(a) Assuming that the Fermi level is at the midgap in the intrinsic silicon, calculate the...
(a) Assuming that the Fermi level is at the midgap in the
intrinsic silicon,
calculate the probability of finding an electron at the bottom of
the conduction
band (E=Ec) for three different temperatures: 0K, 20C, 100C?
(b) How are these probabilities related to the probabilities of
finding a hole
at E=Ev, which is the top of the valence band?
(c) A sample of silicon is doped with 1016 cm-3 of arsenic and
3x1016 cm-3 of
boron. Calculate n, p, and Ef for room temperature and 1000 C.
Homework Answers
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(a) Assuming that the Fermi level is at the midgap in the
intrinsic silicon,
calculate the...
P3. (a) Determine the position of the Fermi level with respect to the intrinsic Fermi level in silicon at T =...
P3. (a) Determine the position of the Fermi level with respect to the intrinsic Fermi level in silicon at T = 300'K that is doped with phosphors atoms at a concentration of 1015 cm. (b) Repeat (a) if the silicon is doped with boron atoms at a concentration of 10'5 cm3. (c) Calculate the electron concentration in the silicon for parts (a) and (b) P1. For the Boltzmann approximation to be valid for a semiconductor, the Fermi level must be...
7. Find the position of the intrinsic Fermi level with respect to Emidgap for silicon, germanium,...
7. Find the position of the intrinsic Fermi level with respect to Emidgap for silicon, germanium, gallium arsenide, and indium arsenide. Use the effective density of states values from problem 5. 8. a. Draw a band diagram for silicon doped 107/cmp-type and label the band gap and the position of the Fermi level. b. Draw a band diagram for gallium arsenide doped 10/cmn-type and label the band gap and the position of the Fermi level. c. Draw a band diagram...
P3. (a) Determine the position of the Fermi level with respect to the intrinsic Fermi level in silicon at T = 300&#...
P3. (a) Determine the position of the Fermi level with respect to the intrinsic Fermi level in silicon at T = 300'K that is doped with phosphors atoms at a concentration of 1015 cm. (b) Repeat (a) if the silicon is doped with boron atoms at a concentration of 10'5 cm3. (c) Calculate the electron concentration in the silicon for parts (a) and (b)
P3. (a) Determine the position of the Fermi level with respect to the intrinsic Fermi level...
(2) In a semiconductor with an energy gap Eg between the valence and the conduction bands we can take Ef (the Fermi ene...
(2) In a semiconductor with an energy gap Eg between the valence and the conduction bands we can take Ef (the Fermi energy) to be halfway between the bands (see figure below): Conduction band Energy gap Eg Valence band Semiconductor a. Show that for a typical semiconductor or insulator at room temperature the Fermi- Dirac factor is approximately equal to exp(-E 2kBT). (Typical Eg for semi-conductors ranges from about 0.5eV to 6eV at T-293K.) b. In heavily doped n-type silicon,...
3. Silicon samples with band-gas 1.1 eV at 300 Kelvin, are doped at four different levels...
3. Silicon samples with band-gas 1.1 eV at 300 Kelvin, are doped at four different levels and have the properties listed below. Case 1: Case 2: Case 3: Case 4: Ex-Ey = 0.15 eV Ef-Ey=0.88 eV EF-Ey = 0.55 eV Ex-Ey = 1.09 eV The four cases above show the position of the Fermi Level Er relative to the valence band edge Ev.at dilterent doping levels. a) identify each sample as degenerate and nondegenerate. b) which nondegenerate case shows heavy...
In a semiconductor it can be shown that the product of the electron and hole densities...
In a semiconductor it can be shown that the product of the electron and hole densities is the square of the intrinsic density, i.e., pm n. Find the equilibrium electron (n) and hole (p) concentrations and the location of the Fermi level (EF) referenced to the conduction band (Ec) or valence band (Ev) in Si at 27°C if the Si contains the following concentrations of shallow dopant atoms: a) 1x1016 cm-3 boron atoms b) 3x1016 cm-3 arsenic atoms and 2.9x1016...
Consider a sample of silicon at 300 K in which the Fermi level is found 0.22...
Consider a sample of silicon at 300 K in which the Fermi level is found 0.22 eV above the top of the valence band. a) What type of semiconductor is this sample? b) Sketch the band diagram, labelling Ev, E., E. EF, E. – EF, EF - Ec, and Ea or Ed as applicable. c) What is the carrier concentration of electrons and holes in this sample at thermal equilibrium?
Draw the band diagram (the relative positions of conduction band edge EC, valence band edge Ev,...
Draw the band diagram (the relative positions of conduction band
edge EC, valence band edge Ev, Fermi level EF) for the four
following cases. Clearly note EC −EF, EF −EV, Ei −EF, EG = EC −EV.
Ei is the intrinsic Fermi level. Take NC=NV =1025 m−3, EG=1.1 eV,
ni=1.5×1016 m−3, kT=0.026 eV.
(Q1.1) p-type, NA=5×1023 m−3.
(Q1.2) p-type, NA=5×1021 m−3.
(Q1.3) n-type, ND=5×1023 m−3.
(Q1.4) n-type, ND=5×1021 m−3.
Q2 Draw the band diagram (the relative positions of conduction band edge...
Silicon at at T-300 K contains acceptor atoms at a concentration of Na-5x10A15 cmA-3. Donor atoms are added forming an n type compensated(counter doped) semiconductor such that the fermi level is 0.2...
Silicon at at T-300 K contains acceptor atoms at a concentration of Na-5x10A15 cmA-3. Donor atoms are added forming an n type compensated(counter doped) semiconductor such that the fermi level is 0.215 eV below the conduction band edge 4. a. What concentration of donor atoms were added. b. What were the concentration of holes and electrons before the silicon was counterdoped c. What are the electron and hole concentrations after the silicon was counter doped.
Silicon at at T-300 K...
Silicon at at T-300 K contains acceptor atoms at a concentration of Na-5x10A15 cmA-3. Donor atoms are added forming an n type compensated(counter doped) semiconductor such that the fermi level is 0.2...
Silicon at at T-300 K contains acceptor atoms at a concentration of Na-5x10A15 cmA-3. Donor atoms are added forming an n type compensated(counter doped) semiconductor such that the fermi level is 0.215 eV below the conduction band edge 4. a. What concentration of donor atoms were added. b. What were the concentration of holes and electrons before the silicon was counterdoped c. What are the electron and hole concentrations after the silicon was counter doped.
Silicon at at T-300 K...
P3. (a) Determine the position of the Fermi level with respect to the intrinsic Fermi level in silicon at T = 300'K that is doped with phosphors atoms at a concentration of 1015 cm. (b) Repeat (a) if the silicon is doped with boron atoms at a concentration of 10'5 cm3. (c) Calculate the electron concentration in the silicon for parts (a) and (b) P1. For the Boltzmann approximation to be valid for a semiconductor, the Fermi level must be...
7. Find the position of the intrinsic Fermi level with respect to Emidgap for silicon, germanium, gallium arsenide, and indium arsenide. Use the effective density of states values from problem 5. 8. a. Draw a band diagram for silicon doped 107/cmp-type and label the band gap and the position of the Fermi level. b. Draw a band diagram for gallium arsenide doped 10/cmn-type and label the band gap and the position of the Fermi level. c. Draw a band diagram...
P3. (a) Determine the position of the Fermi level with respect to the intrinsic Fermi level in silicon at T = 300'K that is doped with phosphors atoms at a concentration of 1015 cm. (b) Repeat (a) if the silicon is doped with boron atoms at a concentration of 10'5 cm3. (c) Calculate the electron concentration in the silicon for parts (a) and (b)
P3. (a) Determine the position of the Fermi level with respect to the intrinsic Fermi level...
(2) In a semiconductor with an energy gap Eg between the valence and the conduction bands we can take Ef (the Fermi energy) to be halfway between the bands (see figure below): Conduction band Energy gap Eg Valence band Semiconductor a. Show that for a typical semiconductor or insulator at room temperature the Fermi- Dirac factor is approximately equal to exp(-E 2kBT). (Typical Eg for semi-conductors ranges from about 0.5eV to 6eV at T-293K.) b. In heavily doped n-type silicon,...
3. Silicon samples with band-gas 1.1 eV at 300 Kelvin, are doped at four different levels and have the properties listed below. Case 1: Case 2: Case 3: Case 4: Ex-Ey = 0.15 eV Ef-Ey=0.88 eV EF-Ey = 0.55 eV Ex-Ey = 1.09 eV The four cases above show the position of the Fermi Level Er relative to the valence band edge Ev.at dilterent doping levels. a) identify each sample as degenerate and nondegenerate. b) which nondegenerate case shows heavy...
In a semiconductor it can be shown that the product of the electron and hole densities is the square of the intrinsic density, i.e., pm n. Find the equilibrium electron (n) and hole (p) concentrations and the location of the Fermi level (EF) referenced to the conduction band (Ec) or valence band (Ev) in Si at 27°C if the Si contains the following concentrations of shallow dopant atoms: a) 1x1016 cm-3 boron atoms b) 3x1016 cm-3 arsenic atoms and 2.9x1016...
Consider a sample of silicon at 300 K in which the Fermi level is found 0.22 eV above the top of the valence band. a) What type of semiconductor is this sample? b) Sketch the band diagram, labelling Ev, E., E. EF, E. – EF, EF - Ec, and Ea or Ed as applicable. c) What is the carrier concentration of electrons and holes in this sample at thermal equilibrium?
Draw the band diagram (the relative positions of conduction band
edge EC, valence band edge Ev, Fermi level EF) for the four
following cases. Clearly note EC −EF, EF −EV, Ei −EF, EG = EC −EV.
Ei is the intrinsic Fermi level. Take NC=NV =1025 m−3, EG=1.1 eV,
ni=1.5×1016 m−3, kT=0.026 eV.
(Q1.1) p-type, NA=5×1023 m−3.
(Q1.2) p-type, NA=5×1021 m−3.
(Q1.3) n-type, ND=5×1023 m−3.
(Q1.4) n-type, ND=5×1021 m−3.
Q2 Draw the band diagram (the relative positions of conduction band edge...
Silicon at at T-300 K contains acceptor atoms at a concentration of Na-5x10A15 cmA-3. Donor atoms are added forming an n type compensated(counter doped) semiconductor such that the fermi level is 0.215 eV below the conduction band edge 4. a. What concentration of donor atoms were added. b. What were the concentration of holes and electrons before the silicon was counterdoped c. What are the electron and hole concentrations after the silicon was counter doped.
Silicon at at T-300 K...
Silicon at at T-300 K contains acceptor atoms at a concentration of Na-5x10A15 cmA-3. Donor atoms are added forming an n type compensated(counter doped) semiconductor such that the fermi level is 0.215 eV below the conduction band edge 4. a. What concentration of donor atoms were added. b. What were the concentration of holes and electrons before the silicon was counterdoped c. What are the electron and hole concentrations after the silicon was counter doped.
Silicon at at T-300 K...
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