# Electron hole
An electron hole is a quasiparticle in condensed-matter physics that represents an unoccupied electron state in an otherwise filled valence band: it behaves as a mobile positive charge carrier with charge +e and a positive effective mass, even though no new particle has been added to the crystal. IUPAC defines it as a conceptual charge carrier opposite to the electron, the absence of an electron at a position where one would be present if the lattice were in its ground state with the valence band normally filled.[1](https://goldbook.iupac.org/terms/view/08826) Holes are one of the two carrier types of semiconductor physics, alongside conduction-band electrons.[2](https://ocw.mit.edu/courses/6-720j-integrated-microelectronic-devices-spring-2007/10707b9dced1bed9ea148baae9689b0b_lecture2.pdf)
| Key fact | Detail |
|---|---|
| Definition | A quasiparticle: a missing electron in a filled valence band, with energy equal to the negative of the missing electron's energy and positive charge.[1](https://goldbook.iupac.org/terms/view/08826) • [3](https://solidstate.quantumtinkerer.tudelft.nl/test_builds/N_A-equal-0/13_semiconductors/) |
| Charge and mass | Charge +e; effective mass in most semiconductors higher than the electron's (heavy-hole mass 0.49 m₀ in Si, 0.45 m₀ in GaAs).[1](https://goldbook.iupac.org/terms/view/08826) • [4](https://apachepersonal.miun.se/~gorthu/halvledare/Effective%20mass%20in%20semiconductors.htm) |
| Creation energy | About 1.1 eV frees a covalent electron in silicon, creating one conduction electron and one hole; kT is only 26 meV at room temperature.[5](https://www.chu.berkeley.edu/wp-content/uploads/2020/01/Chenming-Hu_ch1-3.pdf) |
| Hole mobility at 300 K | 1900 cm²/Vs (Ge), 450 (Si), 400 (GaAs), 150 (InP), 75 (GaP), 30 (GaN), against electron mobilities of 3900, 1500, 8500, 4600, 110, and 1500 cm²/Vs.[6](http://my.ece.ucsb.edu/Mishra/classfiles/data2.pdf) |
| Intrinsic carrier density, Si at 300 K | 1.45×10¹⁰ cm⁻³ (Sze table; a second reference gives 1.02×10¹⁰ cm⁻³), with intrinsic resistivity 2.3×10⁵ Ω-cm.[7](https://electronica.usal.es/docs/Tabla%20semiconductores.pdf) • [8](https://www.taylorfrancis.com/chapters/edit/10.1201/b13001-80/properties-silicon-germanium-john-cressler) |
| Doping roles | In N-type material electrons are majority carriers and holes minority; in P-type the roles reverse.[5](https://www.chu.berkeley.edu/wp-content/uploads/2020/01/Chenming-Hu_ch1-3.pdf) |
| Recent development | A germanium heavy-hole spin qubit reached single-qubit gate fidelities well above 99% even at temperatures above 1 K, and a diamond p-type transistor reached hole mobility of 566–572 cm²/Vs.[9](https://www.nature.com/articles/s41563-024-01857-5) • [10](https://arxiv.science/abs/2602.07424) |
## Physical origin and formation
In a semiconductor at equilibrium, bonding electrons occupy states in the valence band and free electrons occupy states in the conduction band; holes are the empty states in the valence band, and conduction-band electrons and valence-band holes are the mobile carriers.[2](https://ocw.mit.edu/courses/6-720j-integrated-microelectronic-devices-spring-2007/10707b9dced1bed9ea148baae9689b0b_lecture2.pdf) A hole is created when a valence-band electron is excited into the conduction band, leaving a positively charged site in its previous position.[1](https://goldbook.iupac.org/terms/view/08826) In the bond picture, breaking a covalent bond in silicon requires the band-gap energy of about 1.12 eV and yields one negatively charged free electron and one positively charged hole.[11](https://courses.cit.cornell.edu/ece315/Lectures/handout2.pdf)
The excitation can be thermal or optical. [Thermal energy](https://www.edgepedia.org/thermal-energy) can promote an electron across the forbidden band gap into the conduction band, leaving a hole behind, but ordinary temperatures excite only a few electrons this way.[12](https://www.britannica.com/science/hole-solid-state-physics) The numbers show why: kT is 26 meV at room temperature, far below the silicon gap of about 1.1 eV, so thermally generated electron and hole densities are very small without doping; the minimum photon energy for photoconductivity in silicon is likewise about 1.1 eV.[5](https://www.chu.berkeley.edu/wp-content/uploads/2020/01/Chenming-Hu_ch1-3.pdf) Band gaps set this energy scale across materials: 0.18 eV (InSb), 0.67 eV (Ge), 1.12 eV (Si), 1.42 eV (GaAs), 2.25 eV (GaP), 2.7 eV (ZnSe), and 6.0 eV (diamond).[5](https://www.chu.berkeley.edu/wp-content/uploads/2020/01/Chenming-Hu_ch1-3.pdf)
A useful sign convention follows from the hole's inverted energy: hole energy is measured downward in the band diagram, so the valence-band edge Ev is the minimum hole energy, and moving a hole downward in the diagram requires energy.[5](https://www.chu.berkeley.edu/wp-content/uploads/2020/01/Chenming-Hu_ch1-3.pdf)
## The hole as a quasiparticle: charge, mass, and statistics
The quasiparticle description is exact enough to compute with. A hole is a state of a completely filled band with one particle missing; its energy is the negative of the missing electron's energy, Eh = −E, and its charge is positive.[3](https://solidstate.quantumtinkerer.tudelft.nl/test_builds/N_A-equal-0/13_semiconductors/) Its velocity equals that of the missing electron, and its equation of motion is mh dv/dt = +e(E + v×B); equivalently, the hole's wavevector is the negative of the missing electron's wavevector, giving the [Lorentz force](https://www.edgepedia.org/lorentz-force) ℏ dk_h/dt = e(E + v_h×B).[3](https://solidstate.quantumtinkerer.tudelft.nl/test_builds/N_A-equal-0/13_semiconductors/) • [13](https://www.homepages.ucl.ac.uk/~ucapikr/Solid_State_Physics/Section%208.pdf) MIT's solid-state course summarizes the object as a quasiparticle with positive charge and positive mass whose motion is read off the E(k) band diagram.[14](https://web.mit.edu/6.730/www/ST04/Lectures/Lecture23.pdf)
**Effective mass.** Because the hole lives near the top of the valence band, where E(k) curves downward, the missing electron's negative curvature becomes a positive hole mass. The valence band in typical semiconductors splits into three branches at the band maximum: heavy holes, light holes, and split-off holes. For GaAs the values are 0.5 mₑ (heavy), 0.082 mₑ (light), and 0.17 mₑ (split-off), against 0.066 mₑ for electrons.[13](https://www.homepages.ucl.ac.uk/~ucapikr/Solid_State_Physics/Section%208.pdf) In noncubic crystals the mass depends on the direction of motion.[15](https://neurophysics.ucsd.edu/courses/physics_120/The%20Feynman%20Lectures%20on%20Semiconductors.pdf) Simplified single-value tables give mp/m₀ of 0.39 (Si), 0.30 (Ge), 0.50 (GaAs), and 0.30 (InAs), against electron masses of 0.26, 0.12, 0.068, and 0.023.[5](https://www.chu.berkeley.edu/wp-content/uploads/2020/01/Chenming-Hu_ch1-3.pdf)
**Statistics.** The probability of a valence-band state being occupied by a hole is the probability of it not being occupied by an electron, 1 − f(E), where f(E) is the Fermi–Dirac occupation function; the hole concentration follows from the valence-band [density of states](https://www.edgepedia.org/density-of-states) Nv and this probability.[5](https://www.chu.berkeley.edu/wp-content/uploads/2020/01/Chenming-Hu_ch1-3.pdf)
## Hole transport and mobility
A missing electron is equivalent to an added positive charge. Holes generally move more slowly than electrons because they function within the tightly bound valence band rather than the conduction band.[12](https://www.britannica.com/science/hole-solid-state-physics) Both electron and hole mobilities are proportional to the mean free time between scattering events, and drift current density is proportional to the electric field when carrier concentrations are field-independent, which is [Ohm's law](https://www.edgepedia.org/ohms-law).[16](https://ethz.ch/content/dam/ethz/special-interest/chab/icb/shih-lab-dam/documents/IEM-lecture/Lecture_2024/Notes_2024/Lecture_18_2024.pdf) Although electrons and holes drift in opposite directions, the sign of their current-density contributions is the same, so the total drift current is (nqμn + qpμp)·E.[16](https://ethz.ch/content/dam/ethz/special-interest/chab/icb/shih-lab-dam/documents/IEM-lecture/Lecture_2024/Notes_2024/Lecture_18_2024.pdf)
In silicon MOSFETs, the mobility difference can be large. In silicon MOSFETs with identical oxides, an order-of-magnitude mobility difference between electrons and holes was observed and attributed to valence-band nonparabolicity: the nonparabolicity endows holes with a density-dependent transverse effective mass ranging to values significantly larger than the usually quoted band-edge mass of about 0.49 m₀.[17](https://link.aps.org/doi/10.1103/g29w-st3q) The heavy-hole band's constant-energy surfaces are warped, resembling a cube with rounded corners and dented-in faces, which is one root of the discrepancy between density-of-states and conductivity effective masses in silicon.[4](https://apachepersonal.miun.se/~gorthu/halvledare/Effective%20mass%20in%20semiconductors.htm)
## Carrier concentrations and doping
Equilibrium hole and electron densities are computed by integrating the density of states over the valence band for holes and over the conduction band for electrons; the valence-band density of states takes the form g_v(E) ∝ (2m_h)^(3/2)(Ev−E)^(1/2)/(2π²ℏ³).[18](https://ocw.mit.edu/courses/3-024-electronic-optical-and-magnetic-properties-of-materials-spring-2013/94c724ae53bc91ac576f4c709d653fab_MIT3_024S13_2012lec16.pdf) • [3](https://solidstate.quantumtinkerer.tudelft.nl/test_builds/N_A-equal-0/13_semiconductors/) The effective densities of states are Nv = 1.04×10¹⁹ cm⁻³ (Ge), 1.04×10¹⁹ cm⁻³ (Si), and 7.0×10¹⁸ cm⁻³ (GaAs), with Nc = 1.04×10¹⁹, 2.8×10¹⁹, and 4.7×10¹⁷ cm⁻³ respectively; Nc and Nv are both about 10¹⁹ cm⁻³ and differ only because the electron and hole effective masses differ.[5](https://www.chu.berkeley.edu/wp-content/uploads/2020/01/Chenming-Hu_ch1-3.pdf)
Doping fixes which carrier dominates. In an N-type semiconductor the abundant electrons are the majority carriers and the less abundant holes are the minority carriers; in P-type semiconductors the holes are the majority carriers and the electrons the minority.[5](https://www.chu.berkeley.edu/wp-content/uploads/2020/01/Chenming-Hu_ch1-3.pdf) Intrinsic concentrations at 300 K span orders of magnitude: about 2×10¹³ cm⁻³ for Ge, 1×10¹⁰ cm⁻³ for Si, 2×10⁶ cm⁻³ for GaAs, and roughly 10⁻¹⁰ cm⁻³ as tabulated for GaN.[6](http://my.ece.ucsb.edu/Mishra/classfiles/data2.pdf) A reference chapter on electrons and holes at equilibrium also covers the relative industrial importance of germanium, silicon, and gallium arsenide and a qualitative analysis of impurity levels via an extension of the Kronig–Penney model.[19](https://link.springer.com/chapter/10.1007/978-3-319-63154-7_18)
## Hole parameters across materials
| Quantity (300 K unless noted) | Ge | Si | GaAs | InP | GaN |
|---|---|---|---|---|---|
| Band gap (eV) | 0.66 | 1.12 | 1.42 | — | 3.4[6](http://my.ece.ucsb.edu/Mishra/classfiles/data2.pdf) |
| Electron mobility (cm²/Vs) | 3900 | 1500 | 8500 | 4600 | 1500[6](http://my.ece.ucsb.edu/Mishra/classfiles/data2.pdf) |
| Hole mobility (cm²/Vs) | 1900 | 450 | 400 | 150 | 30[6](http://my.ece.ucsb.edu/Mishra/classfiles/data2.pdf) |
| Heavy-hole mass (m₀) | 0.28 | 0.49 | 0.45 | — | 0.80[6](http://my.ece.ucsb.edu/Mishra/classfiles/data2.pdf) • [4](https://apachepersonal.miun.se/~gorthu/halvledare/Effective%20mass%20in%20semiconductors.htm) |
| Light-hole mass (m₀) | 0.044 | 0.16 | 0.082 | — | —[4](https://apachepersonal.miun.se/~gorthu/halvledare/Effective%20mass%20in%20semiconductors.htm) |
| Split-off mass (m₀) | 0.084 | 0.29 | 0.154 | — | —[4](https://apachepersonal.miun.se/~gorthu/halvledare/Effective%20mass%20in%20semiconductors.htm) |
| Intrinsic carrier density (cm⁻³) | 2.4×10¹³ | 1.45×10¹⁰ | 6.7×10⁶ | — | —[7](https://electronica.usal.es/docs/Tabla%20semiconductores.pdf) |
Several reference tables disagree at the level relevant to design. For silicon, Sze's table gives mobilities of 1500 (electrons) and 450 (holes) cm²/Vs, while Cressler's chapter gives 1450 and 500 cm²/Vs.[7](https://electronica.usal.es/docs/Tabla%20semiconductores.pdf) • [8](https://www.taylorfrancis.com/chapters/edit/10.1201/b13001-80/properties-silicon-germanium-john-cressler) The silicon intrinsic carrier concentration is 1.45×10¹⁰ cm⁻³ in the Sze table and 1.02×10¹⁰ cm⁻³ in Cressler's; the germanium value is 2.4×10¹³ versus 2.33×10¹³ cm⁻³.[7](https://electronica.usal.es/docs/Tabla%20semiconductores.pdf) • [8](https://www.taylorfrancis.com/chapters/edit/10.1201/b13001-80/properties-silicon-germanium-john-cressler) The BYU cleanroom database matches the Sze values for silicon.[20](https://cleanroom.byu.edu/Semiconductor-Constants) Effective masses are quoted inconsistently by design: Hu's single hole mass for silicon (0.39 m₀) is a simplified value, while band-resolved tables give heavy-hole 0.49 and light-hole 0.16 m₀.[5](https://www.chu.berkeley.edu/wp-content/uploads/2020/01/Chenming-Hu_ch1-3.pdf) • [6](http://my.ece.ucsb.edu/Mishra/classfiles/data2.pdf) For the silicon hole density-of-states mass, Sze's chapter lists 0.57 as the calculated value and 0.81 as the generally accepted literature value, noting that the two differ because the constant-energy surfaces are not ellipsoids.[21](https://truenano.com/PSD20/chapter2/pdf/ch2_3_7.pdf) [Temperature](https://www.edgepedia.org/temperature) also matters: at 4.2 K the heavy-hole masses are 0.537 (Si) and 0.28 (Ge), with light-hole masses 0.153 and 0.044.[8](https://www.taylorfrancis.com/chapters/edit/10.1201/b13001-80/properties-silicon-germanium-john-cressler)
## Holes, electrons, and positrons
A hole is not antimatter. Electrons and holes in solid-state physics are collective excitations of the material rather than true single particles, a point best understood in the language of effective field theories; this is the basis for distinguishing the hole from the positron.[22](https://physics.stackexchange.com/questions/389/positrons-versus-holes-as-positive-charge-carriers) A 2002 [Physical Review B](https://www.edgepedia.org/physical-review-b) analysis examined the microscopic differences between holes and electrons in nearly full energy bands, including their dependence on doping and the consequences for superconductivity.[23](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.65.184502) The historical confusion is instructive: in the first version of the Dirac sea, Dirac interpreted the hole as a proton, a proton-hole model he retracted about one and a half years later in 1931 and replaced with the hole as an anti-electron.[24](https://link.springer.com/chapter/10.1007/978-3-032-09188-8_7) Within the crystal, the hole's transport behavior parallels the electron's except for sign: opposite drift directions, identical current sign, and a mobility typically lower by roughly an order of magnitude in silicon devices.[16](https://ethz.ch/content/dam/ethz/special-interest/chab/icb/shih-lab-dam/documents/IEM-lecture/Lecture_2024/Notes_2024/Lecture_18_2024.pdf) • [17](https://link.aps.org/doi/10.1103/g29w-st3q)
## Historical development
The hole concept has two converging lineages. In relativistic quantum theory, Dirac's hole theory initially identified the sea's vacancies with protons before the 1931 revision to the anti-electron.[24](https://link.springer.com/chapter/10.1007/978-3-032-09188-8_7) In semiconductor physics, [William Shockley](https://www.edgepedia.org/william-shockley)'s 1950 monograph *Electrons and Holes in Semiconductors* formalized the hole as a positively charged quasiparticle moving through the crystal much like a free electron except for the sign of its charge, using the concepts and terminology of Brillouin zones and energy bands.[25](https://pearl-hifi.com/06_Lit_Archive/14_Books_Tech_Papers/Shockley_William/Electrons_and_Holes_in_Semiconductors_%28To_Pg_400%29.pdf) Hole conduction became technologically central with the transistor: the 1948 [Physical Review](https://www.edgepedia.org/physical-review) announcement by Bardeen and Brattain described a three-element electronic device using a newly discovered principle involving a semiconductor as its basic element.[26](https://journals.aps.org/pr/pdf/10.1103/PhysRev.74.230) Brattain's laboratory notebook entry of 17 November 1947 is recorded as a motivating moment on the path to the junction transistor,[27](https://archive.org/stream/ECL-225/ECL-225-The-Path-of-the-Conception-of-the-Junction-Transistor_djvu.txt) and the surface behavior underlying the invention was recognized by Bardeen in 1947; historical accounts of the MOS transistor also note low hole mobility as a device-relevant limitation from the start.[28](https://dejazzer.com/ece723/resources/Evolution_of_the_MOS_transistor.pdf)
## Devices and recent advances
In P-type regions of devices such as transistors and MOSFETs, holes are the majority carriers; the historical record ties the transistor's invention to the recognition of surface behavior by Bardeen in 1947.[5](https://www.chu.berkeley.edu/wp-content/uploads/2020/01/Chenming-Hu_ch1-3.pdf) • [28](https://dejazzer.com/ece723/resources/Evolution_of_the_MOS_transistor.pdf) Hole mobility is typically lower than electron mobility, and historical accounts of the MOS transistor note low hole mobility as a device-relevant limitation.[17](https://link.aps.org/doi/10.1103/g29w-st3q) • [28](https://dejazzer.com/ece723/resources/Evolution_of_the_MOS_transistor.pdf)
**Hole spin qubits.** The spin–orbit interaction makes the hole exchange anisotropic, a feature that becomes a resource in quantum computing. Two hole-spin qubits in a silicon FinFET demonstrated electrical tunability of the exchange splitting from above 500 MHz to close to zero and a conditional spin-flip in 24 ns; the exchange is anisotropic because of the spin–orbit interaction, enabling two-qubit controlled-rotation gates without a speed–fidelity trade-off, and individual [hole spin qubits](https://www.edgepedia.org/hole-spin-qubit) in bulk-silicon FinFETs operate above 4 K.[29](https://www.nature.com/articles/s41567-024-02481-5) In germanium, a heavy-hole spin qubit operated at low magnetic field showed a dephasing time T₂* of 17.6 μs with single-qubit gate fidelities well above 99% even at temperatures above 1 K, with driving and decoherence originating from electric-field modulations of the highly anisotropic heavy-hole g-tensor.[9](https://www.nature.com/articles/s41563-024-01857-5)
**New p-channel materials.** A p-type transistor using a two-dimensional hole channel on hydrogenated diamond (bandgap 5.6 eV) combined with a high-k SrTiO₃ (k = 30.5) perovskite membrane achieved stable operation with an on-current of about 200 mA/mm, a subthreshold swing of 70 mV/dec, hole mobility of 566–572 cm²/Vs, and an on/off ratio near 10⁹.[10](https://arxiv.science/abs/2602.07424)
## References
1. [IUPAC Gold Book – hole (08826)](https://goldbook.iupac.org/terms/view/08826)
2. [MIT OCW 6.720J Integrated Microelectronic Devices, Lecture 2](https://ocw.mit.edu/courses/6-720j-integrated-microelectronic-devices-spring-2007/10707b9dced1bed9ea148baae9689b0b_lecture2.pdf)
3. [Open Solid State Notes (TU Delft) – Basic principles](https://solidstate.quantumtinkerer.tudelft.nl/test_builds/N_A-equal-0/13_semiconductors/)
4. [Effective mass in semiconductors](https://apachepersonal.miun.se/~gorthu/halvledare/Effective%20mass%20in%20semiconductors.htm)
5. [Chenming Hu, Electrons and Holes in Semiconductors, UC Berkeley](https://www.chu.berkeley.edu/wp-content/uploads/2020/01/Chenming-Hu_ch1-3.pdf)
6. [Room temperature properties of important semiconductors (UCSB)](http://my.ece.ucsb.edu/Mishra/classfiles/data2.pdf)
7. [Properties of Ge, Si, and GaAs at 300 K (Sze, Physics of Semiconductor Devices, 2nd Ed.)](https://electronica.usal.es/docs/Tabla%20semiconductores.pdf)
8. [Properties of Silicon and Germanium (Cressler, Taylor & Francis)](https://www.taylorfrancis.com/chapters/edit/10.1201/b13001-80/properties-silicon-germanium-john-cressler)
9. [Sweet-spot operation of a germanium hole spin qubit, Nature Materials (2024)](https://www.nature.com/articles/s41563-024-01857-5)
10. [Efficient and Robust p-type Transistor based on Ultra-wide-bandgap Semiconductor (arXiv preprint)](https://arxiv.science/abs/2602.07424)
11. [Cornell ECE 315 Lecture 2](https://courses.cit.cornell.edu/ece315/Lectures/handout2.pdf)
12. [Britannica – Hole (solid-state physics)](https://www.britannica.com/science/hole-solid-state-physics)
13. [UCL Solid State Physics §8 – Semiconductors](https://www.homepages.ucl.ac.uk/~ucapikr/Solid_State_Physics/Section%208.pdf)
14. [MIT 6.730 Lecture 23](https://web.mit.edu/6.730/www/ST04/Lectures/Lecture23.pdf)
15. [The Feynman Lectures on Physics Vol. III Ch. 14: Semiconductors](https://neurophysics.ucsd.edu/courses/physics_120/The%20Feynman%20Lectures%20on%20Semiconductors.pdf)
16. [Lecture 18 (ETH Zürich, 2024)](https://ethz.ch/content/dam/ethz/special-interest/chab/icb/shih-lab-dam/documents/IEM-lecture/Lecture_2024/Notes_2024/Lecture_18_2024.pdf)
17. [Transport properties of extremely high mobility electrons and holes in silicon MOSFETs, Physical Review B](https://link.aps.org/doi/10.1103/g29w-st3q)
18. [MIT OCW 3.024 Lecture 16: Density of charge carriers in semiconductors](https://ocw.mit.edu/courses/3-024-electronic-optical-and-magnetic-properties-of-materials-spring-2013/94c724ae53bc91ac576f4c709d653fab_MIT3_024S13_2012lec16.pdf)
19. [Electrons and Holes in Semiconductors at Equilibrium (Springer)](https://link.springer.com/chapter/10.1007/978-3-319-63154-7_18)
20. [Semiconductor Constants (BYU Cleanroom)](https://cleanroom.byu.edu/Semiconductor-Constants)
21. [Detailed description of the effective mass (Sze, Physics of Semiconductor Devices, ch. 2.3.7)](https://truenano.com/PSD20/chapter2/pdf/ch2_3_7.pdf)
22. [Positrons versus holes as positive charge carriers, Physics Stack Exchange](https://physics.stackexchange.com/questions/389/positrons-versus-holes-as-positive-charge-carriers)
23. [Why holes are not like electrons, Phys. Rev. B 65, 184502 (2002)](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.65.184502)
24. [Scattering and the Sea: Antiparticles and Intermediate States (1928–1931) (Springer)](https://link.springer.com/chapter/10.1007/978-3-032-09188-8_7)
25. [William Shockley, Electrons and Holes in Semiconductors (1950)](https://pearl-hifi.com/06_Lit_Archive/14_Books_Tech_Papers/Shockley_William/Electrons_and_Holes_in_Semiconductors_%28To_Pg_400%29.pdf)
26. [Bardeen & Brattain, The Transistor, A Semi-Conductor Triode, Physical Review 74, 230 (1948)](https://journals.aps.org/pr/pdf/10.1103/PhysRev.74.230)
27. [The Path of the Conception of the Junction Transistor, IEEE Trans. Electron Devices (1976)](https://archive.org/stream/ECL-225/ECL-225-The-Path-of-the-Conception-of-the-Junction-Transistor_djvu.txt)
28. [Evolution of the MOS transistor: from conception to VLSI, Proceedings of the IEEE](https://dejazzer.com/ece723/resources/Evolution_of_the_MOS_transistor.pdf)
29. [Anisotropic exchange interaction of two hole-spin qubits, Nature Physics (2024)](https://www.nature.com/articles/s41567-024-02481-5)
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*Topic: Encyclopedia › Physical world and mathematics › Physics › Matter and radiation physics › Condensed matter physics › Electronic and magnetic properties › Band theory and electron transport › Semiconductor materials and carrier physics*
*Initially written Sep 17, 2026 · Reviewed: Sep 19, 2026; Oct 15, 2026 · Edited: Sep 19, 2026; Oct 15, 2026 · Last review: Oct 15, 2026*
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