  We present a consistent overall picture of the electronic structure and
ferromagnetic interaction in CaB$_6$, based on our joint transport, optical,
and tunneling measurements on high-quality {\em defect-controlled} single
crystals. Pure CaB$_6$ single crystals, synthesized with 99.9999 %-pure boron,
exhibited fully {\em semiconducting} characteristics, such as monotonic
resistance for 2--300 K, a tunneling conductance gap, and an optical absorption
threshold at 1.0 eV. {\em Boron-related defects} formed in CaB$_6$ single
crystals synthesized with 99.9 %-pure boron induced {\em mid-gap states} 0.18
eV below the conduction band and extra free charge carriers, with the
transport, optical, and tunneling properties substantially modified.
Remarkably, no ferromagnetic signals were detected from single crystals made
with 99.9999 %-pure boron, regardless of stoichiometry, whereas those made with
99.9 %-boron exhibited ferromagnetism within a finite range of carrier density.
The possible surmise between the electronic state and magnetization will be
discussed.
