Substrate doping ND = 1015 cm-3, polysilicon gate doping density ND = 1020 cm-3, gateoxide thickness tx = 650 A, and oxide-interface charge density Nox = 2 x 1010 cm-2 . UseEsi = 11.7EO and Eox = 397EO for the dielectric coefficients of silicon and silicon-dioxide,respectively.(a) Calculate the threshold voltage V, for VSB = 0.(b) Determine the type and the amount of channel ion implantation which are necessaryto achieve a threshold voltage of V = - 2 V
Question
Substrate doping ND = 1015 cm-3, polysilicon gate doping density ND = 1020 cm-3, gateoxide thickness tx = 650 A, and oxide-interface charge density Nox = 2 x 1010 cm-2 . UseEsi = 11.7EO and Eox = 397EO for the dielectric coefficients of silicon and silicon-dioxide,respectively.(a) Calculate the threshold voltage V, for VSB = 0.(b) Determine the type and the amount of channel ion implantation which are necessaryto achieve a threshold voltage of V = - 2 V
Solution
The threshold voltage (Vt) for a MOSFET can be calculated using the following formula:
Vt = Vfb + 2phi_f + sqrt(2qEsiND*(2*phi_f)/Cox)
where:
- Vfb is the flat-band voltage
- phi_f is the Fermi potential
- q is the elementary charge
- Esi is the permittivity of silicon
- ND is the substrate doping concentration
- Cox is the oxide capacitance per unit area
First, we need to calculate the flat-band voltage (Vfb). This can be done using the formula:
Vfb = phi_ms - Qox/Cox
where:
- phi_ms is the work function difference between the gate material and the semiconductor
- Qox is the oxide-interface charge density
However, since we don't have the work function difference, we'll assume that Vfb is approximately 0.
Next, we calculate the Fermi potential (phi_f) using the formula:
phi_f = kT/q * ln(ND/ni)
where:
- k is the Boltzmann constant
- T is the absolute temperature
- ni is the intrinsic carrier concentration
Assuming room temperature (T = 300K), and using the given value for ND, we can calculate phi_f.
Next, we calculate the oxide capacitance per unit area (Cox) using the formula:
Cox = Eox/tox
where:
- Eox is the permittivity of the oxide
- tox is the oxide thickness
Using the given values for Eox and tox, we can calculate Cox.
Finally, we can substitute all the calculated and given values into the formula for Vt to find the threshold voltage for VSB = 0.
For part (b), to achieve a threshold voltage of V = -2V, we would need to adjust the substrate doping concentration (ND) or the oxide-interface charge density (Qox). This would require ion implantation. The type of ion (p-type or n-type) would depend on the desired threshold voltage and the original type of the substrate. The amount of ion implantation would be determined by the difference between the original and desired threshold voltages.
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