A piezoelectric actuator includes a first electrode, a first piezoelectric body disposed at one side of the first electrode in a thickness direction of the first electrode, an individual electrode disposed at one side of the first piezoelectric body in the thickness direction, a second piezoelectric body disposed at one side of the individual electrode in the thickness direction, a second electrode disposed at one side of the second piezoelectric body in the thickness direction, a wiring that electrically connects to the individual electrode, a first contact, and a second contact. At the first and the second contacts, the first electrode and the second electrode electrically connect to each other. The first contact is disposed at one side of the individual electrode in a perpendicular direction perpendicular to the thickness direction. The second contact is disposed at the other side of the individual electrode in the perpendicular direction.

An optical assembly of a projection exposure apparatus for semiconductor lithography comprises an optical element and an actuator for deforming the optical element. The actuator is subjected to a bias voltage by a controller that is present. A projection exposure apparatus for semiconductor lithography comprises an optical assembly. A method for operating an actuator for deforming an optical element for semiconductor lithography comprises subjecting the actuator to a bias voltage by a controller.

In a piezoelectric device, when viewed in a direction perpendicular to one main surface, an outer shape of a recess is a polygonal shape or a circular shape. When n represents a number of sides of the polygonal shape, r represents a radius of a circumscribed circle of an imaginary regular polygon including n sides with a length identical to a length of a shortest of the sides, and d represents a maximum thickness of a membrane portion, which is located above the recess, of a multilayer portion, r≤197.7dn.sup.−0.6698 when 3≤n≤7, and r≤52.69d when 8≤n or when the outer shape of the recess is a circular shape.

In a piezoelectric device, a layered portion includes, at a position at least above a recess, a single crystal piezoelectric layer and a pair of electrode layers to apply voltage to the single crystal piezoelectric layer. At least a portion of the pair of electrode layers includes a lower electrode layer extending along a surface of the single crystal piezoelectric layer, the surface being closer to a base. The lower electrode layer is present only inside the recess.

Provided is a method for producing a piezoelectric element in which a piezoelectric body substrate piece is subjected to polarization treatment and a piezoelectric element is produced. The method includes a first step in which the piezoelectric body substrate piece is held on a flat plate-shaped slightly adhesive sheet and a second step in which voltage is applied to the piezoelectric body substrate piece held on the slightly adhesive sheet and the piezoelectric body substrate piece is subjected to polarization treatment.

Provided is a piezoelectric ceramics having a gradual change in piezoelectric constant depending on an ambient temperature. Specifically, provided is a single-piece piezoelectric ceramics including as a main component a perovskite-type metal oxide represented by a compositional formula of ABO.sub.3, wherein an A site element in the compositional formula contains Ba and M.sub.1, the M.sub.1 being formed of at least one kind selected from the group consisting of Ca and Bi, wherein a B site element in the compositional formula contains T1 and M.sub.2, the M.sub.2 being formed of at least one kind selected from the group consisting of Zr, Sn, and Hf, wherein concentrations of the M.sub.1 and the M.sub.2 change in at least one direction of the piezoelectric ceramics, and wherein increase and decrease directions of concentration changes of the M.sub.1 and the M.sub.2 are directions opposite to each other.

There is provided a piezoelectric actuator, including: a vibration plate; a first piezoelectric body; a second piezoelectric body; a first electrode disposed on a first surface of the first piezoelectric body; a second electrode disposed on a second surface of the second piezoelectric body; an intermediate electrode disposed on an intermediate surface of the first piezoelectric body and overlapping with the first and second electrodes; an intermediate trace connected to the intermediate electrode on the intermediate surface and drawn out to one side in a first direction beyond the first piezoelectric body and the second piezoelectric body; a first trace overlapping with the intermediate trace in the thickness direction and being conducted with the intermediate trace; and a second trace overlapping with the intermediate trace in the thickness direction and being conducted with the intermediate trace.

An optical element includes a primary electrode, a secondary electrode overlapping at least a portion of the primary electrode, and an electrostrictive ceramic layer disposed between and abutting the primary electrode and the secondary electrode, where the electrostrictive ceramic may be characterized by a relative density of at least approximately 99%, an average grain size of at least approximately 300 nm, a transmissivity within the visible spectrum of at least approximately 70%, and bulk haze of less than approximately 10%. Optical properties of the electrostrictive ceramic may be substantially unchanged during the application of a voltage to the electrostrictive ceramic layer and the attendant actuation of the optical element.

A multilayer piezoelectric element includes a piezoelectric body containing a piezoelectric ceramic material, a first electrode, and a second electrode. The piezoelectric body includes a first main surface and a second main surface opposing each other. The first electrode includes an external electrode formed on the first main surface. The second electrode includes an internal electrode formed inside the piezoelectric body to oppose the external electrode. The piezoelectric body includes an active region between the external electrode and the internal electrode, and includes an inactive region opposite to the active region with the internal electrode interposed therebetween. A stress received by the piezoelectric body from the external electrode is larger than a stress received by the piezoelectric body from the internal electrode. A polarization direction of the active region is a direction directed from the external electrode to the internal electrode.

In a composite component, a semiconductor device is stacked on an elastic wave device. Side electrodes extend from at least one side surface of a piezoelectric substrate of the elastic wave device to at least a side surface of a semiconductor substrate of the semiconductor device and are connected to an IDT electrode and functional electrodes. The side electrodes extend onto at least one of a second main surface of the piezoelectric substrate and a second main surface of the semiconductor substrate.