PH300
Fall 2013
HW9 answer key
1) Find the wavelength of the photon needed to cause an electron to
jump from the valence to the conduction band in (a) germanium, with
a band gap of 0.67 eV (b) silicon with a band gap of 1.1 ev. How
large an energy gap is required for a blue semiconductor laser with
wavelength = 460 nm?
Using λ = hc/E
a) λ = (1240 nm*eV)/ 0.67 eV = 1851 nm
b) λ = (1240 nm*eV)/ 1.1 eV = 1127 nm
Using E = hc/ λ
c) E = (1240 nm*eV)/ 460 nm = 2.696 eV
2) Using the applet at
http://phet.colorado.edu/en/simulation/bound-states
What is the average energy separation of the first excited state for a 6
square well potential with a width of 0.1 nm between wells?
How large is the band gap of a 10 well coulomb potential with a
spacing of 0.3 nm?
E-levels of n = 2 bond (default W, H)
4.34
4.13
3.87
3.61
3.35
3.22
∆E
0.21
0.26
0.26
0.26
0.13
The average ∆E is 0.224 eV
10 well coulomb potential, spacing 0.3nm:
Top of 1st band = -31.25
Bottom of 2nd band = -12.58
The gap between these levels: 18.67ev
3) What was a common device that made use of the semiconductor
properties of material decades before semiconductors were
invented?
Thermocouples and crystal radios
4) Assuming that the average daily solar constant at a particular
place is 200 W/m2, how large an array of 30% efficient solar cells is
required to equal the power output of a typical power plant, about 109
W?
Solar flux = 200 W/m2, Effieciency = 0.30, Plant output = 109 W
(109 W)*(1 m2)/(200 W)*(1/0.30) = 1.67x107 m2 or 16.67 km2
5) A crystal radio can detect AM radio stations. Why does it need a
diode to do this? Why won’t it work without a diode? Your explanation
should include a sketch(es) of voltage vs time.
A) The signal as picked up by the
receiver would cancel out as there are
both positive and negative voltage
contributions.
B) However, in a diode current only
passes through it in one direction, so the
amplitude modulated signal does not
average out to zero but rather a
fluctuating non-zero value C).
Graph obtained from:
http://en.wikipedia.org/wiki/Crystal_radio