Structural Parameters Of Low-dimensional Semiconductor Materials High-resolution X-ray Diffraction Study

In this paper x-ray diffraction dynamical theory and kinematicaI theory fbr low-dimension semi-conductor hetero-epitaxy materials are analyzed particularly and areaPplied to analyze the structure of 1ow-dimension semi-conductor. Originated fYomTakagi-Taupin equation and based waved-optics theory, the recursion fOrmulates ofreflection amplitude for arbitrary structure multi-layer is obtained. A matrix solutionfOr differential equation is presented fOr solving the problem of mathematics'calculation. Originating from x-ray dynamic theory and ignoring the effects of multi-reflection, the general fOrmulate of x-ray kinematical theory are obtained. Therefore,the theoretical system ofx-ray diftYaction is discussed entirely.Computer programs were writte11 using theory above to calculating the arbitrarystructure multi-layer conductor x-ray diftYaction. The experiment data is simulatedusing dynamical and kinematical theory respectively to get the structure parameters ofthe sample. So the validity of our theory are verified.The problem of x-ray diffraction for a parallel quantum wire array is consideredas that of a multi-slit Fraunhofer dif1Yaction. The modal x-ray diffraction of rectanglequantum-wire is established to simulate the experiment result successful to get thebasic parameters of quantum-wires. Considering the shape of quantum-wires, themodal x-ray diffraction of trapeze quantum-wire is established. The relationshipbetween Fourier transfOrms quantum wires shape and x-ray diffraction is presented toobtain the more exact info of parameters. So the fundamental characteristics of x-raydiffraction fOr quantum wire array are investigated.The GaAs/InAs/GaAs quantum-dots is dealed as strain sandwich structure,considering the large strain, using the kinematics theory of x--ray dil1Yaction of multi-layer of , experiment of x-ray diffraction from quantum-dot is simulated successfullyto obtain the strain and thick of each layer. The quantum dots are considered aspyramid shape approximately, therefore the ditTraction of dots is considered asdiffraction from triangle. The transverse period is obtained using the transform ofFourier. The trustiness of this modal is showed through comparing with the resultcome from Triple-Axis diffraction formula and result of STM.The reciprocal space map of x-ray difll-action for quantum-wires is simulatedsuccessfully. Abundant structural intbrmation such as array period, geometric shape,etching depth and strain state, etc. fOr quantum wires are obtained.The theory and model in this paper can be applied convenie11tly to analyze anddesign the structure of low-dimension conductor.