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quiz1solution - Square-barrier tunneling: T "...

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EE 439 Name_______________________________________ Quiz 1 – Sept. 18, 2009 Put your final answers on this sheet and attach any additional sheets behind. You must include your work to get full credit. An electron is fired from an electron gun with energy of 10 eV. The electron is incident on a barrier that is 14 eV high and 0.5 nm wide. What is the probability that the electron will tunnel through? This is a straight application of the tunneling probability equation: T = 16 E U o " E ( ) U o 2 exp " 2 # L ( ) , where " = 2 m U o # E ( ) h 2 = 2 9.11 x 10 # 31 kg ( ) 14 eV # 10 eV ( ) 1.6 x 10 # 19 J / eV ( ) 1.055 $ 10 # 34 J % s ( ) 2 = 1.02 $ 10 10 m # 1 = 10.2 nm # 1 Then T = 16 10 eV ( ) 14 eV " 10 eV ( ) 14 eV ( ) 2 exp " 2 10.2 nm " 1 ( ) 0.5 nm ( ) [ ] = 1.21 # 10 " 4 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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quiz1solution - Square-barrier tunneling: T "...

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