Process variation is the naturally occurring variation in the attributes of transistors (length, widths, oxide thickness) when integrated circuits are fabricated. The amount of process variation becomes particularly pronounced at smaller process nodes (<65 nm) as the variation becomes a larger percentage of the full length or width of the device and as feature sizes approach the fundamental dimensions such as the size of atoms and the wavelength of usable light for patterning lithography masks.
Contents
Process variation causes measurable and predictable variance in the output performance of all circuits but particularly analog circuits due to mismatch. If the variance causes the measured or simulated performance of a particular output metric (bandwidth, gain, rise time, etc.) to fall below or rise above the specification for the particular circuit or device, it reduces the overall yield for that set of devices.
History
The first mention of variation in semiconductors was by William Shockley, the co-inventor of the transistor, in his 1961 analysis of junction breakdown.
An analysis of systematic variation was performed by Schemmert and Zimmer in 1974 with their paper on threshold-voltage sensitivity. This research looked into the effect that the oxide thickness and implantation energy had on the threshold voltage of MOS devices.
sources of variations 1) gate oxide thickness 2) random dopant fluctuations 3) Device Geometry, Lithography in nanometer region
Characterization
Semiconductor foundries run analyses on the variability of attributes of transistors (length, width, oxide thickness, etc.) for each new process node. These measurements are recorded and provided to customers such as fabless semiconductor companies. This set of files are generally referred to as "model files" in the industry and are used by EDA tools for simulation of designs.
Statistical Analysis
Designers using this approach run from tens to thousands of simulations to analyze how the outputs of the circuit will behave according to the measured variability of the transistors for that particular process. The measured criteria for transistors are recorded in model files given to designers for simulating their circuits before simulation.
The most basic approach used by designers is increasing the size of devices which are sensitive to mismatch.
Topology Optimization
This is used to reduce variation due to polishing, etc.
Patterning Techniques
To reduce roughness of line edges, advanced lithography techniques are used.