quiz4solution

quiz4solution - nm Potentially useful equations and data:...

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EE 439 Name_______________________________________ Quiz 4 – Sept 28, 2009 Put your final answers on this sheet and attach any additional sheets behind. You must include your work to get full credit. The light coming from a quantum cascade laser has wavelength of 2 μm. If we assume that the photons are generated by the fall of electrons from the n = 2 level to the n = 1 level of an infinitely deep quantum well, calculate the width of the well. Light with wavelength of 2 μm corresponds to photon energy of 0.62 eV. So we need a well with separation of 0.62 eV between the 1 st and 2 nd levels. E 2 " E 1 = 2 2 # 2 h 2 2 mL 2 " 1 2 2 h 2 2 mL 2 = 3 2 h 2 2 mL 2 . Solving for L L = 3 " 2 h 2 2 m E 2 # E 1 ( ) = 3 2 1.055 $ 10 # 34 J % s ( ) 2 2 9.11 $ 10 # 31 kg ( ) 0.62 eV ( ) 1.6 $ 10 # 19 J / eV ( ) = 1.35
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Unformatted text preview: nm Potentially useful equations and data: Square-barrier tunneling: T " 16 E U o # E ( ) U o 2 exp # 2 $ L ( ) ; = 2 m U o # E ( ) h 2 Energy levels in an infinitely deep quantum well: E n = n 2 2 h 2 2 mL 2 p = h E = h "# = c h = 6.63x10 34 Js = 4.14x10 15 eVs; h = 1.055x10 34 Js = 6.595x10 16 eVs (Plancks constant) c = 3.0x10 8 m/s (speed of light in vacuum) k = 1.38x10 23 J/K = 8.617x10 5 eV/K (Boltzmanns constant, not wave number) m = 9.11x10 31 kg (mass of an electron) q = 1.6x10 19 C (charge of an electron) o = 8.85x10 12 F/m (free-space permittivity) 1 eV = 1.6x10 19 J...
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quiz4solution - nm Potentially useful equations and data:...

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