Recently, there has been a great deal of interest in searching for dark matter and neutrinoless double-beta decay that are so called rare event physics beyond Standard Model using ton-scale high-purity germanium (HPGe) detectors with ultra-low internal radioactive backgrounds [1-8]. The high purity germanium crystal (net concentration range below 10¹⁰/cm³) was grown in pure hydrogen atmosphere. The divacancy-hydrogen center (V₂H) in the crystal will cause trapping of holes which will degrade the performance of nuclear radiation detectors. In order to reduce the impact of V₂H center, the dislocation density must be everywhere between 10² and 10⁴ cm⁻² [9]. For fabricating detectors, the orientation of the Ge crystal is important. High-Purity germanium crystals used for fabricating detectors are usually oriented along <100> direction [10,11]. Although an accurately oriented seed is used for growing a crystal, the grown crystal will deviate from the <100> direction because the seed rod is slightly off-center in the crucible. Therefore, the grown crystals should be oriented before fabricating detectors. X-ray diffraction is an accurate technique to orient crystals [12,13]. However, the equipment and operation of X-ray diffraction is complex.

Based on the structure and crystal growth behavior of Ge, the optical method that has been used in Si crystals [14] is used to orient Ge crystals for cutting since it is extremely simple and effective. Figure 1 shows the morphology of Ge crystal, which is from the structure data of Ge crystal [15]. The interfacial angle between (111) and (100) is 54.72 degrees. The angle between the normal line of (111) facet and another normal line of (100) facet is 54.72 degrees. These normal lines are parallel to <111> and <100> directions, respectively. The interfacial angle between (111) and (11ī) ((1ī1) or (ī11) is 70.53 degrees.

For Ge crystals, because the atom density of (111) facet is the largest, the growth speed of (111) is the slowest one. Therefore, Ge crystals tend to develop (111) facets. If the axial thermal gradient is lower, three {111} facets will be formed in the enlarging process after the dash process. For crystals along <100>, there are four {111} facets and four crystal edges [110]. For Ge crystals along <111>, there are three facets and three crystal edges [110]. Therefore, the reflection of crystal facets can be used to orient the Ge crystals. On the other hand, because of the dissolution speed difference in (111) and (100) facets the etching pits reflection can also be used to orient Ge crystals. In this paper, both crystal facets reflection and etching pits reflection in the orientation of high-purity germanium crystals are discussed.