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For an n channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity
(∂VT/∂ |VBS|) is found to be 50 mV/V at a substrate voltage |VBS| =2V , where VT is the threshold voltage of the MOSFET. Assume that |VBS| >>2φB , where qφB is the separation between the fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given are :
Electron charge ( q) = 1.6× 10−19C
Vacuum permittivity (ε0)= 8.85 × 10−12F / m
Relative permittivity of silicon ( ε si)= 12
Relative permittivity of oxide ( ε ox)= 4
The doping concentration of the substrate is
- a)7.37 ×1015 cm −3
- b)4.37 ×1015 cm −3
- c)2.37 ×1015 cm −3
- d)9.37 ×1015 cm −3
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
For an n channel silicon MOSFET with 10 nm gate oxide thickness, the ...
Given
Gate-oxide thickness,tox 10 nm
Electron charge ( q) = 1.6× 10−19C
Vacuum permittivity (ε0) = 8.85 x 10-12 F / m
Relative permittivity of silicon ( εsi) = 12
Relative permittivity of oxide ( εox) = 4
Threshold voltage when body effect is consider,
As per the question, φF = φB → Both are same
Differentiate equation (i), with respect to VBS ,
Hence, the correct option is (A).
Substrate voltage, 2V
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Community Answer
For an n channel silicon MOSFET with 10 nm gate oxide thickness, the ...
Given:
For an n-channel silicon MOSFET,
Gate oxide thickness, t_ox = 10 nm
Substrate voltage, |V_BS| = 2V
Substrate sensitivity, (∂V_T / ∂|V_BS|) = 50 mV/V
To find:
Doping concentration of the substrate
Solution:
1. Threshold voltage (V_T):
Threshold voltage of a MOSFET can be given by the equation:
V_T = V_T0 + γ(√|V_BS| - √|V_T0|) - 2φ_F
where V_T0 is the threshold voltage at zero bias, γ is the body effect parameter, and φ_F is the Fermi potential.
In this case, |V_BS| >> 2φ_B, where φ_B is the separation between the Fermi energy level (E_F) and the intrinsic level (E_i) in the bulk. Therefore, the body effect can be neglected and the threshold voltage can be simplified to:
V_T = V_T0 - 2φ_F
2. Substrate Sensitivity:
Substrate sensitivity is given by the equation:
(∂V_T / ∂|V_BS|) = γ / (2√|V_BS|)
Given that (∂V_T / ∂|V_BS|) = 50 mV/V and |V_BS| = 2V, we can calculate γ.
50 mV/V = γ / (2√2)
γ = 50 mV/V * 2√2 = 100 mV/V * √2 = 100 * 0.1414 ≈ 14.14 mV/V
3. Doping Concentration:
The body effect parameter (γ) can be related to the doping concentration of the substrate (N_A) using the equation:
γ = (2qε_siN_A) / C_ox
where q is the electron charge, ε_si is the relative permittivity of silicon, and C_ox is the oxide capacitance per unit area.
The oxide capacitance per unit area can be given by the equation:
C_ox = (ε_ox * ε_0) / t_ox
Substituting the values, we have:
C_ox = (4 * 8.85 × 10^-12 F/m) / (10 × 10^-9 m) = 35.4 × 10^-3 F/m^2
Rearranging the equation for γ, we get:
γ = (2qε_siN_A) / C_ox
N_A = (γ * C_ox) / (2qε_si)
Substituting the values, we have:
N_A = (14.14 × 10^-3 * 35.4 × 10^-3) / (2 * 1.6 × 10^-19 * 12)
N_A ≈ 7.37 × 10^15 cm^-3
Therefore, the doping concentration of the substrate is approximately 7.37 × 10^15 cm^-3. Hence, the correct answer is option 'A'.
For an n-channel silicon MOSFET,
Gate oxide thickness, t_ox = 10 nm
Substrate voltage, |V_BS| = 2V
Substrate sensitivity, (∂V_T / ∂|V_BS|) = 50 mV/V
To find:
Doping concentration of the substrate
Solution:
1. Threshold voltage (V_T):
Threshold voltage of a MOSFET can be given by the equation:
V_T = V_T0 + γ(√|V_BS| - √|V_T0|) - 2φ_F
where V_T0 is the threshold voltage at zero bias, γ is the body effect parameter, and φ_F is the Fermi potential.
In this case, |V_BS| >> 2φ_B, where φ_B is the separation between the Fermi energy level (E_F) and the intrinsic level (E_i) in the bulk. Therefore, the body effect can be neglected and the threshold voltage can be simplified to:
V_T = V_T0 - 2φ_F
2. Substrate Sensitivity:
Substrate sensitivity is given by the equation:
(∂V_T / ∂|V_BS|) = γ / (2√|V_BS|)
Given that (∂V_T / ∂|V_BS|) = 50 mV/V and |V_BS| = 2V, we can calculate γ.
50 mV/V = γ / (2√2)
γ = 50 mV/V * 2√2 = 100 mV/V * √2 = 100 * 0.1414 ≈ 14.14 mV/V
3. Doping Concentration:
The body effect parameter (γ) can be related to the doping concentration of the substrate (N_A) using the equation:
γ = (2qε_siN_A) / C_ox
where q is the electron charge, ε_si is the relative permittivity of silicon, and C_ox is the oxide capacitance per unit area.
The oxide capacitance per unit area can be given by the equation:
C_ox = (ε_ox * ε_0) / t_ox
Substituting the values, we have:
C_ox = (4 * 8.85 × 10^-12 F/m) / (10 × 10^-9 m) = 35.4 × 10^-3 F/m^2
Rearranging the equation for γ, we get:
γ = (2qε_siN_A) / C_ox
N_A = (γ * C_ox) / (2qε_si)
Substituting the values, we have:
N_A = (14.14 × 10^-3 * 35.4 × 10^-3) / (2 * 1.6 × 10^-19 * 12)
N_A ≈ 7.37 × 10^15 cm^-3
Therefore, the doping concentration of the substrate is approximately 7.37 × 10^15 cm^-3. Hence, the correct answer is option 'A'.
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For an n channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity(∂VT/∂ |VBS|) is found to be 50 mV/V at a substrate voltage |VBS| =2V , where VT is the threshold voltage of the MOSFET. Assume that |VBS| >>2φB , where qφB is the separation between the fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given are :Electron charge ( q) = 1.6× 10−19CVacuum permittivity (ε0)= 8.85 × 10−12F / mRelative permittivity of silicon ( ε si)= 12Relative permittivity of oxide ( ε ox)= 4The doping concentration of the substrate isa)7.37 ×1015 cm −3b)4.37 ×1015 cm −3c)2.37 ×1015 cm −3 d)9.37 ×1015 cm −3Correct answer is option 'A'. Can you explain this answer?
Question Description
For an n channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity(∂VT/∂ |VBS|) is found to be 50 mV/V at a substrate voltage |VBS| =2V , where VT is the threshold voltage of the MOSFET. Assume that |VBS| >>2φB , where qφB is the separation between the fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given are :Electron charge ( q) = 1.6× 10−19CVacuum permittivity (ε0)= 8.85 × 10−12F / mRelative permittivity of silicon ( ε si)= 12Relative permittivity of oxide ( ε ox)= 4The doping concentration of the substrate isa)7.37 ×1015 cm −3b)4.37 ×1015 cm −3c)2.37 ×1015 cm −3 d)9.37 ×1015 cm −3Correct answer is option 'A'. 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 For an n channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity(∂VT/∂ |VBS|) is found to be 50 mV/V at a substrate voltage |VBS| =2V , where VT is the threshold voltage of the MOSFET. Assume that |VBS| >>2φB , where qφB is the separation between the fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given are :Electron charge ( q) = 1.6× 10−19CVacuum permittivity (ε0)= 8.85 × 10−12F / mRelative permittivity of silicon ( ε si)= 12Relative permittivity of oxide ( ε ox)= 4The doping concentration of the substrate isa)7.37 ×1015 cm −3b)4.37 ×1015 cm −3c)2.37 ×1015 cm −3 d)9.37 ×1015 cm −3Correct answer is option 'A'. 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 For an n channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity(∂VT/∂ |VBS|) is found to be 50 mV/V at a substrate voltage |VBS| =2V , where VT is the threshold voltage of the MOSFET. Assume that |VBS| >>2φB , where qφB is the separation between the fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given are :Electron charge ( q) = 1.6× 10−19CVacuum permittivity (ε0)= 8.85 × 10−12F / mRelative permittivity of silicon ( ε si)= 12Relative permittivity of oxide ( ε ox)= 4The doping concentration of the substrate isa)7.37 ×1015 cm −3b)4.37 ×1015 cm −3c)2.37 ×1015 cm −3 d)9.37 ×1015 cm −3Correct answer is option 'A'. Can you explain this answer?.
For an n channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity(∂VT/∂ |VBS|) is found to be 50 mV/V at a substrate voltage |VBS| =2V , where VT is the threshold voltage of the MOSFET. Assume that |VBS| >>2φB , where qφB is the separation between the fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given are :Electron charge ( q) = 1.6× 10−19CVacuum permittivity (ε0)= 8.85 × 10−12F / mRelative permittivity of silicon ( ε si)= 12Relative permittivity of oxide ( ε ox)= 4The doping concentration of the substrate isa)7.37 ×1015 cm −3b)4.37 ×1015 cm −3c)2.37 ×1015 cm −3 d)9.37 ×1015 cm −3Correct answer is option 'A'. 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 For an n channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity(∂VT/∂ |VBS|) is found to be 50 mV/V at a substrate voltage |VBS| =2V , where VT is the threshold voltage of the MOSFET. Assume that |VBS| >>2φB , where qφB is the separation between the fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given are :Electron charge ( q) = 1.6× 10−19CVacuum permittivity (ε0)= 8.85 × 10−12F / mRelative permittivity of silicon ( ε si)= 12Relative permittivity of oxide ( ε ox)= 4The doping concentration of the substrate isa)7.37 ×1015 cm −3b)4.37 ×1015 cm −3c)2.37 ×1015 cm −3 d)9.37 ×1015 cm −3Correct answer is option 'A'. 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 For an n channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity(∂VT/∂ |VBS|) is found to be 50 mV/V at a substrate voltage |VBS| =2V , where VT is the threshold voltage of the MOSFET. Assume that |VBS| >>2φB , where qφB is the separation between the fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given are :Electron charge ( q) = 1.6× 10−19CVacuum permittivity (ε0)= 8.85 × 10−12F / mRelative permittivity of silicon ( ε si)= 12Relative permittivity of oxide ( ε ox)= 4The doping concentration of the substrate isa)7.37 ×1015 cm −3b)4.37 ×1015 cm −3c)2.37 ×1015 cm −3 d)9.37 ×1015 cm −3Correct answer is option 'A'. Can you explain this answer?.
Solutions for For an n channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity(∂VT/∂ |VBS|) is found to be 50 mV/V at a substrate voltage |VBS| =2V , where VT is the threshold voltage of the MOSFET. Assume that |VBS| >>2φB , where qφB is the separation between the fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given are :Electron charge ( q) = 1.6× 10−19CVacuum permittivity (ε0)= 8.85 × 10−12F / mRelative permittivity of silicon ( ε si)= 12Relative permittivity of oxide ( ε ox)= 4The doping concentration of the substrate isa)7.37 ×1015 cm −3b)4.37 ×1015 cm −3c)2.37 ×1015 cm −3 d)9.37 ×1015 cm −3Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
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For an n channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity(∂VT/∂ |VBS|) is found to be 50 mV/V at a substrate voltage |VBS| =2V , where VT is the threshold voltage of the MOSFET. Assume that |VBS| >>2φB , where qφB is the separation between the fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given are :Electron charge ( q) = 1.6× 10−19CVacuum permittivity (ε0)= 8.85 × 10−12F / mRelative permittivity of silicon ( ε si)= 12Relative permittivity of oxide ( ε ox)= 4The doping concentration of the substrate isa)7.37 ×1015 cm −3b)4.37 ×1015 cm −3c)2.37 ×1015 cm −3 d)9.37 ×1015 cm −3Correct answer is option 'A'. Can you explain this answer?, a detailed solution for For an n channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity(∂VT/∂ |VBS|) is found to be 50 mV/V at a substrate voltage |VBS| =2V , where VT is the threshold voltage of the MOSFET. Assume that |VBS| >>2φB , where qφB is the separation between the fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given are :Electron charge ( q) = 1.6× 10−19CVacuum permittivity (ε0)= 8.85 × 10−12F / mRelative permittivity of silicon ( ε si)= 12Relative permittivity of oxide ( ε ox)= 4The doping concentration of the substrate isa)7.37 ×1015 cm −3b)4.37 ×1015 cm −3c)2.37 ×1015 cm −3 d)9.37 ×1015 cm −3Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of For an n channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity(∂VT/∂ |VBS|) is found to be 50 mV/V at a substrate voltage |VBS| =2V , where VT is the threshold voltage of the MOSFET. Assume that |VBS| >>2φB , where qφB is the separation between the fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given are :Electron charge ( q) = 1.6× 10−19CVacuum permittivity (ε0)= 8.85 × 10−12F / mRelative permittivity of silicon ( ε si)= 12Relative permittivity of oxide ( ε ox)= 4The doping concentration of the substrate isa)7.37 ×1015 cm −3b)4.37 ×1015 cm −3c)2.37 ×1015 cm −3 d)9.37 ×1015 cm −3Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice For an n channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity(∂VT/∂ |VBS|) is found to be 50 mV/V at a substrate voltage |VBS| =2V , where VT is the threshold voltage of the MOSFET. Assume that |VBS| >>2φB , where qφB is the separation between the fermi energy level EF and the intrinsic level Ei in the bulk. Parameters given are :Electron charge ( q) = 1.6× 10−19CVacuum permittivity (ε0)= 8.85 × 10−12F / mRelative permittivity of silicon ( ε si)= 12Relative permittivity of oxide ( ε ox)= 4The doping concentration of the substrate isa)7.37 ×1015 cm −3b)4.37 ×1015 cm −3c)2.37 ×1015 cm −3 d)9.37 ×1015 cm −3Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Electronics and Communication Engineering (ECE) tests.
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