White light source, backlight, liquid crystal display apparatus, and illuminating apparatus

1. A white light source comprising:

an insulating substrate;

a light-emitting diode chip which is provided on the insulating substrate and emits ultraviolet light with a wavelength of 330 nm to 410 nm; and

a phosphor layer which is formed so as to cover the light-emitting diode chip, contains a red emitting phosphor, a green emitting phosphor, and a blue emitting phosphor as phosphors, and the phosphors are dispersed in a cured transparent resin,

wherein when it is assumed that a shortest distance between a surface of the phosphor layer and a peripheral portion of the light-emitting diode chip is t(mm) and the mean free path defined by the following expression (1) is L(mm), the t and L satisfy 3.2≦t/L,

[Expression 1]

L= 1/( n ×σ)  (1)

(n: number of phosphors per unit volume of the phosphor layer (pcs/mm 3 ), and σ: average cross section area of a phosphor in the phosphor layer (mm 2 )).

2. The white light source according to claim 1 , wherein the phosphor layer comprises:

a cylindrical first shape portion formed on the insulating substrate side; and

a dome-shaped second shape portion formed to continue to an end portion of the first shape portion;

and is a cylindrical body having a dome-shaped end surface, and

an axial length of the first shape portion is equal to or greater than 10% of the axial length of the entire phosphor layer.

3. The white light source according to claim 1 , wherein the t and L satisfy 3.2≦t/L≦6.

4. The white light source according to claim 1 , wherein the red emitting phosphor includes at least one kind of phosphor powder with a composition expressed by the following expression (2),

[Formula 1]

(La 1−x−y Eu x M y ) 2 O 2 S  (2)

(where M is at least one element selected from Sb, Sm, Ga, and Sn; and x and y are a value satisfying 0.01<x<0.15 and 0≦y<0.03 respectively); and

phosphor powder with a composition expressed by the following expression (3),

[Formula 2]

(Sr x Ca 1−x )SiAlN 3 :Eu  (3)

(where x is a value satisfying 0≦x<0.4).

5. The white light source according to claim 1 , wherein the green emitting phosphor includes at least one kind of phosphor powder with a composition expressed by the following expression (4),

[Formula 3]

(Ba 1−x−y−z Sr x Ca y Eu z )(Mg 1−u Mn u )Al 10 O 17   (4)

(where, x, y, z, and u are a value satisfying 0≦x<0.2, 0≦y<0.1, 0.005<z<0.5, and 0.1<u<0.5, respectively); and

phosphor powder with a composition expressed by the following expression (5),

[Formula 4]

(Sr 2−x−y−z−u Ba x Mg y Eu z Mn u )SiO 4   (5)

(where, x, y, z, and u are a value satisfying 0.1<x<0.4, 0.005<y<0.21, 0.05<z<0.3, and 0.001<u<0.04, respectively).

6. The white light source according to claim 1 , wherein the blue emitting phosphor includes phosphor powder with a composition expressed by the following expression (6),

[Formula 5]

(Sr 1−x−y−z Ba x Ca y Eu z ) 5 (PO 4 ) 3 Cl  (6)

(where, x, y, and z are a value satisfying 0≦x<0.5, 0≦y<0.1, 0.005<z<0.1 respectively).

7. The white light source according to claim 1 , wherein the phosphor has an average particle diameter of 10 μm to 60 μm.

8. A backlight using the white light source according to claim 1 .

9. A liquid crystal display apparatus having the backlight according to claim 8 .

10. An illuminating apparatus using the white light source according to claim 1 .