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We have investigated the behavior of the superconducting energy gap A in ultrathin films of quench condensed Bi near the superconductor-insulator (SI) transition. From electron tunneling measurements on these films, we conclude that A becomes very small and approaches zero at the SI transition. We studied high-sheet-resistance films with TVo' s as low as 0.19 K. This is a factor of 40 lower than the low-sheet-resistance film Tco of 6.4 K. PACS numbers: 74.65.+n, 74.75.+t, 74.50.+r As the amount of disorder is increased in a metallic system the conduction-electron states begin to localize, and the strength of the effective electron-electron interactions increases. These two effects hinder the formation of the normally superconducting state in a disordered material. The localization of the electrons opposes the formation of a coherent state over distances longer than the localization length. The enhanced repulsive electronelectron interactions will reduce the net attractive interaction that is required for Cooper pairing. In twodimensional systems the effects of increasing disorder on the superconducting state are dramatic and eventually drive a transition from a superconducting to an insulating state [1][2][3][4][5][6].To qualitatively describe this transition it is helpful to consider the superconducting order parameter ^ oc Ao^^e'^ where the amplitude of the order parameter, Ao, is the zero-temperature energy gap and 0 is its phase. If a film is composed of islands that are large enough to have independent superconducting properties then the superconducting state can be weakened by reducing the (Josephson) coupling between the islands. This is accomplished by reducing the tunneling probability between the islands which results in an increase in the normal-state sheet resistance, Ru, of the film. Fluctuations in the phase of the order parameter ensue, which when strong enough destroy the long-range phase coherence across the film [2,6,7]. The situation has been shown to be diflferent for the case where the morphology of the film is more homogeneous, i.e., for disorder on shorter length scales. In systems that are not too close to the superconducting to insulating transition, increases in Ru have been shown to lead to well-defined decreases in the amplitude of the order parameter [7,8] and the mean-field transition temperature, Tco [3][4][5][6][7][8][9][10][11], in direct contrast with the islanded film case. One might expect that very near the superconducting to insulating transition, fluctuations in the amplitude of the order parameter would play a dominant role in driving the transition. Recently, however, it has been argued that even in these systems, phase fluctuations dominate the physics of the superconducting to insulating transition [6,12]. In this paper we present tunneling and transport results on uniformly disordered Bi films that are very close to the superconducting to insulating transition. We find that the energy gap in these films is reduced significantly from its bulk value, showing that the ...