Lattice-mismatched semiconductor structures with reduced dislocation defect densities and related methods for device fabrication

1. A structure comprising:

a substrate comprising a first crystalline semiconductor material;

a non-crystalline layer over the substrate, the non-crystalline layer having a trench extending to a surface of the substrate, the trench defining an area of the surface of the substrate, a sidewall of the trench defining an arbitrary length of the area, the arbitrary length being with respect to trapping dislocations, at least a first portion of the sidewall extending perpendicular to the surface of the substrate; and

a second crystalline semiconductor material disposed at least partially in the trench and adjoining the first crystalline semiconductor material, the second crystalline semiconductor material being lattice mismatched to the first crystalline semiconductor material, threading dislocation segments in the second crystalline semiconductor material arising from the lattice mismatch propagating in a crystallographic direction parallel to the surface of the substrate and at a first angle away from the surface of the substrate, the sidewall being oriented at a second angle to the crystallographic direction, the second angle being between 30° and 60°, the threading dislocation segments terminating at the first portion of the sidewall.

2. The structure of claim 1 , wherein a height of the first portion of the sidewall is at least

1

2

times a width of the area.

3. The structure of claim 2 , wherein the first crystalline semiconductor material is (100) silicon, and the second angle is 45°.

4. The structure of claim 1 , wherein a height of the first portion of the sidewall is at least

6

3

times a width of the area.

5. The structure of claim 4 , wherein the first crystalline semiconductor material is (110) silicon, and the second angle is 45°.

6. The structure of claim 1 , wherein a height of the first portion of the sidewall is at least 2 times a width of the area.

7. The structure of claim 6 , wherein the first crystalline semiconductor material is (111) silicon, and the second angle is 45°.

8. The structure of claim 1 , wherein a width of the area and a height of the first portion of the sidewall are less than the arbitrary length.

9. A structure comprising:

a substrate comprising a first crystalline semiconductor material;

a non-crystalline layer over the substrate, the non-crystalline layer having a trench extending to a surface of the substrate, the trench defining an area of the surface of the substrate, the area having a width and an arbitrary length with respect to trapping dislocations, a sidewall of the trench defining the arbitrary length, at least a first portion of the sidewall extending perpendicular to the surface of the substrate to a height, the height being at least a distance d, the width being no more than 2 time the distance d, where the distance d is determined by

F

I

=

Gb

2

4

⁢

⁢

π

⁢

⁢

d

⁡

(

1

-

v

)

,

where F I =Image force necessary to bend a dislocation to the sidewall, G=Shear modulus, b=Burgers vector, and ν=Poisson's ratio; and

a second crystalline semiconductor material disposed at least partially in the trench and adjoining the first crystalline semiconductor material, the second crystalline semiconductor material being lattice mismatched to the first crystalline semiconductor material, dislocations in the second crystalline semiconductor material arising from the lattice mismatch terminating at the first portion of the sidewall.

10. The structure of claim 9 , wherein the second crystalline semiconductor material is a cubic crystalline semiconductor material.

11. The structure of claim 9 , wherein the height and the width are less than the arbitrary length.

12. The structure of claim 9 , wherein a strain of the second crystalline semiconductor material is less than 2 percent.

13. The structure of claim 9 , wherein the first crystalline semiconductor material is silicon, and the second crystalline semiconductor material is selected from the group consisting of germanium, GaAs, InP, AlSb, InSb, and a combination thereof.

14. A structure comprising:

a substrate comprising a first crystalline semiconductor material;

a non-crystalline layer on a top surface of the substrate, the non-crystalline layer having a trench extending to the top surface of the substrate, the trench having an arbitrary length with respect to trapping dislocations, at least a first portion of a first sidewall of the trench having the arbitrary length extending perpendicular to the top surface of the substrate, a recess being in the first crystalline semiconductor material from the top surface of the substrate and corresponding to the trench, the recess having a second sidewall non-perpendicular to the top surface of the substrate; and

a second crystalline semiconductor material disposed at least partially in the trench and the recess and adjoining the first crystalline semiconductor material, the second crystalline semiconductor material being lattice mismatched to the first crystalline semiconductor material, dislocations in the second crystalline semiconductor material arising from the lattice mismatch propagating from the second sidewall to the first portion of the first sidewall, the dislocations terminating at the first portion of the sidewall.

15. The structure of claim 14 , wherein the second sidewall comprises a (111) crystallographic plane of the first crystalline semiconductor material.

16. The structure of claim 14 , wherein the second sidewall comprises a hexagonal crystallographic surface.

17. The structure of claim 14 , wherein the second crystalline semiconductor material is a hexagonal material.

18. The structure of claim 14 , wherein the dislocations propagate perpendicular to the second sidewall.

19. The structure of claim 14 , wherein the second sidewall defines an angle of 45° with respect to a plane of the top surface of the substrate.

20. The structure of claim 14 , wherein the substrate is (100) silicon.