Prelim Guide: Electrical and Magnetic Properties
|MSE Prelim Guide|
Electrical and Magnetic Properties
- Explain the phenomenon of superconductivity.
- Draw the current-field curve for superconductivity.
- Explain the mechanisms of the superconducting transition from A to C and from B to C.
- What are "hard" and "soft" superconductors?
- Draw a schematic of the energy-level diagram of a p-n junction
- What is the physical origin of the small current in a reverse biased p-n junction?
- What are you working on? (if your answer contains the work "magnetic":)
- Draw domain configuration of a macroscopic magnet and explain why it is magnetic.
- How does this change in an applied field?
- Why would you want to add Si to Fe magnets?
- Plot resistivity vs. T for:
- a metal. Explain the effects of impurities. What determines the residual resistivity at low T?
- a superconductor. Explain superconductivity (better than BN&T explanation, please)
- an ionic crystal. Explain the slopes.
- a semiconductor. Explain the slopes. Suppose there is a shallow dopant?
- why is there a fourth slope for an extrinsic semiconductor at low temperatures? Explain freeze-out and compensation.
- Draw a Fermi level vs. T plot showing the shallow donor freezing out and compensation.
- Write an equation relating carrier concentration to conductivity.
- Draw r vs. T for a metal and for a semiconductor.
- How is r affected by defects in a superconducting metal?
- Draw s vs. 1/T for a semiconductor.
- What happens at low temp?
- Explain the slopes.
- How would you measure the carrier concentration in a semiconductor?
- What happens to the voltage gradient if the charge carriers are holes rather than electrons?
- How would you measure the band gap of a semiconductor?
- How would you measure the resistivity of a metal?
- How is the carrier concentration in a metal affected by an increase in temperature?
Spring 1985: E. Haller
- Plot E vs. x for a semiconductor acceptor, and for a donor.
- Draw a p-n junction. What happens when it is joined and why?
- With a bias applied, how do diffusion current and voltage current vary? How does this explain the rectifying property of the junction?
- Plot s vs. T for a metal and for a semiconductor. Why are the curves different?
Fall 1985: E. Weber
- Plot resistivity vs. T for a metal. What is the cause of residual resistivity at 0K?
- Why does the slope change, and how?
- Plot resistivity vs. T for a superconductor.
- Explain the dependence of conductivity on temp for an insulator.
- How can an ionic material conduct electricity?
- Plot conductivity vs. temp for a semiconductor. What are the slopes? Why is there a factor of 1/2 in them?
- If you know only one point on this graph, how can you find the Fermi energy?
- Explain dia-, para- and ferromagnetism. What happens to a diamagnetic material if no field is applied? What is an example of a paramagnetic material? *Can calcium be paramagnetic?
- Why does ferromagnetism become paramagnetism at high temperature? How is this called thermodynamically?
Spring 1986: E. Weber
- Draw resistivity vs. temperature for a metal.
- What is responsible for permanent resistivity at 0K?
- What is the main factor determining the slope of the part for T>0K?
- Draw resistivity vs. T for a superconductor. Describe the mechanism for superconductivity.
- Draw s vs 1/T for a semiconductor. What is responsible for the slope of the initial region?
- Describe the Hall effect. How do electrons and holes move in this situation?
- How can you measure the band gap of an ionic material, optically? Draw a schematic of the measuring system.
Fall 1986: E. Haller
- Describe some types of magnetism.
- Why are some materials ferromagnetic while others are not?
- How do the electrons line up in a ferromagnetic material?
- What happens if a magnetic field is applied? Do the spins change spontaneously?
- Draw a B vs. H curve.
- What is this called?
- What does the area correspond to?
- What happens if we continue the curve instead of making H periodic?
- What do you call materials with large/small hysterisis areas?
- Which would you use for a computer? Which would you use for a transformer?
- Draw E vs. x for a semiconductor.
- Why does a semiconductor look metallic?
- What if you looked under infrared light?
- Draw the band diagram for a p-n junction.
- What are the charges from (mobile and immobile)?
- What does the donor level refer to?
- What happens when the two regions are initially brought into contact? Why does this stop?
- What are the different currents?
- Apply now a reverse bias.
- Why is there still a current?
- What is the effect of temperature?
- Are there any holes in the n-region? How many? How does this depend on T?
- How many electrons are there in the n-region?
- Know also the Hall effect.
Spring 1987: E. Haller
- Pick a topic from the board (semiconductors picked)
- Explain band gap theory, density of states for metals, semiconductors, insulators, p and n doping.
- (Misc. Haller question - Explain the Meissner effect)
Fall 1987: E. Weber
- Plot resistivity vs. T for a metal, a semiconductor and an insulator.
- Why doesn't resistivity drop to zero for metals at low T?
- What is the (currently believed) mechanism for superconductivity?
- For a semiconductor, plot lnN vs. 1/T. Explain the reasons for the different slopes.
- Briefly explain the difference between paramagnetism and diamagnetism.
Spring 1988: E. Haller
- Draw the band structure (E vs. x) of a heterojunction p-n junction. What accounts for the contact potential?
- Draw a schematic plot of charge density vs. position. From this, draw electric field and potential vs. position. Why is the potential vs. position curve different from that of the band diagram?
- Draw r vs. T for a superconductor. To what value does r drop? How can you tell?
- What experiment can you perform to demonstrate that superconductivity is not just the disappearance of electrical resistivity? Show this on a H-T diagram.
- What is the difference between types I and II superconductors? Can you make a type I into a type II? How?
- Assume you solidify molten iron and cool it to room temperature in the absence of magnetic fields. Is it magnetized? In what way? Show the domains. *What happens to the domains as you increase an applied field?
Spring 1988: E. Haller
- What material do you work with? What happens if it is put in a magnetic field?
- What if you put BaTiO3 in an electric field?
- What is the capacitance of the parallel plate capacitor with and without a dielectric between the plates? Write an equation relating q, C and V.
- Change the voltage to V0. Remove the battery and insert a dielectric. What happens?
- Suppose you do the same thing with the battery attached?
- What happens if you apply an AC current to the capacitor? How is the dielectric affected? What types of polarizations are there? What are their cutoff frequencies?
- Can a microwave heat perfectly solid ice?
Spring 1989: E. Haller
- (Choose a topic from the board)
- Describe the Hall effect in detail.
- How could you determine the Hall coefficient experimentally?
- How could you determine the mobility from Hall effect measurements?
- Draw the m vs. T plot for an n-type semiconductor.
- Describe a p-n junction.
- Show a reverse-biased p-n junction and show the driving force for electron movement across the junction.
Fall 1989: E. Weber
- Why does the resistivity of a metal increase with temperature? Why doesn't it reach 0 at 0K?
- What is the mechanism of superconductivity, as we understand it now?
- What is the difference between direct and indirect band gaps?
- Show an Arrhenius plot of conduction in ionic solids
- What are para- and diamagnetism? What are their temperature dependences? At very low temperatures, paramagnetic materials become ferromagnetic - why?
Spring 1991: E. Haller
- Pick one: dielectrics, semiconductors, magnetic materials, optical materials.
- On semiconductors: What is the crystal structure of semiconductors? What is the coordination? How can the four outer electrons form 4 equivalent bonds when 2 are "s" and two are "p"?
- Draw a  projection of silicon. Where are the electrons in this picture? Can you go from here to an energy-band diagram?
- Where are the electrons at 0K? Is the valence band completely full? Down to the last electron? Write and graph the fraction of filled states as a function of energy, both at 0K and at some elevated temperature.
- What if you wanted more electrons present - what would you do? What were the populations of electrons and holes before? What are they now? What is this law called?
Fall 1991: E. Weber
- What is the difference between diamagnetism, paramagnetism and ferromagnetism?
- What happens atomistically (to the individual electrons) to give these properties?
- Explain the temperature dependence of the mobility.
- Why does resistivity increase with temperature in a metal? Why is the curve linear at high temperatures?
Spring 1993: Weber
- How does the resistance vary with temperature from a metal to a semiconductor to an insulator? Draw a curve for each.
- What is causing the increase in resistance for a metal?
- Do you know any numbers of conductivities for materials?
- How would the resistance of a metallic alloy that forms an ordered compound vary above and below the ordering temperature?
- Describe paramagnetism, diamagnetism, and ferromagnetism. Why are some materials paramagnetic, while others are diamagnetic? Why are some para and some ferromagnetic? What are the two competing thermodynamic forces? What's antiferromagnetism?
- Illustrate ionic conductivity in a solid. What are the slopes of s vs. 1/T? What determine the vacancy concentration in the low T region. Plot n vs. 1/T for a semiconductor. Why do the slopes change? Draw E vs. x. How does the Fermi level change with T? How would you determine the Fermi level from the concentration? write the equation. experimentally how would you determine carrier concentration? (4pt probe, Hall effect) In GaAs, midgap donors of 1E18 and shallow acceptors of 1E16 cm^-3. Where is the fermi level?
Fall 1993: Haller
- Choose a topic. (Semiconductors) What type of elements are intrinsic semiconductors? Donors? Acceptors? Draw E vs. k diagram for Si, for a direct band gap material. Where are electrons and holes? Describe the various means by which electronic transitions can occur. Then at very low temperatures.
- Draw the band diagram for a pn junction.
- Give an expression for the number of electron and holes in each region. Where are the space charges located? What is the region near the interface called? Is it possible to widen this depletion zone, how?
- For the topic of capacitors, main question: How does the capacitance change when you increase the reverse voltage?
Spring 1994: Haller
- What types of magnetism exist?
- Give examples of materials with each type. How does magnetism come about?
- How come Fe does not display magnetic properties?
- Why does it form domains?
- What are the boundaries of the domains called?
- Draw a detailed sketch of a Bloch Wall.
- How thick is it?
- How could your original sketch of the 2 domains reduce their energy?
- How could we change the domain structure?
- Does it take energy?
- Draw what happens as we apply a magnetic field to your iron sample?
- Why would you use Fe in a 60 Hz transformer?
- What would you use at 1 MHz?
- What is minimized when you cool ferromagnetic? Is iron magnetized when you cool it from melt?
- Discuss three types of magnetism.
- Draw hysteresis curve identify important points on the curve. What limits maximum B?
- Compare max B for Fe and Co.
- Discuss hard and soft magnets.
- A typical magnet has a field of about what?
- What types of magnet in a transformer, why?
- Draw band diagram for Si in E vs k and E vs x space. What's the band gap?
- Draw band diagram for GaAs. What's the difference between GaAs and Si?
- What happens with GaAs at high E?(answer: decreases mobility because mass gets heavier)
- With no doping why do you have electrons in the conduction band and holes in the valence band?
Fall 1994: Weber
- How do you MEASURE if a material is paramagnetic or diamagnetic? (Use inhomogeneous B field)
- Draw metal resistivity curve vs. T.
- At zero kelvin will an ideal, pure metal be a superconductor?
- How does impurity affect the curve?
- Draw Ionic (insulator) conductivity vs. T.
- Describe the different regions.
- Draw a general curve for metal resistivity again. Say the metal is niobium which has a superconducting transition. Draw on the same curve what the resistivity curve for niobium would look like. What is the mechanism for superconductivity?
- Draw a simple band diagram for a semiconductor (intrinsic). (shows periodic table). Say I add phosphorus (assume this is silicon) how does the band diagram change? What if I add boron? What about Zn? What about sulfur? What are the typical values for energy difference between shallow sites and the conduction or valence band? Say this band diagram is for GaAs. What would it look like if I had an As on a Ga site? What is this called?
- Why is the electron on the Phosphorus atom delocalized in a Si semiconductor? Is it a property of the Si or the P? (Dielectric constant of Si)
- How does the Fermi energy vary with temperature for an n-type semiconductor?
Spring 1995: Haller
- Draw a p-n junction. Are all of the carriers mobile on both sides? What would be the motion of the minority carriers? What type of current is that? *Draw the I-V characteristics of a pn diode. Does it have a linear relationship in the lower region? (no, exponential) What happens at the breakdown voltage? Are there different types of breakdown voltages? Why is it beneficial to operate a zener diode in the range of 50% zener breakdown? (thermal effects of zener and avalanche breakdown cancel each other) Draw a transistor (npn). Which region is the base, emittor, collector? How would you create a gain from it?
Fall 1995: Weber
- How can one find the energy of formation of a vacancy? What doping level is needed to find the effect of solubility of Fe in Si? Explain the difference between diamagnetism and paramagnetism. What is the lowest energy state for a ferromagnet which is first raised to a high T and then slowly cooled?
Fall 1996: Weber
- Describe the mechanisms of conductivity for insulators, metals, and semiconductors?
- Explain the slope of conductivity vs. Temp. for an ionic compound.
- What is the charge of a Na vacancy in NaCl?
- Explain conductivity vs. T for a metal?
- How does the number of carriers vary with T for a metal?
Spring 1998: Haller
- Choice of 2 out of four: magnetic materials, semiconductors, dielectrics and optics, superconductors. Magnetics: draw a hysterysis curve for soft and hard magnet. How does BvsH and MvsH go as they saturate? What kind of applications use hard and soft magnets? What material is a typical magnet made of? Why does a magnet form domains and what are the boundaries between domains called? Sketch the domain wall.
Spring 1999: Haller
- PLot how the resistivity change with temperature for supreconductor (Nb)
- How to prove that reisitivity is zero for superconductor
- What happen if we applied field on superconductor. Why? Who found induction current? (Faradey) What you know about BCS theory? How long the Cooper Pair is? Is there any other electron in between? How long a Cooper Pair can exist? How large bonding energy between this Cooper Pair is. Just below Tc,
how many fraction of electron can form Cooper Pairs? What is Type I and Type II superconductor and how can you make it. Pure Nb is Type I or II?
- How about YBCO?
Fall 1999: Sands
- We are discussing electrical properties today. (Gives a log conductivity vs 1/T plot with A,B,C,D curves overlaid). Take a minute to review this and then discuss each curve. (There is an extrinsic seminconductor w/o compensation, superconductor, pure metal and dirty metal. The pure metal has a slight dependence on T, the dirty metal is constant w/ T). What are the various regimes and slopes of the semiconductor curve? Explain the temperature dependence of the pure metal curve.
- What is the source of resistivity here? What about for this curve (dirty metal)? Do you know a typical resistivity for a good conducting metal?
- (Draws M-H loop). What is the significance of this point (coercivity)?
- Explain the rectifying behavior of either a pn junction or a Schottky diode. (chose pn junction) What happens in forward bias?
Spring 2000: E. Haller
- Draw in E vs. k space the difference between a direct band gap and an indirect gap semiconductor. How would you determine if a semicond. is direct or indirect?
- Plot abosorption vs. energy. What is the linear absorption coefficient? How do the plots for direct and indirect semicond. differ and why?
- Describe in the E vs. k diagram the mechanism by which a direct and indirect semicond. absorbs. Why is the indirect absorption process less likely?
- Why do photons create a vertical transition while phonons a horizontal one? Whatâ€™s the band gap of Si? Whatâ€™s the â€œdirectï¿½? gap of Si? How much energy does a phonon carry? Based on this information, what can you say about the two peaks in an indirect semicond. absorption? What about the heights of the peaks. Are they the same? Whatâ€™s the difference in engery between the two peaks?
- If this measurement was done at low T, there are very few phonons. Why does the indirect transition still occur?
- If you have diode made of indirect semicond material, can electrons and holes recombine? The answer is yes to some degree. How do they recombine if conservation of momentum still needs to be satisfied and there are no phonons in your crystal?
- What about absorption in semi-insulating GaAs?
- If you have a recombination event at a deep trap or level, where does the energy go? The energy that is then absorbed is about 20 times more than that of a phonon. So can phonons still be generated?
Fall 2000: Weber
- How does no. of carriers vary with temp. in metals? What is a typical value?
- Give ï¿½?ï¿½ or ï¿½?ï¿½ vs T for metals, semiconductors (compensated and uncompensated) and ionic material (Extrinsic dominated by defects, intrinsic has 2x the slope). Explain the mechanisms in each. In ionic conductivity, why does the number of vacancies in extrinsic regime exceed the equilibrium number? Can you name and explain main types of magnetism. Also, explain why a paramagnetic material turns ferromagnetic? What happens above Curie Temp.? If you had to guess what metals on the periodic table would be diamagnetic (one d or two d electrons), which would you guess?
Spring 2001: Haller
- Pulls out the prelim guide. Flips through it. "Have you seen this?" Picks a question. Magnetic Materials - describe the types of magnetic materials. Tell me a simple experiment you can do in order to determine if a material is diamagnetic or paramagnetic? (Use a magnet and see if the material is attracted to or repelled from the magnet). What happens as you increase the applied field? What if you increase it beyond the saturization magnetization, then what happens? Draw the hysteresis curve. What is the difference between the behavior of B and M on the hysteresis curve, when you get beyond the saturation point?
- Curie point - what happens if you heat a magnet above the Curie Point? Why, does the exchange energy get smaller? (No, but it is dominated by the thermal energy in the system). Who was the first person to describe the exchange energy?
What does iron look like if you cool it from the melt? Is there a net magnetic field? Why do domains form? What are the domain walls called? How thick are they? What happens as I start to apply a field to the domain walls? What does the area in the curve represent? Would the hysteresis curve which you have drawn be good for a transformer? What would happen if you used a hard magnetic material for a transformer? What kind of material should you use for memory? What two properties are important (switchable, but not erasable).
- What types of magnetism exist? How does magnetism come about? How come Fe does not display magnetic properties? Why does it form domains? What are the boundaries of the domains called?Draw a detailed sketch of a Bloch Wall. How thick is it? How could your original sketch of the 2 domains reduce their energy? How could we change the domain structure? Does it take energy? Draw what happens as we apply a magnetic field to your iron sample? Discuss three types of magnetism. Draw hysteresis curve identify important points on the curve. What limits maximum B? What is an easy way to tell if a material is para- or diamagnetic? (Bring it up to one end of a bar magnet) Discuss hard and soft magnets. What types of magnet in a hard disk, why?
Spring 2002: E.E. Haller
- Picked magnetism. List types of magnetism. What differentiates ferro- from para-? (what is necessary?) Who first postulated this? Draw a **B** vs H curve.
- What is the slope of this curve at high fields (mu_naught). How are B and H related in a vacuum? What applications are ferrites used for? Why would they be better than metals (insulators)? How will eddy currents affect the magnetic response of a material (in terms of frequency - answer-> can't respond to high frequencies). For magnetic recording materials, there are two competing design criteria that need to be balanced - what are they and what demands do they put on the material chosen? Move on to p-n-p junction. What are its parts? How must it be biased for use as an amplifier? What part does the collector play? What about the emitter? What conditions (geometric) must the base satisfy?
He decides to talk about Shottky barriers. We then talk about what the band diagram in E-x space looks like. We have an interlude where we talk about the Work function and how you measure it. (Know who got the nobel prize for photoelectric effect) Then we finish drawing the band diagram. Then I draw a regular P-n junction. He asks about the switching of the two barriers which one is faster and why (minority carrieres). Talk about diffusion and drift currents. Then we started talking about superconductors. Cooper pairs how they form how strong is the bond between them. What is electron? Some basic stuff about elecron, such charge, mass and spin.
- Draw the electronic potential vs. distance in periodic lattice. Draw E-k for free electrons and electrons in lattice. What is band gap? Can the electrons move in valence band, and why? Fermi level and mass action law. How many types of currents in P-N junction, what are they? Draw the band diagram for p-n junction, how do the electrons and holes move in that... Now put a forword bias, how do the currents change? Now put a reverse bias, how do they change? When a p-n junction first put together, what will happen? Where do the positive and negative charges come from in the depletion zone? Draw I-V curve? What is the reverse current in this curve? Does it change with V? Write the current equation of p-n junction? what is the material character in this equation? What's the charge density, E-field, and potential across the junction. Driving force for the forward bias current and reverse bias current. What are the types of magnetism? Which two are related among dia, para, and ferro? What is the physical reason for ferromagnetism? Discuss Bloch walls.
Fall 2002: Haller
- Semiconductors: Questions about the hydrogenic model for shallow dopants and freeze out curves.
- What is an intrinsic semiconductor, what is an extrinsic semiconductor? Draw the band diagram of both. How does mobility vary with temperature? How does the Fermi level vary with T? How does the electrons concentration change with T? How does the p-n junction current change with applied voltage?
- What is a semiconductor, what is doping, how to get n type or p type semiconductor.
- Magnetism: What is magnetism? What are the different types of magnetism seen in materials? Describe all of them? What class of materials are usually ferromagnetic? (metals) What are ferrites and what kinds of application are they important in?
- If you say that Fe is ferromagnetic, would you expect a piece of iron quenched from the melt to be a magnet? Why not? Talked about domains, and domain wall motion. How thick is a domain wall, why? How much energy does it cost to move a magnetic dipole in a magnetic field?
- Draw an M vs. H curve for a soft ferromagnet? Now do the same for a hard one. How does this differ from the B vs. H curve? What is the slope of the B vv. H curve at high fields?
- If you need a material for a hard disk, what kind of material would you choose and why? What are the two competing criteria?
Spring 2003: Dubon
- If two crystals have the same bandgap why would they have different resistivities? (Resistance due to carriers, Probability of occupation is a function of density of states which could be different even though the bandgap was the same.) Magnetism: How does a magnetic field affect a paramagnetic material? (Draw a H vs. B diagram.) Whatâ€™s going on within the material at different points within the curve. Why doesnâ€™t the curve follow the same path in both directions? Is there a linear region, why?
Fall 2003: Suzuki
- What causes resistance in materials? Draw conduction or resistance versus temperature for a metal, semiconductor and insulator. Explain the physical/quantum meaning to these curves. What is the slope of each curve. What are the mathematical relations? What happens when a magnetic field is applied to a material? What are the various types of magnetism? Describe each. Describe the optical appearance of a metal, semiconductor and insulator using their band structure. (reflectiveness, color, transparency) Why is copper reddish? (This was her first prelim and the optical part might have been a little out of scope but good to know anyway.)
Spring 2004: Haller
- Allows me to choose from 4 topics. I choose magnetism. Asks for the different classifications of magnetic behavior. Describe diamagnetic, paramagnetic, and ferromagnetic behavior and give an atomistic description of what gives rise to each of these behaviors. How I would test to see if a material is diamagnetic (see how it is deflected by an inhomogeneous field)? Asks how a paramagnetic material would behave in the field. I had said all materials have a diamagnetic response, he asks, if that is true, then why do we also see other magnetic behavior. Asks me for the energy of a magnetic dipole (E = Î¼B). Asks me what would be the effect of temperature on a paramagnetic material in the present of a magnetic field. Asks me questions about iron, a ferromagnet. If you had a chuck of iron, would it be magnetic? I said it is ferromagnetic, but it may not have a net magnetic moment. Asks why. Asks me to draw the microstructure. I draw a multicrystalline structure with different orientations of easy directions and a showing a detail of one grain with several domains. Asks me why the domains form. Asks me if there external field for my domain structure will be zero (not completely zero, there can be some field from corners and edges). Asks me what gives rise to the magnetostatic energy. Draw a B vs M curve. Why does it have the shape it does? What if it were a single crystal.
- Allows me to choose two topics and then picked the second one (i.e. the one I didnâ€™t know). Electrons in solids: For a metal how do you model electrons quantum mechanically? What are the boundary conditions? How many electrons can be placed in a particular energy level? What is the density of states in thee dimensions? How will the electrons fill the energy levels? How do you determine probability of filling particular energy levels? How is the density of states changed for a semiconductor? How does it change in a thin metallic film? Show the conductivity or resistivity vs. temperature for a metal and a semiconductor. Over how many orders of magnitude can the conductivity of a semiconductor be effectively controlled?
- Magnetism questions: What types of magnetism are found in materials? Why do they arise? Do all materials exhibit diamagnetism? Plot them on an MvsH curve. Why do ferromagnets have domains? Where are the field lines? What does the area under the curve represent? How would you engineer a material to have different curves? Why would you add Si to Fe?
- Magnetism questions: Brings out a box of magnetic devices, asks me what they are and how they work. What happens if you plug a transformer into the wall? What is magnetostatic energy? How do you minimize it? What are domains? Bloch walls? Who came up with a theory of induction? What are eddy currents? Draw a hysteresis loop for iron? Why are domain walls a finite thickness?
- Magnetism questions: Brings out a box of magnetic devices, asks me what they are â€“ see a transformer, some magnetic tape, and something that is a ferrite (answer that it is a ferrite after he says it is non-conducting). Three types of magnetism? Comparison on Dia- and Paramagnetism. How could you tell the difference? Which direction does each go when placed in inhomogeneous magnetic field. Then onto ferromagnetism. Mechanism of dipoles because of exchange energy. Onto domain, lots of questions because drawing wasnâ€™t quite right â€“ how to minimize external field. Questions about details of Bloch walls. Back to the transformer, soft vs. hard hysteresis loops. End with a few materials questions about how to make a soft magnet.
- Two topics: Semiconductors and Electrons in a Solidâ€¦questions dealing with modeling electrons quantum mechanically and extrapolating that to an electron in a 3D boxâ€¦What is the nearly free electron model and how does it relate to materials? (this was his connection to semiconductors) Why does Si have a bandgap and what type of material is it at T=0K? Why does the Fermi Energy not sit EXACTLY in the middle of the bandgap in intrinsic Si? Why does Phosphorous work as a shallow dopant in Si but NOT Nitrogen?
- Chose superconductivity: What was the experiment in 1911 when they discovered superconductivity? Why did they do it? (because they could- they had developed new cooling technology) Difference between type I and II superconductors. Which one do you want to use generally? Graph the relation between H and B. How do you predict what will be a good superconductor? How do superconductors work? Whatâ€™s in between electron pairs? How long do they last? Can there be other electrons in between? How are they coupled to the lattice?
- Given electron transport. What is electron transport dependent on? Start by talking about electrons as fermions. Why are there free electrons in a metal? Talk about bonding. How many free electrons per atom? How would you determine the density of carriers. Derive the Hall effect. How would you measure it? Back to electrons in a metal, how do you need to think about them quantum mechanically (as waves). How are the wavefunctions related. Draw a 1-D potential well. Solve for the wavefunctions and the energy eigenvalues. Draw solutions to the potential well. Asks you for the equation of an energy eigenfunction that you drew. Back to the metal. What determines the number of electron energy states available? How do the density of states vary with energy.
- Insulators: What defines an insulator? Show me an equation (q=cV) What is the equation for capacitance? How does capacitance vary with size of capacitor, distance between the plates, and type of insulator between the plates? What were Faradayâ€™s experiments? What are two ways dipoles form? What is waters dielectric constants? How does this relate to an appliance in the home? (microwave) Explain how microwaves work? Then we switched to semiconductor metal junctions? And Iâ€™m spent.
- Chose p-n junctions and metal-n-type semiconductor junctions. Draw the metal-n-type junction. Show me the work function for both. Locate the electrons in both. Show what happens for the forward and reverse bias. What happens to the Fermi level when you apply a reverse and forward bias? What directions are the electrons flowing? Draw the current vs. voltage for the junction. Draw the p-n junction. Show me the work function for both. Show what happens for the forward and reverse bias. What happens to the Fermi level when you apply a reverse and forward bias? Locate the electrons in both. Spoke about energy barriers. What directions are the electrons flowing? Draw the current vs. voltage for the junction. What is responsible for the current in the forward and reverse directions? What applications are n-p junctions used for? Talked a little about traffic lights and InGaN. We spoke a little about direct and indirect band gaps, photon and phonon emission.
Fall 2004: Ramesh
- Magnetic properties: why does iron become magnetized? Why do domains form? Can oxides be ferromagnetic? (Yes, iron oxide = ferromagnetic). *Superexchange interactions. Spin polarized materials â€“ manganese oxides. Ionic conduction â€“ how to measure activation barrier for ion diffusion. How to make Ohmic contacts â€“ not platinum!
- Are there any conducting polymers? How can you make a polymer conducting? He suggested a benzene ring and asked what would happen if I add a benzene ring. I explained to him what happens. Then he asked about a metallic polymer. Then talked about magnetism and why it exists. What is a ferromagnet? Give examples. What is the difference between the ferromagnet you stated and antiferromagnetism?
- Describe the different band gaps. Which type is Si? What is the energy level of a p-type and an n-type semiconductor. Is an atom of Fe magnetic? Ferromagnetic? Where does the magnetism come from?
- Jumped right in to double exchange. Do you know the slater-pauling curve? How could you stabilize a manganate as ferromagnetic? Why would the nickel in Ni2MnGa not contribute to the moment? Talked about life.
Wanted to talk about magnetism in relation to shape memory materials (my research concerns a non-magnetic shape memory alloy). Wasn't familiar with these, so discussed ferromagnetism in general. Why are some materials (even with unpaired electron spins) not ferromagnetic while others are? No discussion of electronic properties.
- Why are ferrites interesting in magnetics (because they are insulators) and what kind of magnetism do they display (ferrimagnetic)? Why does Fe display ferromagnetic behavior (talked about exchange interaction). Is the same mechanism responsible for the ferromagnetic behavior of dilute magnetic semiconductors?(No) If not, what do you think the mechanism is? (hole-mediated)
- Is there a way to make several antiferromagnetic/paramagnetic materials ferromagnetic through alloying? What is the mechanism for this to occur.
Spring 2005: Haller
- Gives choice of: semiconductors, magnetism, optical properties, or superconductors; pick one.
- What are the different types of conductivity?
- At low temperature, where are the electrons in a semiconductor? What is the electron population away from the Fermi energy?
- What does the density of states look like for metals? For semiconductors? What is the energy dependence?
- Draw a simple band structure (energy vs. spatial coordinate) for an n-type and a p-type semiconductor. Why is the Fermi level (chemical potential) closer to valence band in one of the diagrams but closer to the conduction band in the other?
- If the material is GaAs, what elements could be used as donors? As acceptors? On which sites would each sit? Draw donor and acceptor levels on a diagram.
- What is an intrinsic/extrinsic semiconductor? Is there really such a thing as an intrinsic semiconductor?
- What is the formula that determines the number of carriers in each material (n-/p-type)? Why must the Fermi-Dirac distribution be used? What is the dependence of the density of states on energy? If and n = 1015, what is p?
- What is a donor/acceptor? Describe excitation of electrons/holes from donors/acceptors into the appropriate band. What is the band gap of silicon? What are typical ionization energies for silicon dopants? Why is the ionization energy of a donor nearly the same irrespective of which element acts as the donor?
- How can you tell the difference between a semiconductor doped with x donors, vs 2x donors, or x acceptors? (Mobility measurements will be different due to the presence of a greater number with [x] donors versus [2x] donors and [x] acceptors? Of scattering centers for second case).
- Is there a simple way to model the orbit of electrons around donors (holes around acceptors)? What is this relation and upon what material properties does it depend?
- Draw a P atom in a field of Si atoms. How is the Bohr radius of the extra electron affected? What causes this effect?
- Draw E vs k. How is the mass of the electron represented in this graph? How does this affect the ionization energy?
- How can you characterize whether a semiconductor is intrinsic or extrinsic with compensatory doping?
- What determines the resistivity (or conductivity) of a semiconductor? How does carrier mobility depend upon temperature in an extrinsic semiconductor? â€¦in an intrinsic semiconductor?
- Draw a p-n junction, starting with Ef. Show the 4 currents present. How do these currents arise? Which current is most dependent on T? Draw the IV characteristics of the junction.
- Write an equation for the diffusion current. If the minority carrier lifetime is increased, what happens to the diffusion current?
- Draw carrier concentration vs 1/T. The high temp regime is the intrinsic regime. If I have an extrinsic semiconductor with doping levels Na and Nd, what is the carrier concentration at very low temperature? (kT~1mV)
Fall 2005: Suzuki
A few straightforward questions (answer for the last one not as straightforward).
- why are the group I,II elements metallic?
- Draw a bar magnet. Draw the poles and the field lines. If I take another magnet and place it at various points around this one, how will it align?
- Can an atom be magnetic? What is the origin of magnetism? (Details! Coulomb, pauli, exchange, all conceptually.)
- Describe diamagnetism, paramagnetism, ferromagnetism.
- What is Lens Law?
- What are Bloch walls, what size are Bloch walls?
- Describe the parts of a hysteresis curve. How are the curves different for hard and soft magnets?
- How is energy dissipated?
- What is magnetostatic energy?
Spring 2006: Haller
No choosing your topic this semester, I walked in and he said, "How comfortable are you with semiconductors?" Asked me to define the difference between intrinsic and extrinsic. Is it possible to be all intrinsic/all extrinsic/ both? Draw the freeze-out curve for Si and Germanium (asked for the band gap energies for both). How would you model dopants (I didn't know)? Walked me through the basics of the hydrogen model (why the dielectric constant and effective mass are important).
Fall 2006: Ramesh
Let's talk about magnetism. Here are two materials Fe and Cu. What determines if these solids are magnetic or not? Draw the electronic configuration of Fe and Cu. (i.e. 1s22s22p2...) (just know the valences of the 3d transition metals beforehand) Now draw the electrons in the atomic orbitals. (i.e. draw five boxes (as you do in chemistry class) representing orbitals and fill them with arrows representing electrons)
Why is Fe magnetic and Cu not? (well actually they both have magnetic moments, but Fe is ferromagnetic Cu just shows paramagnetism) Talked about the energy favorability of having electrons with aligned spin in Fe: exchange energy vs "band energy" How do electrons know that another electron is spin up or down? In other words, why do electrons align? Would a ferromagnet be magnetic at high temperature?
An alloy of Al, something, and something, it is ferromagnetic even though its constitutive elements are not. Would this chunk of material be magnetic or do you have to do something to it? Why do domains form? If you had an infinitely large chunk of Fe, would it have domains? Would it have magnetostatic energy? At what point will domains form if you start decreasing the size of the chunk? What applications could you think of for Fe since it is magnetic.
If you have up spins and down spins and you apply a magnetic field, what happens? Now suppose we have also added an electrical potential. Is it possible to control the electrical properties in this device? (Yes, you have a larger current if you conduct with up spins, if they are aligned parallel to the mag field. If it is possible to control whether up or down spin electrons conduct, you would have a larger population of the spins that are parallel with your mag field.)
Draw the Iron-Carbon phase diagram. What is the crystal structure of iron? Does the crystal structure change as you raise the temperature? Why does iron go from BCC to FCC and then back to BCC? Similar questions as those listed above regarding domains, magnetostatic energy, the demagnetizing field, etc. He also asked about the the origin of echange energy and whether it was directional or not. Is a material required to be crystalline in order to be magnetic? What about a metallic glass? (No, it doesn't. Yes, metallic glasses can be magnetic. He was trying to get to the point that exchange energy is non-directional and depends on separation distance.)
Spring 2006: Haller
As he has done before, Prof. Haller let you choose what topic you wanted to talk about from three options (semiconductors, optical, magnetic, superconductors, and so on...).
- What is a semiconductor and how do its properties compare to that of other materials? (conductivity)
- Can you write an expression for the conductivity of a material?
- What are the dominant terms?
- How does conductivity vary with temperature?
- Why is it different for metals and semiconductors?
- Does the temperature have a different effect on the mobility of an electron in a metal vs. in a semiconductor?
- Draw the band diagram for a n-type semiconductor.
- Suppose that this is Si, what is the band gap?
- What is the energy difference (in eV) between the conduction band and the Fermi level in n-doped Si?
- How do you dope Si?
- If instead of Si, you have GaAs, how do you dope it to be either n or p-type?
- When you dope it, what happens to the extra + or - charge? Doesn't the atom have to follow the Lewis Octet rule?
- Topics to choose from, although not everyone had the same choices: magnetism, semiconductors, and insulators. Chose magnetism. Everything contained in the few pages of Barrett, Nix, and Tetelman. Know it all. Explain how domains change as you proceed through a hysteresis loop. Know how to explain the type of hysteresis loop you draw, if asked to draw one. I drew a very hard hysteresis loop. If a sample is placed in a gradient magnetic field, which way will the sample move if FM, DM, PM. Know who discovered domain walls, and who postulated existance of domains - first and last names. Really impress him by knowing where they came from.
- Magnetics -- describe different ferro, para, and diamagnetism. What test can you do to determine whether a material is a para or a dia. Draw the hysteresis loop for a ferromagnet and explain. Difference between hard and soft magnets and their applications.
- What are the types of magnetism? Is there such a thing as antiferrimagnetic? How could you tell paramagnetic, diamagnetic and ferromagnetic apart?
Talk about hysteresis. Where is the energy loss? Draw domain structure. What about if you applied a field? Why do you use ferrites? What would you use for a transformer? How do you make a magnet harder? What about for magnetic tape?
- Choose between semiconductors, fiber optics, or dielectrics. Chose semiconductors. Draw band diagram of intrinsic semiconductor. How does it change if you put in a donor or acceptor? Draw carrier density versus temperature curve and explain significance of different slopes. What is a common donor/acceptor concentration in a semiconductor?
- Pick from three areas: Semiconductors, Superconductors or Magnetic Materials. I choose semiconductors. Define a semiconductor. (I did in terms of conductivity) Define conductivity and resistivity. Asked for more about semiconductors. (Discussed number of charge carriers). What is carrier concentration in a metal? Why is the number of carriers lower in a semiconductor? (Talked about filled vs. unfilled bands). Asked me to draw a band structure. How would it look for a metal? How would it look for a semiconductor? How would I make an N or P type semiconductor? What elements could I use? Why is GaAs semiconductor used for optical devices instead of Si?
- Magnetics: What are the different types of magnetism? Draw M vs. H for a ferromagnetic material. How can you tell if a material is para or dia magnetic? Describe magnetic domains (width and energy considerations). How do they grow with an applied field. What is hysteresis? How does it relate to energy loss? Hard vs. soft. What is usefull about ferrimagnetism, and what are some applications of it.
Fall 2007 - Dubon
- We're going to talk about...SUPERCONDUCTIVITY. What is a superconductor? Why does it act as a perfect diamagnetic? (Lenz's law current repels the field) Where is this current? (around the outside of the super conductor). How can you verify whether you have a super conductor or not (Magnetize the superconductor and cool it)? What's the difference between type I and type II? Can you draw the curves for this (H vs. M)? What's the difference between a paramagnet, diamagnet, and ferromagnet? Can you draw these on the same plot? How's a paramagnet different than a ferromagnet? What makes a semiconductor different than a metal? Ended up drawing density of states, fermi probability, described fermi energy. Questions were quick and numerous.
Spring 2008: Professor Haller
Magnetism: What kinds of magnetism are there? Give examples of each. How does Ferromagnetism come about? What is the long range order? Why does it form domain? What is the domain structure when you solidify Fe from melt? What happens to its magnetization when you apply field? Is M parallel to H? What about B? Does M eventually saturate? What happens when you reverse the applied field? What is happening to the domain? What does the area mean? Draw a hard and soft magnet. What would you use for computer? What about transformer? What material is used for transformer? What else do they add to the material? What shape are the transformers? Why?
Superconductor: What happens to Tc if we used a different isotope of Hg?
3 choices (different for everyone): The electron, Kronig-Penney Model (pg. 174 Kittel) and Optics (seriously).
- Chose The electron
- Write down everything you know about the electron
- What is the charge?
- What is the mass?
- Talked about wave-particle duality
- What is the wavelength of the electron related to? Derive this. Who came up with this?
- What is the wavelength at room temperature?
- Switched to solar cells:
- Draw a solar cell
- What happens when I put a p and n type semiconductor together?
- What is the driving force for transfer of charge?
- What limits the lifetime of electrons in p-type material?
- How long do they live in silicon?
- What does an impurity look like in an E v k diagram?
- What two elements drastically reduce minority carrier lifetimes in silicon?
Fall 2008: Haller
He's friendly but also quick to tell you you're wrong! He starts the day with a list of 4 to 6 topics on the chalkboard. He lets you pick. As the day goes on, he erases the topics that have been chosen by several students, leaving the little discussed topics for the students who take his section last. Be wise here! He will also ask if you know key figures in history, like who discovered something, but although he'll be impressed if you know, he also loves to tell you the answer AND a story! The topics were semiconductors, superconductivity, magnetism...but you can expect others, like the electron, the solar cell, etc.
- Semiconductors: What's the difference between an intrinsic and extrinsic semiconductor? What might you use to dope Si? Describe the different between p vs n doping and draw a picture. Draw a picture showing As-doped Si. Draw a picture of B-doped Si. Draw a graph showing how the carrier concentration in the conduction band of n-type Si depends on temperature. Who calculated the radius of an electron orbiting the hydrogen atom? What is the energy of the electron orbiting hydrogen? Relate the semiconductor to the photovoltaic cell. Talk about band gaps of semiconductors (know relative sizes for prominent semiconductor types, like Si, Ge, etc.). Relate band gaps to wavelength of light. Don't call the band of Si small just because it's only a few eV!!
- Magnetism: What are the types. What's the physical source of the types. What's the difference between diamagnets and paramagnets (attract or repel). Domain walls: How thick are they, and how do they move? Exchange energy. Draw hysteresis loops for hard and soft magnets. What do you use hard magnets for? What do you use soft magnets for? He got excited when I said I'd never seen a transformer, and he pulled out his box of transformers to show me. How do they cut out eddy currents? They make the magnets into thin slabs!
Spring 2009: Suzuki
- What is the equation for conductivity in pure Cu wire/metal? [sigma=mu N e = e tau/ m N e = e^2 N tau/ m]
This conductivity is not the measured conductivity, so what could be different? Use N at the fermi level and the reduced mass. In other words, What is mobility in terms of the â€œtime to collisionâ€? Why does this conductivity expression not model conductivity in Cu well?
- Why does Cu look shiny and why is it reddish? How does the electromagnetic wave affect the metal? Draw the density of states for Cu and explain why it has a reddish hue [the transition from the denser area of the d band to the fermi level has a gap equal to blue light, so copper looks red]. The 4s state looks like a very narrow arc of a circle with the thin d states in the middle of the 4s.
- Explain what a diamagnetic material is and how it can float in a magnetic gradient (she shows a piece of graphite floating over some magnets aligned to give a steep gradient). Write down the expression for the force on the magnet with respect to the magnetic field. Write the potential energy in terms of the Magnetization and Magnetic Field vectors. Draw the gradient field of the magnet. [F=-grad. U U=-m dot H, F=m grad H.] Show how the directions of these vectors is a force opposing the gravity pulling down the magnet. When a diamagnet is in a magnetic field gradient show why the diamagnet floats.
Fall 2009: Haller
As in previous years, three topics were written on the board (superconductivity, semiconductors, magnetism). Choose one. Questions below are specific to which topic the student chose. Just to give some general advice for Haller: read Barret, Nix, and Tetelman. He asks questions that come pretty much straight from this book; however, don't rely on it exclusively! The last edition was in 1973, and a lot has changed in 35 years. For example, giant magnetoresistance wasn't discovered until the 80's, and new types of superconductors (especially high-Tc materials) have been developed.
First student chose semiconductors. Many of the questions that he asked came out of what I had drawn for the previous question. His opening question was thus: explain the difference between an intrinsic and extrinsic semiconductor. I drew an intrinsic freeze-out curve, demonstrated asymptote of the carrier concentration at low temperatures, due to unavoidable impurities. I then drew an extrinsic case, showing a saturation regime. He wanted to make sure I understood that in the extrinsic case you have many orders of magnitude greater carrier concentration at the saturation point than in the intrinsic case, but in BOTH cases you have saturation at low temps. How do you get carrier concentration from this plot? I answered Nd is the extrinsic saturation level that I drew. He quickly corrected me: it’s Nd-Na. Always have some concentration of acceptors, even 99.99999% pure germanium has acceptors.
He then asked if I knew the hydrogenic model. I began by discussing phosphorous n-type doping in silicon, drew a crystal demonstrating a single ionized core atom with a large effective Bohr radius for the electron, discussed its relatively weak binding energy. He then asked me for the equation to describe the binding energy of the dopant. I wrote an equation, screwed up on a few terms, so he urged me to correct it. First, split the dielectric constant it into two components: E0 for hydrogen and E for the substrate matrix (e.g. Si). Now, he suggested that the dielectric constant was much more influential. So I changed it so that it was squared. Next was my location of the effective mass, which was initially in the denominator. Clearly that’s wrong, since he’s mentioning it. Can’t just move it to the numerator, he wants you to understand why it belongs in the numerator. He says draw a direct-gap E vs K plot. Done. What’s the effective mass? I say it’s the curvature of the bands, wrote D2E/Dk2. Not right. Does a steeper slope have a larger effective mass or a smaller effective mass than a wider slope? It’s the inverse of D2E/Dk2. Okay. Effective mass belongs in the numerator. What’s the binding energy for hydrogen? 13.6 eV. What’s the dielectic constant for silicon? No idea… looked it up afterwards and it’s 11.7. Asks for germanium. Again, no clue. He informs me that it’s 16. Okay. What is the range of effective masses for semiconductors? He tells me about InSb, effective mass of 0.1. And that’s the end.
Second student chose magnetism. What do you know about magnetism? (I start by saying there are two categories, induced and spontaneous and give examples of each.) He asks me to explain paramagnetism. Then ferromagnetism. If I have single crystalline Fe, what does the domain structure look like? What happens if I apply a magnetic field? What two energies are competing in domain orientation? Wanted me to say Weiss came up with the domain theory (magnetic domains are also called Weiss domains.) What does the magnetization look like at a domain boundary? (Bloch wall) Does it change orientation gradually or not? Over how far a distance is this change (~1000 Angstroms). We then talked about hysteresis curves for hard and soft magnets, citing examples of devices that use each. What is the quantity represented in the area of a hysteresis curve (the energy to go around the loop). If this is so, what kind of magnet do I want for a transformer? He then wanted me to talk intelligently about transformers. He then asked me if there was anything else I knew about magnetism, asked me to describe diamagnetism.
Third student chose magnetism. He hands me a piece of chalk and asks how can I check to see what type of magnetism this material exhibits. Haller actually led me to the answer, I didn’t know how to answer this. But the answer is that if you apply a very strong divergent magnetic field, the material will either be repelled (diamagnetic) or attracted (paramagnetic) to the field. Simply place the chalk on a string and see which way it pulls in relation to the magnetic field.
Name some materials that are paramagnetic. Why are they paramagnetic? What materials can you think of that are diamagnetic. Why? What materials exhibit ferromagnetic properties? (Nickel, iron, and cobalt). Why are these materials ferromagnetic? What causes spontaneous magnetism? Are there other materials that exhibit spontaneous magnetism? (Yes, antiferromagnets and ferrimagnets) What are domains? What causes domains to develop? If I casted an iron material from liquid, will it have domains? Why? What type of magnetostatic force would you expect from this material? (very small to zero magnetostatic force since domain formation will reduce magnetostatic force). Draw me what you think the domains would look like in the material. What happens between the domains? (There is a Bloch wall) Does this Bloch wall have a magnetic moment? What determines the size of the domain wall? (Two competing forces – exchange energy and MAE). In iron, what is the typical size of the Bloch wall?
Due to a large class size, two professors handled the prelim this semester.
- Plot resistivity versus temperature for a metal, a semiconductor and an insulator. Explain each.
- What is the equation for conductivity for Cu? (sigma = n e mu). What is mu?
- If we measure the conductivity, it isn't the calculated value. Why?
- She wants you to talk about n as a function of DOS at fermi level, and how this equation is semi-classical and doesn't completely describe what's going on.
- Plot magnetization versus T for a ferromagnet. Same for paramagnet and diamagnet (with a very small applied field). (Ferromagnet: looks like eta vs T for mutation; paramagnet: Weiss-Curie plot; diamagnet: M is independent of T, horizontal line)
- Explain what happens when a metal and semiconductor are joined. (Schottky barrier if work function of metal is greater than that of semiconductor, ohmic if less)
- Can you show what a plot of an ohmic contact versus a Schottky contact would look like?
- What is origin of magnetism in atoms? What is the exchange interaction?
Unlike previous years, this year he chose which topics to ask students rather than giving us a choice. He started out by saying that he wanted the simplest explanations possible.
- Plot the resistivity of a metal and a semiconductor.
- What is the equation for resistivity? (rho = 1/sigma = 1/(n*e*mu))
- Explain the plots using that equation. (In metals, n is constant with temperature, e is constant with temp and mu decreases because of phonon vibrations, the mean free path is shorter).
- What is an intrinsic semiconductor?
- Draw a freeze-out curve for a semiconductor, explain each part. (Include slopes and y axis intercepts, also had me add the section of the slope for compensated material and explain it.)
- What is the slope in the freeze out curve in the intrinsic region? What leads to the 1/2 term in the slope? (two particles are generated - an electron and a hole) What will happen if 3 particles are generated? (1/3 instead of 1/2)
- Draw a band diagram for an insulator, semiconductor, metal. Why should the band be exactly filled?
- What is the crystal structure of silicon?
- Talked about Energy band diagram for addition of donors and acceptors and how compensation works. What is the typical ionization energy for donors?
- What model can be used for the donors? (Hydrogenic model). Write the equations for it. How do you use that to calculate the energy? (multiply by effective mass and divide by epsilon^2)
- Plot a p-n junction and explain what is happening once the materials are connected (e's from from n to p side, h's from p to n sides, depletion layer makes e-field and balances flow out). plot charge, e-field, potential vs x. Relate it to Poisson's equation.
- Draw the resitivity Vs T for normal metal (like Cu) and a superconductor.
- Explain why the curve is like that. He wanted you to be more careful about the qualitative height of the resitivity for both of them in normal state.
- Asked about the mechanism of superconductivity - talk about Cooper pairs, then Messiner effect.
- Asks me to tell him about dielectrics. (I ask what he wants to know, and he kinda shrugs. I mention that they are insulators and start talking about capacitance.)
- Explain Faraday's experiments. (I ask what those were, and he outlines the parallel-plate capacitor, add a dielectric at constant voltage or constant charge experiments.)
- What happens in each case, by how much do the voltage and charge change? Why does this happen?
- How does polarization work? (I draw a nucleus and electron cloud relatively displaced). What about for water?
- Draw capacitance as a function of frequency (I can't; he talks me through water having a resonance at microwave oven frequency, then drops it).
- What are the various mechanisms of polarization? Which one is fastest?
- Which metal conducts electrons fastest?
- Anything else you want to say about dielectrics?
Haller is very intimidating but will talk you through things if you don't get it right away; I think he sometimes asks questions he doesn't expect you to know with the expectation that he will have to explain. E.g. what is the dielectric constant of water, of plastics, etc--he was perfectly happy to give me the answers, from which I had to reason something about the polarization mechanisms.
Student 1: Magnetism
- Write down as many types of magnetism as you can.
- Which of these is the weakest and give an example?
- Explain ferromagnetism. Why do domains form? What happens when you apply a magnetic field? Why is iron not good for use in transformers (eddy current losses)? What do they commonly do to avoid this problem?
- What is the equation for susceptibility and for the relation between B, H, and M?
- Draw the curve of M vs. H behavior. What is this called? What does the area inside the curve mean?
- Showed me some magnetic tape. What type of hysteresis curve would you want for a material used in magnetic tape and why?
- What else do you want to tell me about magnetism?
- Overall he was very nice and he would stop throughout the exam to chat about the people that discovered things. He was impressed if you knew some of the history of the field.
Student 2: Semiconductors
- Draw the band diagrams of metal, semiconductor, and insulator. Give 2 examples of each.
- Give examples of indirect and direct semiconductors. What are their bandgaps? Draw the absorption vs wavelength plot for each.
- What is the equation for the conductivity of metals. What is the limiting factor.
- Describe the mobility.
- Draw the conductivity of metals and semiconductors as a function of temperature.
- Explain the basic principle of LED/PV. Draw its band diagram.
- What model do we use to describe extrinsic carriers? (hydrogen model)
- How do we modify the hydrogen model to describe n-type carriers in Si? What are the approximate values of effective mass, relative permittivity for silicon? What is the orbital radius? Will there be free carriers at room temperature?
- How abundant is Si on Earth?
Asked me about my research (tin-doped indium oxide nanocrystals
- So tin and indium are metals, but they become semiconducting when they are oxidized. Why?
- Asked me to draw some band structures. Asked me why metals are conductive and why semiconductors are not.
- Talked about the conduction band of a semiconductor and how to find the number of electrons in a conduction band, and why these electrons conduct electricity.
- When you increase temperature, how does the fermi level change?
- Let’s talk about a metal some more. What is the density of electrons in aluminum?
- How far above the conduction band minimum is the fermi level in aluminum?
- What is the kinetic energy of the aluminum atoms themselves in the lattice?
- So the electrons at the fermi level in aluminum have a very high potential energy while the atoms have a very low energy. Thermodynamics says that we’d expect the electrons to thermally equilibrate with the atoms. Why don’t they?
Asked me about research and chatted about PV materials. Questions are pretty in depth. He always started with drawing the band diagram and Fermi level. Also asked me why electron’s effective mass is smaller than hole’s .
Asked me about research. (TEM characterization of polymer electrolyte)
- How do you measure the conductivity of the electrolyte? The mobility of a conductor? (Hall effect) What is the normal magnitude of mobility? Explain the experimental setup for Hall effect. Why can you measure a potential in that direction? (the balance between the Lorentz force and electrical force.)
- Do you know hopping mechanism? (Explain that the electrons would hop in insulators.) Can you measure Hall effect of the hopping mechanism? Why?
- Why are you using electron diffraction for characterization? What is the equation to calculate the wavelength? How about X-ray? How to calculate the wavelength of X-ray? Since they can both attain very small wavelength, why not use X-ray? (hard to focus on a small area. Electrons are charged particles, easy to focus by electromagnetic lens.) But there is a way to focus X-ray, do you know that? (Wave plate)
Asked me about my research (determining corrosivity of oil at temperature).
- Asked me about ion mobility in the solution. What effects the mobility of the ions? How does temperature effect the mobility?
- We talked about the scattering cross section and the mfp with respect to brownian motion.
- How could be determine the mobility of the ions experimentally? How do you perform Hall effect measurements on this material?
Spring 2012: Dubon
- Draw a pn junction diagram. Why must the fermi-levels be equal in a pn junction? Explain what's happening in reverse and forward bias. Why is the interface called the "depletion region?"
- Draw the IV curve for a diode. Write down the Shockley diode equation. Why is there an exponential term in the diode equation? What does the prefactor mean; how is the prefactor manifested on the IV curve?
- A metal-semiconductor junction can also have rectifying behavior--draw an n-type semiconductor to metal rectifying (Shottky) junction. How does it demonstrate rectifying behavior (draw it in forward and reverse bias)?
- What exactly is the fermi level? What is the fermi distribution?
- What is the density of states? What dependence does the density of states have on the energy? Derive that dependence. (particle in a 3D box model).
- How do we know the relative value of the different energy bands for one material compared to another? (Work function, material in vacuum and energy required to remove electron.