Basic Transistor Physics
David Giessel
University of Alaska Fairbanks
Physics 212 Web Project, Spring 2003

   Transistor gate switching speed is an area of primary concern in nearly all digital applications. Everyone wants faster stuff. The problem is being able to provide this without increasing power consumption or cost. There are many factors involved in determining the maximum frequency of a transistor which will be discussed here. A primary limiting factor is gate temperature.

   Gate temperature is a byproduct of the resistance that is inherent to all electrical circuits. There is a small resistance in the wiring, there is resistance in the silicon substrate (which results in leakage current), and there is resistance within the gate. Gate temperature has a nearly linear corelation to operating frequency. We know that resistance is a product of temperature, resistivity, and cross sectional area. From this we can infer that lower gate temperature means higher gate speed. And conversely higher gate temps will result in lower frequency. Clearly operating at or below room temperature would be ideal (although operating below room temperature involves exotic cooling solutions such as thermal electric coolers). Electromigration (a side effect of gate overheating) is illustrated below. Material is actually moved in the wire to create a "void" and "hillock." Clearly having a hole in your wiring is not a good thing. This shows why processor cooling is of critical importance.

   What are some factors that affect gate temperatures? Well temperature is a direct reflection of wattage. Wattage in a processor is a product of the power used per gate multiplied by the number of gates (the activity of gates is also important as inactive gates use very little power). When you start switching 50 million gates (approximately the number of gates in a Pentium 4 processor) wattage can add up pretty quick. Individual gate temperature is a product of gate voltage (when voltage increases current also increases). And gate voltage is directly related to the size of the gate (smaller gates require less voltage to be turned on or off and therefore less power).

So how does one reduce individual transistor power output? By shrinking the gate wiring and size.