脈衝雷射激發引致彈性波傳與電磁輻射之有限元素分析

Abstract

壓電晶體能夠利用壓電效應，將機械能和電磁能互相轉換，在這些晶體結構中，壓電效應主要由材料本身的晶格變形來實現，電場與機械應變之間的耦合強度取決於單一材料的固有特性，因此耦合相對較弱，在過去，很多研究都致力於提高能量耦合強度。 而壓電超晶格是一種具有週期性的結構的壓電材料，它通常由兩種不同極化方向的壓電晶體交替排列而成，通常透過施加外部電場(電磁式激發)，將輸入的機械能和電磁能透過強耦合的方式產生出電磁輻射。相較於前面提到的壓電晶體，壓電超晶格具有較強的能量耦合程度。然而，電磁式激發中的電極會影響電場的分布，因此，本研究將會專注於機械式激發的部分。雖然多數的機械式激發方法都會直接接觸材料而影響波傳，但在過去研究中，有學者利用非破壞性檢測的脈衝雷射，在材料的表面和內部激發出不同種類的機械波傳，而脈衝雷射不須直接接觸材料，因此是眾多的機械式激發方法中，不錯的嘗試。 本論文的研究目的主要分成兩部分，第一部分為探討壓電晶體弱耦合射出電磁波的理論和模擬，透過等效電路模型和赫茲電偶模型推論出輻射功率，並利用商用有限元素COMSOL模擬軟體的壓電模組和電磁波模組來模擬弱耦合的現象，算出遠場輻射的功率，再和理論解模型去做比對。第二部分則是模擬脈衝雷射激發壓電超晶格的波傳現象，先列出基本的運動方程式和熱傳導方程式，然後聯立解出此微分方程式的諧振解，得到溫度隨時間變化的函數。接著再用COMSOL模擬軟體的熱傳模組和固體力學模組兩者耦合的熱膨脹模組來驗證先前的結果，好觀測出體波在鈮酸鋰晶體中傳遞的情況。

Piezoelectric crystal is a kind of material that can convert mechanical energy and electric energy by utilizing piezoelectric effect. When piezoelectric crystal is subjected to external mechanical stress or vibration, it will generate charge separation or movement, which in turn will generate voltage and electric field. If we equate the electric field to an external current, it can be used as an excitation source to radiate electromagnetic waves like an antenna. While piezoelectric superlattice is a kind of piezoelectric material with periodic structure, which usually consists of piezoelectric crystals alternately arranged in two different polarization directions, with phonons representing mechanical wave propagation, photons representing electromagnetic wave propagation, and polariton generated by strong coupling of mechanical and electromagnetic waves. Compared to weakly coupled piezoelectric crystals, this material can radiate electromagnetic waves of greater energy. Piezoelectric superlattices are usually excited by electromagnetic inputs. Mechanical excitation is not common in practice because it usually touches the material and affects the wave propagation phenomenon. However, pulse lasers do not require direct contact with the material and are therefore a good alternative to mechanical excitation methods. By using the principle of thermal expansion and contraction, thermal stress is continuously generated around the material, which can be used as a high-frequency vibration source. This paper is divided into two parts, the first half of which is to explore the theory and simulation of weakly coupled electromagnetic waves emitted from piezoelectric crystals. The radiant energy is deduced from the equivalent circuit model and the Hertzian dipole model, and the weakly coupled phenomenon is simulated by using piezoelectric and electromagnetic wave modules of the COMSOL simulation software, and compared with the theoretical model. In the second half, the wave propagation phenomenon of pulsed laser in piezoelectric superlattice and the temperature change of the crystal are simulated. The distribution of heat flow inside the two-dimensional isotropic material is given first, so as to list the basic equations of motion and thermal conduction equations, and finally the harmonic solution of this differential equation is solved jointly to get the function of temperature change with time. Then, the thermal expansion module of COMSOL simulation software is used to verify the previous results, and the laser parameters are adjusted after confirming the accuracy, so as to further determine what kind of pulse laser specification is needed to produce the results of BAW with a frequency of 76 MHz.