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quiz2solution - Square-barrier tunneling: T "...

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EE 439 Name_______________________________________ Quiz 2 – Sept. 21, 2009 Put your final answers on this sheet and attach any additional sheets behind. You must include your work to get full credit. An proton (mass = 1.67x10 –27 kg) with energy of 100 eV is incident on a square barrier with energy of 110 eV. Calculate the thickness that the barrier must have in order for the tunneling probability to be 1%? Inverting the probability equation for barrier thickness, L, L = " 1 2 # ln TU o 2 16 E U o " E ( ) $ % ( ) . " = 2 m U o # E ( ) h 2 = 2 1.67 $ 10 # 27 kg ( ) 110 eV # 100 eV ( ) 1.6 $ 10 # 19 J / eV ( ) 1.055 $ 10 # 34 J % s ( ) 2 = 6.93 $ 10 11 m # 1 = 693 nm # 1 Then, L = " 1 2 693 nm " 1 ( ) ln 0.01 ( ) 110 eV ( ) 2 16 100 eV ( ) 110 eV " 100 eV ( ) # $ % % ( ( = 0.0035 nm Potentially useful equations and data:
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Unformatted text preview: 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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quiz2solution - Square-barrier tunneling: T "...

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