Flashcards

Week 4 LNs

R S C Solid State Year 4 English 35 cards

Nearly free electron band structure What can be said of the effective crystal potential for a valence electron? What…

Cards in this deck (35)

1Nearly free electron band structure What can be said of the effective crystal potential for a valence electron? What determines size of band splitting? Sketch the potenial as a function of x and sketch the energy as a function of wave vector k (original unshifted) label the fourier components VgECP is periodic
Vg determines size of band gap at G/2
2Define the nearly free electron modelIn solid-state physics, the nearly free electron model (or NFE model and quasi-free electron model) is a quantum mechanical model of physical properties of electrons that can move almost freely through the crystal lattice of a solid. The model is closely related to the more conceptual empty lattice approximation. The model enables understanding and calculation of the electronic band structures, especially of metals.
This model is an immediate improvement of the free electron model, in which the metal was considered as a non-interacting electron gas and the ions were neglected completely.
3Describe the band diagrams of the nearly free electron band structureTo understand how band structure changes relative to the Fermi level in real space, a band structure plot is often first simplified in the form of a band diagram. In a band diagram the vertical axis is energy while the horizontal axis represents real space. Horizontal lines represent energy levels, while blocks represent energy bands. When the horizontal lines in these diagram are slanted then the energy of the level or band changes with distance. Diagrammatically, this depicts the presence of an electric field within the crystal system. Band diagrams are useful in relating the general band structure properties of different materials to one another when placed in contact with each other.
4For band structures define spin orbit coupling at its presence in band structures of Germanium.a relativistic effect that causes splitting of the electronic bands in many materials, including semiconductors it also lifts degeneracies
5Define and state the isotropic effective mass Describe the dependence on the curvature and effective massEffective mass is a property of an electron (or hole) in a quantum structure that defines how it responds to external forces, set by the band structure of the material.
6For a semiconductor; Sketch E vs k showing both conduction and valence bands State the relations (holes and electrons) for; wave vector energy velocity effective mass charge electric current
7For intrinsic semiconductors; Why are the perfect crystals? Define and state the roles of the free charge carriers.Charge carriers are essentially free electrons and holes that enable electrical conduction. In intrinsic semiconductors, the concentration of these carriers is governed by the inherent properties of the material and temperature rather than by impurities, known as 'doping'. They arise from electronic excitation (thermal or optical) as they are excited from valence into conduction band with some free holes in the valence band and free electrons in the conduction band moving. There are no free charge carriers at 0 Kelvin.
8For intrinsic semiconductors; Describe the role of electrical conductivitythe electrical conductivity at finite temperature has a temperature dependence which comes from the temperature dependence of the carrier concentrations
9Define the charge carrier mobilityThe strength of an applied electric field to the resulting drift velocity of the charge carriers
Higher mobility gives a higher drift velocity, with the same electric field in the case for a lower mobility there in this case gives a lower drift velocity
10Describe the drude model for intrinsic semiconductorsfree electron gas where the electrons can undergo scattering with a scattering rate,
The greater the frequency of scattering events, therefore, the lower the mobility.
11Describe the parabolic band approximationConsidering electrons/holes in states near the band extrema,
12In intrinsic semiconductors in regards to holes and electrons contribution to thermal conductivity; describe their; charges, direction of motion, currentsopposite charges
move in opposite directions
currents in the same direction
13For the carrier concentrations n and p; Describe their effective masses Conduction and Valence band edge energies ni = pi relationto describe the overall shape of the density of states, the mass gives the curvature and hence describes the density of states
They relate to the fermi level between each other
For every free electron in the conduction band there is a hole in the valence band, this removes the fermi level, chemical potential to give the relation. Strong exponential temperature dependence
14For intrinsic charge carrier densities, ni = pi at 300K, describe the band gap energyni has a sensitive dependence to the band gap
15Define Doping, donors, acceptorsDoping is a process in which impurities are artificially added to control the properties of semiconductors
D: extra valence electron donated to crystal conduction band from pentavalent materials such as P
A: one electron missing An impurity atom in a semiconductor which can accept or take up one or more electrons from the crystal and become negatively charged. An atom which substitutes for a regular atom of the material but has one less valence electron may be expected to be an acceptor atom, source from trivalent materials such as Al
16Describe the donor and acceptor levels in the band gap for semiconductorsThe electrons and hole are weakly bound, H model gives binding energies to the correct order of magnitude, the electrons and holes are released easily at room temperature
17Describe the law of mass action: The product np is constant for a particular semiconductor at a given temperature, irrespective of doping!
18For the charge carrier conc vs reciprocal temperatures in the following graph, describe the extrinsic function dotted lineAt sufficiently high temperatures (thermal energy much higher than binding energy) all electrons from donors will be excited to conduction band adding to the free electron concentration giving the value at the donor concentration (dotted line y axis).
At very low temp there is no thermal excitation, all electrons return to impurity centre and not contribute to thermal conductivity. Gives a slope for the donors at the end and a smooth transition between.
19State the following relations; all donors in terms of ionised and neutral donors, and so forth for acceptors Define charge neutrality What if both donors and acceptors existthe charge neutrality level is the energy level at which the surface (or interface) is electrically neutral. If you have no surface states, the charge neutrality level would be the same as the Fermi-level (in equilibrium)
If both exist need to be solved numerically
20For doping a pure n type semiconductor; at low doping levels describe what laws hold and what can be neglected. Relation for free electrons in conduction band.
21Explain this graph of a pure n type semiconductor in terms of extrinsic and intrinsic contributionsAt very high T, intrinsic contribution dominates as there are many more electrons in total in the crystal than the amount introduced as impurities.
At the intermediate T the increase in temp decreases exponential term, ND is smaller than effective no of states in conduction band, n and ND becomes constant. All electrons are released from donors.
Freeze out range; At very low T there is not enough thermal energy within the material to fully ionize the impurity atoms, excitation depends on number of donors and states at start and end of excitation, this with the boltzman like term and the facts that doping atoms are not completely ionized, which leads to a reduction of the charge carrier concentration, gradient from the binding energy of the electrons in the donors, provides the behavior at the freeze out range.
22State and explain the prop relation between mobilities of phonons and temperature
23State and explain scattering by charged defectsdoped SC, electron removed from impurity centre, charged defects scattered around the crystal.
24For pn junctions; describe this case in terms of fermi energy at thermal equilibrium and the concept of space chargeIn this area there are no free charge carriers, since the free electrons of the n-conductor, and the holes of the p-doped crystal in the vicinity of the interface recombine with each other, which means that the electrons fill the holes.
The electrons, abundant in the N-type region, will cross the junction in order to recombine with holes present in the P-type region. Therefore, a negative static space charge builds up in the P region (the trivalent boron atoms have a static negative charge since they release a positively-charged hole in the valence band) whereas a positive space charge builds up in the N-type zone for the same reasons. The small volume in which this space charge is created is called the space charge zone or depletion zone. Because there is a strong electric field in this area, the density of free carriers is negligible at thermal equilibrium. In addition, the frontier between the depletion zone and the neutral parts of the junction is very sharp
25For pn junctions; describe internal electric fieldJust after the P- and N-type semiconductors have been drawn closer, a potential barrier appears for both holes an electrons. Indeed, the static space charges accumulated at the borders of the junction (positive charges in the N zone, negative charges in the P zone) create an electric field pointing from N towards P, which prevents diffusion and further recombination of electrons and holes: diffusion is then rapidly stopped by the buildup of this internal electric field. In addition, because of the existence of this double layer of charges on both sides of the junction, the electrostatic potential varies sharply inside the depletion zone and the potential difference Vd, called the diffusion potential (or built-in potential) reaches non-negligible values (e.g. 0.8V for Si).
26For pn junctions in thermal equilibrium; describe using a multimeter to measure voltages at the PN junctionHowever, if we attempt to measure a voltage by connecting a multimeter at both sides of the PN diode, we will find a zero voltage drop, because a multimeter measures a difference in electrochemical potentials, not just electrostatic potentials. Indeed, here the electrochemical potential is constant throughout the crystal, including in the space charge zone, because this potential takes into account not only the electric field but also the concentration gradient of charge carriers. The diffusion potential due to this gradient compensates exactly for the electrostatic potential.
27For pn junctions; describe the thermal equilibrium caseWhen the junction meets thermal equilibrium, the Fermi energy has a constant value throughout the whole device. The energies of conduction and valence bands are therefore shifted up or down, and exhibit a smooth variation across the depletion region As a consequence, there is an electrostatic potential energy difference appearing between the P and N region,.
28Explain minority and majority carriersOn the p side, the holes constitute the dominant carriers and so are called majority carriers. A few thermally generated electrons will also exist in the p side; these are termed minority carriers. On the n side, the electrons are the majority carriers, while the holes are the minority carriers.
29Explain diffusion voltageThere is a difference in the concentration of holes and electrons at the two sides of a junction. The holes from the p-side diffuse to the n-side, and the electrons from the n-side diffuse to the p-side. These give rise to a diffusion current across the junction.
30For pn junctions; describe n and p diffusion currents, n and p drift currents
31For pn junctions write down the balanced currents equationsMinority carriers that reach the junction are swept across the depletion region due to drift. At equilibrium, the net current (diffusion and drift current) is zero for both electrons and holes because the diffusion current is equal and opposite to the drift current for both carriers.
32Describe the differences of reverse and forward bias for pn junctions
33For the schottky model, pn junctions; describe the n and p regions, space charge
34For the schottky model, pn junctions; Write down the four possible relations for the space charge per region What can be found from them?
35For schottky model; pn junctions, interpret the following1, Thickness is prop to square root of diffusion voltage, approx to the square root of band gap. Go from germanium to silicon, increase the band gap making the
2, Thickness prop to 1/ sq root of conc, conc of same order, higher doping means smaller regions
3, If dopings are unequal, assymetric junction
4, thickness is scaled with the dielectric constant