Term
| What are the assumptions of the free electron model? |
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Definition
-the nucleus is fixed
- e- are floating around
no interaction between ions and e-
ignore e-, e- interactions |
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Term
| currents shift the center of the fermi sphere?Why does this current decay? |
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Definition
electron-electron scattering. The free electron model ignores this. If an electron e1 and e2 scatter off each other they would have to end up in some new states e3 and e4. For this to happen:
e3+e4< e1+e2. The smaller the temperatur ethe less likely this is. |
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Term
| List some sources of scattering in materials |
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Definition
| crystal defects, thermal vibrations |
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Term
| Name some materials for which the free electron model is nearly perfect. |
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Definition
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Term
| The energy gap on the ziman model is the same as the fourier component of what? |
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Definition
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Term
| Where do semiconductors deviate from the free electron model? |
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Definition
| at the zone boundary. for a 1-D crystal at k = pi/a |
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Term
| give three equivalent statements of bragg's law? WHich of these statements can be used to construct brillouin zones and why? |
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Definition
k' = k-g; mg = g(k-g/2)=0; mlambda = 2d sin(theta)
the second statement- since it says that you have diffraction or standing waves at the perpendicular bisectors of the lattice vectors. These perpendicular bisectors intersect to form the brillouin zones |
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Term
| How many electrons are in each band and why? |
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Definition
if you take a 1-D crystal:
k varies from -pi/L to pi/L and each state occupies 2pi/a and each state can hold 2e-:
Number e- = 2(2pi/L)/ (2pi/a) = 2L/a
as a approaches L you get 2 electrons per band. |
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Term
| What model do you use on transition metals? How does this model work? why? |
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Definition
| the tight binding model because electrons in d metals are highly localized due to the shape of d-orbitals. This model assumes that e- are confined to a band, adusting the band width allows you to determine how much e- interact. The narrower the band the more localized the e- are. |
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Term
| What is Bloch's Theorem and what does it allow us to do? |
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Definition
| Uk(r+a) = U(r). Bloch's Theorem just states periodicity. It allows us to translate bewteen reduced and extended zone schemes |
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Term
| What tool can you use to directly measure band structure? |
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Definition
| ARPES - this techniques shoots photons at a metal and measures tbe kinetic energy and momentum of e- that are pulled off. Using conservation of kinetic energy and momentum, you can get an idea of the band gap, etc. |
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Term
| Distortion of the Fermi Surface changes what? |
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Definition
| the average electron energy |
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Term
| What determines electrical properties of a material |
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Definition
| the density of states at the fermi surface |
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Term
| What are the peaks in a density of states plot near the zone boundary called? What happens to the gradient of the density of states at these peaks? |
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Definition
| vont Hove singularities. It goes to a minimum |
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Term
| A fermi surface that lies within a zone had a ____ energy than the free electron case |
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Definition
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Term
| What determines the rho l of a material? |
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Definition
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Term
| What is Mathiessen's rule? How do you use it? |
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Definition
1/l = 1/lphonons + 1/limpurities + 1/lthickness.
You can use it to find the resistivity of a device. You know the resistivity times the scattering from the band structure. |
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Term
| Give the three temperature dependence regimes for resistivity |
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Definition
1) low temperatures T< debye temperature
resistivity proportional to T^3
2)very low temperatures: T<< debye temperature
proportional to T^5 ( T^2 dependence comes from changing of velocity of e- and T^3 dependence same as for low temperatures
3) high temperature T>> debye temperatures:
proportional to T |
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Term
| How do you get piezoresistance in a material? |
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Definition
| In a semiconductor you can change the curvature of bands by changing the lattice structure. This can be done simply by stretching /deforming the crystal. Changes in band structure result in changes in resistance. |
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Term
| ferrimagnetism? antiferrimagnetism? ferromagnetism? paramagnetism? diamagnetism? |
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Definition
ferrimagnetism- local spins that are next to each other are opposite, but the material has a net magnetic moment, since opposing spins aren't equal
antiferrimagnetism- local spins are opposite but the net magnetic moment is zero
ferromagnetism- material exhibits a net magnetic moment
paramagnetism- material will allign with a magnetic field
diamagnetism- material is repelled by magnetic field |
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Term
| mean field ferromagnetism |
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Definition
| mean field stabilizes spins- resulting in a net magnetic moment |
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Term
| superexchange as related to magnetism |
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Definition
| bonds are coupled so the spin of one e- affects the spin of another. e.g in O2- in spinels |
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Term
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Definition
| magnetism that arises from a change in the rel. energy of spin up and spin down states |
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Term
| How does the stoner model work? |
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Definition
- calculates a mean field and uses this to determine a difference in the enegry of spin up and spin down states
- uses stoner criterion to decide whether the energy is stabilized or not |
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Term
| What are sources of magnetic anisotropy? |
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Definition
shape-favors magnetic alignment along the axis (e.g thin films magnetic alignment almost always in plane)
domains |
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Term
| Which "forces" on domain walls re reversible? |
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Definition
| initial movement of domain wall due to an applied field, dipole rotation |
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Term
| What are soft magnetic materials?applications? |
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Definition
| hard axis behavior- transformers |
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Term
| hard magnets? applications? |
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Definition
| easy axis behavior- magnetic data storage |
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Term
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Definition
| when magnetic moments are in the same direction the device has a low resistance; when they are opposite it has a high resistance used in solid state memory. |
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Term
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Definition
| If you heat a material for an extended amount of time, e- will be promoted to higher states in the material. Then if you heat the material again, these e- will relax and light will be emitted. |
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Term
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Definition
stimulated emission has to exceed spontaneous emission.
-population inversion |
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