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Nanoboyutlu yarıiletkenlerin yoğunluk fonksiyoneli kuramı ile tasarımı ve bilgisayar benzetimi

Computer simulation and design of nanoscale semiconductors by using density functional theory

  1. Tez No: 532312
  2. Yazar: HİKMET HAKAN GÜREL
  3. Danışmanlar: PROF. HİLMİ ÜNLÜ
  4. Tez Türü: Doktora
  5. Konular: Fizik ve Fizik Mühendisliği, Physics and Physics Engineering
  6. Anahtar Kelimeler: Bant yapısı, Basınç, Sonlu farklar yöntemi, Sıcaklık, Yarı iletkenler, Yoğunluk fonksiyonu teorisi, Band structure, Pressure, Finite differences method, Temperature, Semiconductors, Density function theory
  7. Yıl: 2011
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Bilişim Enstitüsü
  11. Ana Bilim Dalı: Hesaplamalı Bilim ve Mühendislik Ana Bilim Dalı (disiplinlerarası)
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: Belirtilmemiş.

Özet

Yoğun bilimsel araştırma geliştirme faaliyetleri, mevcut bilişimve elektronik haberleşme teknolojisinin belkemiği olan silikonyarıiletken cihazların boyutlarını ancak 2020 yıllarında 10-20nanometre boyutlarına indirebileceğini göstermektedir. Elektronikve optoelektronik cihazların boyutlarının ve hacimlerininküçültülmesinin bu cihazların hızlarının artırılması anlamınagelen bu yeni üretim yöntemi malzeme tasarımında birçok bilimselve teknolojik problemleri de beraberinde getirmektedir. Geleceğinelektronik ve optik cihazlarının tasarımında ve geliştirilmesindehesaplamalı nanobilim ve mühendislik önemli bir olgu olarakkarşımıza çıkmaktadır. Hatta, şu anda hayal edilmesi çok zor olanyeni bilim dallarının ve teknolojik ürünlerinin ortayaçıkmasındaki hesaplamalı bilim ve mühendisliğin önemi dünyada öndegelen temel bilimciler ve mühendisler tarafından kabul edilmekteve gelişmiş ülkeler bu konuda cesur biçimde maddi ve insangücüyatırımları yapmaktadır. Elektronik ve optik cihazların üretimindekullanılan nanoboyutlu yarıiletken malzemelerin elektronik veoptik özelliklerinin tasarımı ve bunlardan üretilecek olannanoyapı cihazların performansının tayini ve benzetimi bilimselolarak temel fiziksel ilkelere dayanan ve uygulamada gerçekçi olanmodeller ve simülasyon yöntemleri gerektirmektedir.Bu doktora tezinin hesaplamaları“YoğunlukFoksiyoneli Teorisi (Density Functional Theory) (DFT)”ilegerçekleştirilmiştir. Nanoboyutlu yarıiletkenlerin elektronik ve optiközelliklerinin büyütme, arayüz gerilme (ing. strain), alaşım yüzdesi, sıcaklık ve basınçkoşulları altında tasarımı ve bilgisayar benzetimi yapılacaktır.Nanoyapı yarıiletken malzemelerin bant aralıkları, arayüzpotansiyel engelleri, etkin kütle ve optik geçirgenlik gibi temelfiziksel parametrelerin değerleri enerji-momentum uzayı'ndahesaplanan enerji değerlerinden elde edilecek deneysel ve diğerhesaplama yöntemlerinden elde edilen sonuçlarlakarşılaştırılacaktır.

Özet (Çeviri)

Intensive scientific research and development activities show that the existing information technology and electronic communication is the bases of the size of silicon semiconductor devices, but 2020 is the future of the 10-20 nanometer dimensions. Size and volume of electronic and optoelectronic devices were minimized to increase the speed of the device; however this brings about many scientific and technological design problems in their new production methods.Electronic and optical devices of the future design and development of nano science and computational engineering is quite important role. In fact, today it is hard to imagine, the new diciplines and technological products of the emergence of the computational science and engineering in the world the importance of the leading life scientists and engineers, by accepting and advanced countries in this respect the brave material and manpower to make investments.Electronic and optical devices used in the production of nano-sized semiconductor materials electronic and optical properties of the design and production of these nano structure with the performance of the device and the determination of simulation as a scientific basis, based on physical principles and practice are realistic models and simulation methods are needed.In recent decades, III-V, II-VI and III-N based materials have been studied intensively. III?V compound semiconductors provide the materials basis for a number of well-established commercial technologies, as well as new cutting-edge classes of electronic and optoelectronic devices. Just a few examples include high-electron-mobility and heterostructure bipolar transistors, diode lasers, light-emitting diodes, photodetectors, electro-optic modulators, and frequency-mixing components.Group II?VI semiconductors and their heterostructures are well known to form ternary and quaternary alloys with a direct fundamental band gap over most of alloy composition range with high absorption coefficients, which can be used as materials for fabricating thin film heterojunction photovoltaic (PV) devices. The principal energy gaps of ternary and/or quaternary II?VI semiconductor alloys can cover various light spectra over the entire composition and lattice parameters can be tailored independently to fabricate photovoltaic devices on suitable lattice matched substrates.Group III- nitride compounds (GaN, AlN, InN) and their ternary alloys (AlGaN, InGaN, InAlN) have been the subject of intense work in recent years due to the possibility to achieve blue or ultraviolet light emitting and laser diodes, blue resonant-cavity light emitting diodes, surface-emitting lasers, and solar blind ultraviolet photodetectors, as well as high-power high-frequency field-effect transistors.There are many theoretical and experimental studies because of their potentials in making optical and electronic applications. Current growth techniques give an opportunity to control of the growth conditions and material properties of semiconductor structures. Usage of these materials in device applications needs a reliable modeling of their structural, electronic and optical properties.The calculations of the Phd. Thesis carried out by using Density Functional Theory (DFT). The DFT calculations of cubic semiconductors carried out by using the full potential linear augmented plane-wave method plus local orbitals as implemented in the WIEN2k code. Main aim is to predict the electronic properties of III-V, II-VI and III-N related binaries. Results are given for electronic properties (e.g., band structure, density of states, band gaps and band widths) of III-V, II-VI and III-N related binaries. The proposed model uses various exchange-correlation potential to determine band gaps of semiconductors at $\Gamma$, L and X high symmetry points of Brillouin zone. Self-consistent iteration is used for calculation and the iteration repeated until converges to less than $10^{-4}$ Ryd.Most of the theoretical calculations have been performed by using density functional theory (DFT) for semiconductors. DFT calculations give satisfactory ground state properties such as total energies, lattice constant, and bulk modulus. On the other hand, the calculations performed by using conventional DFT give unsatisfactory electronic properties such as band gaps and effective masses. Calculated band gaps are much smaller than those of experimental and theoretical data. Using different approaches such as GW approximation or hybrid functionals overcomes the band gap problem. Even GW and hybrid functionals result in band gap error on the order of $10-20\%$ compared to experimental data.Since the calculated band gaps are much smaller than those of experimental and theoretical data, the exchange correlation potential contribution to the DFT band gap was shifted by using a scissor operator. The difference between the local density approximation (LDA) and experimental band gaps, $\Delta E$, scales with the electronic part of the dielectric constant $\varepsilon_\infty$ as $\Delta E \sim 9.1/\varepsilon_\infty$. Local spin density approximation (LSDA) and generalized gradient approximation (GGA) band gap calculations were shifted by using the scissor operator for III-V, II-VI and III-N related binaries. These calculated energies (especially band gaps) and other physical parameters compared with the available experimental data and other theoretical results. The results show a good agreement with the available experimental and theoretical data.On the other hand, Modified Becke-Johnson (MBJLDA) density potential is presented for Cd and Zn based binaries. In the present calculations using MBJLDA, it was obtained satisfactory band gap values according to the experimental data and there is no need to shift or correct the calculated band gaps as LSDA or GGA.Due to the band gap problem in DFT, using different parameterized schemes (LDA, LSDA, GGA, MBJLDA) results in different values. In some cases, the difference between present results and cited values are rather big. Different parameterized schemes was compared with available theoretical and experimental data since main goal is to show how different methods affect band gap and band properties.After obtaining optimized results for III-V, II-VI and III-N binaries, the model was extended to ternary semiconductors such as AlGaAs, CdSTe, ZnSSe and AlGaN etc. Computer simulation and design of electronic and optical properties of ternary semiconductors carried in terms of interface strain, composition percentage and band offset. The calculated band properties give a good agreement with the available experimental and theoretical data.Temperature and pressure are an important issues for semiconductors. Different materials behave differently under various pressure and temperature conditions. These conditions especially affect to electronic band properties such as band gap (direct or indirect band gap) and effective mass (mobility of the electrons). In order to show how different conditions affect band properties, band gap properties of III-V, II-VI and III-N binaries it was calculated under high pressure and temperature . These calculated energies compared with the available experimental data and other theoretical results.Reduction in dimensionality produced by confining electrons to a thin layer leads to change in their behavior. The dimensionality refers to number of degrees of freedom. For example, the electron is confined across two directions in the quantum wire.To understand the behavior of the low dimensional semiconductors such as quantum well, quantum wire and quantum dot, it was solved the Schrödinger's equation. It is impossible to solve Schrödinger's equation analytically for a various potential profiles. Under these circumstances it is possible to solve Schrödinger's equation numerically using any numerical technique such as finite difference method. In this context, it was calculated the well, wire and dot ground state energies as a function of well width or wire (dot) radius. Different composition values allow us to define potential barriers. Using basic concept of the finite difference method and potential profile it can be easily solved the Schrödinger's equation. The calculated energies compared with the available analytical results.In conclusion, the present thesis focuses on DFT band gap problem. It is suggested a scissor operator for semiconductor binaries and ternaries. It was also calculated band properties as a function of composition, strain, pressure and temperature. All these calculated properties compared with the available experimental data and other theoretical results. Our model gives a good agreement with the available experimental and theoretical data for a wide range semiconductors.

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