EE5508_Semiconductor_Fundamentals-C2_1

EE5508_Semiconductor_Fundamentals-C2_1 - EE5508...

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EE5508-PII-C2-1 1 EE5508 Semiconductor Fundamentals Part II Chapter 2-1 2011 Spring (G.C. Liang) Source P ++ Channel I/N OX OX Drain N ++ gate gate
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Schedule EE5508-PII-C2-1 2 2011 Spring (G.C. Liang) 2011/3/1 Lecture 7 Chapter 1 2011/3/8 Lecture 8 2011/3/15 Lecture 9 2011/3/29 Lecture 10 Chapter 2 2011/4/5 Lecture 11 2011/4/12 Lecture 12 Chpater 3
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EE5508-PII-C2-1 2011 Spring (G.C. Liang) 3 Outline • Fundamentals – Optical processes – Light emission • Devices – LEDs – Lasers – Photodiodes • Photodetectors • Photovoltaics
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EE5508-PII-C2-1 2011 Spring (G.C. Liang) 4 Light? What is light? Electromagne2c wave (Classical point of view) photon (Quantum Theory) Maxwell Equations D= ρ ; D= ε E ; D: electrical flux density B =0; B= μ H ; B: magnetical flux density ∇ × E=- B t ∇ × H = D t + J assume ρ = 0 and J = 0 ∇ × ∇ × E=- t ∇ × B ∇ × ∇ × E=(- 2 E + ( E )) = −∇ 2 E ( D=0) ∇ × B = ∇ × ( μ H ) = μ D t ∇ × ∇ × E=- t ∇ × B → ∇ 2 E = μ 2 D t 2 = μ ε 2 E t 2 = 1 V 2 2 E t 2 E = e i 2 πν ( t x / V ) = e i ( ω t kx ) ;
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EE5508-PII-C2-1 2011 Spring (G.C. Liang) 5 Photon energy= ω Electromagnetic wave (photond) can interacts with electrons in semiconductor light absorption or emission.
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EE5508-PII-C2-1 2011 Spring (G.C. Liang) 6 Relationships between Optical Constants Absorption coefficient We describe the radiation as a plane wave of frequency propagating in the x direction with a velocity v : ν ε = ε 0 e i 2 πν [ t x / V ] where v = c / n c , with c: velocity of propagation in vacuum and n c = n i κ (the index of refraction) 1 V = n c c = n c i κ c Then, ε = ε 0 e i 2 π vt e i 2 π vxn / c e 2 π v κ x / c The last term is a damping factor.
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EE5508-PII-C2-1 2011 Spring (G.C. Liang) 7 The fraction of the incident power available after propagating a distance x: power ε 2 P ( x ) P (0) = ε ( x ) 2 ε (0) 2 = e α x α = 4 πνκ c ; α :absorption coefficient. κ : the imaginary part of n c , is called the extinction coefficient. We relate the complex dielectric constant with n , κ as follows: ε c = ε 1 + i ε 2 ε c = n c ε = n 2 κ 2 ε 2 = 2 n κ
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EE5508-PII-C2-1 2011 Spring (G.C. Liang) 8 Reflection coefficient x y z t=0 In region I, E = ( E in e ikz + E r e ikz ) H = ( H in e ikz H r e ikz ) = ( E in / η 1 e ikz E r / η 1 e ikz ) In region II, E = ( E t e ikz ) H = E t / η 2 e ikz Z=0 I II
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at boundary E i + E r = E t E i E r η 1 = E t η 2 E i + E r E i E r = η 2 η 1 E r E i = η 2 η 1 η 1 + η 2 r E t E i = 2 η 2 η 1 + η 2 τ EE5508-PII-C2-1 9 2011 Spring (G.C. Liang) η 1 = μ 1 ε 1 and η 2 = μ 2 ε 2 assume μ 1 μ 2 r = n 1 n 2 n 1 + n 2 R = rr * = | r | 2 R = E r E i 2 = rr * = | r | 2 = ( n 1 n 2 )( n 1 n 2 ) * ( n 1 + n 2 )( n 1 + n 2 ) * R = ( n 1 n 2 )( n 1 n 2 ) * ( n 1 + n 2 )( n 1 + n 2 ) * = (1 n + i κ )(1 n + i κ ) * (1 + n i κ )(1 + n i κ ) * = ( n 1) 2 + κ 2 ( n + 1) 2 + κ 2 = ( n 1) 2 ( n + 1) 2 ; κ =0, totally transparent 1; κ → ∞ , totally reflecting n 1 = 1 n 2 = n i κ For normal incidence, n 1
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