Maybe you're thinking of the triode, which AT&T did have a monopoly on around 1915, when they deployed the first transcontinental long-distance service using vacuum tubes to boost the signal. They bought deForest's patents and filed many more of their own on amplification circuits.

They had direct-dial long-distance by 1951, using relays and tubes.

The transistor started making a difference in telephony with the release of the 1ESS switch in 1965. But transistors were a commodity by then.