The typical transistor's characterization test-bench schematic for nominal MOS devices is displayed below:

SPICE simulations[edit]

In general to characterize MOS transistors we'd like to perform several simulation sweeps, starting from the following three DC simulation sweeps.

1. First we should to plot the normalized I/V transfer curves for the transistor for different applied Vgs bias voltages.

• The normalized Id drain current vs. Vds drain-source voltage for different Vgs gate bias voltages.
• Also the normalized Id current vs. Vgs gate-source voltage for different Vbs back-gate bias voltages.

2. Second using the same reference minimum length transistor, we should plot all design parameters vs. Veff (as a proxy for inversion level).

3. Lastly, we want to inspect the variation in design parameters vs. Vgs for different length transistors.

• This will also help make the point for advantages and disadvantages of devices as we shrink device length.

Ultimately, what we really care about is getting an idea around trade-offs and the attainable design parameters we can obtain from a single transistor.

DC analysis (sweep): Large signal parameters[edit]

Typically, we start by plotting the large-signal normalized transistor I/V transfer curves.

Id vs Vds for different Vgs bias[edit]

We sweep Vds, and subsequently increment Vgs in steps up to our max supply voltage.

For the I/V characterization curves, normally a minimum transistor length and a nominal width and number of fingers is chosen. (however this is not as critical as transfer curves will be normalized by width)

Id vs Vgs for different Vbs (back-gate) bias[edit]

We also sweep vgs, and subsequently sweep the back gate bias voltage.

DC analysis (sweep): Design parameters vs. Veff (for various Vbs)[edit]

Next, we move onto small-signal device parameters. Typically, nominal design parameters should be plotted for a reference minimum-length transistor with various back-gate Vbs.

Most important are the design parameter plots for Vbs=0V (i.e. with no back-gate voltage): These plots are most useful for starting choosing a Veff bias point to start a design.

Note in cases where the source is not at the same potential as the bulk, it is illustrative to see how design parameters change for the same applied Vgs, mainly as the threshold increases one needs to increase the Vgs bias voltage in order to attain the same Veff which governs inversion and hence small signal operating parameters. Additionally for Vbs < 0 note the back-gate transconductor comes into play which must hence be included in the small signal model of operation as the body effect will modulate the output current (in some instances understanding the contribution of this effect can be advantageous as in the case of the common-drain configuration, whereas in others it can be detrimental as in the case of the source follower).

DC analysis (sweep): Design parameters vs. Veff (for various lengths)[edit]

Small-signal design parameters should also be plotted for a set of transistors with lengths spanning from minimum to nominally maximum (roughly following technology nodes progression is a good rule of thumb) to help compare trade-offs in choosing device dimensions (width chosen as before).

For MOS transistors characterization, the following are important dimension, device and design parameters for different operating regions.

Transistors dimension parameters[edit]

MOS transistors are physically defined primarily by the following parameters:

Length (L)[edit]

The actual physical device length

Width (W)[edit]

The total width (W) of a transistor device (in a planar process) is dependent on:

• Wf: Finger's width, and
• Nf: Number of fingers

and

• m: Parallel multiplier
  • Number of identical devices in parallel

The total width (W) then being the finger's width times the number of fingers multiplied times the number of identical transistors in parallel:

W=(Nf*Wf)*m

Device parameters[edit]

Some important transistor device and bias parameters are the following:

Vgs, Vds, Vbs[edit]

The gate-to-source, drain-to-source and bulk-to-source DC bias voltages.

Vth[edit]

The Device threshold voltage and transition point from cutoff (sub-threshold weak inversion) to moderate inversion ("ON").

Veff or Vov[edit]

The effective overdrive voltage. A proxy for understanding the device inversion level. Used widely as a design parameter in analog design.

More formally defined as Veff = Vgs - Vth

Vdsat[edit]

Minimum active (saturation) voltage (MOS), i.e. the minimum voltage across drain to source that keeps devices in active-sat. While traditionally equal to Veff for longer channel devices, for short-channel devices it is no longer the same, but serves as a close proxy.

Id[edit]

The DC drain current at biased operating point.

cxx[edit]

Device parasitic capacitances. Most important here being lumped capacitances to ground Cgg and Cdd (also Css and Cbb), but also mutual capacitances between terminals -- these are especially important for stability at high-frequencies.

Note these are highly non-linear, hence for analog design these must be considered as small signal quantities.

rds or 1/gds[edit]

Device output drain-source resistance (or the inverse, drain-source conductance). This small signal device parameter (i.e. defined at operating point) is largely dependent on relative length and is absolutely critical for enabling large intrinsic device voltage gain.

Active design parameters[edit]

Most important after specifying and simulating device parameters is understanding the performance limits of your devices so as not to engage in designs where it is not possible to meet your goals. Some very important transistor design parameters are the following (note lowercase indicates small signal parameters):

gm[edit]

Transconductance gain due to nominal input "gate", defined as Iout/Vin. Often specified as design requirement to synthesize larger analog block.

gmb[edit]

Transconductance gain due to bulk/substrate back-gate, defined as Iout/Vbs. This design parameter must be considered when source and bulk are not at the same potential, it can be exploited sometimes beneficially to yield larger total device transconductance for lower power.

gm/Id[edit]

Transconductor current efficiency, in a nutshell how much DC bias current do you need to spend to yield a desired transconductance gain. Typically specified in S/A.

The gm/Id design parameter, can also be used as a proxy for understanding the device inversion level. (but now in terms of other useful design parameters)

Keep in mind, the maximum gm/Id range has tended to be constant over technology nodes (< 30)

gm/W[edit]

Transconductor area efficiency, in a nutshell how much IC width (proportional area) do you need to spend to yield a desired transconductance gain. Typically specified in S/um.

Id/W[edit]

Current density. How much current can you support for a given device width. Typically specified in mA/um.

This parameter is often times used alternatively to gm/W at larger currents where reliability and electron migration are a concern.

ao[edit]

Device intrinsic voltage gain: the maximum voltage gain attainable from a single device at DC. Defined as Vout/Vin and typically unit-less or V/V.

Can be calculated from design parameters as: ao = gm x rds (or equally gm / gds)

Ft or GBW[edit]

Unity-gain frequency: the frequency where the device current gain (Iout/Iin) is 1. Beyond this point the device is typically no longer an amplifier.

Note current gain also applies to MOSFET transistors, recall at larger frequencies the gate impedance is actually finite. Typically it often makes little sense to operate devices near their Ft frequency as there is an exponential decreasing gain returns to power spent. (often times limiting the bandwidth to Ft/10 is more reasonable)

The simulator often provides most accurate Ft approximations, else a good rough approximation for Ft is Ft=gm/Cgg.

Another alternative useful design parameter is the GBW: the gain-bandwith-product which is defined as GBW= a x f. It is equal to Fc (when Fc is known) or can be also computed at other frequencies above Fc assuming a dominant pole approximation.

Fc[edit]

Device -3dB bandwidth corner frequency. Assuming a dominant pole approximation, a rough approximation being Fc=gm/Cload (Fc=gm/Cdd for self-loaded case). These parameter is often more useful for understanding the speed of larger amplifier stages. (e.g. in the case of Opamps)

FoM[edit]

Typical device figure-of-merit for given technology, defined as FoM = gmid x Ft. Typically biasing at max FoM represents a good operating point for transistors when high-speed power-efficient operation is desired.

Triode design parameters[edit]

Only applicable to devices operated mainly as "switches" between triode (Vgs ~ Vdd and Vds ~ 0) and cutoff regions (at Vgs ~ 0). Applications being digital circuits and discrete-time sampled circuits among many others.

Typically, the minimum the switch ON resistance relative to it's OFF resistance for the same output capacitance, the better the switch.

Switches are also defined by their maximum bandwidth, defined as W3db = 1 / (Ron*Cout)

Ron[edit]

Effective/averaged ON resistance of the switch device in triode. The minimum the ON resistance of the switch, the better.

Roff[edit]

Effective/averaged OFF resistance of the switch device in cutoff. The larger the OFF resistance of the switch, the lower the leakage power of the switch. Additionally a larger OFF resistance avoids incurring sampling errors in discrete-time circuits.

Cout[edit]

Effective output capacitance of the switch device in triode. Typically, the minimum the output capacitance of the switch (for the same Ron), the better the bandwidth for the same power.

Cgate[edit]

Lumped averaged input capacitance of the switch device to switch ON/OFF. Sets the required power for the driver to fully switch gate given switching frequency.

Below are different MOS transistor characterization testbenches and results for transistors operation in various regions (as discussed above).