“Implanting” dopant atoms into a silicon wafer is similar to firing a shotgun – looking very closely on sufficiently small volumes of the target you might find no pellets, one pellet, two pellets or more, because the pellets are distributed at random. Similarly for state of the art very small transistors with a channel length of about twenty millionths of a millimeter (twenty nanometers): One trillion atoms (1012) implanted into one square centimeter are at average just four atoms in a transistor channel of that length and width. Due to the randomness of the implantation you might find in some transistor channels three, two, one or no dopant atom – or more than four. All these transistors then turn on and off at different voltages. On a computer chip you have some billion (109) transistors. Imagine the confusion of all of them turning on and off at different voltages. Even more severe, for very small transistors not only the number of dopant atoms in the channel may vary at random: Also the size and shape may vary between transistors because variations in the fabrication process cannot be completely avoided.
Why are smartphones with more than one billion of transistors on the area of a thumbnail still working? Because industry and research do care, by adapting the fabrication processes, the transistors and the circuits in a way to ensure that the final variations are small enough not to ruin your device. A prerequisite for this is to simply know how large the impacts of the process variations are on your devices. Here, simulation comes into play: You can virtually fabricate the transistor or chip on the computer and study here how strongly the device behavior is changed due to changes in the fabrication flow, like the random distribution of implanted dopant atoms. The figure shows an example for random dopant fluctuations and the distribution of electrons in a state-of-the art transistor. However, the problems become more severe when transistors shrink further.
Very sophisticated simulation programs are needed to assess and minimize the impact of process variations on transistors and chips. These must start with the simulation of the fabrication equipment and process, and then simulate the behavior of the transistors and finally that of the electronic circuits. Such a system of simulation programs has been developed within the project “Circuit Stability Under Process Variability and Electro-Thermal-Mechanical Coupling” (SUPERTHEME) which has been funded by the European Union from October 2012 to December 2015 within its Seventh Framework Programme. For the first time, the combined impact of process variations occurring at different steps of the fabrication process can be predicted. This helps the industry to select and adapt their process flows, transistor structures and electronic circuits to assure that nanoelectronic chips still work in spite of these process variations. This holds both for very small digital transistors, as used in smartphones, and for larger analog circuits used for example for sensing applications, where it is important that nominally identical transistors also behave identical in real application.
Key software developed within SUPERTHEME is already being commercialized by the Scottish software house Gold Standard Simulations (GSS) which has been one partner within the SUPERTHEME consortium coordinated by Fraunhofer IISB in Erlangen, and has strongly grown among others by exploiting results from SUPERTHEME. The success of SUPERTHEME has been enabled by the combination of expertize and commitment of a semiconductor company (ams), four equipment companies (ASML, HQ-D, IBS and LASSE), the software house GSS, the research institutes Fraunhofer IISB and IIS/EAS, the University of Glasgow and the Technical University Wien. The software is already being used at leading edge semiconductor companies in Europe and beyond and helps to develop better products e.g. for computing, communication and sensing. Quite surely the SUPERTHEME software will be used in the development of quite a lot of nanoelectronic products which you might buy and use in future. One example might be your next smartphone, which can guide your use of spices in the kitchen by searching for new recipes.