Isma'il I (reigned 1501-1524) was supported by the Qizilbash - tribes of mostly (but not exclusively) Azerbaijani soldiers who were (initially) fanatically loyal to him. Isma'il eventually grew to distrust the Qizilbash and tried rather unsuccessfully to reduce their influence after the battle of Chaldiran, where the traditional Safavid forces were soundly defeated by gunpowder-armed Ottomans. After this battle, everything changed - he essentially fell into a deep depression for the rest of his life, taking up alcohol and dressing in the black clothes of mourning. The Qizilbash lost their devotion to (and respect for) Isma'il after the battle, and they acted increasingly independently. This was a source of significant weakness for the Safavids for quite some time.

When Isma'il died, the Qizilbash tribes fought amongst each other for the right to be "regent" to his son Tahmasp I (reigned 1524-1576). Tahmasp regained control as an adult (significantly executing the powerful Qizilbash chieftain Husayn Khan Shamlu), and managed to successfully reduce Qizilbash power somewhat by enslaving Georgians, Circassians, and Armenians as ghilman (plural of ghulam). These ghilman were initially used as elite palace and harem guards who would be utterly dependent on and loyal to the Shah. It wasn't until the reign of Shah Abbas I (reigned 1588-1629) that the power of the Qizilbash was finally broken however, when he significantly increased ghilman conscription, expanded their role, replaced the Qizilbash systematically in positions of government, and introduced a standing army. From then on, the ghilman were used and equipped quite similarly to Sipahi, with native Iranian musketeers and artillery in support.

Sources:

Converting Persia: Religion and Power in the Safavid Empire by Rula Jurdi Abisaab, Safavid Iran: Rebirth of a Persian Empire by Andrew J. Newman, and Iran Under the Safavids by Roger Savory