Abstract: Methods of forming and analyzing doped monocrystalline silicon each comprise the steps of providing: a vessel, particulate silicon, a dopant, and a float-zone apparatus. The vessel for each method comprises silicon and defines a cavity. The methods each further comprise the steps of combining the particulate silicon and the dopant to form treated particulate silicon, and disposing the treated particulate silicon into the cavity of the vessel. The methods yet further comprise the step of float-zone processing the vessel and the treated particulate silicon into doped monocrystalline silicon with the float-zone apparatus. The analytical method further comprises the step of providing an instrument. The analytical method yet further comprises the steps of removing a piece from the doped monocrystalline silicon, and determining the concentration of the dopant in the piece with the instrument.