Amid rumors that a big design change is in store for the 2017 iPhone as a way to celebrate the 10th anniversary of the handset, we could see something dramatic such as a bezel-less edge-to-edge display. A number of concepts have been designed showing such a design, and some fakes have also used it. Recent speculation has Apple embedding TouchID, the front-facing camera, and the speakers under the screen of a future model. Doing all that would make it easier for Apple to produce an iPhone with an edge-to-edge screen.
While this is all speculation for the moment, there actually is some proof that Apple is thinking about such a look for a future iPhone. A patent application originally filed on March 5th 2015, titled "Man-machine interface for controlling access to electronic devices," includes a method called "ultrasound imaging." Using this method would allow Apple to embed TouchID inside an iPhone screen.
"The most accurate but least common finger-scanning technology is ultrasound imaging. In this type of sensor, two transducers are placed on the x- and y-axes of a plate of glass–one each for receiving and transmitting–for propagating ultrasound waves through a glass plate; when the finger is placed on top of the glass, the finger impedes the waves and the receiving transducer can measure the alteration in wave patterns. This type of scanner is very new and largely untested in a variety of conditions, but initial results show promise for the technology. It combines the large plate size and ease of use of the optical scanners with the ability to pervade dirt and residue on the scanner, an advantage of capacitive scanners."-Apple patent filing"
According to Patently Apple, Apple has two other patents dealing with the placement of TouchID under the screen. And its June 2015 purchase of the fingerprint related IP from Privaris also points to Apple using this design in the not too distant future. Putting the fingerprint scanner under the screen doesn't guarantee that Apple will go with the edge-to-edge look, but it does remove one of the major obstacles in its way.
Apple files patent for yet another way to embed TouchID in the display