Germanium Crystals

Germanium (Ge) was the material used in the first transistor, which was invented by Bardeen, Brattain, and Shockley at Bell Laboratories in 1947. This marked a significant milestone in the semiconductor industry. However, due to its practical superiorities and intrinsic properties, silicon (Si) soon became the preferred material over Ge. As a result, Si became the primary material in the industry, driving the miniaturization and large-scale integration of modern electronic devices. While Ge was initially used in limited fields such as g-ray detectors and infrared optics, it experienced a period of disinterest. However, since the 1990s, Ge has once again garnered keen interest for its applications in ultrafast electronic devices and its favorable intrinsic carrier mobility. As a result, numerous research groups around the world, particularly in Belgium, have renewed their efforts to develop Ge as a material for mainstream semiconductors. This resurgence has led to the promotion of large-crystal growth and the fabrication of electronic devices by Belgian research groups and companies.

Basic properties

1. Mechanical Properties:
   • Strength and Fracture: Ge's mechanical strength is lower than that of Si. Its yield strength increases with decreasing temperature until it reaches a ductile-to-brittle transition. Ge has a stress-intensity factor (K_IC) of 0.6 MPa m¹/², compared to Si's 0.7 MPa m¹/².
   • Dislocation Motion: Dislocations in Ge move faster than in Si. Their velocity is affected by temperature, stress, and impurities. For example, Ga and O impurities suppress dislocation nucleation, whereas As does not. This is useful for controlling dislocation behavior in various applications.
2. Thermal Conductivity:
   • Challenges: Ge's lower thermal conductivity than Si leads to greater thermoelastic stress during crystal growth. This makes it challenging to produce large, dislocation-free Ge crystals.

Growth Techniques and Challenges

Germanium crystal growth techniques have improved to address production challenges. Single crystal growth starts with a dislocation-free Ge seed crystal, which is dipped into the Ge melt to initiate growth. Sometimes, silicon (Si) seeds are used, resulting in a dilute SiGe alloy. To reduce dislocation generation, the Dash necking technique is employed, which involves reducing the crystal diameter to about 2-4 mm, allowing dislocations from the seed to escape through the thin neck, resulting in a dislocation-free crystal. The Low Temperature Gradient (LTG) CZ method has been developed to grow large Ge crystals with minimal dislocation densities, using a temperature gradient of less than 1 K/cm. Additionally, oxygen doping has proven effective in growing oxygen-enriched Ge crystals with extremely low dislocation densities by using oxygen atoms from GeO₂ powder in a B₂O₃-covered melt to suppress dislocation generation.

Physical Properties and Dislocations

Germanium's physical properties, particularly its mechanical strength and dislocation behavior, pose distinct challenges. Ge exhibits lower mechanical strength than silicon, with its yield strength increasing as temperature decreases until a ductile-to-brittle transition is reached. The stress-intensity factor (K_IC) for Ge is 0.6 MPa m¹/², slightly lower than Si's 0.7 MPa m¹/². Dislocations in Ge move more rapidly than in Si, and their velocity is influenced by temperature, stress, and impurities. For example, impurities such as gallium (Ga) and oxygen (O) can suppress dislocation nucleation, while arsenic (As) does not have the same effect. This ability to control dislocation behavior through impurity doping is crucial for optimizing material performance in various applications. Additionally, Ge's lower thermal conductivity than Si contributes to greater thermoelastic stress during crystal growth, complicating the production of large, dislocation-free Ge crystals.

Basic Properties of Germanium (Ge) and Silicon (Si)

Property	Germanium (Ge)	Silicon (Si)
Atomic Weight (M)	72.64	28.09
Atomic Radius (r, nm)	0.123	0.117
Lattice Constant (a, nm)	0.56575	0.5431
Density (ρ, g/cm³)	5.33	2.33
Atomic Number in a Unit Volume (N, cm⁻³)	4.42 × 10²²	5 × 10²²
Bandgap (@0K/@RT, eV)	0.74/0.66	1.17/1.12
Intrinsic Carrier Density (@RT, cm⁻³)	2.5 × 10¹³	1.45 × 10¹³
Effective Mass
- Electron Density of State (mₑᵈ/m₀)	0.19	0.16
- Longitudinal (mₗₑ/m₀)	1.64	0.98
- Transversal (mₜₑ/m₀)	0.082	0.19
- Hole Density of State (mₕᵈ/m₀)	0.34	0.81
- Light (mₗₕ/m₀)	0.044	0.16
- Heavy (mₕₕ/m₀)	0.28	0.49
Mobility
- Electron (mₑ, cm²/Vs)	3900	1500
- Hole (mₕ, cm²/Vs)	1900	450
Dielectric Constant (ε)	16.0	11.9
Refractivity (n)	4.01	3.42
Elastic Constant (@RT)
- C₁₁ (GPa)	129	166
- C₁₂ (GPa)	48.3	64.0
- C₄₄ (GPa)	67.1	79.6
Shear Modulus (G, GPa)	48.9	60.5
Strength (@TM/@(2/3)TM, GPa)	0.3/25	1.0/40
Surface Energy (111, γ, erg/cm²)	1060	1230
Linear Thermal Expansion (@RT/@TM, K⁻¹)	5.9 × 10⁻⁶ / 2.6 × 10⁻⁶	9 × 10⁻⁶ / 4.4 × 10⁻⁶
Thermal Conductivity (@RT/@TM, W/m·K)	58/24	157/31
Gibbs Standard Free Energy of Dioxide Formation (@TM, ΔG, kJ/mol)	3.41	6.80

Physical Properties and Dislocations

1. Mechanical Properties:
   • Strength and Fracture: Ge's mechanical strength is lower than that of Si. Its yield strength increases with decreasing temperature until it reaches a ductile-to-brittle transition. Ge has a stress-intensity factor (K_IC) of 0.6 MPa m¹/², compared to Si's 0.7 MPa m¹/².

• Dislocation Motion: Dislocations in Ge move faster than in Si. Their velocity is affected by temperature, stress, and impurities. For example, Ga and O impurities suppress dislocation nucleation, whereas As does not. This is useful for controlling dislocation behavior in various applications.

1. Thermal Conductivity:
   • Challenges: Ge's lower thermal conductivity than Si leads to greater thermoelastic stress during crystal growth. This makes it challenging to produce large, dislocation-free Ge crystals.

Applications

1. Infrared Optics:
   • Optical Transmission: Ge is transparent in the infrared range from 1.85 to 15 µm and is used in infrared and far-infrared optical components, such as lenses and windows. Large-diameter single crystals are grown to meet the high refractivity and low birefringence requirements of these applications.
   • Avalanche Photodiodes (APDs): Ge can be used in APDs for infrared detection, with doping enhancing sensitivity and response.
2. Radiation Detection:
   • Gamma-Ray Detection: Ge's high atomic number, density, and carrier mobility make it ideal for gamma-ray detection. High-purity Ge crystals are used in detectors for dark matter and neutrinoless double-beta decay experiments. Crystals are typically grown in an H₂ atmosphere to avoid contamination and deep-level centers.
3. Electronics and Photonics:
   • CMOS Technology: Ge is explored as a channel material in MOSFETs due to its higher electron and hole mobility compared to Si. Techniques such as strain engineering and Ge-on-insulator substrates are used to enhance performance.
   • Solar Cells: Ge is used as a substrate for epitaxial growth of GaAs compounds in high-efficiency triple-junction solar cells for space applications.
4. GeSi and GeSn Alloys:
   • GeSi Alloys: Ge₁₋ₓSix alloys are used in thermoelectrics, photodetectors, and tunable monochromators. They offer adjustable lattice parameters and band gaps for various applications.
   • GeSn Alloys: Ge₁₋ₓSix alloys expand the bandgap and lattice parameter engineering of Ge-based materials. They exhibit a transition from indirect to direct bandgap semiconductors at around 8% Sn content, which is useful in infrared optoelectronics.

Conclusion

Germanium crystals have seen significant advances in growth techniques, mechanical properties, and applications. While they are now comparable to silicon in many respects, they still face challenges, including lower mechanical strength and difficulty producing large, dislocation-free crystals. However, with ongoing research and development, including techniques such as oxygen doping and advanced alloy systems, Ge remains a valuable material in various high-tech applications, from infrared optics to advanced electronics and radiation detection. The unique properties of Ge, combined with innovative engineering, hold promise for future advancements in semiconductor technology.

Cole Morace

• Yonenaga, I. (2019). Germanium crystals. Single Crystals of Electronic Materials, 89–127. doi:10.1016/b978-0-08-102096-8.00004-5