Low-curvature and large-diameter GaN wafers are in high demand for the development of GaN-based electronic devices. Recently, we have proposed the coalescence growth of GaN by the Na-flux method and demonstrated the possibility of enlarging the diameter of high-quality GaN crystals. In the present study, 2 in. GaN wafers with a radius of curvature larger than 100 m were successfully produced by the Na-flux coalescence growth technique. FWHMs of the 002 and 102 GaN X-ray rocking curves were below 30.6 arcsec, and the dislocation density was less than the order of 102 cm−2 for the entire area of the wafer.

This paper presents a deep learning-aided iterative detection algorithm for massive overloaded multiple-input multiple-output (MIMO) systems where the number of transmit antennas n is larger than that of receive antennas m. Since the proposed algorithm is based on the projected gradient descent method with trainable parameters, it is named the trainable projected gradient-detector (TPG-detector). The trainable internal parameters, such as the step-size parameter, can be optimized with standard deep learning techniques, i.e., the back propagation and stochastic gradient descent algorithms. This approach is referred to as data-driven tuning, and ensures fast convergence during parameter estimation in the proposed scheme. The TPG-detector mainly consists of matrix-vector product operations whose computational cost is proportional to mn for each iteration. In addition, the number of trainable parameters in the TPG-detector is independent of the number of antennas. These features of the TPG-detector result in a fast and stable training process and reasonable scalability for large systems. Numerical simulations show that the proposed detector achieves a comparable detection performance to those of existing algorithms for massive overloaded MIMO channels, e.g., the state-of-the-art IW-SOAV detector, with a lower computation cost.INDEX TERMS massive MIMO, overloaded MIMO, detection algorithm, deep learning VOLUME 4, 2016

In a previous study, we successfully obtained large-diameter, low-dislocation-density GaN wafer using the Na-flux multi-point seed (MPS) technique. However, the lattice constants of the GaN wafer grown by this technique expanded due to oxygen concentration in pyramidal facets. We here invented a breakthrough technique for the promotion of lateral growth, and succeed in suppressing pyramidal facet growth by residual flux formed after extraction of the MPS-GaN substrate from the Na-Ga melt in a crucible. The surface of the grown wafer was fully composed of the c-plane and showed low oxygen concentration, so expansion of lattice constants could be successfully prevented.

In this review, the history of research and development of the Na-flux method for growing single GaN crystals is summarized from its discovery in 1994 until the present. Underlying the development of the Na-flux method, which has become one of the more important technologies for growing high quality GaN crystals, there have been several important innovations without which it would have been impossible to achieve current technical levels. Here, we describe the development of the Na-flux method through these innovations, including a method for controlling nucleation by adding carbon, single- and multipoint seed techniques, and a hybrid of the flux-film coated and multipoint seed approaches.

Homoepitaxial hydride vapor phase epitaxy (HVPE) growth on GaN substrates grown with a Na-flux method, which is the most promising approach for fabrication of large-diameter, low-dislocation-density, fast-growing GaN wafers, was attempted for the first time. We found that, when different growth methods are combined, the differences in oxygen concentrations between a seed and grown crystal must be eliminated to maintain the crystallographic quality of the seed. Two kinds of Na-flux-grown seed crystals were prepared; one had a surface composed of c, {101̅2}, and {101̅1} planes, the other a surface composed entirely of c-planes. Both crystals were sliced, ground, mirror-polished, and applied for 500-μm-thick HVPE growth. In the former sample, the seed crystal generated fine cracks, and the epitaxially grown layer had a rough surface and included many dislocations; the latter sample showed no fault. For clarifying the mechanism of crystal degradation, we investigated the lattice constants of each growth sector using an X-ray microbeam and found that lattice constants in the {101̅1}-growth sector were expanded compared to those in other growth sectors due to oxygen impurities. These values were estimated to be much larger than those of HVPE crystals, resulting in the crystal degradation after the HVPE growth by a lattice mismatch.