By Jan Grym

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The 1D simplification allows using the wave operator like a function of the z coordinate only: (47) (r,z) = (z)eikr, where k=(kx,ky) is the wave vector in the (x,y) plane. So the carrier are quantized in the z direction and are free to move in the r=(x,y) plane, with a continuous energy component. After phase transformation and imposing the constraint of vanishing for the first derivative of the wave function, the envelope 1D time-independent reduced equation (46) is: (48) z W E z 2 m where is reduced Planck constant, mzz is the effective masses in mo units, W is potential energy, (z) is the 1D envelope wave functions and Ez is the eingenvalue energy.

H. Ryu, and M. 6 kV 4H-SiC Asymmetrical GTO Thyristor," Material Science Forum, pp. 353-356. L. K. Gummel, Large-Signal Analysis of A Silicon, IEEE Trans. Electron Devices, vol. ED-16,pp 64-77, Jan 1969. J. B. Fedison, “High Voltage Silicon Carbide Junction Rectifiers and GTO Thyristors”, PhD Thesis, Rennsealer Polytecnic Institute, New York, May 2001. H. Sakata, M. Zahim, “Device Simulation of SiC-GTO”, IEEE Power Conversion Conference”, vol. 1, April 2002, pp. 220-225. A. 1. Introduction Semiconductor manufacturing spans across many manufacturing areas, including wafer manufacturing where electronic circuitry is built layered on a wafer, chip manufacturing that involves circuit probing and testing, and product manufacturing from which the final IC (integrated circuits) products are assembled, and finally tested.

Rowland, “SiC Materials progress, Status & Potential Roadblocks,” Proc. IEEE, vol. 90, no. 6, pp. 942-955, 2002. J. A. , and A. ” Proc. of the IEEE, vol. 90, pp. 956-968, 2002. Iterative Solution Method in Semiconductor Equations 37 A. K. Agarwal, P. A. Ivanov, M. E. Levinshtein, J. W. Palmour, S. L. Rumyantsev, S. H. Ryu and M. 6 kV 4H-SiC Asymmetrical GTO Thyristor," Material ScienceForum, vol. 353-356, pp 743-746,2001. R. R. Siergiej, J. B. Casady, A. K. Agarwal, L. Rowland. S. Seshadri, S. Mani, P.