In the last decade, silicon carbide (SiC) has emerged as a potential material for high-frequency electronics and optoelectronics applications that may require elevated temperature processing. SiC exists in more than 200 different crystallographic forms, referred to as polytypes. Based on their remarkable physical and electrical characteristics, such as better thermal and electrical conductivities, 3C-SiC, 4H-SiC, and 6H-SiC are considered as the most distinguished polytypes of SiC. In this article, physical device simulation of a light-emitting diode (LED) based on the unique structural configuration of 4H-SiC and 6H-SiC layers has been performed which corresponds to a novel material joining technique, called diffusion welding/bonding. The proposed single quantum well (SQW) edge-emitting SiC-based LED has been simulated using a commercially available semiconductor device simulator, SILVACO TCAD. Moreover, by varying different design parameters, the current-voltage characteristics, luminous power, and power spectral density have been calculated. Our proposed LED device exhibited promising results in terms of luminous power efficiency and external quantum efficiency (EQE). The device numerically achieved a luminous efficiency of 25% and EQE of 16.43%, which is at par performance for a SQW LED. The resultant LED structure can be customized by choosing appropriate materials of varying bandgaps to extract the light emission spectrum in the desired wavelength range. It is anticipated that the physical fabrication of our proposed LED by direct bonding of SiC-SiC wafers will pave the way for the future development of efficient and cost-effective SiC-based LEDs.