We demonstrate what is to our knowledge the first ultrabroadband monolithically grown AlGaAs/CaF(2) semiconductor saturable-absorber mirror (SESAM) that covers nearly the entire gain spectrum of a Ti:sapphire laser. A large high-reflectivity bandwidth of more than 300 nm is provided by a device consisting of only six material layers. This fluoride SESAM had a modulation depth of 2.2%, a fast recovery time constant of less than 150 fs, and a slow recovery time constant of 1.2 ps. Using this SESAM inside a Ti:sapphire laser produced self-starting sub-10-femtosecond pulses.