The Fermi energy level in a silicon sample at T = 300 K is as (Eg/4) close to the top of the valence band. (a) Is the material n type or p type? (b) Calculate the values of n0 and p0.
(a) The given information implies that the Fermi level is located in the valence band and is closer to the top by an amount of Eg/4, where Eg is the bandgap energy of silicon. This indicates that the majority carriers are holes, and the material is p-type.
(b) At thermal equilibrium, the product of the electron and hole concentrations, n0p0, is given by:
n0p0 = ni^2
where ni is the intrinsic carrier concentration of silicon, which is approximately equal to 1.5 x 10^10 cm^-3 at T = 300 K. Since the material is p-type, the hole concentration is higher than the electron concentration, i.e., p0 > n0.
The position of the Fermi level can also be related to the carrier concentrations by the following equation:
n0/Nc * p0/Nv = exp[(Ef - Ev)/kT]
where Nc and Nv are the effective densities of states in the conduction and valence bands, respectively, k is the Boltzmann constant, and T is the temperature in Kelvin.
Since the Fermi level is closer to the top of the valence band by an amount of Eg/4, we have:
Ef - Ev = -Eg/4
Substituting the appropriate values and simplifying, we get:
n0 * p0 = (Nc*Nv/4) * exp(Eg/4kT)
Using the values for silicon, we have:
Nc = 2.8 x 10^19 cm^-3 Nv = 1.04 x 10^19 cm^-3 Eg = 1.12 eV k = 8.62 x 10^-5 eV/K
Substituting these values, we get:
n0 * p0 = 4.62 x 10^19 cm^-6
Since p0 = n0 * exp(Eg/4kT), we can substitute for p0 to obtain:
n0^2 * exp(Eg/4kT) = 4.62 x 10^19 cm^-6
Taking the natural logarithm of both sides, we get:
2ln(n0) + Eg/4kT = ln(4.62 x 10^19)
Solving for n0, we get:
n0 = sqrt(4.62 x 10^19 / exp(Eg/2kT))
Substituting the values, we get:
n0 = 1.26 x 10^15 cm^-3
Therefore, the hole concentration is:
p0 = n0 * exp(Eg/4kT) = 5.21 x 10^16 cm^-3
The Fermi energy level in a silicon sample at T = 300 K is as (Eg/4)...
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?
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...
(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,...
1. Sketch the Fermi-dirac probability function at T= 0 K and T=300 K for function of E above and below EF. 2. Find (EP) 3. Describe Fermi Energy. What are the significances of Fermi energy level in semiconductor device physics? 4. Sktech Density of State Diagram, Fermi-dirac probability function diagram vs. E from there sketch n(E)vs.E and p(E)vs. E for N-type and P-type semiconductors, respectively. 5. A semiconductor has the following parameters: a. Eg = 1.12 eV, x = 4.05...
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...
Please help me 1. In degenerate p-type silicon, a. The Fermi energy is above the valence energy and below the intrinsic Fermi energy b. The Fermi energy is below the valence energy c. The Fermi energy is above the conduction energy d. The Fermi energy is below the conduction energy and above the intrinsic Fermi energy 2. A semiconductor has No 5X 1010 cm3 and N-2X 1018 cm2. It is a. b. C. d. N-type and electrons are the majority...
1. Sketch the Fermi-dirac probability function at T=0 K and T=300 K for function of E above and below EF. 2. Find f(EP). 3. Describe Fermi Energy. What are the significances of Fermi energy level in semiconductor device physics? 4. Sktech Density of State Diagram, Fermi-dirac probability function diagram vs. E from there sketch n(E)vs.E and p(E)vs. E for N-type and P-type semiconductors, respectively. 5. A semiconductor has the following parameters: a. Eg = 1.12 eV, x = 4.05 eV,...
(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...
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...