## 1 Introduction
The underlying physics behind NDC can be attributed to phenomena such as inter-valley transfer at high electric fields, avalanching breakdown, and the quantum mechanical properties of the electronic system. In essence, NDC arises from the interaction between electronic states within the system and the external voltage bias. The presence of resonant states is closely linked to the occurrence of NDC. Resonant states manifest as sharp peaks in the density of states within the system. These resonant states can lead to the formation of a current bottleneck, resulting in a reduction of current flow as the applied voltage increases. In recent years, significant progress has been made in comprehending and controlling NDC behavior across various electronic systems [1]. Further research in this field is anticipated to yield the development of new materials and devices with improved performance and functionality, especially within the realm of strained Si/SiGe heterostructures [16; 17; 18]. In this study, we focus on utilizing the strained Si/SiGe heterostructure (Figure 1), which is a semiconductor structure composed of alternating layers of silicon and silicon-germanium (SiGe) films. These layers possess distinct properties, including different crystal structures and electronic band structures, resulting in intriguing electrical characteristics at their heterojunctions. One remarkable attribute of strained Si/SiGe heterostructures is their ability to exhibit negative differential conductance [7]. This phenomenon strongly depends on the thickness of the SiGe layer and the applied voltage and can be finely adjusted by modifying the composition and thickness of the SiGe layer. The tunability of negative differential conductance in strained Si/SiGe heterostructures presents an opportunity to design custom devices with specific performance attributes. By precisely controlling the composition and thickness of the SiGe layer, the NDC behavior can be tailored to meet specific design requirements. Consequently, strained Si/SiGe heterostructures have emerged as a versatile semiconductor platform, facilitating band structure and strain engineering. This, in turn, enables the enhancement of conventional microelectronic device performance and the exploration of novel concepts. In essence, strained Si/SiGe heterostructures offer a unique semiconductor structure capable of exhibiting negative differential conductance. This property has opened avenues for band structure and strain engineering, enabling divers. In summary, a 2D numerical simulation of the amplification of space charge waves using negative differential conductance in a typical MOS silicon-germanium (SiGe)-based field effect transistors (FET) and complementary metal oxide semiconductor (CMOS) technology at 4.2 K is presented in this paper. The results show the amplification and non-linear interaction of space charge waves in a strained Si/SiGe heterostructure occurs for frequencies up to approximately 60 GHz at T = 1.3 K, 47 GHz at T = 4.2 K, and 40 GHz at T = 77 K. In addition to deep space applications, these types of devices have potential uses in terrestrial applications which include magnetic levitation transportation systems, medical diagnostics, cryogenic instrumentation, and superconducting magnetic energy storage systems. As a future work, the 2D analysis for amplification of space charge waves in strained Si/SiGe heterostructure at 1.3 K will be interesting.