If your physical home button is dead on your phone this app can help you.

It's a very simple app :
With this app you can create a software button in the center bottom of you screen and add several actions to this button.

Actions you can do with the button :
_Home
_Recent apps
_Pull down notification
_Settings
_A custom app
_Back (Experimental)
_Screenshot (Pro version)

/! If your device has a navigation bar (Home Back and MultiTask buttons) on the screen the touch area will be above the navigation bar ! /!

Permission :
Read Phone State => Needed (and only used) to load applications list
Write Internal Storage => Save screenshots