Lecture05 :Threshold voltage and its components | EC6203

Summary

This detailed script explains the process of estimating the threshold voltage of a MOS transistor, covering key components such as the work function difference, gate voltage required for strong inversion, and voltage compensation for depletion and trapped charges. The transcript also explores the effect of substrate bias (V_SB) on the threshold voltage, including its modification with a body effect coefficient (gamma). By breaking down these concepts, the script provides a comprehensive understanding of how threshold voltage is influenced by various factors in MOSFET operation, essential for designing and analyzing semiconductor devices.

Takeaways

• 😀 The threshold voltage of a MOSFET is the minimum gate voltage needed to establish strong inversion and initiate conduction between the source and drain.
• 😀 The threshold voltage is affected by several key components: the work function difference, surface potential change, depletion charges, and trapped charges in the oxide interface.
• 😀 The first component of threshold voltage is the work function difference (Φms), which adjusts the energy bands at the gate-channel interface to flatten them.
• 😀 The second component is the gate voltage needed to establish a surface potential of -2Φf for strong inversion, where Φf is the Fermi potential.
• 😀 The third component compensates for the depletion charges formed when majority carriers are repelled, leaving behind negative charges in the semiconductor.
• 😀 Depletion charges generate a voltage, which is calculated using the formula V = Q/C, where Q is the depletion charge and C is the capacitance of the oxide.
• 😀 The fourth component accounts for the charges trapped in the oxide and at the oxide-semiconductor interface, which can alter the threshold voltage.
• 😀 Trapped charges in the oxide layer are a result of fabrication imperfections, such as voids and vacancies, which capture electrons and affect the MOSFET's behavior.
• 😀 The final expression for threshold voltage (Vt) is given by: Vt = Vt0 + γ(√(-2Φf + Vsb) - √(-2Φf)), where γ is the body factor that quantifies the effect of substrate bias.
• 😀 When the substrate bias voltage (Vsb) is zero, the threshold voltage simplifies to Vt0, but nonzero Vsb increases the threshold voltage due to a higher depletion charge.
• 😀 The body factor (γ) is defined as √(2qN_aε_si / C_ox) and influences how sensitive the threshold voltage is to changes in substrate bias.

Q & A

What is the threshold voltage of a MOSFET?

The threshold voltage is the minimum gate voltage required to establish strong inversion in the MOSFET, where the energy band bends sufficiently to create a conductive channel between the source and drain.

What is the strong inversion condition in a MOSFET?

Strong inversion occurs when the total bending in the energy band of the MOSFET reaches -2.5V, allowing for the formation of a conductive channel.

What is the first component that affects the threshold voltage?

The first component is the work function difference between the gate and the channel, often referred to as φms or φgc, which determines the initial bending of the energy bands at zero bias.

Why is the flat band voltage important in determining the threshold voltage?

The flat band voltage (Vfb) corresponds to the voltage at which the energy bands of the gate and channel align, effectively removing the initial band bending due to work function differences.

What is the second component of threshold voltage related to?

The second component is the amount of gate voltage required to establish the surface potential φ = -φf, corresponding to the strong inversion condition where the surface potential changes by -2φf.

How does depletion charge affect the threshold voltage?

Depletion charge occurs when majority carriers are repelled from the interface, leaving negative ions behind. This charge creates a voltage drop, which must be compensated by the gate voltage to maintain proper channel formation.

What is the basic equation used to calculate the voltage developed by depletion charges?

The voltage developed by depletion charges can be calculated using the formula V = Q/C, where Q is the depletion charge and C is the capacitance, which is given by Cox = ε/ tox for the oxide capacitance per unit area.

What is the role of oxide capacitance in threshold voltage?

Oxide capacitance (Cox) plays a critical role in determining the voltage that needs to be applied to offset the depletion charge voltage. It depends on the dielectric constant of the oxide and the oxide thickness.

What is the significance of trapped charges and oxide interface charges in MOSFET operation?

Trapped charges and oxide interface charges, which arise due to defects in the oxide layer and the mismatch in the crystal structures of the oxide and semiconductor, contribute to shifts in the threshold voltage, often requiring adjustments in the gate voltage.

What is the final expression for the threshold voltage considering all components?

The final expression for threshold voltage is: Vt = Vt0 + γ * sqrt(-2φf + Vsb) - sqrt(-2φf), where γ is the body factor and Vsb is the substrate bias voltage.

How does the substrate bias voltage (Vsb) affect the threshold voltage?

The substrate bias voltage (Vsb) impacts the threshold voltage by modifying the depletion charge, which is reflected in the body factor γ. A non-zero Vsb increases the threshold voltage, whereas Vsb = 0 results in the nominal threshold voltage Vt0.

What does the body factor (γ) represent in a MOSFET?

The body factor γ represents the influence of the substrate bias on the threshold voltage. It is calculated as γ = sqrt(2qNaεSi/Cox), and its unit is typically the square root of voltage.