The Picosecond Avalanche Detector is a multi-junction silicon pixel detector based on a (NP)$_{drift}$(NP)$_{gain}$ structure, devised to enable charged-particle tracking with high spatial resolution and picosecond time-stamp capability. It uses a continuous junction deep inside the sensor volume to amplify the primary charge produced by ionizing radiation in a thin absorption layer. The signal is then induced by the secondary charges moving inside a thicker drift region. A proof-of-concept monolithic prototype, consisting of a matrix of hexagonal pixels with 100 μm pitch, has been produced using the 130 nm SiGe BiCMOS process by IHP microelectronics. Measurements on probe station and with a $^{55}$Fe X-ray source show that the prototype is functional and displays avalanche gain up to a maximum electron gain of 23. A study of the avalanche characteristics, corroborated by TCAD simulations, indicates that space-charge effects due to the large primary charge produced by the conversion of X-rays from the ^55Fe source limits the effective gain.