Open chamber photoluminescent lamp

Information

  • Patent Grant
  • 6762556
  • Patent Number
    6,762,556
  • Date Filed
    Tuesday, February 27, 2001
    23 years ago
  • Date Issued
    Tuesday, July 13, 2004
    20 years ago
Abstract
An apparatus and method are disclosed for an open chamber photoluminescent lamp. The photoluminescent planar lamp is gas-filled and contains photoluminescent materials that emit visible light when the gas emits ultraviolet energy in response to a plasma discharge. The lamp comprises first and second opposing plates manufactured from a glass material having a loss tangent ≦0.05%. In another embodiment the first and second plates have a dielectric constant greater than 5. In yet another embodiment, the first and second plates have a volume resistivity greater than 1×1012 Ωcm. A plurality of sidewalls are coupled to peripheral edges of the first and second plates so that the sidewalls and opposing surfaces of the first and second plates define an interior portion that contains the gas and photoluminescent material, and first and second spaced-apart electrodes disposed along an exterior surface of at least one of the first and second plates to create an electric field when electrical power is applied thereto whereby the electric field interacts with the gas contained by the interior chamber.
Description




TECHNICAL FIELD




This invention relates to planar photoluminescent lamps, and more particularly, to a planar photoluminescent lamp having two electrodes and which emits light by fluorescent phenomena.




BACKGROUND OF THE INVENTION




Thin, planar, and relatively large area light sources are needed in many applications. Backlights must often be provided for liquid crystal displays (LCD) to make them readable in all environments. Because present active matrix LCDs allow only up to approximately 5% light transmission, the backlights must produce enough light to permit readability in low light conditions. Thin backlights for LCDs are desired to preserve as much as possible the LCDs' traditional strengths of thin profile, low cost, and readability in high ambient lighting conditions while permitting readability at numerous angles.




Many demanding challenges exist for engineering a thin planar source of uniform light. If incandescent lamps or LEDs are used as the light source, then optics for dispersing and diffusing light from the multiple point sources to the planar viewing surface must be provided to avoid local bright or dim spots. Despite recent advances, LEDs are spectrally limited, which reduces their applicability for situations where white light is desired. Additionally, provision must be made to dissipate the heat generated by the incandescent or LEDs or alternatively, to utilize only high-temperature materials for LCDs. Electroluminescent lamps suffer from having a relatively low brightness but are sometimes selected as solutions that require only low light display outputs.




Another choice for generating light for a display is photoluminescent technology, including fluorescent lamps. Fluorescent lamps have the advantage of being relatively efficient and capable of generating sufficiently bright light. Tubular fluorescent lamps of about 2 mm in diameter are often used as a backlight, but have the undesirable property of uneven light distribution. Planar fluorescent lamps are well known in the art, having been described, for example, in U.S. Pat. Nos. 3,508,103; 3,646,383; and 3,047,763. Typically, such lamps in the prior art are formed by molding a housing and a cover, each from a piece of glass and sealing the glass pieces to form a sealed enclosure. A selected gas and a fluorescent material are placed in the sealed enclosure for emitting light when an electrical field is applied. Typical fluorescent lamps often have bare metal electrodes, which are exposed to ionized particles of the gas thereby causing undesirable sputtering effects.




Where the enclosure is formed entirely from glass, fabrication can be difficult and the resulting lamp is often quite fragile. A stronger lamp can be made by using thicker pieces of glass to form a lamp having thicker walls. However, increased glass thickness results in a undesirably thicker and heavier lamp, is more difficult to fabricate and may attenuate some light output.




Planar fluorescent lamps having sidewalls formed from metal with a serpentine channel defined by internal walls are known from U.S. Pat. Nos. 2,508,103 and 2,405,518. The sidewalls and internal walls of the serpentine channel provides support for the top and bottom covers. However, longer serpentine channels require undesirably higher electrode voltages that are necessary to ionize the selected gases. Large display areas using planar fluorescent lamps having such internal walls require that many planar fluorescent lamps be tiled together to provide large areas of illumination.




A need remains therefor, for a thin, lightweight, planar lamp having a substantially uniform display that is easily manufacturable, is readily scaleable to larger display sizes, is temperature tolerant, and is relatively durable.




SUMMARY OF THE INVENTION




The limitations of prior lamps are overcome by the present invention, which is an open chamber photoluminescent lamp and a method of producing an open chamber photoluminescent lamp. In a sample embodiment, a gas-filled photoluminescent planar lamp contains a photoluminescent material that emits visible light in response to ultraviolet energy emitted from an ionized gas. The lamp contains first and second opposing glass plates that are made from glass material having a loss tangent of less than around 0.05%. A plurality of sidewalls are coupled to the peripheral edges of the first and second plates so that a chamber is formed that contains the gas and photoluminescent material. The lamp also contains first and second electrodes disposed along an exterior surface of at least one of the first and second plates so that an electrical field is created when electrical power is applied to the electrodes so that the electric field interacts with the gas contained within the chamber.




In another embodiment, the lamp may further contain a plurality of spacers that are distributed between the first and second glass plates at predetermined locations so that the first and second plates will be maintained at a predetermined distance from each other. The spacers may be further manufactured from glass material that is transmissive to ultraviolet radiation. The lamp may further contain a plurality of spacers positioned between the first and second plates so that the first and second plates will be maintained at a distance of less than around 0.5 mm from each other.




In yet another embodiment, the lamp contains sidewalls that are sized to maintain the first and second plates at a distance of less than around 0.5 mm between the first and second plates.




In yet another embodiment the first plate is less than around 1 mm thick. The lamp may be further constituted such that the distance from the exterior surface of the first plate to the exterior surface of the second plate is less than around 5.0 mm.




In yet another embodiment, the electrodes are disposed along the exterior surface of only one of the first and second plates. Alternatively, the first electrode may be disposed along the exterior surface of the first plate and the second electrode may be disposed along the exterior surface of the second plate.




In further embodiments, the lamp comprises a first plate having a dielectric constant of greater than around 5, the lamp comprises at least one plate being manufactured from planar glass material that is substantially free of sodium, and the lamp further comprises a layer of photoluminescent material applied to an inner surface of at least one of the first and second plates to luminesce in response to ionization of the contained gas.




In another example embodiment, a gas-filled photoluminescent planar lamp contains a photoluminescent material that emits visible light when the gas emits ultraviolet energy in response to a plasma discharge. The lamp contains first and second opposing glass plates that are made from glass material having a dielectric constant greater than 5.0. A plurality of sidewalls are coupled to the peripheral edges of the first and second plates so that a chamber is formed that contains the gas and photoluminescent material. The lamp also contains first and second electrodes disposed along an exterior surface of at least one of the first and second plates so that an electrical field is created when electrical power is applied to the electrodes so that the electric field interacts with the gas contained within the chamber.











BRIEF DESCRIPTION OF THE DRAWINGS





FIG. 1

is a schematic of the invention in cross-section.





FIG. 2

is a top plan view of an example of the patterning of a top electrode.





FIG. 3

is a bottom plan view of an example of the patterning of a bottom electrode.





FIG. 4

is a top plan view of an example of the patterning of spacers.





FIG. 5

is a fragmentary cut-away cross-sectional view of a planar lamp according to one embodiment of the invention.





FIGS. 6-9

are top plan views, of alternative electrode patterns used in planar lamps.





FIGS. 10 and 11

are schematics of alternate embodiments of the invention.











DETAILED DESCRIPTION OF THE INVENTION





FIG. 1

illustrates a lamp


10


having a single open chamber


12


. The chamber


12


is an interior portion of the lamp


10


formed by the sealed enclosure of a pair of opposing planar plates, namely a bottom plate


14


and a top plate


16


, and sidewalls


18


being coupled to the peripheral edges of the bottom and top plates. The chamber


12


contains an ultraviolet-emissive gas (not shown) such as Mercury vapor in a noble gas environment, which environment in one embodiment may comprise Xenon, Argon, and the like. Although mercury vapor is frequently used in fluorescent lamps, it is well known to use other gases, such as Argon, Xenon, a mixture of inert and halogen gases and the like, either alone or in combination to produce the desired spectral characteristics. In addition, it is known to vary the lamp pressure to alter the spectral characteristics of the lamp for a given gas. Furthermore, it is known to use photoluminescent materials other than phosphors to generate visible light energy in response to excitation by UV radiation. Accordingly, the present invention is not limited by the lamp pressure, the type of photoluminescent material, or type of gas used to fill the lamp


10


.




Ultraviolet-transmissive spacers


20


are spaced apart and distributed between the plates


14


and


16


to support the plates and thereby minimize the danger of implosion due to net positive external atmospheric pressures. For the purpose of clarity, not all spacers


20


are shown, nor are they drawn to scale, in

FIGS. 1-9

.




A bottom planar electrode


22


and a top planar electrode


24


in one embodiment are on the exterior surfaces of the plates


14


and


16


, respectively. The electrodes


22


and


24


are coupled to opposite sides of an alternating current (AC) power supply. Alternatively, the bottom electrode


22


is coupled to the AC power supply and the top electrode


24


is coupled to ground. The electrodes


22


and


24


are used to create an electric field by capacitive coupling through the dielectric of the plates


14


and


16


, which in turn produces a stable and uniform plasma from the ultraviolet-emissive gas in the chamber


12


. The plasma acts as a uniform source of ultraviolet light, which is a condition conducive to uniform visible light generation.




At least one of the electrodes is designed to permit light to exit from the chamber


12


. Usually the top electrode


24


is transparent or finely drawn as to permit light to pass by without causing undesirable gradations in the produced illumination.

FIG. 2

illustrates one embodiment where the top electrode


24


comprises conductive lines patterned as a grid on the exterior surface of the plate


16


using a laser or ultraviolet (UV) light and an aqueous development process to yield highly conductive lines of a silver-based compound (such as Fodel® as produced by DuPont®) drawn to widths of about 5-150μ, with a spacing of about 40-1000μ. For the purpose of clarity, not all lines of the top electrode


24


are shown in FIG.


2


.




The bottom electrode


22


may be deposited on the exterior surface of the bottom plate


14


using a conventional, and more economical, screen printing process.

FIG. 3

illustrates one embodiment where the bottom electrode


22


is deposited as a series of parallel lines that are wider than the top electrode


24


. The width of the lines of the bottom electrode


22


may be wider than the line of the top electrode


24


because the bottom surface of chamber


12


reflects, and does not pass, the light produced by the lamp. In an example embodiment, a reflective coating such as TiO


2


or Al


2


O


3


may be deposited on the exterior surface of the bottom plate


14


so that more light is reflected towards the top surface. Thus, the width of the lines of the bottom electrode


22


does not cause undesirable gradations in the produced illumination. For the sake of clarity, not all lines of bottom electrode


22


are shown in FIG.


3


.




In another example embodiment, the electrodes


22


and


24


may be disposed so that one of the electrodes


22


and


24


is on an exterior surface and a second electrode is on an interior surface. In yet another embodiment both electrodes


22


and


24


may be disposed on the same surface in a coplanar arrangement, as illustrated in

FIGS. 6

to


9


.




It will be understood by those skilled in the art that the number and shape of lines of the electrodes


22


and


24


and the spacers


20


may be varied greatly without departing from the scope of the invention. It will also be apparent to those skilled in the art that the electrodes may be also placed on the interior surfaces of the plates


14


and


16


, or even on the exterior surface of one plate and the interior surface of its opposing plate. In the exemplary embodiment, the electrodes


22


and


24


are disposed on the exterior surfaces of the plates


14


and


16


, so as to maximize the distance between the electrodes, and minimize near-field effects, which effects result in undesirable non-uniform illumination across the face of the lamp


10


. In another variation of the embodiment, the electrodes


22


and


24


may also be interdigitated so that substantial lengths of conductors of the top electrode


24


do not directly overlie substantial lengths of conductors of the bottom electrode


22


.




According to one aspect of the invention, the bottom plate


14


and the top plate


16


are made from an alkaline earth aluminosilicate glass having suitable characteristics such as a high operating temperature, high transmissivity of light at the desired output wavelength, low coefficient of thermal expansion, low thermal shrinkage, high dielectric strength, and high volume resistivity. For example, Corning® type 1737F glass has been found to be suitable and provides a coefficient of thermal expansion of 37.6×10


−7


/° C. through a temperature range of 0°-300° C., a dielectric constant of less than about 6 (and greater than 5 at frequencies above 100 Hz) through a temperature range of 0-300° C., a dielectric strength of over 1000 V/mil, and a loss tangent of less than about 0.05% for frequencies above 100 Hz through a temperature range of 0-300° C. The glass is also substantially free of mobile sodium and potassium ions, which can cause solarization under exposure to ultraviolet light.




As is known in the art, glass is often used as a dielectric element in a capacitor. The parallel plates


14


and


16


of the lamp


10


along with the electrodes


22


and


24


essentially form a capacitor where the glass of the plates function as a dielectric. Unfortunately, glass is also a conductor that decreases in resistivity as the temperature increases. When glass having a low volume resistivity is used, the current flowing through the glass generates heat, which further reduces the resistance of the glass. The lowering of the resistance of glass cause more current to flow, which unfavorably causes the temperature of the glass to increase even more and may ultimately lead to failure of the device. This undesirable positive feedback may be overcome by using glass having a volume resistivity sufficiently high enough to prevent the glass from warming appreciably. In a typical embodiment of the present invention, glass having a volume resistivity of over 1×10


12


Ωcm at room temperature has been found to be suitable.




Because the lamp


10


operates as a capacitor, it is desirable to use materials with a high dielectric constant so as to increase the effective capacitance and thus increase current flow through the lamp. However, glass having high dielectric constants also tend to have low volume resistivity, which has the undesirable characteristics described above. Glass used in the plates


14


and


16


is selected to have a reasonably high dielectric constant (e.g., greater than 5) while also maintaining a high volume resistivity (e.g., greater than 1×10


12


Ωcm). Accordingly, the selected glass will have a loss tangent of less than 0.05%. As is known in the art, the loss tangent of a material is the ratio of the imaginary part to the real part of the relative permeability of the material. Another way to increase the effective capacitance for a given glass material is to decrease the spacing between the plates


14


and


16


. As will be described in greater detail below, the lamp


10


is constructed to reduce the separation between the plates


14


and


16


.




The integrity of the sealed chamber


12


provided by the bottom plate


14


and the top plate


16


is partially a function of the thickness of the plates, the arrangement and number of the spacers


20


provided between the plates, and net atmospheric pressures. The net atmospheric pressure is the difference between external atmospheric pressure and the pressure of the gasses within the chamber


12


. The glass of the plates


14


and


16


must be strong and thick enough to withstand external atmospheric pressure exerted against spans of the plates that are not supported directly by the spacers


20


to prevent implosion of the lamp


10


. In one embodiment, the thickness of the bottom plate


14


and the top plate


16


is approximately 1 mm or less for each plate, and the spacers


20


are arranged on 0.25 in. (6.35 mm) centers. The spacers


20


are typically highly UV-transmissive glass beads, and have a diameter selected to match the height of the sidewall


18


, as shown in FIG.


1


. The UV-transmissive characteristic of the spacers


20


allows UV light generated in the chamber


12


to pass through the spacers unimpeded and thus reduce undesirable dim spots in the lamp


10


. The spacers


20


are distributed uniformly across the chamber


12


so as to provide support “columns” for the faces of the plates


14


and


16


at a height equal to the sidewall


18


. In the exemplary embodiment, the spacers


20


are approximately 0.020 in. (0.51 mm) in diameter and are resistant to solarization.

FIG. 4

illustrates the placement of the spacers


20


that may conveniently be affixed to the bottom plate


14


during assembly of the lamp. Assembly details are provided below.




The sidewall


18


is also 0.020 in. (0.51 mm) in height and 0.040-0.100 in. (1-2.5 mm) in width. The sidewall


18


is comprised of a material suitable for use as a devitrifying frit (or solder glass) and has a coefficient of thermal expansion selected to match the coefficient of thermal expansion of the glass used for the plates


14


and


16


.





FIG. 5

is a fragmentary cut-away view of the lamp


10


according to one embodiment illustrating the constituents of the chamber


12


, the plates


14


and


16


, and the electrodes


22


and


24


. A 60μ-thick reflective layer


26


of Al


2


O


3


or BaTiO


3


is deposited on the interior surface of the bottom plate


14


that is subjacent to chamber


12


. Reflective layer


26


is used at the bottom of the lamp to reflect light that is directed downwards from the chamber


12


so that the reflected light is emitted through the top of the lamp. A 60μ-thick bottom phosphor layer


28


of rare earth phosphors and Al


2


O


3


is deposited on the reflective layer


26


. The rare earth phosphors are selected to emit red, green, and blue light in the presence of ultraviolet radiation produced from the plasma of the ultraviolet-emissive gas (not shown) contained by the chamber


12


. Suitable rare earth phosphors that fluoresce in response to ultraviolet radiation are well known in the art. One skilled in the art will also appreciate that electroluminescent materials (which emit light when subjected to an alternating electric field) such as ZnS may be effectively used as well.




An electron emissive coating (not shown) comprising a thin film (around 0.5μ) of MgO may be optionally applied to the interior surface of the bottom plate


14


before the reflective layer


26


is applied. One skilled in the art will appreciate that MgO has a high coefficient of secondary electron emission, which increases the efficiency and ionization of the contained gas in producing ultraviolet light. The coefficient of secondary electron emission is the ratio of secondary electrons (electrons that are ejected from a metallic surface as a result of incident electrons colliding with the metallic surface) to incident electrons, which here are produced by ionizing the gas. As is known in the art, a thin film of MgO also functions as a passivation layer, which here protects the glass from erosion and solarization of the glass by the incident electrons, ions, and UV energy.




The spacers


20


are affixed to the bottom phosphor layer


28


with an organic binder (not shown) on 0.25 in. centers, in a pattern such as exemplified in FIG.


4


. As discussed above, it will be readily apparent to those skilled in the art that other suitable arrangements of spacers


20


may be made.




Referring again to

FIG. 5

, an electron emissive coating


32


comprising a thin-film (around 0.5μ) of MgO is applied to the interior surface of the top plate


16


that defines the top of the chamber


12


. One skilled in the art will appreciate that the emissive coating may be omitted, although the omission will result in less satisfactory results. A top phosphor layer


34


is a 15μ-thick layer of rare earth phosphors and Al


2


O


3


that is applied to the exposed surface of the passivation layer


32


. An optional side phosphor layer


30


of rare earth phosphors similar in thickness and composition to the top or bottom phosphor layers


26


-


28


may be applied to a portion of the interior surface of the sidewall


18


that intervenes between the bottom phosphor layer


28


and the top phosphor layer


34


to increase the brightness of lamp


10


. The components of the lamp


10


are assembled within a vacuum furnace (not shown). The vacuum furnace is used in a conjoined process step to evacuate atmospheric gasses from the chamber


12


, fill the chamber


12


with an ultra-violet emissive gas, and seal the chamber


12


.




As noted above, the specific pattern of the electrodes


22


and


24


can be varied without detrimental effect on the quality and uniformity of light produced by the lamp


10


. For example,

FIGS. 6-9

illustrate some selected alternatives for the arrangement of the electrodes


22


and


24


for the lamp


10


.

FIG. 6

illustrates the arrangement of the electrodes


22


and


24


wherein the electrodes are arranged as a series of straight, interdigitated fingers.

FIG. 7

illustrates the electrode pattern of a lamp wherein the electrodes


22


and


24


are arranged as a series of “wavy,” interdigitated fingers.

FIGS. 8-9

illustrate alternative arrangements for the top electrode


24


that can be used with a circular lamp body


40


.

FIG. 8

illustrates the electrode of a lamp having electrodes


22


and


24


being arranged as two interdigitated spirals.

FIG. 9

illustrates the electrode pattern of a lamp having a electrodes


22


and


24


being disposed as a series of concentric semi-circles.

FIG. 10

illustrates the top electrode


24


being disposed on the interior surface of the top plate


16


.

FIG. 11

illustrates the bottom electrode


22


being disposed on the interior surface of bottom plate


14


.




From the foregoing it will be appreciated that, although specific embodiments of the invention have been described herein for purposes of illustration, various modifications may be made without deviating from the spirit and scope of the invention. For example, while the preferred embodiment of the invention uses electrodes on the exterior surfaces of the plates, the use of electrodes on at least one of the interior surfaces of the plates for planar fluorescent lamps is known, and may be used without departing form the scope of the invention. Accordingly, the invention is not limited except as by the appended claims.



Claims
  • 1. A gas-filled photoluminescent planar lamp containing a photoluminescent material to emit visible light in response to ultraviolet energy emitted from an ionized gas, the lamp comprising:first and second opposing glass plates manufactured from a glass material that has a dielectric constant of about 5 or greater and a loss tangent of about 0.05% or less when at a temperature of 20° C.; a plurality of sidewalls coupled to peripheral edges of the first and second plates to define a chamber that contains the gas and photoluminescent material; and first and second electrodes disposed along an exterior surface of at least one of the first and second plates to create an electric field when electrical power is applied thereto to create an electric field that interacts with the gas contained within the chamber.
  • 2. The lamp of claim 1, further comprising a plurality of spacer beads distributed between the first and second plates and having predetermined dimensions to maintain the first and second plates at a predetermined distance from each other.
  • 3. The lamp of claim 2 wherein the plurality of spacers are manufactured from a glass material that is transmissive to ultraviolet radiation.
  • 4. The lamp of claim 1, further comprising a plurality of spacers positioned between the first and second plates to maintain the first and second plates at a distance of about 0.5 millimeters or less from each other.
  • 5. The lamp of claim 1 wherein the sidewalls are sized to maintain the first and second plates at a distance of about 0.5 millimeters or less between the first and second plates.
  • 6. The lamp of claim 1 wherein the first plate is less than around 1 millimeter thick.
  • 7. The lamp of claim 1 wherein a distance from the exterior surface of the first plate to the exterior surface of the second plate is less than around 5.0 millimeters.
  • 8. The lamp of claim 1 wherein the first and second electrodes are disposed along the exterior surface of only one of the first and second plates.
  • 9. The lamp of claim 1 wherein the first electrode is disposed along the exterior surface of the first plate and the second electrode is disposed along the exterior surface of the second plate.
  • 10. The lamp of claim 1 wherein the first plate is composed of an aluminosilicate glass.
  • 11. The lamp of claim 1 wherein at least one of the first and second plates is manufactured from a glass material being substantially free of sodium.
  • 12. The lamp of claim 1, wherein the photoluminescent material comprises a layer of fluorescent and reflective material applied to an inner surface of at least one of the first and second plates wherein the layer luminesces in response to ionization of the contained gas.
  • 13. A gas-filled photoluminescent planar lamp containing a photoluminescent material to emit visible light in response to ultraviolet energy emitted from an ionized gas, the lamp comprising:first and second opposing glass plates manufactured from a glass material having a volume resistivity of greater than 1×1012 Ωcm; a plurality of sidewalls coupled to peripheral edges of the first and second plates to define a chamber that contains the gas and photoluminescent material; and first and second electrodes disposed along an exterior surface of at least one of the first and second plates to create an electric field when electrical power is applied thereto to create an electric field that interacts with the gas contained within the chamber.
  • 14. The lamp of claim 13, further comprising a plurality of spacers distributed between the first and second plates and having predetermined dimensions to maintain the first and second plates at a predetermined distance from each other.
  • 15. The lamp of claim 13 wherein the first and second electrodes are disposed along the exterior surface of only one of the first and second plates.
  • 16. The lamp of claim 13 wherein the first plate has a dielectric constant of greater than around 5.
  • 17. The lamp of claim 13 wherein at least one of the first and second plates is manufactured from a glass material being substantially free of sodium.
  • 18. A gas-filled photoluminescent planar lamp containing a photoluminescent material to emit visible light, the lamp comprising:a chamber having a gas and photoluminescent material therein, the chamber being composed of a light transmissive front plate, a back plate and a plurality of sidewalls coupled to the peripheral edges of the front plate and the back plate to define the chamber; a front electrode positioned adjacent the front plate; a back electrode positioned adjacent the back plate; the front and back plates being parallel to each other and flat, the first plate being composed of a glass material having a dielectric constant of about 5 or greater and a resistivity of about 1 1012 Ωcm or greater when at a temperature of 20° C.; a plurality of spacer beads positioned inside of the chamber, the spacer beads being composed of transparent glass material and having a diameter approximately equal to the distance between the front plate and the side plate in order to maintain the integrity of the chamber of the lamp to prevent implosion and to maintain the front plate and the back plate at a predetermined distance from each other.
  • 19. The planar lamp according to claim 18 wherein the front electrode contains a plurality of grid members having a first pattern and the back electrode contains a plurality of grid members having a second pattern, different than the first pattern and having portions of the back electrode grid which are offset from electrically conductive portions of the front electrode grid.
  • 20. The lamp according to claim 18 wherein the back electrode is composed of wider electrically conductive lines than the front electrode.
  • 21. The lamp according to claim 19 wherein the back electrode has a larger composite surface area than the front electrode.
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