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Estimate of Avalanche Breakdown Voltage in 4H-SiC

Fig. 1. Ionization Rate as a function of electric field in Silicon Carbide at room temperature.
Published impact ionization coefficients of (0001) 4H-SiC are used to fit a power-law-approximated effective impact ionization, which is accurate in the range of electric field strengths from 1.5 to 5MV/cm. This power law approximation is used to generate 1D equations for critical electric field, avalanche breakdown voltage, and depletion layer width of 4H-SiC devices as a function of doping concentration. One-dimensional avalanche breakdown of 4H-SiC Schottky diodes was simulated for various epi layer doping levels, to evaluate the fidelity to these and other published 1D breakdown equations. Our (RPI) equations best fit the Schottky diode simulation and correlate well with published 4H-SiC device results.

Measured sets of impact ionization coefficients have been published for the 4H-polytype of Silicon Carbide, as well as approximated sets of 1D breakdown equations for calculation of drift layer requirements for design of SiC power devices. This type of equations is useful as a starting point in new device design, and so having accurate analytical equations are important for development of new device structures. Fidelity of these equations with simulation using accepted ionization coefficients and with published experimental device results can be used to compare and contrast the accuracy of these analytical approximations.

A power law relationship was fit to accepted impact ionization coefficients, as shown in Fig. 1. The fitted equation for ionization rate as a function of electric field is given in equation (1). This relationship approximates the published impact ionization coefficients well for electric fields of 1.5 to 5MV/cm. Solving the ionization integral using this relationship leads to 1D equations (2), (3), and (4).

4H-SiC Schottky diodes were simulated with varied doping concentrations, using the Konstantinov impact ionization coefficients. Our equations show strong fidelity to simulation, and published device results (Fig. 2, 3). As expected, physical devices lie slightly below the calculated BVPP due to termination, cell structure, etc. By contrast, other sets of previously published equations overestimate the breakdown voltage by up to 80%.

Fig. 2. Blocking voltage versus drift layer doping concentration. Schottky simulations were run using the Konstantinov impact ionization coefficients.
Fig. 3. Depletion layer width versus drift layer doping concentration, with non-punch-through blocking voltage on the secondary y-axis. Schottky simulations were run using the Konstantinov impact ionization coefficients.