A p-channel enhancement-mode MOSFET with 50 nm thick HfO2 high-k gate dielectric (ϵr=25) has a

step 1 In this question we have to find the cutoff frequency for the ideal case and for the other case.

A p-channel enhancement-mode MOSFET with 50 nm thick HfO2...

A p-channel enhancement-mode MOSFET with $50 \mathrm{~nm}$ thick $\mathrm{HfO}_{2}$ high-k gate dielectric $\left(\epsilon_{r}=25\right)$ has a threshold voltage of $-0.6 \mathrm{~V}$. The effective hole channel mobility is $150 \mathrm{~cm}^{2} / \mathrm{V}-\mathrm{s}$. What is the drive current for a $50 \mu \mathrm{m}$ wide and $2 \mu \mathrm{m}$ long device at $V_{G}=-3 \mathrm{~V}$ and $V_{D}=-0.05 \mathrm{~V} ?$ What is the saturation current at this gate bias? Sketch a cross section of the device schematically showing the inversion layer if gate and drain are both at $-3 \mathrm{~V}$. Below that sketch qualitatively the variation of channel potential with position.

Key Concepts

Channel Potential Variation

The variation of channel potential along the MOSFET length is important for understanding device behavior. A schematic cross-section of the device will show the inversion layer and illustrate how the channel potential drops from source to drain, reflecting the gradual change in carrier concentration and electric field distribution along the channel.

Inversion Layer Formation

Under sufficient gate bias (beyond the threshold voltage), an inversion layer is formed at the semiconductor-oxide interface. This thin, conductive layer of carriers (holes for a p-channel device) facilitates the conduction from source to drain, making it a critical aspect of MOSFET operation.

Operation Regions of MOSFETs

MOSFETs typically operate in different regions based on the applied voltages. In the linear (ohmic) region, the current increases linearly with the drain voltage until channel pinch-off occurs. Beyond this, in the saturation region, the current plateaus at a maximum value due to channel pinch-off, defining the saturation current.

Threshold Voltage

In a MOSFET, the threshold voltage is the point at which the gate voltage is sufficient to create an inversion layer, enabling significant channel conduction. It is the critical voltage that marks the transition from the off-state to the on-state in enhancement-mode devices.

Carrier Mobility

Carrier mobility, in this context referring to the effective hole mobility, is a measure of how quickly holes can move through the channel when an electric field is applied. This parameter directly impacts the device’s drive current and overall performance.

Gate Capacitance

Gate capacitance, especially in MOSFETs with high-k dielectrics such as HfO2, is determined by the dielectric constant and thickness of the gate insulator. It influences the amount of charge that can be induced in the channel for a given gate voltage, thereby affecting the device’s drive current.

Channel Dimensions

The width and length of the MOSFET channel play a crucial role in defining device performance. A wider channel provides more conduction paths and thus a higher drive current, whereas a shorter channel reduces the resistance, leading to improved device speed and higher currents.

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