GATE EC 2021 Set 1 — Question 40
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Electronic Devices → MOS Capacitor & MOSFET → Body Effect & Channel Modulation
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Question
For an n-channel silicon MOSFET with 10 nm gate oxide thickness, the substrate sensitivity () is found to be 50 mV/V at a substrate voltage V, where is the threshold voltage of the MOSFET. Assume that, , where is the separation between the Fermi energy level and the intrinsic level in the bulk. Parameters given are
Electron charge (q) = C
Vacuum permittivity () = F/m
Relative permittivity of silicon () = 12
Relative permittivity of oxide () = 4The doping concentration of the substrate is
Electron charge (q) = C
Vacuum permittivity () = F/m
Relative permittivity of silicon () = 12
Relative permittivity of oxide () = 4The doping concentration of the substrate is
Correct answer
(A) 7.37 × 10¹⁵ cm⁻³
Solution
The substrate sensitivity is given by the derivative of the threshold voltage with respect to the substrate bias .
The formula for threshold voltage is .
The substrate sensitivity is:Given the condition , we can approximate this as:We are given:
Substrate sensitivity = 50 mV/V = 0.05
VUsing these values, we can find the body effect parameter, :The body effect parameter is also defined as:where is the substrate doping concentration, is the electron charge, is the permittivity of silicon, and is the gate oxide capacitance per unit area.First, let's calculate :
Now, we can solve for from the formula for :We need the permittivity of silicon, :
Now, substitute all the known values:The options are in units of cm⁻³. To convert from m⁻³ to cm⁻³, we use the relation , so .This matches option (A).
The formula for threshold voltage is .
The substrate sensitivity is:Given the condition , we can approximate this as:We are given:
Substrate sensitivity = 50 mV/V = 0.05
VUsing these values, we can find the body effect parameter, :The body effect parameter is also defined as:where is the substrate doping concentration, is the electron charge, is the permittivity of silicon, and is the gate oxide capacitance per unit area.First, let's calculate :
Now, we can solve for from the formula for :We need the permittivity of silicon, :
Now, substitute all the known values:The options are in units of cm⁻³. To convert from m⁻³ to cm⁻³, we use the relation , so .This matches option (A).
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