Transcript 물실2오리엔테이션
물리실험II 오리엔테이션 • • • • FRESNEL EQUATIONS, BREWSTER'S LAW FARADAY EFFECT MUON DECAY MEASUREMENT OF LOW RESISTANCES : 4 PROBE METHOD, LOCK- IN AMPLIFIER FRESNEL EQUATIONS, BREWSTER'S LAW 𝑛1 cos 𝜃𝑖 − 𝑛2 cos 𝜃𝑡 𝑅𝑠 = 𝑛1 cos 𝜃𝑖 + 𝑛2 cos 𝜃𝑡 2 𝑛1 cos 𝜃𝑡 − 𝑛2 cos 𝜃𝑖 𝑅𝑃 = 𝑛1 cos 𝜃𝑡 + 𝑛2 cos 𝜃𝑖 2 FRESNEL EQUATIONS, BREWSTER'S LAW He-Ne Laser Polarizer Half-cylindrical Lens Photometer FARADAY EFFECT Linear polarization= Right hand circular polarization + Left hand circular polarization Verdet constant, FARADAY EFFECT Flint glass (SF6) Analyzer 5 color tunable He-Ne laser system Polarizer Teslameter MUON DECAY Muon(𝝁): an elementary particle similar to the electron. Charge -1, spin ½, about 200 times the mass of electron’s Mean lifetime = 2.197 × 10-6S Non-Relativistic Relativistic MUON DECAY 𝑑𝑁 = −𝑁 𝑡 𝑑𝑡/𝜏 𝑁 𝑡 = 𝑁0 exp(−𝑡/𝜏) 𝑁= 𝑁0 exp(−𝑡/𝜏) + 𝐶 (background count) mesured MEASUREMENT OF LOW RESISTANCES : 4 PROBE METHOD, LOCK- IN AMPLIFIER 4 probe method MEASUREMENT OF LOW RESISTANCES : 4 PROBE METHOD, LOCK- IN AMPLIFIER Signal is multiplied by the gain of Amplifier (g) Signal in : Reference : High frequency(2f) signals can not pass through Low-pass filter MEASUREMENT OF LOW RESISTANCES : 4 PROBE METHOD, LOCK- IN AMPLIFIER Dual lock in amplifier ∝ Voltage(amplitude) on Reactance Signal in Reference signal ∝ Voltage(amplitude) on Resistance MEASUREMENT OF LOW RESISTANCES : 4 PROBE METHOD, LOCK- IN AMPLIFIER CONTENTS Holography Energy gap of Ge Hall effect SQUID Holography Objective Two-beam transmission hologram을 제 작하는 과정을 통해 holography의 기본 적인 원리를 이해한다. Holography Holography? http://en.wikipedia.org/wiki/Holography Coherent한 두 빛을 어떤 면에서 만나게 하면 두 빛의 위상차에 따른 간섭무늬가 만들어진다. Holography Setup He-Ne laser PFG-01 film Energy Gap of Ge Objective 온도에 따른 undoped Ge의 conductivity σ를 측정하고, 이를 통해 undoped Ge의 band gap Eg를 구한다. Energy Gap of Ge Small band gap of Ge 작은 band gap http://en.wikipedia.org/wiki/Electron_band_structure 약간의 thermal energy를 공급하는 것으로도 전자가 band gap을 극복하여 sample의 conductivity가 변한다. Energy Gap of Ge Evaluation (1/2) eni ( n p ) j (e)ni vn epi v p j E (Ohm' s law) μn, μp: mobility of electron and hole ni, pi: electron, hole concentration vn, vp: electron, hole drift velocity e: elementary charge [2] http://en.wikipedia.org/wiki/Electron_mobility (e)ni vn eni v p Intrinsic semiconductor인 pure Ge는 thermal equilibrium 상태에서 valence band hole과 conduction band electron 수가 동일. vn n E vp pE Definition of drift velocity[2]. Energy Gap of Ge Evaluation (2/2) eni ( n p ) k: Boltzmann constant σ0: constant coefficient Eg: band gap of pure Ge at 0 K 4.77 10 4 eV / K (Ge), 235 K (Ge) [6]. ni T 3/ 2 exp( Eg' / 2kT ), [3,4]. T 3 / 2 , [2]. 2 T Eg' Eg , [5]. T 2 1 T E g 0 exp T 2kT 따라서 각 온도 에 따른 σ를 측 정하면 curve fitting을 통해 Eg 를 구할 수 있다. [2] http://en.wikipedia.org/wiki/Electron_mobility [3] Zeynep Dilli (2008-2009), Intrinsic and Extrinsic Semiconductors, Fermi-Dirac Distribution Function, the Fermi level and carrier concentrations [4] http://ecee.colorado.edu/~bart/book/book/chapter2 /ch2_6.htm [5] http://en.wikipedia.org/wiki/Band_gap [6] Jerome Keith Miller, "PROBING III-V SEMICONDUCTOR HETEROSTRUCTURES USINGTIME RESOLVED PUMP-PROBE TECHNIQUES", Ph. D. Dissertation, Vanderbilt Universit y, Nashville, Tennessee, 2006. Energy Gap of Ge Setup Hall effect module Power supply Multimeter for power voltage Energy Gap of Ge Hall effect module On: sample에 걸리는 전류 측정 Off: sample 온도 측정 Display Ge sample Module 전원 공급 단자(교류) 전류 조정 knob Ge sample heating On/Off power voltage 측정을 위한 multimeter 연결 Hall effect module 전, 후면 Hall effect in n-Ge, p-Ge Objective 특정 온도에서 n-type Ge와 p-type Ge의 Hall coefficient를 측정한다. 이후 온도를 바꾸면서 Hall coefficient의 변화를 관찰 한다. Hall mobility와 electron concentration을 측정한다. Hall effect in n-Ge, p-Ge Hall effect Hall effect는 uniform magnetic field B에 놓여 있는 전도체에 current I가 흐르면, Lorentz force에 의해 charge carrier가 B와 I에 수직으로 힘을 받아 한쪽으 로 몰리는 현상이다. IB VH R H d Hall coefficient Hall effect in n-Ge, p-Ge Doping type N-type P-type Hall effect in n-Ge, p-Ge Hall coefficient RH in semiconductor is expressed as following 1 p h2 ne2 RH e ( p h ne ) 2 μ denotes the mobility Hall coefficient RH can be rearranged to be n-type *conditionn nd ni ; p pi ni . p-type *conditionn ni pi ; p pa pi . n2 1 T 2 nd 2 3 d g nd N 0 T exp 4 k T T 2 b 1 RH e 2 n2 d N 2T 3 exp 1 T nd n d 0 k T g T 2 4 b p2 1 T 2 a g pa N 02T 3 exp 4 k T T b 1 RH e p2 1 T 2 2 3 a p N T exp a 0 k T g T 4 b [3] http://en.wikipedia.org/wiki/Hall_effect [4] Kasap, Safa. "Hall Effect in Semiconductors" 1 1 u 2 2 1 1 u pa 1 u2 2 2 pa 1 u 2 u e / h RH turns out to be the function of temperature! Hall effect in n-Ge, p-Ge Setup IB VH R H d Teslameter Power supply Multimeter for VH, VI Two solenoids Hall effect module Hall effect in n-Ge, p-Ge Hall effect module Hall voltage 측정을 위한 multimeter 연결 On: sample에 걸리는 전류 측정 Off: sample 온도 측정 Display Ge sample Ge sample heating On/Off Module 전원 공급 단자(교류) 전류 조정 knob 회로 voltage 측정을 위한 multimeter 연결 Hall effect module 전, 후면 SQUID Objective Superconducting quantum interference device (SQUID)를 사용한 실험을 통해 Josephson junction의 특성과 magnetic flux quantization의 존재를 확인한다. SQUID Josephson junction Superconductor Single Josephson junction I-V curve in Josephson junction http://en.wikipedia.org/wiki/Josephson_junction SQUID Magnetic flux quantization in SC ring h 0 2e SQUID SQUID SQUID Result SQUID Setup Control box SQUID probe and N dewar