TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: In the structure (S2): the first crystalline material and the second crystalline material each comprise indium gallium phosphide, the semiconductor substrate comprises silicon, the third crystalline material comprises indium phosphide, and the fourth crystalline material comprises indium gallium arsenide; or the first crystalline material comprises indium phosphide, the second crystalline material comprises indium gallium arsenide, and the semiconductor substrate comprises silicon. In the structure (S3), the first crystalline material and the second crystalline material each comprise indium gallium phosphide, the semiconductor substrate comprises silicon, the third crystalline material comprises indium phosphide, and the fourth crystalline material comprises indium gallium arsenide.    TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Components: The structure (S1) comprises the defect-trapping layer disposed between the first and second photovoltaic sub-cells and an addition defect-trapping layer disposed between the second and third photovoltaic sub-cells. In the structure (S2), the first solar sub-cell comprises a wetting layer (1140) disposed between the first crystalline material and the first surface of the semiconductor substrate. The structure (S2) further comprises a second contact on a second surface of the semiconductor substrate, where the second surface is opposite from the first surface. The structure (S2) further comprises: a second dielectric layer on a second surface of the semiconductor substrate, where the second surface is opposite from the first surface, and the second dielectric layer has a second trench which extends to the second surface of the semiconductor substrate; a second solar sub-cell disposed in the second trench, where the second sub-cell comprises a third crystalline material comprising defects terminating at respective sidewalls of the second trench, the second sub-cell further comprises a fourth crystalline material, where the third crystalline material is disposed between the second surface of the semiconductor substrate and the fourth crystalline material, and the fourth crystalline material is substantially free from defects; and a second contact on the second solar sub-cell, where at least a portion of the second contact extends into the second trench. In the structures (S2) and (S3), the semiconductor substrate comprises a second solar sub-cell and a third solar sub-cell. In the structures (S2) and (S3): the first solar sub-cell comprises a bandgap of greater than or equal to 1.82 eV, the third solar sub-cell comprises a bandgap of greater than or equal to 1.15 eV, and the second solar sub-cell comprises a bandgap of greater than or equal to 0.61 eV. In the structure (S3), the first crystalline material and the second crystalline material are a same material. The structure (S3) further comprises wetting regions disposed in respective ones of the first trenches and disposed between the first crystalline material and the first surface of the semiconductor substrate. The structure (S3) further comprises: a second dielectric layer on a second surface of the semiconductor substrate, where the second surface is opposite from the first surface, the second dielectric layer has a second many trenches extending to the second surface of the semiconductor substrate; a second trapping region comprises a third crystalline material disposed in each of the second trenches, where the third crystalline material comprises defects arising from a lattice-mismatch terminating at respective sidewalls of the second trenches; a fourth crystalline material on the second trapping region, where the second trapping region is disposed between the second surface of the semiconductor substrate and the fourth crystalline material, the fourth crystalline material coalesce between neighboring ones of the second trenches and on a surface of the second dielectric layer distal from the semiconductor substrate to form a second continuous layer, and the second continuous layer is substantially free from defects; a second solar sub-cell on the second continuous layer; and a second contact on the second solar sub-cell, where the second solar sub-cell is disposed between the second continuous layer and the second contact.