Generate a plot estimating wavelength (in nm) vs. energy (in meV) for electrons, phonons, and
photons in the 0 - 200 meV energy range. The equations for particle wavelength (i.) are below
where h is Plank's constant, m' is the effective mass, Vs is velocity, E is energy, and c is the
speed of light. For Silicon m "=0.26 mo, Vs = 8433 m/s, and the Debeye temperature is Op=645K.
This implies a phonon cutoff at 55 meV, i.e. phonons at wavelengths with E>55 meV are not
allowed. Comment on which particles are Fermions, Bosons, and Boltzons, along with which
heat transfer mechanism is associated with each particle.
Electrons: i = V2MILE h ; Phonons: i = Photons: 2 hc E
Power Dissipation in CPUs
1 cm x 1 cm computer processor has 1x109 transistors on it. Each transistor occupies an area
0.1um2. The processor is in contact with an environment that has an effective thermal conductivity
of 10W/m-K, and heat must travel a distance of 1mm before it is completely removed from the
processor. Plot the temperature of the processor as a function of the power dissipated by the
transistors from InW to 100 nW. Comment on the energy challenges associated with cloud
computing and data centers.
Thermal Conductivity of Metals
Create a table of electrical conductivity (S/m) and thermal conductivity (W/m-K) for Mo, Fc, W, Ti, Cr,
Co, Ni, Cu, Ag, Al, Au. Create a plot of thermal conductivity vs. electrical conductivity at T-300 K.
Using the "polyfit" and "polyval" commands perform a linear fit to the data. Plot the data as scatter
points and overlay your linear fit. Comment on the slope and the particles carrying the heat in metals.
Also, comment on how you may reduce the thermal conductivity of a metal.
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h=6.62606957e-34; %m^2 kg/s
c=299792458; %speed of light in m/s
E=0.5:1:200; %in meV
Ep=0.5:1:55; %in meV
%wave length in meters
ylabel('Wavelenghth Lambda (nm)')
title('Electron wavelength as a function of energy')