the surface - emission cathodes of the invention are constructed so that the cathode body has a free surface over which electrons are efficiently accelerated after injection from a conductive contact . the junction between the free surface and the contact has the property that the height of the barrier to tunneling from the contact to floating surface states associated with the free surface of the cathode body is lower than both the barrier to emission from the contact to vacuum and the barrier to injection from the contact into the conduction band of the cathode body material . thus under an applied potential , electrons are injected from the contact into floating surface states associated with the free surface . after acceleration , electrons leave the free surface , either emitted to vacuum or injected into another medium .