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In a non-degenerate bulk semiconductor with electron density n = 1016 cm-3 , the value of EC -EFn= 200 meV , where EC and EFn denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as 26 meV and the intrinsic carrier concentration is 1010 cm-3 . For n = 0.5 x1016 cm-3 , the closest approximation of the value of ( EC - EFn) , among the given options, is
- a)174 meV
- b)182 meV
- c)226 meV
- d)218 meV
Correct answer is option 'D'. Can you explain this answer?
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In a non-degenerate bulk semiconductor with electron density n = 1016...
Calculation of EC - EFn for n = 1016 cm-3
Given, n = 1016 cm-3 and EC - EFn = 200 meV
We know that, ni^2 = n*p, where ni is intrinsic carrier concentration, n is electron density and p is hole density. At room temperature, ni = 1010 cm-3. Therefore, p = ni^2/n = 1010/1016 = 10^-6 cm-3 (since the material is non-degenerate)
Now, using the relation n*p = (Nc*Nv)*exp(-Eg/kT), where Nc and Nv are effective densities of states in the conduction and valence bands respectively, Eg is the bandgap energy, k is Boltzmann constant and T is temperature, we can find Eg. Assuming T = 300 K, we get Eg = 1.12 eV or 1100 meV.
Now, using the relation EFp - Ev = Eg - (kT/q)ln(Nv/Nc), where EFp is the hole Fermi level energy and q is the electronic charge, we can find Ev. Assuming EFp = 0 (since the material is non-degenerate), we get Ev = -1100 meV.
Therefore, EFn = Ev + EC - Eg = -1100 meV + EC - 1100 meV = EC - 2200 meV.
Now, using the relation (EC - EFn)/kT = ln(n/Nc), we can find Nc. Assuming T = 300 K, we get Nc = 2.86 x 10^19 cm-3.
Using the relation EC - EFn = (kT/q)ln(n/Nc), we can find EC - EFn for n = 0.5 x 1016 cm-3.
Calculation of EC - EFn for n = 0.5 x 1016 cm-3
Given, n = 0.5 x 1016 cm-3 and Nc = 2.86 x 10^19 cm-3
Using the relation EC - EFn = (kT/q)ln(n/Nc), we get EC - EFn = (26 meV/q)ln(0.5 x 1016/2.86 x 10^19) = 218 meV.
Therefore, the closest approximation of the value of (EC - EFn) for n = 0.5 x 1016 cm-3 is 218 meV, which is option D.
Given, n = 1016 cm-3 and EC - EFn = 200 meV
We know that, ni^2 = n*p, where ni is intrinsic carrier concentration, n is electron density and p is hole density. At room temperature, ni = 1010 cm-3. Therefore, p = ni^2/n = 1010/1016 = 10^-6 cm-3 (since the material is non-degenerate)
Now, using the relation n*p = (Nc*Nv)*exp(-Eg/kT), where Nc and Nv are effective densities of states in the conduction and valence bands respectively, Eg is the bandgap energy, k is Boltzmann constant and T is temperature, we can find Eg. Assuming T = 300 K, we get Eg = 1.12 eV or 1100 meV.
Now, using the relation EFp - Ev = Eg - (kT/q)ln(Nv/Nc), where EFp is the hole Fermi level energy and q is the electronic charge, we can find Ev. Assuming EFp = 0 (since the material is non-degenerate), we get Ev = -1100 meV.
Therefore, EFn = Ev + EC - Eg = -1100 meV + EC - 1100 meV = EC - 2200 meV.
Now, using the relation (EC - EFn)/kT = ln(n/Nc), we can find Nc. Assuming T = 300 K, we get Nc = 2.86 x 10^19 cm-3.
Using the relation EC - EFn = (kT/q)ln(n/Nc), we can find EC - EFn for n = 0.5 x 1016 cm-3.
Calculation of EC - EFn for n = 0.5 x 1016 cm-3
Given, n = 0.5 x 1016 cm-3 and Nc = 2.86 x 10^19 cm-3
Using the relation EC - EFn = (kT/q)ln(n/Nc), we get EC - EFn = (26 meV/q)ln(0.5 x 1016/2.86 x 10^19) = 218 meV.
Therefore, the closest approximation of the value of (EC - EFn) for n = 0.5 x 1016 cm-3 is 218 meV, which is option D.
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Community Answer
In a non-degenerate bulk semiconductor with electron density n = 1016...
Given
(i) Electron density, n1 = 1016 cm-3
(ii) (EC - EFn)1 = 200 meV
(iii) Intrinsic carrier concentration, ni = 1010 cm-3
(iv) We have to find ( Ec -EFn)2 for electron density, n2 = 0.5 x 1016 cm-3
Since, electron density for n - type semiconductor is given by,
Where, n = Electron density, Nc = Effective density of states at the edge of conduction band.
Dividing equations (i) and (ii),
(EC - EFn)2 - 200 x 10-3 = 26 In 2
(EC - EFn)2 = 26 In 2 + 200
(EC - EFn)2 = 218 meV
Hence, the correct option is (D).
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In a non-degenerate bulk semiconductor with electron density n = 1016 cm-3 , the value of EC -EFn= 200 meV , where EC and EFn denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as 26 meV and the intrinsic carrier concentration is 1010 cm-3 . For n = 0.5 x1016 cm-3 , the closest approximation of the value of ( EC - EFn) , among the given options, isa)174 meVb)182 meVc)226 meVd)218 meVCorrect answer is option 'D'. Can you explain this answer?
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In a non-degenerate bulk semiconductor with electron density n = 1016 cm-3 , the value of EC -EFn= 200 meV , where EC and EFn denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as 26 meV and the intrinsic carrier concentration is 1010 cm-3 . For n = 0.5 x1016 cm-3 , the closest approximation of the value of ( EC - EFn) , among the given options, isa)174 meVb)182 meVc)226 meVd)218 meVCorrect answer is option 'D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about In a non-degenerate bulk semiconductor with electron density n = 1016 cm-3 , the value of EC -EFn= 200 meV , where EC and EFn denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as 26 meV and the intrinsic carrier concentration is 1010 cm-3 . For n = 0.5 x1016 cm-3 , the closest approximation of the value of ( EC - EFn) , among the given options, isa)174 meVb)182 meVc)226 meVd)218 meVCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a non-degenerate bulk semiconductor with electron density n = 1016 cm-3 , the value of EC -EFn= 200 meV , where EC and EFn denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as 26 meV and the intrinsic carrier concentration is 1010 cm-3 . For n = 0.5 x1016 cm-3 , the closest approximation of the value of ( EC - EFn) , among the given options, isa)174 meVb)182 meVc)226 meVd)218 meVCorrect answer is option 'D'. Can you explain this answer?.
In a non-degenerate bulk semiconductor with electron density n = 1016 cm-3 , the value of EC -EFn= 200 meV , where EC and EFn denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as 26 meV and the intrinsic carrier concentration is 1010 cm-3 . For n = 0.5 x1016 cm-3 , the closest approximation of the value of ( EC - EFn) , among the given options, isa)174 meVb)182 meVc)226 meVd)218 meVCorrect answer is option 'D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about In a non-degenerate bulk semiconductor with electron density n = 1016 cm-3 , the value of EC -EFn= 200 meV , where EC and EFn denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as 26 meV and the intrinsic carrier concentration is 1010 cm-3 . For n = 0.5 x1016 cm-3 , the closest approximation of the value of ( EC - EFn) , among the given options, isa)174 meVb)182 meVc)226 meVd)218 meVCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a non-degenerate bulk semiconductor with electron density n = 1016 cm-3 , the value of EC -EFn= 200 meV , where EC and EFn denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as 26 meV and the intrinsic carrier concentration is 1010 cm-3 . For n = 0.5 x1016 cm-3 , the closest approximation of the value of ( EC - EFn) , among the given options, isa)174 meVb)182 meVc)226 meVd)218 meVCorrect answer is option 'D'. Can you explain this answer?.
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