  The D-Egg, an acronym for ``Dual optical sensors in an Ellipsoid Glass for
Gen2,'' is one of the optical modules designed for future extensions of the
IceCube experiment at the South Pole. The D-Egg has an elongated-sphere shape
to maximize the photon-sensitive effective area while maintaining a narrow
diameter to reduce the cost and the time needed for drilling of the deployment
holes in the glacial ice for the optical modules at depths up to 2700 meters.
The D-Egg design is utilized for the IceCube Upgrade, the next stage of the
IceCube project also known as IceCube-Gen2 Phase 1, where nearly half of the
optical sensors to be deployed are D-Eggs. With two 8-inch high-quantum
efficiency photomultiplier tubes (PMTs) per module, D-Eggs offer an increased
effective area while retaining the successful design of the IceCube digital
optical module (DOM). The convolution of the wavelength-dependent effective
area and the Cherenkov emission spectrum provides an effective photodetection
sensitivity that is 2.8 times larger than that of IceCube DOMs. The signal of
each of the two PMTs is digitized using ultra-low-power 14-bit
analog-to-digital converters with a sampling frequency of 240 MSPS, enabling a
flexible event triggering, as well as seamless and lossless event recording of
single-photon signals to multi-photons exceeding 200 photoelectrons within 10
nanoseconds. Mass production of D-Eggs has been completed, with 277 out of the
310 D-Eggs produced to be used in the IceCube Upgrade. In this paper, we report
the des\ ign of the D-Eggs, as well as the sensitivity and the single to
multi-photon detection performance of mass-produced D-Eggs measured in a
laboratory using the built-in data acquisition system in each D-Egg optical
sensor module.
