He secured funding and lab space, and went to work on the problem with Brattain and John Bardeen.
The key to the development of the transistor was the further understanding of the process of the electron mobility in a semiconductor. It was realized that if there was some way to control the flow of the electrons from the emitter to the collector of this newly discovered diode, one could build an amplifier. For instance, if you placed contacts on either side of a single type of crystal the current would not flow through it. However if a third contact could then "inject" electrons or holes into the material, the current would flow.
Actually doing this appeared to be very difficult. If the crystal were of any reasonable size, the number of electrons or holes required to be injected would have to be very large-—making it less than useful as an amplifier because it would require a large injection current to start with.
That said, the whole idea of the crystal diode was that the crystal itself could provide the electrons over a very small distance, the depletion region. The key appeared to be to place the input and output contacts very close together on the surface of the crystal on either side of this region.
Brattain started working on building such a device, and tantalizing hints of amplification continued to appear as the team worked on the problem. Sometimes the system would work but then stop working unexpectedly. In one instance a non-working system started working when placed in water.
Ohl and Brattain eventually developed a new branch of quantum mechanics known as surface physics to account for the behavior. The electrons in any one piece of the crystal would migrate about due to nearby charges. Electrons in the emitters, or the "holes" in the collectors, would cluster at the surface of the crystal where they could find their opposite charge "floating around" in the air or water. Yet they could be pushed away from the surface with the application of a small amount of charge from any other location on the crystal.
Instead of needing a large supply of injected electrons, a very small number in the right place on the crystal would accomplish the same thing. Their understanding solved the problem of needing a very small control area to some degree. Instead of needing two separate semiconductors connected by a common, but tiny, region, a single larger surface would serve. The emitter and collector leads would both be placed very close together on the top, with the control lead placed on the base of the crystal.
When current was applied to the "base" lead, the electrons or holes would be pushed out, across the block of semiconductor, and collect on the far surface. As long as the emitter and collector were very close together, this should allow enough electrons or holes between them to allow conduction to start. The Bell team made many attempts to build such a system with various tools, but generally failed. Setups where the contacts were close enough were invariably as fragile as the original cat's whisker detectors had been, and would work briefly, if at all.