What was the reason for the conquest of the Balkan Peninsula by the Ottoman Turks?

The Turks first appeared in the Balkans in the middle of the 14th century under Sultan Orhan (reigned from 1324 to 1362). In those years, a civil war was going on in Byzantium and one of the warring parties turned to the Turks for help. They captured the Cimpe fortress in 1353 and from that moment began their expansion on the peninsula. Also, the Byzantine emperor John IV Palaeologus used the help of the Ottoman army in the war against the Serbs and Bulgarians (the Byzantines lacked their own soldiers). The Ottoman expansion on the peninsula proceeded in two stages:

Until 1402 (before the defeat by Tamerlane).
Until the beginning of the 16th century (then expansion into Hungary began).