The alveoli-capillary membrane's surface area is the key determinant of oxygen transfer efficiency from air to blood.

“If you look at how oxygen gets from outside the body into the bloodstream, the critical passage is across the membrane in the lung. It's called the alvea capillary membrane. The alveis is part of the lung and the blood runs through capillaries which are these the smallest tubes in the circulatory system and at that point oxygen can go from the airfilled alveis into the blood. The key element is the surface area. The bigger the surface area, the more oxygen that can pass through.”