The present invention relates to a reactor (1) for epitaxial deposition of semiconductor material on substrates (100), comprising: a reaction chamber (2) provided with a cavity (20) defined by a lower wall (21), an upper wall (22) and lateral walls (23, 24); a susceptor (3), positioned inside said cavity (20), and adapted to support and heat substrates (100) during epitaxial deposition; a heating system (6) adapted to heat said susceptor (3); an upper plate (7) that is positioned above said upper wall (22) and that overlies said susceptor (3) so that it reflects thermal radiation emitted by said susceptor (3) towards said susceptor (3). A liquid flow (LF) is provided in or on said upper plate (7) to cool said upper plate (7). A gaseous flow (GF) is provided between said upper wall (22) and said upper plate (7) to promote the transfer of heat from said upper wall (22) to said upper plate (7).