Nitride semiconductor wafer including different lattice constants

1. A nitride semiconductor wafer comprising:

a silicon substrate having a major surface;

a lower strain relaxation layer provided on the major surface and including a nitride semiconductor, the lower strain relaxation layer having a first lattice constant;

an intermediate layer provided on the lower strain relaxation layer and including a nitride semiconductor;

an upper strain relaxation layer provided on the intermediate layer and including a nitride semiconductor; and

a functional layer provided on the upper strain relaxation layer and including a nitride semiconductor, the intermediate layer including:

a first lower layer provided on the lower strain relaxation layer and including a nitride semiconductor, the first lower layer having a second lattice constant larger than the first lattice constant;

a first doped layer provided on the first lower layer and including a nitride semiconductor, the first doped layer having a third lattice constant larger than the second lattice constant and containing an impurity at a concentration of 1×10 18 cm −3 or more and less than 1×10 21 cm −3 ; and

a first upper layer provided on the first doped layer and including a nitride semiconductor, the first upper layer having a fourth lattice constant larger than the third lattice constant and larger than the second lattice constant.

2. The wafer according to claim 1 , wherein

a composition ratio of the first doped layer is different from a composition ratio of the first lower layer, and also different from a composition ratio of the first upper layer.

3. The wafer according to claim 1 , wherein the impurity includes at least one of silicon (Si), magnesium (Mg), manganese (Mn), iron (Fe), oxygen (O), and carbon (C).

4. The wafer according to claim 1 , wherein the intermediate layer further includes:

a second lower layer provided on the first upper layer and including a nitride semiconductor, the second lower layer having a fifth lattice constant smaller than the fourth lattice constant;

a second doped layer provided on the second lower layer and including a nitride semiconductor, the second doped layer having a sixth lattice constant larger than or equal to the fifth lattice constant and containing an impurity at a concentration of 1×10 18 cm −3 or more and less than 1×10 21 cm −3 ; and

a second upper layer provided on the second doped layer and including a nitride semiconductor, the second upper layer having a seventh lattice constant larger than or equal to the sixth lattice constant and larger than the fifth lattice constant.

5. The wafer according to claim 4 , wherein the intermediate layer further includes a second strain relaxation layer provided between the first upper layer and the second lower layer and including a nitride semiconductor, the second strain relaxation layer having a eighth lattice constant smaller than the fifth lattice constant.

6. The wafer according to claim 5 , wherein the second strain relaxation layer is Al z2 Ga 1-z2 N (0<z 2 ≦1).

7. The wafer according to claim 4 , wherein

the second lower layer includes Al xa2 In ya2 Ga 1-xa2-ya2 N (0≦xa 2 ≦1, 0≦ya 2 <1, xa 2 +ya 2 ≦1),

the second doped layer includes Al xb2 In yb2 Ga 1-xb2-yb2 N (0≦xb 2 <xa 2 , ya 2 ≦yb 2 <1, xb 2 +yb 2 ≦1), and

the second upper layer includes Al xc2 In yc2 Ga 1-xc2-yc2 N (0≦xc 2 <xb 2 , yb 2 ≦yc 2 <1, xc 2 +yc 2 ≦1).

8. The wafer according to claim 1 , wherein

the first lower layer includes Al xa1 Ga 1-xa1 N (0<xa 1 ≦1),

the first doped layer includes Al xb1 Ga 1-xb1 N (0<xb 1 <xa 1 ), and

the first upper layer includes Al xc1 Ga 1-xc1 N (0≦xc 1 <xb 1 ).

9. The wafer according to claim 1 , wherein

the lower strain relaxation layer is AlN.

10. The wafer according to claim 1 , wherein

the upper strain relaxation layer is Al z0 Ga 1-z0 N (0<z 0 ≦1).

11. The wafer according to claim 1 , wherein

a thickness of the first doped layer is 20 nanometers or more and 150 nanometers or less.

12. The wafer according to claim 1 , wherein

a thickness of the first lower layer is 100 nanometers or more and 500 nanometers or less.

13. The wafer according to claim 1 , wherein

a thickness of the first upper layer is 100 nanometers or more and 500 nanometers or less.

14. The wafer according to claim 1 , wherein

a first density of dislocations extending in a direction from the first lower layer toward the first upper layer in the functional layer is lower than a second density of dislocations extending in the direction in the first lower layer.

15. The wafer according to claim 1 , wherein

the first lower layer includes Al xa1 In ya1 Ga 1-xa1-ya1 N (0≦xa1<1, 0≦ya1<1),

the first doped layer includes Al xb1 In yb1 Ga 1-xb1-yb1 N (0≦xb1<1, 0≦yb1<1),

the first upper layer includes Al xc1 In yc1 Ga 1-xcl-yc1 N (0≦xc1<1, 0≦yc1<1),

the xa 1 is different from the xb 1 and different from the xc 1 the xb 1 is different from the xc1, and

the ya1 is different from the yb1 and different from the yc1, the yb1 is different from the yc1.

16. The wafer according to claim 1 , wherein

the first lower layer includes Al xa1 In ya1 Ga 1-xa1-ya1 N (0<xa1<1, 0≦ya1<1, xa1+ya1≦1),

the first doped layer includes Al xb1 In yb1 Ga 1-xb1-yb1 N (0≦xb1<1, 0≦yb1<1, xb1+yb1≦1,

the first upper layer includes Al xc1 In yc1 Ga 1-xc1-yc1 N (0≦xc1<1, 0≦yc1<1, xc 1 +yc1≦1),

the xa1 is different from the xb1 and different from the xc1, the xb1 is different from the xc1,and

the ya1 is different from the yb1 and different from the yc1 the yb1 is different from the yc1.

17. The wafer according to claim 1 , wherein

the first lower layer includes Al xa1 Ga 1-xa1 N (0<xa1≦1),

the first doped layer includes Al xb1 Ga 1-xb1 N (0<xb1<xa1), and

the first upper layer includes Al xc1 Ga 1-xc1 N (0≦xc1<xb1).