Bjt connected as diode
It is no different than using small base current to control a larger collector current. The emitter current is base current plus collector current, Ie = Ib + Ic. It's just that collector current is beta times base current, so Ic = beta * Ib. So, Ie = (beta+1) * Ib. For whatever the beta happens to be at this bias point where Vb equals Vc because they are shorted.