1 / 39

MSE-630 Week 2

MSE-630 Week 2. Conductivity, Energy Bands and Charge Carriers in Semiconductors. Objectives:. To understand conduction, valence energy bands and how bandgaps are formed To understand the effects of doping in semiconductors

nichole
Download Presentation

MSE-630 Week 2

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MSE-630 Week 2 Conductivity, Energy Bands and Charge Carriers in Semiconductors

  2. Objectives: • To understand conduction, valence energy bands and how bandgaps are formed • To understand the effects of doping in semiconductors • To use Fermi-Dirac statistics to calculate conductivity and carrier concentrations • To understand carrier mobility and how it is influenced by scattering • To introduce the idea of “effective mass” • To see how we can use Hall effect to determine carrier concentration and mobility

  3. MSE-512 ELECTRICAL CONDUCTION • Ohm's Law: DV = I R voltage drop (volts) resistance (Ohms) current (amps) • Resistivity, r and Conductivity, s: --geometry-independent forms of Ohm's Law E: electric field intensity resistivity (Ohm-m) J: current density conductivity • Resistance: 3

  4. MSE-512 Resistivity and Conductivity as charged particles mobility, m = Where is the average velocity is the average distance between collisions, divided by the average time between collisions, t d

  5. MSE-512 CONDUCTION IN TERMS OF ELECTRON AND HOLE MIGRATION • Concept of electrons and holes: • Electrical Conductivity given by: hole mobility # electrons/m3 # holes/m3 electron mobility 11

  6. MSE-512 CONDUCTIVITY: COMPARISON -1 • Room T values (Ohm-m) 4

  7. As the distance between atoms decreases, the energy of each orbital must split, since according to Quantum Mechanics we cannot have two orbitals with the same energy. The splitting results in “bands” of electrons. The energy difference between the conduction and valence bands is the “gap energy” We must supply this much energy to elevate an electron from the valence band to the conduction band. If Eg is < 2eV, the material is a semiconductor.

  8. MSE-512 CONDUCTION & ELECTRON TRANSPORT • Metals: -- Thermal energy puts many electrons into a higher energy state. • Energy States: -- the cases below for metals show that nearby energy states are accessible by thermal fluctuations. 6

  9. MSE-512 ENERGY STATES: INSULATORS AND SEMICONDUCTORS • Semiconductors: --Higher energy states separated by a smaller gap. • Insulators: --Higher energy states not accessible due to gap. 7

  10. MSE-512 PURE SEMICONDUCTORS: CONDUCTIVITY VS T • Data for Pure Silicon: --s increases with T --opposite to metals electrons can cross gap at higher T material Si Ge GaP CdS band gap (eV) 1.11 0.67 2.25 2.40 10

  11. Simple representation of silicon atoms bonded in a crystal. The dotted areas are covalent or shared electron bonds. The electronic structure of a single Si atom is shown conceptually on the right. The four outermost electrons are the valence electrons that participate in covalent bonds. Electron (-) and hold (+) pair generation represented b a broken bond in the crystal. Both carriers are mobile and can carry current. Portion of the periodic table relevant to semiconductor materials and doping. Elemental semiconductors are in column IV. Compound semiconductors are combinations of elements from columns III and V, or II and VI.

  12. Doping of group IV semiconductors using elements from arsenic (As, V) or boron (B, III) Intrinsic carrier concentration vs. temperature.

  13. MSE-512 INTRINSIC VS EXTRINSIC CONDUCTION • Intrinsic: # electrons = # holes (n = p) --case for pure Si • Extrinsic: --n ≠ p --occurs when impurities are added with a different # valence electrons than the host (e.g., Si atoms) • N-type Extrinsic: (n >> p) • P-type Extrinsic: (p >> n) 12

  14. MSE-512 Equations describing Intrinsic and Extrinsic conduction • Using the Fermi-Dirac equation, we can find the number of charge carrier per unit volume as: • Ne = Noexp(-Eg/2kT) • Nois a preexponential function, • Egis the band-gap energy and • kis Boltzman’s constant (8.62 x 10-5 eV/K) • If Eg > ~2.5 eV the material is an insulator • If 0 < Eg < ~2.5 eV the material is a semi-conductor • Semi-conductor conductivity can be expressed by: • s(T) = so exp(-E*/nkT) • E* is the relevant gap energy (Eg, Ec-Ed or Ea) • n is 2 for intrinsic semi-conductivity and 1 for extrinsic semi-conductivity

  15. MSE-512 DOPED SEMICON: CONDUCTIVITY VS T • Data for Doped Silicon: --s increases doping --reason: imperfection sites lower the activation energy to produce mobile electrons. • Comparison:intrinsic vs extrinsic conduction... --extrinsic doping level: 1021/m3 of a n-type donor impurity (such as P). --for T < 100K: "freeze-out" thermal energy insufficient to excite electrons. --for 150K < T < 450K: "extrinsic" --for T >> 450K: "intrinsic" 13

  16. When we add carriers by doping, the number of additional carrers, Nd, far exceeds those in an intrinsic semiconductor, and we can treat conductivity as s = 1/r = qmdNd Dopant designations and concentrations Resistivity as a function of charge mobility and number

  17. Simple band and bond representations of pure silicon. Bonded electrons lie at energy levels below Ev; free electrons are above Ec. The process of intrinsic carrier generation is illustrated in each model. Simple band and bond representations of doped silicon. EA and ED represent acceptor and donor energy levels, respectively. P- and N-type doping are illustrated in each model, using As as the donor and B as the acceptor

  18. Behavior of free carrier concentration versus temperature. Arsenic in silicon is qualitatively illustrated as a specific example (ND = 1015 cm-3). Note that at high temperatures ni becomes larger than 1015 doping and n≈ni. Devices are normally operated where n= ND+. Fabrication occurs as temperatures where n≈ni Probability of an electron occupying a state. Fermi energy represents the energy at which the probability of occupancy is exactly ½. Fermi level position in an undoped (left), N-type (center) and P-type (right) semiconductor. The dots represent free electrons, the open circles represent mobile holes.

  19. The density of allowed states at an energy E. Integrating the product of the probability of occupancy with the density of allowed states gives the electron and hole populations in a semiconductor crystal.

  20. Effective Mass In general, the curve of Energy vs. k is non-linear, with E increasing as k increases. E = ½ mv2 = ½ p2/m = h2/4pm k2 We can see that energy varies inversely with mass. Differentiating E wrt k twice, and solving for mass gives: Effective mass is significant because it affects charge carrier mobility, and must be considered when calculating carrier concentrations or momentum Effective mass and other semiconductor properties may be found in Appendix A-4

  21. Substituting the results from the previous slide into the expression for the product of the number of holes and electrons gives us the equation above. Writing NC and NV as a function of ni and substituting gives the equation below for the number of holes and electrons:

  22. In general, the number of electron donors plus holes must equal the number of electron acceptors plus electrons The energy band gap gets smaller with increasing temperature. Fermi level position in the forbidden band for a given doping level as a function of temperature.

  23. In reality, band structures are highly dependent upon crystal orientation. This image shows us that the lowest band gap in Si occurs along the [100] directions, while for GaAs, it occurs in the [111]. This is why crystals are grown with specific orientations. The diagram showing the constant energy surface (3.10 (b)), shows us that the effective mass varies with direction. We can calculate average effective mass from:

  24. MSE-512 P-N RECTIFYING JUNCTION • Allows flow of electrons in one direction only (e.g., useful to convert alternating current to direct current. • Processing: diffuse P into one side of a B-doped crystal. • Results: --No applied potential: no net current flow. --Forward bias: carrier flow through p-type and n-type regions; holes and electrons recombine at p-n junction; current flows. --Reverse bias: carrier flow away from p-n junction; carrier conc. greatly reduced at junction; little current flow. 14

  25. MSE-512 Piezoelectrics Field produced by stress: x = electric field s= applied stress E=Elastic modulus d = piezoelectric constant g = constant Strain produced by field: Elastic modulus:

  26. APPLIED MAGNETIC FIELD • Created by current through a coil: • Relation for the applied magnetic field, H: current applied magnetic field units = (ampere-turns/m) 2

  27. With Magnetic core: In Air: mo=1.257 x 10-6 Wb/(A-m)

  28. MAGNETIC SUSCEPTIBILITY • Measures the response of electrons to a magnetic field. • Electrons produce magnetic moments: Adapted from Fig. 20.4, Callister 6e. • Net magnetic moment: --sum of moments from all electrons. • Three types of response... 4

  29. Magnetic domains align in presence of magnetic field, H

  30. Hysteresis Loop

  31. Soft and Hard Magnetic Materials

  32. Typical properties of soft and hard magnetic materials

  33. MAGNETIC STORAGE recording medium recording head • Information is stored by magnetizing material. • Head can... --apply magnetic field H & align domains (i.e., magnetize the medium). --detect a change in the magnetization of the medium. • Two media types: --Particulate: needle-shaped g-Fe2O3. +/- mag. moment along axis. (tape, floppy) --Thin film: CoPtCr or CoCrTa alloy. Domains are ~ 10-30nm! (hard drive) 9

  34. Magnetic Forces

  35. MSE-512 Sheet Resistivity R = = = = = Sheet resistivity is the resistivity divided by the thickness of the doped region, and is denoted W/□ rs is the sheet resistivity L w If we know the area per square, the resistance is

  36. Conductivity Charge carriers follow a random path unless an external field is applied. Then, they acquire a drift velocity that is dependent upon their mobility,mnand the strength of the field,x Vd = -mnx The average drift velocity, vav is dependent Upon the mean time between collisions, 2t

  37. Charge Flow and Current Density Current density, J, is the rate at which charges, cross any plane perpendicular to the flow direction. J = -nqvd = nqmnx = sx n is the number of charges, and q is the charge (1.6 x 10-19 C) The total current density depends upon the total charge carriers, which can be ions, electrons, or holesJ = q(nmn + pmp) x OHM’s Law: V = IR Resistance, R(W) is an extrinsic quantity. Resistivity, r(Wm), is the corresponding intrinsic property. r = R*A/l Conductivity, s, is the reciprocal of resistivity: s(Wm)-1 = 1/r

More Related