## 1 Introduction  
In the past decade, Si photonics has become one of the hottest research domains in the World since it holds great promise for maintaining the performance roadmap known as Moore's Law. As short-distance data exchange rates approach 10 Gb/s, metal interconnection is facing a number of inevitable issues such as slow resistance-capacitance limit speed and large heat dissipation. Under these circumstances, it is well known that for data communication beyond 10 Gb/s, optical signal delivery is more advantageous compared to today's copper interconnections. As a result, combining sophisticated process techniques, low cost and mass production, Si based Electro-Photonic IntegratedCircuits (EPIC) emerge as one of the most promising solutions for next generation interconnection techniques. In fact, long-haul combinations have been based on fiber optics techniques for the last 30 years. The wavelength used for the majority of long-distance data transitions is in the 1.3-1.55 \(\upmu\)m range, corresponding to the minimum loss window of silica optical fiber. If the same wavelength can be utilized in the future short-distance data transfers including inter-chip, chip-to-chip and Fiber-To-The-Home (FTTH) communications, all end users will be able to connect directly to the external servers without the need for wavelength conversion, making global communication much easier and cheaper. As a result, Si EPIC working in 1.3-1.55 \(\upmu\)m wavelength has become aggressively pursued by researchers worldwide. To date, enormous efforts have been invested in Si photonics techniques and critical breakthroughs and milestones have been achieved. Various passive components [1], active devises like lasers [2], and high speed modulators [3] have been reported. Being the device that ends the optical path, photodetectors, which convert light back into electrical signals, are vital component for Si photonic integrated circuits. In fact, the trigger of the past decade's Si photonics upsurge was the first successful demonstration of the high-efficiency Germanium photodetector [4]. Although Si photodetectors have been widely used in optical receivers in the wavelength range around 850 nm, its relatively large bandgap of 1.12 eV corresponding to an absorption cutoff wavelength of \(\sim\)1.1 \(\upmu\)m hinders Si photodetectors' application in the longer wavelength range of 1.3 and 1.55 \(\upmu\)m. For a more seamless integration with current long-haul communication technology, a material with strong absorption coefficient in the 1.30-1.55 \(\upmu\)m is very desirable. Among the available choices, III-V compound semiconductors possess the advantage of high absorption efficiency, high carrier drift velocity and mature design and fabrication technology for optical devices. Therefore, integration of high performance III-V photodetectors onto the Si platform by flip-chip bonding or direct heteroepitaxy has been widely reported. However, the introduction of III-V materials into Si process is at the expense of high cost, increased complexity and potential introduction of doping contaminants into the Si CMOS devices since III-V materials also act as dopants for group IV materials. Germanium, a group IV material the same as Si, avoids the cross contamination issue. Though Ge is also an indirect bandgap (E\({}_{\text{g}}\) = 0.66 eV) material like Si, its direct bandgap of 0.8 eV is only 140 meV above the dominant indirect bandgap. As a result, Ge offers much higher optical absorption in 1.3-1.55 \(\upmu\)m wavelength range, thus making Ge-based photodetectors promising candidates for Si photonics integration. However, the 4% lattice mismatch between Ge and Si places challenging obstacle towards monolithic integration of high-quality low dislocation density Ge devices through Ge on Si heteroepitaxy. Nevertheless, to date, device-grade single-crystalline Ge films have been demonstrated by many groups with practical high performance Ge photodetectors. In this review paper, we first introduce in Section 2 the various Ge growth techniques.