Semiconductor Spin Qubits

The performance and potential of semiconductor spin qubits are inextricably linked to the material platform used. The physical properties of the material, including its band structure, carrier effective mass, spin-orbit coupling, piezoelectricity, and the presence of nuclear spins, determine the qubit's coherence time, control methods, compatibility with existing manufacturing processes, and scalability.

Band Structure

The band structure determines whether the band gap is direct or indirect. A direct band gap allows carriers to be excited from the valence band to the conduction band without the need for phonon coupling, leading to higher efficiency in coupling with photons. Furthermore, the degeneracy and symmetry of the band structure are relevant; in qubits, a magnetic field is often applied to split the spin energy states, and the choice of field direction is related to the crystal lattice structure. Degenerate or symmetric energy states can easily allow carriers to couple with other bands and decohere from the selected magnetic field state.

Carrier Effective Mass

Carriers in solid-state materials are not the same as free electrons in a vacuum. A large number of electrons in a crystal structure form a band structure with a ground state known as the Fermi sea. Carriers are excitations of this band structure and can be positively or negatively charged. Because carriers interact in complex ways with the crystal lattice and other electrons, their "inertia" of movement differs from that of a bare electron, which is described by an "effective mass." The magnitude of the effective mass determines the "wavelength" of the carrier at low temperatures. A longer wavelength makes it easier for the wave functions of two quantum dots to overlap, allowing quantum interactions to be realized with larger device dimensions.

Spin-Orbit Coupling (SOC)

Interestingly, spin-orbit coupling is a relativistic phenomenon. Spin is a natural mathematical structure in a consistent relativistic quantum field framework. Furthermore, as an electron moves rapidly around an atomic nucleus, the electric field of the nucleus, due to the electron's relative motion, will appear to have a magnetic field component from the electron's perspective (this is also a relativistic effect). This magnetic field then interacts with the electron's spin magnetic moment.

Spin-orbit coupling is a double-edged sword for qubit control. The advantage is that stronger SOC allows for the control of an electron's spin state via electric fields (a relativistic electromagnetic conversion), which is superior to magnetic field control for integrated circuits. However, the disadvantage is that phonon disturbances in the crystal structure can easily lead to decoherence.

Piezoelectricity

The piezoelectric properties of a material allow for the generation of electric field signals through mechanical stress, which can be used to manipulate spin states similarly to the methods mentioned above. However, the disadvantage is also that phonon disturbances are more likely to generate electric field noise, leading to decoherence.

Material Nuclear Spins

Because an electron has a spin of \(\frac{1}{2}\), if the atomic nuclei of the material also have non-zero nuclear spins, spin-spin interactions will occur, which can very easily lead to decoherence. Using isotopically purified materials with zero-spin isotopes as the substrate can effectively increase coherence times.

Key Material Properties

The three most common semiconductor materials are Gallium Arsenide (GaAs), Silicon (Si), and Germanium (Ge).

Property	Gallium Arsenide (GaAs)	Silicon (Si)	Germanium (Ge)
Primary Carrier	Electrons	Electrons / Holes	Holes
Band Gap Structure	Direct	Indirect	Indirect Highly degenerate electron bands
Carrier Effective Mass	Small	Large	Small
Spin-Orbit Coupling	Strong	Electrons: Weak Holes: Stronger	Strong and tunable
Piezoelectricity	Yes	-	-
Nuclear Spin Environment	Ga and As are all spin-\(\frac{3}{2}\)	>90% is 28Si (spin-0), can be isotopically purified	Main isotopes 70Ge, 72Ge, 74Ge are all spin-0
Typical Coherence Time \(T_2^*\)	Short (~tens of ns)	Longer (ms) due to low nuclear spin	Long (~hundreds of ns, constantly improving)
Gate Control Method	Electrical (SOC/Exchange)	Magnetic (ESR) or Electrical (SOC/Exchange)	All-electrical (Strong SOC)
CMOS Compatibility	No	Excellent (Si-MOS) / Good (Si/SiGe)	Good (compatible with Si processes)
Technology Maturity	Pioneering, less active now	Leading platform	Rapidly emerging platform

Gallium Arsenide (GaAs)

Gallium arsenide is a classic example of a III-V compound semiconductor and was a pioneering material for research in spintronics and spin qubits. Due to its very high crystal growth quality, atomically flat heterostructure interfaces can be grown using molecular beam epitaxy (MBE), forming a high-quality two-dimensional electron gas (2DEG). This provided an excellent foundation for defining high-quality quantum dots. Additionally, GaAs has a small carrier effective mass, which allows for a larger quantum coherence length, making it easier to achieve quantum interactions between qubits.

However, the GaAs platform has a fatal, intrinsic flaw: both of its constituent atoms—gallium (Ga) and arsenic (As)—have stable isotopes with non-zero nuclear spins (both are spin-\(\frac{3}{2}\)). This means that an electron spin in a quantum well is surrounded by a randomly fluctuating bath of tens of thousands of nuclear spins. The electron spin couples strongly with these nuclear spins. This random nuclear magnetic field acts as a powerful source of magnetic noise, causing rapid decoherence of the electron spin.

This unavoidable interaction limits the coherence time \(T_2^*\) of electron spins in GaAs to a very short range, typically only a few tens of nanoseconds. Due to this difficult-to-overcome limitation, research focus has gradually shifted from GaAs to Group IV semiconductor materials with a much cleaner nuclear spin environment: silicon.

Silicon (Si)

Silicon is the cornerstone of the modern electronics industry, with the global multi-trillion-dollar semiconductor industry built upon Si-based CMOS technology. Building quantum computing on a silicon platform undoubtedly provides a clear and feasible path to leveraging this mature and vast industrial ecosystem for large-scale manufacturing. In addition to its compatibility with CMOS technology, silicon possesses a physical advantage as a spin qubit material due to its predominantly zero-spin nuclear environment.

Isotopic Purification and the Leap in Coherence Time

Silicon's most prominent advantage is its extremely favorable nuclear spin environment. Naturally occurring silicon consists mainly of three isotopes: ²⁸Si (~92.2%), ²⁹Si (~4.7%), and ³⁰Si (~3.1%). Among these, only ²⁹Si has a non-zero nuclear spin (spin-\(\frac{1}{2}\)), while the vast majority, ²⁸Si and ³⁰Si, are spin-zero isotopes. This means that even in natural silicon, the density of nuclear spins that can cause hyperfine interactions with electron spins is already much lower than in GaAs.

Furthermore, using industrial techniques such as centrifugal enrichment, it is possible to produce highly isotopically purified silicon, specifically increasing the abundance of ²⁸Si to over 99.9%. This isotopically purified ²⁸Si crystal provides an environment for electron spins that is almost completely free of magnetic noise, virtually eliminating this decoherence mechanism. This breakthrough has led to a leap of several orders of magnitude in the coherence time of spin qubits in silicon, from microseconds in natural silicon to milliseconds or even seconds in isotopically purified silicon. Such long coherence times provide a solid hardware foundation for achieving high-fidelity quantum operations that far exceed the fault-tolerance threshold.

Si-MOS vs. Si/SiGe Heterostructures

In the development of silicon-based spin qubits, there are two mainstream device structure platforms:

• Si-MOS: This structure is physically almost identical to the CMOS transistors that make up modern CPUs and memory chips. It typically consists of a silicon channel, a silicon dioxide (SiO₂) insulating layer, and a metal gate on top. The biggest advantage of Si-MOS is its compatibility with standard industrial manufacturing processes, making it the most direct path to large-scale, low-cost fabrication of quantum processors. However, the Si/SiO₂ interface inevitably has some charge defects, which can cause significant charge noise and affect qubit performance.

• Silicon/Silicon-Germanium (Si/SiGe) Heterostructures: This approach uses epitaxial growth to create a Si/SiGe heterostructure, where a thin film of pure silicon is grown on top of a silicon-germanium alloy layer. Due to differences in the band structure, electrons are confined within the pure silicon layer, far from the surface interface defects, which effectively reduces charge noise. This generally leads to higher qubit performance, including higher fidelity and longer coherence times. However, the fabrication process for Si/SiGe heterostructures is more complex and costly than for standard Si-MOS.

Germanium (Ge)

The Ge platform combines some of the advantages of both GaAs and Si, and brings its own unique strengths:

• Nuclear Spin Environment: Similar to silicon, the natural isotopes of germanium are predominantly spin-zero, providing a low nuclear spin noise environment and the potential for long coherence times.

• Strong and Tunable Spin-Orbit Coupling: This is germanium's most prominent advantage. Unlike the extremely weak SOC in silicon, germanium (especially holes in its valence band) has a very strong intrinsic SOC. This strong SOC means that electric fields can be used very efficiently to manipulate hole spins (via EDSR), enabling fast, all-electrical single-qubit gates without relying on complex micromagnet structures as in silicon, thus simplifying device design and fabrication.

• Smaller Effective Mass: The effective mass of holes in germanium is smaller than that of electrons in silicon. This means that larger, more easily processable quantum dots (around 50-100 nm) can be fabricated, which to some extent relaxes the extreme demands on lithography technology.

In recent years, research based on Ge/Si nanowires and planar Ge/SiGe heterostructures has made rapid progress, successfully demonstrating high-quality hole quantum dots, coherent manipulation, and longer coherence times than for holes in silicon. The all-electrical control characteristics and good compatibility with silicon processes make the germanium platform a highly attractive and promising option for achieving fast and scalable quantum computing.

Originally written in Chinese by the author, these articles are translated into English to invite cross-language resonance.