Photonic Materials /[광자 재료] -...

The Science & Engineering of Materials

Photonic Materials /[광자 재료]

Chapter 20. Photonic Materials

1. 왜 하늘은 파랗게 보이는가? 2. 광섬유(광통신용)는 어떻게 작동하는가? 3. 어떤 요인이 재료에서 빛의 투과 또는 흡수를 조절하는가? 4. Laser의 용어는 무엇을 의미하는가? 5. 루비 레이저는 무엇으로 만들어 지는가? 6. 형광등의 작동원리는 인광현상을 포함하는가?

용어 정의: Laser, X-ray, fluorescence, LED, Photon, Solar cell, dispersion


Introduction

Optical properties of materials are related to the interaction of a material with electromagnetic radiation in the form of wave or particles of energy called photons(광자)

Gamma (γ) rays are produced by change in the structure of the nucleus of the atom; x-rays, ultraviolet radiation, and the visible spectrum are produced by changes in the electronic structure of the atom. Microwaves and radio waves are low-energy, long-wavelength radiation caused by the vibration of atoms or the crystal structure. [단파장(high frequency) 높은 E]

When photons interact with a material, a variety of optical effects can be produced, including absorption, transmission, scattering, diffraction, reflection, refraction, and the generation of voltage. 질문: 상기 Light들에 대해 에너지가 높은 순서대로 열거해 보세요!!


20.1. The Electromagnetic Spectrum

λhchvE ==

Light is energy, or radiation, in the form of wave or particles called photons that can be emitted from a materials.

Energy: E [eV]

Wavelength: λ [nm]

Frequency: v

Photon either as a particle of energy E or as a wave with a characteristic wavelength and frequency.

= 1240 / λ

예제: 가시광의 파장은 400~800 nm이다. 이에 해당하는 Energy[eV]를 구하시오.

빛(light): 에너지, 복사파


20.1. The Electromagnetic Spectrum

[전자기파 스펙트럼] [파장대별 빛의 명칭!!]

[Fig. 20-1]

Microwaves are radio waves with wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz (0.3 GHz) and 300 GHz.[1]

Microwave

http://en.wikipedia.org/wiki/Radio_waveshttp://en.wikipedia.org/wiki/Wavelengthhttp://en.wikipedia.org/wiki/Frequencyhttp://en.wikipedia.org/wiki/Hertz


20.1. The Electromagnetic Spectrum [Fig. 20-1]

[재료의 밴드갭 Eg와 빛의 파장 관계!!]

λ = 1240 / Eg


20.2. Refraction, Reflection, Absorption, and

Transmission

• All materials interact in some way with light. Photons cause a number of optical phenomena when they interact with the electronic or crystal structure of a material.

• The photons may give up their energy to the material, in which case absorption occur.

• The photons may give up their energy, but photons of identical energy are immediately emitted by the material; in this case, reflection occur.

• The photons may not interact with the electronic structure of the material; in this case, transmission occur.

• Even in transmission, however, photons are changed in velocity and refraction occur.

tar IIII ++=0

[Fig. 20-2]

빛의 진행 방향은 굴절률(n)에 의해 변화함!!

θi

Incident or refracted angle에서 기준이 되는 선은?


The absorption index (k) as a function of wavelength: 각각의 재료에 따른 파장의 함수로 나타낸 흡수계수 k. 가시광 영역에서 금속과 반도체는

흡수계수가 높게 나타난다. 이유는? Eg의 크기로 설명 됨!!!


Transmission [Fig. 20-2]

λ = 1240 / Eg


Refraction

εµ ⋅=

1c

Even when a photon is transmitted, the photon causes polarization of the electrons in the material and, by interacting with the polarized material, loses some of its energy.

The speed of light : C

Permittivity: ε

Permeability: μ

t

iVaccum

ccn

θθ

λλ

sinsin0 ===

n : index of refraction

Θi : incident beam angle[진공]

Θt : refracted beam angle[물질]


Transmission: refraction [굴절]

참고: 재료가 쉽게 분극되면, 광자와 재료의 상호작용이 크게 나타남


Index of refraction of selected materials for photons of wavelength 5890Å.


Transmission: refraction

모든 재료의 굴절계수는 1보다 크다. 이유를 굴절계수의 정의를 사용해서 설명하시오.

[Table 20-1]

t

iVaccum

ccn

θθ

λλ

sinsin0 ===

Light가 진공에서 물질내부로 진입시

** [굴절율(계수)]을 정의하세오.


When a ray of light enters from material 1 into material 2, if the refractive index of material 1 (n1) is greater than that of material 2 (n2), then the ray bends away from the normal and toward the boundary surface.[1,9]

t

i

nn

cc

θθ

sinsin

1

2

2

1 ==Snell’s law



(Eq. 20-7a)

[Fig. 20-3]

매우 중요: 입사각과 굴절각(θt)의 정의 방법, Snell의 법칙 암기와 적용

재료 1 재료 2

조건: n1 > n2 공기 물


(b) Diagram a light beam in glass fiber for Example 20-1: 광섬유가 공기로 둘러 쌓여(clading) 있을 때를 가정함.

[예제 20-1] : 광섬유를 통과하는 빛의 손실을 없게하기 위한 조건은??


Transmission: refraction [Fig. 20-3]

광섬유, n=1.50

공기


∞=≅== kccn

000

0

εε

εµµε

The electronic polarization is the one that controls the refractive index of materials.

Relationship between the index of refraction (n) and the high frequency dielectric constant (k∞) of the material[비자성 재료의 경우].



** 굴절율(n)의 정의 방법!!


λλ ddnDispersion =)(

Dispersion of a material is defined as the variation of the refractive index with wave length.

This dependence of the refractive index on wavelength is nonlinear.

The dispersion within a material means light pulses of different wavelengths, starting at the same time at the end of an optical fiber, will arrive at different times at the other end. Thus, material dispersion plays an important role in fiber optics. This is one of the reasons why we prefer to use a single wavelength source of light for fiber-optics communications.

Dispersion also causes chromatic aberration in optical lenses.

Since dielectric polarization (P) is equal to the dipole moment per unit volume and the high frequency dielectric constant is related to the refractive index, we expect that, for the same material, a denser form or polymorph will have a higher refractive index.[굴절율의 정의에서 유추 가능함]




When a beam of photons strikes a materials, the photons interact with the valence electrons and give up their energy. In metals, the radiation of almost any wavelength excites the electrons into higher energy levels. One might expect that, if the photons are totally absorbed, no light would be reflected and the metal would appear to be black. In aluminum or silver, however, photons of almost identical wavelength are immediately reemitted as the excited electrons return to their lower energy levels-that is, reflection occurs. Since virtually the entire visible spectrum is reflected, these metals have a white, or silvery, color. In metals, the reflectivity is typically on the order of 0.9 to 0.95, whereas the reflectivity of typical glasses is nearer to 0.05. The high reflectivity of metals is one reason that they are opaque.


Transmission: reflection [반사]

** 빛의 흡수와 반사 및 color?


2)11(

+−

=nnR

2)(i

i

nnnnR

+−

=

The reflectivity R gives the fraction of the incident beam that is reflected and is related to the index of refraction. If the material is in a vacuum or in air:

If the material is in some other medium with an index of refraction of ni, then

There are many applications where we want materials to have very good reflectivity such as mirrors and certain types of coatings on glass.


Transmission: reflection

결론: 상기에서 보듯이, 높은 굴절계수 n를 갖는 재료는 높은 반사도를 갖는다.

굴절율과 반사도의 관계


)exp(0 xII α−=

That portion of the incident beam (that is not reflected by the material) is either absorbed or transmitted through the material. The fraction of the beam that is absorbed is related to the thickness of the material and the manner in which the photons interact with the material’s structure. The intensity of the beam after passing through the material is given by

x : path through which the photons move α : linear absorption coefficient Io : Intensity of the beam after reflection at the front surface I : Intensity of the beam when it reaches the back surface


Transmission: absorption

하늘이 파란색을 갖는 이유는 파란빛의 파장이 공기와 심하게 산란되기 때문임. 높은 원자번호를 갖는 원자와 낮은 광자에너지의 경우 심하게 산란을 일으킴. 광전효과는 광자의 E가 전자와 핵사이의 결합을 절단하는데 충분해야 발생함.

tar IIII ++=0


The linear absorption coefficient relative to wavelengths for several metals.

Note the sudden decrease in the absorption coefficient for wavelengths greater than the absorption edge.

As the energy of the photon increases (or the wavelength decreases) less absorption occurs until the photon has energy equal to that of the binding energy. At this energy, the absorption coefficient increase significantly: absorption edge. [흡수단의 의미와 응용사례: 단색 X선 제조]


Transmission: absorption [Fig. 20-4]

AE


Characteristic emission lines and absorption edges for selected elements


Transmission: absorption [Table 20-2]


1. I reflected at front surface = RI0 , I after reflection = (1-R)I0 2. I after absorption = (1-R)I0 exp (-αx)

3. I reflected at back surface =R(1-R)I0 exp(-αx)

4. I transmitted = I after absorption – I reflected at back = (1-R)I0 exp(-αx) – R(1-R)I0 exp(-αx)

= (1-R)(1-R)I0 exp(-αx)

It = I0(1-R)2exp (-αx)


Transmission: Transmission [Fig. 20-5]

Original beam이 입사시, 반사, 흡수, 투과의 분율

공기 물질

굴절률이 작은 곳에서 큰 물질로 빛의 진행 경우:


• The intensity of the transmitted beam depends on the wavelength of the photons in the beam. If, however, longer wavelength photons are absorbed more than the shorter wavelength photons, we expect the transmitted light to appear blue or green.

• There are two cutoff frequencies in dielectric materials. The short, wavelength-side absorption edge is determined by the bandgap (Eg) of the dielectric. The long, wavelength-side absorption edge is determined by the interaction of relatively low energy photons with the lattice vibrations or phonons.

• Thus, for dielectric materials, there exists a “window” in which the transmission occurs easily. This will be between wavelengths that correspond to the optical absorption edge and the higher wavelength edge dictated by the phonon-photon interactions.

• The intensity of the transmitted beam also depends on microstructural features (ex., Porosity, Crystalline precipitates).

Typically, smaller pores or precipitates cause a greater reduction in the transmission of light.


Transmission: Transmission

투과된 빛의 세기와 color의 예측 방법


Relationships between absorption and the energy gap (Eg):

(a) Metal: no band gap (b) Dielectrics and intrinsic

semiconductors: Eg

(c) Extrinsic semiconductors:

Ea or Ed의 크기와 Photon E


Transmission: Transmission [Fig. 20-6]

빛의 흡수가 일어나는 원인을 에너지갭의 크기와 연관시켜 이해!!

λ = 1240 / Eg


(a) Photoconduction in semiconductors involves the absorption of a stimulus by exciting electrons from the valence band to the conduction band. Rather than dropping back to the valence band to cause emission, the excited electrons carry a charge through an electrical circuit. [Eg와 photoconduction 위한 최대 입사빔의 파장 관계]

(b) A solar cell takes advantage of this effect

gEhc

=maxλ


Transmission: Photoconduction [Fig. 20-7]


Elements of a photonic system for transmitting information involves a laser or LED to generate photons an electrical signal, optical fibers to transmit the beam of photons efficiently, and an LED receiver to convert the photons back into an electrical signal. [광통신의 원리]


Transmission: Solar cells & LEDs [Fig. 20-8]

light의 발생

light의 전송

Light의 수신/변환 Example 20-1 의 조건 만족


20.3. Selective Absorption, Transmission, or

Reflection

• In certain materials, replacement of normal ions by transition or rare earth elements produces a crystal field, which creates new energy levels within the structure. This phenomenon occurs when Cr3+ ions replace Al3+ ions in Al2O3. The new energy levels absorb visible light in the violet and green-yellow portions of the spectrum. Red wave-lengths are transmitted, giving the reddish color in ruby. [루비가 빨간색 나는 이유]

• Glasses can also be doped with ions that produce selective absorption and transmission (ex., Photochromic glass).

• Electron or hole traps, called F-centers, can also be present in crystals. When fluorite (CaF2) is produced so that there is excess calcium, a fluoride ion vacancy is produced. To maintain electrical neutrality, an electron is trapped in the vacancy, producing energy levels that absorb all visible photons-with the exception of purple.

• Polymers-particularly those containing an aromatic ring in the backbone can have complex covalent bonds that produce an energy level structure that causes selective absorption.


Effect of ions on colors produced in glasses.

20.3. Selective Absorption, Transmission, or

Reflection [Table 20-3]

**Glass에 doping된 이온이 Color를 내는 이유 energy gap내에 extra energy level를 만들어 특정 파장을 흡수하기 때문.

숙제: Example 20-1,2,3,4 1: Fiber Optic System의 설계 2: Polyesthylene에서 빛의 전달 3: 임계 energy gap 결정 4: Radiation shield의 설계


20.4. Example and Use of Emission Phenomena:

Gamma Rays

Gamma (γ) ray, which are very high-energy photons, are emitted during the radioactive decay of unstable nuclei of certain atoms.

The energy of the gamma rays therefore depends on the structure of the atom nucleus and varies for different materials.

The gamma rays can be used as the radiation source to detect defects lying within a material (a nondestructive test).

Gamma ray의 파장범위: < 1Å


X-rays, which have somewhat lower energy than gamma rays, are produced when electrons in the inner shells of an atom are stimulated.

The stimulus could be high-energy electrons or other x-rays. When stimulation occurs, x-ray of a wide range of energies are emitted. Both a continues and a characteristic spectrum of x-rays are produced.

Suppose that a high-energy electron strikes a material. As the electron decelerates, energy is given up and emitted as photons. Each time the electron strikes an atom, more of its energy is given up.[연속 스펙트럼]

Each interaction, however, may be more or less severe, so the electron gives up a different fraction of its energy each time and produces photons of different wavelengths. A continuous spectrum is produced [연속 X선 스펙트럼의 생성 원리].


X-rays 전자의 감속!!


• The minimum wavelength of x-rays produced is called the short wavelength limit λswl. The short wavelength limit decreases, and the number and energy of the emitted photons increase, when the energy of the stimulus increases.

• The incoming stimulus may also have sufficient energy to excite an electron from an inner-energy level into an outer-energy level. The exited electron is not stable and, to restore equilibrium, electrons from a higher level fill the empty inner level. This process leads to the emission of a characteristic spectrum of x-rays that is different for each type of atom. [특성 X선 스펙트럼의 생성 원리].


X-rays

연속스텍트럼과 특성스펙트럼이 발생하는 원인을 이해 해야 함 : 그림 20-10과 20-11를 결부시켜 설명.


The continuous and characteristic spectra of radiation emitted from a material.

Low-energy stimuli produce a continuous spectrum of low-energy, long-wavelength photons.

A more intense, higher energy spectrum is emitted when the stimulus is more powerful until, eventually, characteristic radiation is observed.


X-rays [Fig. 20-10]

* 연속스펙트럼 발생 원리: 높은 에너지의 전자가 재료에 입사하면 재료와 상호작용으로 전자는 감속되면서 연속스펙트럼을 발생. [그림 20-9 참조].


Characteristic x-rays are produced when electrons change from one energy level to a lower energy level, as illustrated here for copper.

The energy and wavelength of the x-rays are fixed by the differences between the energy levels.


X-rays

λ = 1240 / Eg

[Fig. 20-11]

Kα 와 Kβ 의 발생원리상 차이점? 파장의 길이는?

Transition!!


Luminescence(발광) occurs when the incident radiation excites electrons from the valence band, through the energy gap, and into the conduction band. When the electrons drop back to the valance band, photons are emitted. If the wavelength of these photons is in the visible light range, luminescence occurs.

In fluorescence(형광), all of excited electrons drop back to the valance band and the corresponding photons are emitted within a very short time (~10-8 seconds) after the stimulus is removed.

Phosphorescent(인광) materials have impurities that introduce a donor level within the energy gap. The stimulated electrons first drop into the donor level and are trapped. The electrons must then escape the trap before returning to the valance band. There is a delay before the photons are emitted. When the source is removed, electrons in the traps gradually escape and emit light over some additional period of time [2 steps drop].


Luminescence


In metals, there is no energy band gap, so luminescence does not occurs

Luminescence is the conversion of radiation or o ther forms o f energy to visible light.


Luminescence [Fig. 20-14]

λ = 1240 / Eg

(a)


Fluorescence occurs when there is an energy gap (Eg).

In fluorescence, all of the excited electrons drop back to the valence band and the corresponding photons are emitted within a very short time (~10-8 sec) after the s t i m u l u s i s r e m o v e d .



(b)

λ = 1240 / Eg

* 발광이 나타나기 위한 Eg의 범위를 구하라[단, 가시영역은 400~800nm로 가정]


Phosphorescence occurs when the photons are emitted over a period of time ( > 10-8 sec) due to donor traps in the energy gap.

Phosphorescent materials have impurities that introduce a donor level within the energy band gap.

τt

II

−=)ln(0

τ : relaxation time



* 형광과 인광의 차이를 에너지 밴드 구조 측면에서 구분 설명하시오.

λ = 1240 / (Eg-Ed)


LEDs are p-n junction devices engineered so that the Eg is in the visible spectrum.

A voltage applied to the diode in the forward-bias direction causes holes and electrons to recombine at the junction and emit photons.

GaAs, GaP, GaAlAs, and GaAsP are typical materials for LEDs.


Light –Emitting Diodes

Diagram of a light-emitting diode (LED).

A forward-bias voltage across the p-n junction produces photons.

[Fig. 20-15]

* LED를 정의하시오. [Cf. Direct band Gap]


λ = 1240 / Eg

Sapphire substrate

GaN buffer layer

n-GaN

InGaN

P-GaN

P-electrode

n-electrode

Active region

+ _


Light –Emitting Diodes


In certain materials, electrons excited by a stimulus produce photons which, in turn, excite additional photons of identical wavelength. Consequently, a large amplification of the photons emitted in the material occurs [레이저 발생 원리].

The output of the laser is a beam of photons that are parallel, of the same wavelength, and coherent. In a coherent beam, the wavelike nature of the photons is in phase, so that destructive interference does not occur.

Lasers are useful in heat treating and melting of metals, welding, surgery, mapping, transmission and processing of information, and a variety of other applications, including reading of the compact disks used to produce noise-free stereo recordings. [Laser의 응용사례]

LASER: Light Amplification by Stimulated Emission of Radiation


Lasers


The laser converts a stimulus into a beam of coherent photons. The mirror on one side is 100% reflecting, the mirror on the right transmits partially. [Laser 장치의 구조]


Lasers [Fig. 20-16]


Creation of a laser beam from a semiconductor: (a) 전자가 전도대로 여기됨, (b) 전자 1개가 홀 1개와 재결합 하면서 광자 1개를 생성, 그 광자가 재결합을 통해서 2개의 광자가 생기도록 자극함, (c) 광자들이 반사되면서 더 많은 광자를 생성하도록 자극함, (d)일부의 광자는 Laser빔으로 방출되고 나머지는 재결합을 유도하도록 stimulate. [ laser의 발생원리 설명].


Lasers [Fig. 20-17]

VB

CB


Schematic cross-section of a GaAs laser. Because the surrounding p-and n-type GaAlAs layers have a higher energy gap and a lower index of refraction than GaAs, the photons are trapped in the active

GaAs layer. [p-and n-type GaAlAs layers의 기능에 대해 이해].


Lasers [Fig. 20-18]

λ = 1240 / Eg

Eg


When a material is heated, electrons are thermally excited to higher energy levels, particularly in the outer energy levels where the electrons are less tightly bound to the nucleus. The electrons immediately drop back to the normal levels and release photons, an event known as thermal emission.

By measuring the intensity of a narrow band of the emitted wavelengths with a pyrometer, we can estimate the temperature of the material. [온도가 높아지면, 강도는 높아짐] .


Thermal Emission [열전자 여기]

Intensity in relation to wavelengths of photons emitted thermally from a material. As the temperature increases, more photons are emitted from the visible spectrum.

[Fig. 20-19]

color

λ = 1240 / Eg


20.5. Fiber Optics Communication System

Schematic of a fiber-optic based communication system. [광통신의 개념도]

[Fig. 20-20]

[발신기]

[수신기]

[광전달]

** Fiber에 들어온 광은 케이블 표면으로 못 나가도록 100% 굴절되도록 설계해야함.


Generating the signal: The light should be coherent and monochromatic (Laser, LED). By varying the voltages applied to the devices, the intensity of the photon beam can be varied. The intensity of the beam can then be exploited to convey information.

Transmitting the Beam: Optical fibers transmit the information. The optical fiber must have exceptional transparency and must not leak any light (Ultra high purity silica, Refractive index control, Graded refractive index).

Receiving the signal: The job of a receiver in the fiber optic system is to convert the optical signal into an electronic signal (Semiconductor photodiodes).

20.5. Fiber Optics Communication System

** Fiber 광통신의 원리를 설명하시오!!


Fig. 20-21. A step index glass fiber, in which the index of refraction is slightly different in each glass.

20.5. Fiber Optics Communication System [Fig. 20-21]

** Fiber에 들어온 광은 캐이블 표면으로 못 나가도록 설계. cladding에서 100% 굴절 되어 core 로 광이 되돌아 오게 해야 함 굴절 계수 조합!!

(a)


The profile of a refractive index in a graded refractive index (GRIN) fiber.


(b)

Fiber의 굴절 계수를 순차적으로 변화(중심은 높고, 주변은 낮게)시키는 기술인 GRIN.

고

저


The path of rays entering at different angles.


(c)

** 핵심사항: Fiber의 굴절 계수가 cladding 재료의 굴절계수보다 크게 설계하면, 빛은 fiber를 벗어나지 않고 긴 거리를 절달 가능함.

[낮은 굴절계수]

[높은 굴절계수]


1. Example 20-7, 8, 9를 이해하고 풀이과정을 제출하시오. 20-7: X-ray filter의 설계 20-8: XRD를 위한 X-ray의 제조 20-9: Energy Dispersive X-ray Analysis

2. 다음의 용어를 정의하시오 Laser, X-ray, fluorescence, LED, Photon, Solar cell, dispersion

숙 제

Chapter 20. Photonic Materials

슬라이드 번호 1슬라이드 번호 2슬라이드 번호 3슬라이드 번호 4슬라이드 번호 5슬라이드 번호 6슬라이드 번호 7슬라이드 번호 8슬라이드 번호 9슬라이드 번호 10슬라이드 번호 11슬라이드 번호 12슬라이드 번호 13슬라이드 번호 14슬라이드 번호 15슬라이드 번호 16슬라이드 번호 17슬라이드 번호 18슬라이드 번호 19슬라이드 번호 20슬라이드 번호 21슬라이드 번호 22슬라이드 번호 23슬라이드 번호 24슬라이드 번호 25슬라이드 번호 26슬라이드 번호 27슬라이드 번호 28슬라이드 번호 29슬라이드 번호 30슬라이드 번호 31슬라이드 번호 32슬라이드 번호 33슬라이드 번호 34슬라이드 번호 35슬라이드 번호 36슬라이드 번호 37슬라이드 번호 38슬라이드 번호 39슬라이드 번호 40슬라이드 번호 41슬라이드 번호 42슬라이드 번호 43슬라이드 번호 44슬라이드 번호 45슬라이드 번호 46슬라이드 번호 47

Photonic Materials /[광자 재료] -...

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