MOSFET Threshold Voltage Extraction: How to Get Power Management Right from the Beginning

PublishTime： 2023-08-14 Article Source：Keysight blogs

The endurance of your smartphone battery amidst your relentless multitasking is nothing short of an engineering marvel. The increasing longevity of batteries highlights the delicate balance circuit designers and modeling engineer strike in power management. With electronic devices becoming ubiquitous, from mobile gadgets to servers and networking equipment, the race intensifies for power-efficient, scalable semiconductor devices. These essential components must minimize power consumption while fitting into densely packed integrated circuits.

Metal-Oxide Field-Effect Transistors, or MOSFETs, stand out in this progressive trajectory.

Developed in the 1960s, these transistors have become a mainstay in electronic devices, thanks to their power efficiency, scalability, and manufacturability. In fact, your smartphone might carry billions of nanoscale MOSFETs.

For designers aiming to optimize power management, accurate modeling of MOSFETs – the full characterization of the device performance by a mathematical formula and their fitting parameters – is essential.

Threshold voltage: A critical parameter for MOSFET modeling

The threshold voltage (V_th) is a crucial parameter to extract for accurate MOSFET modeling. Over the decades, experts have fine-tuned the definition of Vth. It means the gate voltage where a MOSFET transitions from weak to strong inversion. In simple terms, Vth is the voltage where conduction of current begins. As devices become more compact, zeroing in on the precise V_th has become imperative for ensuring optimal functionality and energy efficiency in both digital and analog applications.

However, finding a definitive threshold in the drain current (I_D) vs. gate-source voltage (V_GS) characteristic relationship is no easy feat, due to the continuous nature of the physical phenomena at play. This challenge has given rise to numerous methods to extract the value of threshold voltage. This article will help properly understand these methods and influential factors to ensure accurate and consistent V_th extraction.

How to extract the threshold voltage

There are two popular methods for extracting the threshold voltage (V_th). Depending on the device and application, these methods offer varying degrees of precision and relevance.

Linear Extrapolation Method (ELR)

The linear extrapolation method (ELR) determines V_th by locating the gate voltage (V_g) axis intercept of the linear extrapolation of the drain current (I_d) –V_g curve at its point of maximum transconductance (g_m). The value of V_th is calculated by subtracting V_d/2 to Vg intercept point to minimize the effect of different values of drain voltage (Vd). As shown in Figure 1, there are four key steps:

1. Find g_{m_peak}

2. Calculate I_{d_appx} based on I_d at g_{m_peak}

3. Find V_cross based on I_{d_appx}

4. Substract V_cross by V_d/2 to get the value of V_th

Figure 1. Calculating the threshold voltage using Linear Extrapolation Method (ELM)

However, the ELR method has certain limitations. Mobility degradation effects and the impact of significant source and drain series parasitic resistances can skew the I_d-V_g curve, thereby rendering the extracted threshold voltage value imprecise.

Constant Current Method (CC)

The constant-current method (CC) evaluates the threshold voltage as the value of the gate voltage, V_g, corresponding to a given arbitrary constant drain current (I_d). Usually, drain voltage (V_d) is less than 100mV to bias the transistor at a linear region. Both source and body nodes are connected to the ground.

I_d is equal to (W_m/L_m) * I_con, where W_m and L_m are the mask channel width and length respectively. I_con is an arbitrary value. While a typical value of I_con is 1e^-7, it may be different for different process nodes. Despite the simplicity of the CC method, the outcome heavily depends on the assigned drain current value I_con. This selection can introduce significant variations in the extracted threshold voltage.

Figure 2. Extracting V_th using Constant Current Method

Key factors affecting the threshold voltage

Variations in threshold voltage (V_th) can have significant implications for the performance and reliability of the devices. Several factors, both internal and external, can influence the threshold voltage of a MOSFET.

Oxide layer thickness

The type of oxide and the thickness of the layer can alter the threshold voltage. A thinner oxide layer results in a reduced threshold voltage, and vice versa.

Temperature

Although not directly related, temperature variations do impact threshold voltage. For instance, a 30°C change can change the threshold voltage by about 500mV.

Random dopant fluctuation (RDF)

RDF entails reducing random dopant fluctuation by minimizing dopant density. This can alter MOSFET characteristics, including the threshold voltage.

Considerations for precise V_th extraction

Getting V_th of a MOSFET right is like making sure the brick in the foundation of your house is solid. Here are some key considerations for ensuring an accurate V_th extraction.

Maintaining consistent condition

The bedrock of any scientific measurement is consistency. This means maintaining uniform experimental conditions when extracting V_th. Changes as subtle as temperature variations or swapping out equipment can introduce discrepancies in your readings.

Averaging results

To increase the reliability and accuracy of V_th extraction, perform multiple measurements and calculate an average.

Staying updated with the latest tools

The precision and accuracy of measurement tools have improved over the years. Tools like Keysight's PathWave Device Modeling solution offer modern features designed to improve modeling accuracy and time-to-release. For instance, with automated measurements, you can not only ensure accuracy but also save valuable time.

Consider the impact of device geometry and scaling

As MOSFETs get scaled down, they are more susceptible to short-channel effects. These effects can have a significant influence on the threshold voltage. So it’s essential to consider these effects when extracting V_th for compact electronic devices.

Choosing a reliable partner

Ever found yourself scratching your head over Vth extraction or wishing there was an easier way to compare results from different methods?

Keysight's PathWave Model Builder (MBP) is a comprehensive model generation solution designed to take the guesswork out of the threshold voltage extraction for MOSFETs. Its built-in extraction packages are tailored for standard industry models, and we’ve even included a customizable modeling strategy interface to ensure you have the flexibility you need.

Figure 3. V_th vs. Length in PathWave Model Builder (MBP)

Inside MBP, you'll find both CC and ELR methods smoothly integrated into the libraries and are just a click away on the IMV (InterMediate Variable) page.

In the realm of power electronics, the significance of device modeling becomes increasingly paramount. As devices push the boundaries of efficiency and miniaturization, understanding the intricacies of MOSFET threshold voltage extraction is not just an academic exercise but a necessity. Accurate device modeling forms the bedrock of efficient power electronic systems, ensuring that components work optimally and synergistically. As we advance further into an era dominated by ultra-low-power devices, leveraging precise methodologies and state-of-the-art tools for MOSFET modeling will be the cornerstone for groundbreaking innovations in power electronics.

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