films in electronic devices has been the thermal oxidation of silicon. On the other hand, oxide films can be grown on silicon by an electrochemical process (1-4). The electrochemical process has a number of advantages, low cost and the use of room temperature, which makes this process a very good candidate for growing insulator layers on hydrogenated amorphous silicon films. Amorphous Si:H films are unstable at high temperature (above 300~176 since the H evolves and causes the films to lose their desirable properties. Oxide insulation layers are also used to make low-cost, high-efficiency solar cells and integrated thin film transistor arrays (TFT) for image sensor and large-area liquid displays (5, 6). Another potential application is growing very thin silicon dioxide layers (20-200A) for short channel MOSFET and EPROM devices (7). Many theoretical papers, e.g., (8)(9)(10)(11)(12)(13)(14), in addition to experimental investigations, e.g., (15-28), have followed the original work by Cabrera and Mott (8); however, still more work is necessary for a complete understanding and adequate control of the anodic process.In this paper, an anlaytical model for the constant voltage anodic oxidation of silicon has been developed. The experimental results and an empirical relation found by Jain et al.(3) are compared with the theoretical growth rate equations. Theoretical ModelTwo basic steps for the constant voltage anodic oxidation of Si are illustrated in Fig. 1. First, it is assumed that the anions are transported across the oxide film and, second, that the anions react with the silicon surface.The first assumption of this model is that anions are the dominant species moving across the oxide. It has been a controversial issue for the anodic oxidation of silicon whether, during growth, the cation, the anion, or both, are moved across the thickening oxide film. Schmidt and Owen (1) labeled an oxide film on silicon by anodizing it in tetrahydrofurfuryl alcohol containing 32p as phosphate. When this radioactive film ...

Electrokinetic transport and separations in fluidic nanochannels

“…The relative conductivity increases with decreasing kh because the relative number of ions with respect to the reservoir increases. The ae-potential can be varied by surface chemical modification [88] or electric voltage bias [2,81,[89][90][91][92][93][94][95][96][97][98][99] (see also below). Figure 2a shows a perfect symmetry in the ae-potential dependence of the conductivity of KCl solution, while Fig.…”

“…The fluid transport asymmetry can be used to design a dynamic valve that will allow for a larger flow in one direction and be controlled by modulating the potential at the channel wall [2,81,[89][90][91][92][93][94][95][96][97][98][99]. If the divalent ions tend to strongly adsorb at the channel wall then the magnitude of the ae-potential will decrease and the observed electric conductivities and fluid flow rates will be reduced accordingly.…”

“…The idea of manipulating the ae-potential of a fluidic channel was first formulated by Ghowsi and Gale [90][91][92]. Such voltage bias is supposed to change the ae-potential at wall-solution interface, and therefore can be used to control the current and fluid transport in the channel.…”

“…That is why many researchers try to design nanochannel devices that incorporate this principle to create a fluidic "field effect transistor" [2,81,89,[93][94][95][96][97][98][99]. The relationship between the applied external voltage and the shift in the ae-potential is rather complicated [90][91][92]. A relatively simple expression can be obtained for slit-shaped channel and assuming that no current is leaking across the dielectric channel wall [81] Dz…”

“…where Dae is the shift in the interfacial potential (originally equal to ae 0 ), s is the surface charge (s 0 ¼ Àee 0 rC wall j ), d is the thickness of the dielectric layer at the channel wall, and e d is the relative permittivity of the material [90][91][92]. The charge s is a function of the total potential z 0 þ Dz and (Eq.…”