3.46 PHOTONIC MATERIALS AND DEVICES Lecture 10: LEDs and Optical Amplifiers

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1 3.46 PHOTONIC MATERIALS AND DEVICES Lctu 0: LEDs and Optical Amplifis Lctu Rfncs:. Salh, M. Tich, Photonics, (John-Wily, Chapts 5-6. This lctu will viw how lctons and hols combin in smiconductos and nat photons. Th study of liht mission in matials is a ky facto fo th undstandin of optolctonic dvics such as LEDs, Optical Amplifis and Lass. P E A E Photon flux: φ =I = I = optical pow dnsity P = optical pow A = bam aa v Non-quilibium R = non thmal nation at (cai injction at G 0 = thmal nation at n= n 0 + Δn p= p 0 + Δp Δ n =Δp Δn n, p 0 0 Δn Δn Injction cai at quation: d( = R dt = xcss cai combination tim (low injction lvl appoximation G 0 = n 0 p 0 G 0 + R =np R = Δn + 3 ( h pais/ cm s = Δ n(n 0 + p 0 n0 ( + p Photonic Matials and Dvics Lctu 0: LEDs and Optical Amplifis Pof. Lionl C. Kimlin Pa of 8

2 Lctu Rcombination: Non-quilibiumquilibium Rcombination at = = +n = adiativ n = non-adiativ σ v n taps Photon thmal quilibium 6 3 GaAs n i =.8 0 cm = 0 G 0 = n i = 34 Photons 3 cm s 0 3 cm thicknss of lay: t = μm = x 0-4 cm ( α 0 4 cm /s φ =( n t = cm v i E =.4 V = J s I =φe = W/cm v vy low pow Intnal Quantum Efficincy Rcombination = las of ny adiatin hυ non-adiatin hν phonon, Au η= i = +n η= n i = : faction of non-quilibium +n cais that combin adiativly R V = injctd (pais/s volum of activ matial φ= photon flux = η i RV A Δn = t 3.46 Photonic Matials and Dvics Lctu 0: LEDs and Optical Amplifis Pof. Lionl C. Kimlin Pa of 8

3 Lctu Intband combination GaAs: η i = 0.5 Si: η i = GaAs : 50 ns, η = 0.5, Δ = 0 7 i n cm 3 R =Δn / = 0 4 photons/cm / s t = μm φ =Rt = 0 0 cm s v I =φ E = 46 W/cm v LED: 00 μ mittd pow = 9 mw m 00 μm aa Spontanous mission Rat = (ν = sp ρ( ν f (ν 3 π ρν ( = (m (hν E optical joint dnsity of stats = + (ducd mass m m m v c Emission condition f(ν = f (E [ f(e ] c v pob C E mpty pob V E filld E = E hν m m c E = E c + (hν E V φ= (ν ν A SP d 0 3 V(m = (k Τ 3 E xp FC E FV E A π kt Photonic Matials and Dvics Lctu 0: LEDs and Optical Amplifis Pof. Lionl C. Kimlin Pa 3 of 8

4 Lctu ( low injction ( Δ n< n, p 0 R Δ n (E f(ν FC 0 E FV ( hih injction ( Δ n> n 0, p 0 (E E FV = E + (3π 3 FC (Δn m 3 Spctal dnsity of mission at (h = D(hν E xp ν E sp KT wak injction D = (m 3 xp (E FC E FV E π kt sam shap as thmal quilibium: (h = D 0 (hν E xp ν E sp KT Wh D xp (E E FC FV D k T 0 ν = Pak fquncy P hν =E + k T P λ : bandap wavlnth E : bandap ny.4 V μm λ = E 3.46 Photonic Matials and Dvics Lctu 0: LEDs and Optical Amplifis Pof. Lionl C. Kimlin Pa 4 of 8

5 Lctu FWHM Δν =.8k T /h Hz (k T in V units Δλ =.45λ P k T μm λ = μ m p k T(300K = 0.05 V LED Dvics Intnal photon flux R = I/ = injction at V I = cunt = cha/ - V = activ hih injction lvls Δ n> n 0,p 0 ( I Δ n = V t Intnal quantum fficincy η i photon flux lcton flux A φ=η i I A Extnal quantum fficincy η = xt xtnal photon flux lcton flux I φ =η A out xt C Sufac mission 3.46 Photonic Matials and Dvics Lctu 0: LEDs and Optical Amplifis Pof. Lionl C. Kimlin Pa 5 of 8

6 Lctu. Absoption (hν E η =xp ( αt. intfac (n 4n η = = (n+ (n + = 0.68 fo GaAs (n= Total flction η = cos θ 3 c n = 4% of GaAs η xt =η η η 3 η i output pow = P 0 = h νφ 0 hν I Pout =η xt Pow convsion wall plu fficincy η W mittd optical pow input lctical pow P out hν = = η xt IV V volta dop acoss dvic Rsponsivity R P 0 = Vη W I.4 W R =η xt λ ( μm A 0 =η xt hν Typical: η xt =.5% R = 0-50 μw/ma 3.46 Photonic Matials and Dvics Lctu 0: LEDs and Optical Amplifis Pof. Lionl C. Kimlin Pa 6 of 8

7 Lctu P 0 (μw I(mA Luminous pfomanc (displays lumns IV = P 0 y snsitivity IV η xt (% 3.46 Photonic Matials and Dvics Lctu 0: LEDs and Optical Amplifis Pof. Lionl C. Kimlin Pa 7 of 8

8 p-typ a b c. Typical LED dvic and chip confiuations. (a Cosssction of a LED lamp. Th LED chip, typically 50 x 50 x 50 micomts, is mountd in a flctin cup fomd in lad fam. Cla poxy acts as a lns, as wll as pfomin oth functions. (b A convntional homojunction LED chip can b mad with GaAsP:N/GaP stuctus to mit at d and yllow wavlnths, and with GaP:N/GaP stuctus to mit at n wavlnths. (c In a d-mittin AlGaAs doubl-htostuctu chip, th nti stuctu is own by LPE and can b ith n-typ o p- typ on top. (d An AllnGaP doubl-htostuctu with a GaP window lay fo d, yllow, o n mitts. Th Al concntation in th p-typ activ ion is adjustd to iv th dsid colo. d 3.46 Photonic Matials and Dvics Lctu 0: LEDs and Optical Amplifis Pof. Lionl C. Kimlin Pa 8 of 8

Assignment 6. Solution: Assumptions - Momentum is conserved, light holes are ignored. Diagram: a) Using Eq a Verdeyen,

Assignment 6. Solution: Assumptions - Momentum is conserved, light holes are ignored. Diagram: a) Using Eq a Verdeyen, Assignment 6 Solution: Assumptions - Momentum is conserved, light holes are ignored. Diagram: a) Using Eq..4.5a Verdeyen, ΔE c = E 2 E c = Using Eq..4.5b Verdeyen, ΔE v = E v E = b) Using Eq.2.9 Verdeyen,