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quiz1solution - Square-barrier tunneling T" 16 E U o E...

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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 J·s = 4.14x10 –15 eV·s; h = 1.055x10 –34 J·s = 6.595x10 –16 eV·s (Planck’s constant) c = 3.0x10 8 m/s (speed of light in vacuum) k = 1.38x10 –23 J/K = 8.617x10 –5 eV/K (Boltzmann’s constant, not wave number) m = 9.11x10 –31 kg (mass of an electron) q = 1.6x10 –19 C (charge of an electron) ε o = 8.85x10 –12 F/m (free-space permittivity) 1 eV = 1.6x10 –19 J...
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quiz1solution - Square-barrier tunneling T" 16 E U o E...

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