雾化辅助化学气相沉积法氧化镓薄膜生长研究

采用自主设计搭建的雾化辅助化学气相沉积系统设备,开展了Ga₂O₃薄膜制备及其特性研究工作。通过X射线衍射研究了沉积温度、系统沉积压差对Ga₂O₃薄膜结晶质量的影响。结果表明,Ga₂O₃在425~650 ℃温度区间存在物相转换关系。随着沉积温度从425 ℃升高至650 ℃,薄膜结晶分别由非晶态、纯α-Ga₂O₃结晶状态向α-Ga₂O₃、β-Ga₂O₃两相混合结晶状态改变。通过原子力显微镜表征探究了生长温度对Ga₂O₃薄膜表面形貌的影响,从475 ℃升高至650 ℃时,薄膜表面粗糙度由26.8 nm下降至24.8 nm。同时,高分辨X射线衍射仪测试表明475 ℃、5 Pa压差条件下的α-Ga₂O₃薄膜样品半峰全宽仅为190.8″,为高度结晶态的单晶α-Ga₂O₃薄膜材料。     

Periods of generalized Fermat curves

Let $k,n\ge 2$ be integers. A generalized Fermat curve of type $(k,n)$ is a compact Riemann surface S that admits a subgroup of conformal automorphisms $H\le \text{Aut}(S)$ isomorphic to ${\mathbb{Z}}_k^n$, such that the quotient surface $S/H$ is biholomorphic to the Riemann sphere $\stackrel{?}{\mathbb{C}}$ and has $n+1$ branch points, each one of order k. There exists a good algebraic model for these objects, which makes them easier to study. Using tools from algebraic topology and integration theory on Riemann surfaces, we find a set of generators for the first homology group of a generalized Fermat curve. Finally, with this information, we find a set of generators for the period lattice of the associated Jacobian variety.     

Hilbert’s Nullstellensatz for analytic trigonometric polynomials

This paper proves such a new Hilbert’s Nullstellensatz for analytic trigonometric polynomials that if ${\left\{f_j\right\}}_{j=1}^{n\ge 2}$ are analytic trigonometric polynomials without common zero in the finite complex plane $?$ then there are analytic trigonometric polynomials ${\left\{g_j\right\}}_{j=1}^{n\ge 2}$ obeying ${\sum }_{j=1}^{n\ge 2}{f}_j{g}_j=1$ in $?$, thereby not only strengthening Helmer’s Principal Ideal Theorem for entire functions, but also finding an intrinsic path from Hilbert’s Nullstellensatz for analytic polynomials to Pythagoras’ Identity on $?$.