Small speaker with high SPL?

In order to increase sound pressure level, we need to vibrate more air molecule by more power under unit time.For the two sizes speakers, the area of diaphragms of the 15mm speakers are around 176mm square (7.5*7.5*3.14),and the 20mm size speakers are around 314mm square(10*10*3.14). The 20mm speakers are only bigger by5 mm/ 25%, however, the diaphragm are bigger by 78%. Therefore when we input the same power, the 20mmspeakers can vibrate more air at the same time, and it result in higher sound pressure level.Generally, the speaker in bigger size can provide lower frequency response which is better for human’saudition. On the other side, we can also provide the smaller speakers more power to make higher soundpressure level, but it is limited by,1. Acceptability of the diaphragms2. Thermolysis of the speakers3. After increasing the power, frequency response will change too(because thicker diaphragm, heavier coil..etc)Therefore, what we can do is reform the material and the structure of the speakers to increase sound pressure level,but if it is possible to choose the bigger size, the problem of the lower sound pressure level will be improved immediately.