Fractional Order Theory in a Semiconductor Medium Photogenerated by a Focused Laser Beam

Abstract

In this paper, the fractional order theory has been applied for thermal, elastic and plasma waves to determine the carrier density, displacement, temperature and stress in a semiconductor medium. The thermal, elastic and plasma waves in a semi-infinite medium photogenerated by a focused laser beam were analyzed. The Laplace transformation is used to express the governing equation and solved analytically by applying eigenvalue approach methodology in that domain. A semiconducting material like as silicon was considered. According to the numerical results and graphics, the fractional order parameter and thermal relaxation time may play an important role in the behavior of all physical quantities.Keywords Ñ èñïîëüçîâàíèåì äðîáíîãî èñ÷èñëåíèÿ äëÿ îïèñàíèÿ òåïëîâûõ, óïðóãèõ è ïëàçìåííûõ âîëí îïðåäåëåíû êîíöåíòðàöèÿ íîñèòåëåé çàðÿäà, ñìåùåíèÿ, òåìïåðàòóðà è íàïðÿaeåíèÿ â ìàòåðèàëå ïîëóïðîâîäíèêà. Ïðîâåäåí àíàëèç ðàñïðîñòðàíåíèÿ òåïëîâûõ, ïëàçìåííûõ è óïðóãèõ âîëí â ïîëóáåñêîíå÷íîé ñðåäå ïðè âîçäåéñòâèè ñôîêóñèðîâàííîãî ëàçåðíîãî ëó÷à. Ìåòîäîì ïðåîáðàçî-âàíèÿ Ëàïëàñà íàéäåíî îïðåäåëÿþùåå ñîîòíîøåíèå, êîòîðîå ðåøåíî àíàëèòè÷åñêè íà îñíîâå ñîáñòâåííîãî çíà÷åíèÿ â äàííîé îáëàñòè. Èññëåäîâàíèå ïðîâåäåíî äëÿ ìàòåðèàëà ïîëóïðîâîäíèêà ñî ñâîéñòâàìè êðåìíèÿ. Ðåçóëüòàòû èññëåäîâàíèÿ ïîêàçàëè, ÷òî äðîáíûé ïàðàìåòð ïîðÿäêà è âðåìÿ òåïëîâîé ðåëàêñàöèè ìîãóò ñèëüíî âëèÿòü íà èçìåíåíèå âñåõ ôèçè÷åñêèõ âåëè÷èí.Êëþ÷åâûå ñëîâà: äðîáíîå èñ÷èñëåíèå, ôîòîòåðìîóïðóãèå âîëíû, ïîäõîä íà îñíîâå ñîáñòâåííûõ çíà÷åíèé, ëàçåðíûé ëó÷, ïðåîáðàçîâàíèå Ëàïëàñà