The son of an electrical engineer from Jefferson City, Missouri, Kilby failed his entrance to the Massachusetts Institute of Technology. He was drafted into the army, spending most of his time attempting to reduce the size of radio sets for jungle-warfare units. After demobilization, he was admitted to the University of Illinois. After graduating in 1947 he began work for Centralab, Milwaukee, Wisconsin, producing parts for television sets and hearing aids.

In 1952 Centralab decided to use the transistors recently developed by William Shockley and Kilby was sent to Bell Laboratories at Murray Hill, New Jersey, to learn about the new device. In 1958 he moved to Texas Instruments, Dallas, the firm that had had the foresight in 1954 to switch from germanium to silicon transistors. Engineers at TI, and elsewhere, had come up against the difficulty of fitting on a transistor the number of parts and connections demanded by their designs. It was here in July 1958, while the rest of the laboratory was on holiday, that Kilby came up with what was later termed ‘the Monolithic Idea’.

His basic intuition was that silicon alone could fill most electronic demands. Undoped, it was a resistor; as a p–n junction, a capacitor. It should be possible to build a whole circuit out of a single piece of material by using different doping levels; no connections would be called for. He built a test circuit and it worked. It was, in fact, the first integrated circuit. Kilby was awarded patent rights in 1967, having first fought off a challenge from Robert Noyce. On appeal the decision was reversed and, in 1968, the patent was awarded to Noyce.

Kilby also worked for Texas Instruments on the development of what was the first pocket calculator, the Pocketronic. It was launched on April 14 1971, weighed 2.5 pounds, cost £150, and could only perform the four main arithmetical functions. By this time Kilby had left TI in 1970 to work in Dallas as a self-employed inventor. He also served as a distinguished professor of electrical engineering at the University of Texas from 1978 to 1985.