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# SEMICONDUCTOR DEVICES ECEN 3320

GPA 3.9

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This 3 page Class Notes was uploaded by Mrs. Lacy Schneider on Thursday October 29, 2015. The Class Notes belongs to ECEN 3320 at University of Colorado at Boulder taught by Staff in Fall. Since its upload, it has received 18 views. For similar materials see /class/231792/ecen-3320-university-of-colorado-at-boulder in ELECTRICAL AND COMPUTER ENGINEERING at University of Colorado at Boulder.

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Date Created: 10/29/15

9 4 V39 05 gt1 9 0 Problems Calculate the packing density of the body centered cubic the face centered cubic and the diamond lattice listed in example 21 p 28 At what temperature does the energy bandgap if silicon equal exactly 1 eV Prove that the probability of occupying an energy level below the Fermi energy equals the probability that an energy level above the Fermi energy and equally far away from the Fermi energy is not occupied At what energy in units of kT is the Fermi function within 1 of the MaxwellBoltzmann distribution function What is the corresponding probability of occupancy Calculate the Fermi function at 65 eV ifEF 625 eV and T 300 K Repeat at T 950 K assuming that the Fermi energy does not change At what temperature does the probability that an energy level atE 595 eV is empty equal 1 Calculate the effective density of states for electrons and holes in germanium silicon and gallium arsenide at room temperature and at 100 0C Use the effective masses for density of states calculations Calculate the intrinsic carrier density in germanium silicon and gallium arsenide at room temperature 300 K Repeat at 100 OC Assume that the energy bandgap is independent of temperature and use the room temperature values Calculate the position of the intrinsic energy level relative to the midgap energy EMUgap EC EV2 in germanium silicon and gallium arsenide at 300 K Repeat at T 100 OC Calculate the electron and hole density in germanium silicon and gallium arsenide if the Fermi energy is 03 eV above the intrinsic energy level Repeat if the Fermi energy is 03 eV below the conduction band edge Assume that T 300 K The equations 2634 and 2635 derived in section 26 are only valid for nondegenerate semiconductors ie EV 3kT lt EF lt EC 3kT Where exactly in the derivation was the assumption made that the semiconductor is nondegenerate A silicon wafer contains 1016 cm393 electrons Calculate the hole density and the position of the intrinsic energy and the Fermi energy at 300 K Draw the corresponding band diagram to scale indicating the conduction and valence band edge the intrinsic energy level and the Fermi energy level Use ni 1010 cm39 A silicon wafer is doped with 1013 cm393 shallow donors and 9 x 1012 cm393 shallow acceptors Calculate the electron and hole density at 300 K Use ni 1010 cm393 The resistivity of silicon wafer at room temperature is 5 Qcm What is the doping density Find all possible solutions How many phosphorus atoms must be added to decrease the resistivity of ntype silicon at room temperature from 1 Qcm to 01 Qcm Make sure you include the doping dependence of UI ON 00 O N O N 4 the mobility State your assumptions A piece of ntype silicon Nd 1017 cm393 is uniformly illuminated with green light 7 550 nm so that the power density in the material equals 1 mWcm a Calculate the generation rate of electronhole pairs using an absorption coefficient of 104 cm39l b Calculate the excess electron and hole density using the generation rate obtained in a and a minority carrier lifetime due to ShockleyReadHall recombination of 01 ms c Calculate the electron and hole quasiFermi energies based on the excess densities obtained in b A piece of intrinsic silicon is instantaneously heated from 0 K to room temperature 300 K The minority carrier lifetime due to ShockleyReadHall recombination in the material is 1 ms Calculate the generation rate of electronhole pairs immediately after reaching room temperature E E If the generation rate is constant how long does it take to reach thermal equilibrium Calculate the conductivity and resistivity of intrinsic silicon Use n 1010 cm393 u 1400 cmzVsec and up 450 cmzVsec Consider the problem of finding the doping density which results the maximum possible resistivity of silicon at room temperature m 1010 cm393 u 1400 cmzVsec and up 450 cmzVsec Should the silicon be doped at all or do you expect the maximum resistivity when dopants are added If the silicon should be doped should it be doped with acceptors or donors assume that all dopant are shallow Calculate the maximum resistivity the corresponding electron and hole density and the doping density The electron density in silicon at room temperature is twice the intrinsic density Calculate the hole density the donor density and the Fermi energy relative to the intrinsic energy Repeat for n 5 n and n 10 m Also repeat forp 2 m p 5 n andp 10 m calculating the electron and acceptor density as well as the Fermi energy relative to the intrinsic energy level What photon energy in electron volt corresponds to a wavelength of 1 micron What wavelength corresponds to a photon energy of 1 eV 1 billion photons with a wavelength of 03 micron hit a detector every second How large is the incident power The expression for the Bohr radius can also be applied to the hydrogenlike atom consisting of an ionized donor and the electron provided by the donor Modify the expression for the Bohr radius so that it applies to this hydrogenlike atom Calculate the Bohr radius of an electron orbiting around the ionized donor in silicon Sr 119 and m 026 Mg Calculate the density of electrons per unit energy in electron volt and per unit area per cubic centimeter at 1 eV above the band minimum Assume that me 108 Mg N UI N O N 00 LA 0 LA Calculate the probability that an electron occupies an energy level which is 3kT below the Fermi energy Repeat for an energy level which is 3kT above the Fermi energy Calculate and plot as a function of energy the product of the probability that an energy level is occupied with the probability that that same energy level is not occupied Assume that the Fermi energy is zero and that kT 1 eV The effective mass of electrons in silicon is 026 Mg and the effective mass of holes is 036 Mg If the scattering time is the same for both carrier types what is the ratio of the electron mobility and the hole mobility Electrons in silicon carbide have a mobility of 1000 cmzVsec At what value of the electric field do the electrons reach a velocity of 3 X 107 cms Assume that the mobility is constant and independent of the electric field What voltage is required to obtain this field in a 5 micron thick region How much time do the electrons need to cross the 5 micron thick region A piece of silicon has a resistivity which is specified by the manufacturer to be between 2 and 5 Ohm cm Assuming that the mobility of electrons is 1400 cmzVsec and that of holes is 450 cmzVsec what is the minimum possible carrier density and what is the corresponding carrier type Repeat for the maximum possible carrier density A silicon wafer has a 2 inch diameter and contains 1014 cm393 electrons with a mobility of 1400 cmzVsec How thick should the wafer be so that the resistance between the front and back surface equals 01 Ohm The electron mobility is germanium is 1000 cmzVsec If this mobility is due to impurity and lattice scattering and the mobility due to lattice scattering only is 1900 cmzVsec what is the mobility due to impurity scattering only

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