## 1 Introduction  
THz band communication technology has garnered significant attention due to its potential for high data transmission rates, and it is likely to be utilized in future 6G communications [1; 2; 3; 4; 5]. The current research focus is on enhancing the transmission power of THz signals, optimizing beam control technology, and developing efficient integrated-circuit designs. The main beam control technologies currently include transmission array beam control [6; 7; 8; 9], reflection array beam control [10; 11], and phased-array technology [12]. Among them, phased-array technology has become a key technology for THz beam control because it can support a wider available frequency band, as well as spatial coexistence and multiplexing. By adjusting the phase of each antenna element in the array, the phased array can precisely control the radiation beam, thereby improving signal directionality and enhancing communication quality. However, the design of phased-array antennas (PAAs) for the THz band is extremely challenging due to the extremely small size of antennas in this frequency range. In addition, the operating bandwidth of the THz band is generally wide, but achieving stable gain within a wide operating bandwidth is also not easy. To achieve precise control of the beam in the THz band, beam control chips are indispensable. The fabrication processes for THz beam control chips mainly include compound semiconductor processes and silicon-based processes. Compound semiconductor processes, such as gallium arsenide (GaAs), indium phosphide (InP), and gallium nitride (GaN), offer advantages like high output power and low noise figure for reception. However, they have the drawbacks of low integration density and high cost. Silicon-based processes, including complementary metal-oxide-semiconductor (CMOS) and silicon-germanium (SiGe), may have average performance but benefit from high integration density and low cost. In [13], the authors introduce a scalable approach for implementing millimeter-wave and THz fully integrated circuits based on standing waves which addresses the challenges of power generation and beam steering in a compact form factor. In [14], working on a scalable THz 2-D PAA, the authors further emphasize the potential for high-resolution imaging and spectroscopy in the millimeter-wave and THz frequencies. The fully integrated 16-element PAA transmitter in SiGe BiCMOS for 60 GHz communications, as detailed in [15], exemplifies PAA technology for high-data-rate wireless communications. In [16], the authors provide a thorough review of terahertz beam-steering technologies, comparing traditional methods with emerging reconfigurable metasurface-based approaches. In [17], the authors introduce a 0.32 THz four-transmitter PAA using Chiplets in 130-nm SiGe BiCMOS technology, demonstrating significant output power and beam-steering capabilities. This work represents a significant step towards scalable and efficient THz communication systems. In [18], the authors present an optimization methodology for THz PAAs that incorporates mutual coupling effects. Their algorithm, implemented in PyAEDT, offers a high-fidelity optimization technique for accurate and fast EIRP pattern synthesis. In [19], the authors discuss millimeter-wave and sub-THz PAA imaging systems that utilize electro-optic up-conversion and optical beamforming. Their work is a significant contribution to the development of imaging systems that operate beyond the capabilities of current technology. In recent years, there have been reports related to PAAs in the THz band. In [20], the authors use lens-coupled annular-slot antennas to design a 1 \(\times\) 5 PAA which can achieve a 1-D beam scanning of 62\({}^{\circ}\) at 200 GHz. In [21], a 0.59 THz beam-steerable coherent-radiator array based on 40 nm CMOS is proposed, and it can achieve a 1-D beam scanning of 30\({}^{\circ}\).