It is well known that reconstruction problems, as the

cross-disciplinary subject, have been studied in numerous contexts

including statistical physics, information theory and computational

biology. My major contributions to the this field are to figure out

the tightness of the Kesten-Stigum reconstruction bound for both the

2q-state symmetric model with triple mutation probabilities and

the asymmetric binary channel on trees. Furthermore, we determine

asymptotics for the reconstruction thresholds on regular trees of

large degree.

GaN-based high electron mobility transistors (HEMTs) and monolithic microwave integrated circuits (MMICs) have emerged as a leading technology for power amplification at high frequency. N-polar GaN-based HEMTs are very promising to achieve high output power and high efficiency for solid-state millimeter wave power amplifiers. The advantages come from both the GaN material, and the polarization engineering enabled by the N-polar orientation. Harnessing these advantages, Romanczyk et al. reported a record-high 8.84 W/mm power density at 94 GHz from a N-polar GaN deep-recessed HEMT with a SiN gate dielectric.To further boost the high-frequency and high-power performance in N-polar GaN HEMTs, improving the gate structure is critical to enhancing both stability and gain during device operation. This dissertation is devoted to the evaluation of gate structures on N-polar GaN including MIS- and Schottky structures. Part of the evaluation is conducted through the MIS-capacitor and Schottky diode structures to understand the interface properties. Another part of the evaluation wis in the form of N-polar GaN deep recess HEMTs to pursue the high performance at 94 GHz. A series of MIS- capacitors consisting of SiN and AlSiO with different thicknesses on N-polar GaN were fabricated to investigate their interface states. An improved model combining the effects from interface states and bulk hole traps is proposed to extract the interface state density accurately. Based on the model, the Dit can be obtained by extrapolating the trap density to a zero-thickness dielectric. The average Dit value and the bulk trap parameters can be thereby quantified. The results, model and analysis presented provide new insights into studying Dit of various dielectrics on GaN and other wide-bandgap semiconductors. Schottky barrier diode of ruthenium (Ru) deposited by atomic layer deposition on N-polar GaN was investigated. The Schottky diodes showed near-ideal thermionic current behavior under forward bias and reverse bias at various temperatures. The barrier height was extracted to be 0.77 eV at room temperature. The combination of the 0.77 eV barrier and thermionic current characteristic resulted in < 2 µA/cm2 reverse current at -5 V, which is a record-low value for N-polar GaN Schottky diodes. ALD Ru gate was adopted into the N-polar GaN deep recess MIS- and Schottky HEMTs. The ALD Ru effectively fills the narrow T-gate stems aiding realization of shorter gate lengths with lower gate resistance than in prior work. For the ALD Ru MIS-HEMTs, the gate length was scaled down to 48 nm resulting in the demonstration of a record-high 8.1 dB linear transducer gain measured at 94 GHz by load-pull techniques. This increased gain has enabled a record 33.8% power-added efficiency (PAE) with an associated output power density (PO) of 6.2 W/mm. The Ru/N-polar GaN Schottky-HEMT operating at W-band has also shown good large signal performance. The fabricated Schottky HEMT with LG of 60 nm has a high peak extrinsic transconductance of 798 mS/mm with a gate leakage in pinch-off below 3  10-4 A/mm at VDS = 5V. The Schottky-HEMT shows high PAE of 27.1% and PO of 4.87 W/mm at 94 GHz and VDS,Q = 16V. The peak PAE is 31.8% with associated PO of 3.31 W/mm at VDS,Q = 12V.