quiz5solution

# quiz5solution - E = 2 h 2 w 2 mL 2 = 2 1.055" 10 34 J \$...

This preview shows pages 1–2. Sign up to view the full content.

EE 439 Name_______________________________________ Quiz 5 – Nov. 6, 2009 Put your final answers on this sheet and attach any additional sheets behind. You must include your work to get full credit. A finite-height quantum well has barriers that are 0.5-eV high and a well width of 1 nm. Find the first quantized energy level of the well. The characteristic equation for finding the energies of the even-symmetry states of a finite-height quantum well: w tan w = R 2 " w 2 where w = mEL 2 2 h 2 and R = mU o L 2 2 h 2 . For the given well configuration, R = 9.11 " 10 # 31 kg ( ) 0.5 eV ( ) 1.6 " 10 # 19 J / eV ( ) 10 # 9 m ( ) 2 2 1.055 " 10 # 34 J \$ s ( ) 2 = 1.81 Inserting this value into the characteristic equation, w tan w = 3.27 " w 2 . Use some type of iteration on this transcendental equation (calculator equation solver, enlightened guessing, or whatever), leads to a value of w = 0.99. Then we can find the corresponding energy:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: E = 2 h 2 w 2 mL 2 = 2 1.055 " 10 # 34 J \$ s ( ) 2 0.99 ( ) 2 9.11 " 10 # 31 kg ( ) 10 # 9 ( ) 2 = 2.39 " 10 # 20 J = 0.15 eV Potentially useful equations and data: Square-barrier tunneling: T " 4 E U o # E ( ) U o 2 exp # \$ 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...
View Full Document

## This document was uploaded on 03/27/2010.

### Page1 / 2

quiz5solution - E = 2 h 2 w 2 mL 2 = 2 1.055" 10 34 J \$...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online