A review of some charge transport properties of silicon

doi:10.1016/0038-1101(77)90054-5

Solid-State Electronics

Volume 20, Issue 2, February 1977, Pages 77-89

https://doi.org/10.1016/0038-1101(77)90054-5 Get rights and content

Abstract

This paper reviews the present knowledge of charge transport properties in silicon, with special emphasis on their application in the design of solid-state devices. Therefore, most attention is devoted to experimental findings in the temperature range around 300 K and to high-field properties. Phenomenological expressions are given, when possible, for the most important transport quantities as functions of temperature, field or impurity concentration. The discussion is limited to bulk properties, with only a few comments on surface transport.

References (93)

W. Fawcett et al.
J. Phys. Chem. Solids
(1970)
M.A.C.S. Brown
J. Phys. Chem. Solids
(1961)
C. Hamaguchi et al.
J. Phys. Chem. Solids
(1966)
W.E. Spear
J. Phys. Chem. Solids
(1961)
C.B. Norris et al.
IEEE Trans. Electron Devices
(1967)
M. Martini et al.
C.Y. Duh et al.
IEEE Trans. Electron Devices
(1967)
C.Y. Duh et al.
Solid-St. Electron.
(1968)
W. Einle
Electron. Lett.
(1967)
P. Norton et al.
Phys. Rev.
(1973)
L. Gherardi et al.
Lett. Nuovo Cimento
(1975)

D.M. Caughey et al.

C. Canali et al.

Solid-St. Commun.

(1973)

C. Canali et al.

Phys. Rev. Lett.

(1973)

D.K. Ferry

Phys. Rev.

(1975)

C. Canali et al.

Phys. Letters

(1970)

A. Dargys et al.

Phys. Stat. Solidi

(1972)

G. Baccarani et al.

Solid-St. Electron.

(1977)

J.R. Schrieffer

Phys. Rev.

(1955)

N.St.J. Murphy et al.

Solid-St. Electron.

(1969)

K. Hess et al.

J. Appl. Phys.

(1974)

T. Sato et al.

J. Phys. Soc. Japan

(1971)

J.M. Ziman

R.A. Smith

Semiconductors

(1959)

P.N. Butcher

Electrons in Crystalline Solids

W. Fawcett

Electrons in Crystalline Solids

E.M. Conwell

J.R. Chelikowsky et al.

Phys. Rev.

(1974)

J.C. Hensel et al.

Phys. Rev.

(1965)

C. Canali et al.

Phys. Rev.

(1975)

G. Dresselhaus et al.

Phys. Rev.

(1963)

O. Kane

J. Phys. Chem. Solids

(1965)

G. Ottaviani et al.

Phys. Rev.

(1975)

H.D. Rees

J. Phys. C: Solid State Physics

(1972)

C. Hammar

J. Phys. C: Solid State Physics

(1973)

J.R. Haynes et al.

Phys. Rev.

(1949)

J.R. Haynes et al.

Phys. Rev.

(1951)

E.J. Ryder et al.

Phys. Rev.

(1951)

W. Shockley

Bell. System Tech. J.

(1951)

E.J. Ryder

Phys. Rev.

(1953)

A.C. Prior

J. Phys. Chem. Solids

(1959)

K. Seeger

Phys. Rev.

(1959)

J. Zucker et al.

J. Appl. Phys.

(1961)

A.F. Gibson et al.

J. Phys. Chem. Solids

(1961)

J.G. Ruch et al.

Phys. Rev.

(1968)

C. Canali et al.

J. Phys. Chem. Solids

(1971)

T.W. Sigmon et al.

Appl. Phys. Lett.

(1969)

C. Canali et al.

Appl. Phys. Lett.

(1975)

Cited by (957)

Formation and specific contact resistivity of NiGe on polycrystalline Ge made by flash lamp annealing
2024, Journal of Alloys and Compounds
Flash lamp annealing (FLA) is an ultra-short annealing method, which excellently meets the requirements of thin-film processing and microelectronics. Due to the relatively high hole mobility, thin Ge layers are highly interesting as a transistor channel material or generally as a functional layer in CMOS technology and for low-cost electronics. One possibility to realize ohmic contacts with low contact resistance is the use of metal germanides, especially the stoichiometric NiGe phase. In this work, NiGe contacts on thin Ge films were fabricated by magnetron sputtering followed by FLA. The evolution of microstructure was traced by transmission electron microscopy, energy-dispersive X-ray spectroscopy, and X-ray diffraction. Electrical measurements focused on the determination of contact resistance by the circular transfer length method. The contacts were fabricated by two different approaches, and the influence of different process steps on the layer morphology and uncertainty of the measurement was studied. Finally, we show that FLA as a thermal treatment with a low thermal budget is able to form NiGe on p-type Ge with a low contact resistance similar to that achieved by other thermal treatments.
Predictability of thermoelectric figure of merit for the single crystal from first principles
2024, International Journal of Heat and Mass Transfer
The first-principles calculations have been widely used to predict the thermoelectric figure of merit (ZT) for the single crystal, but such precise calculations are confined to phonon-limited intrinsic system, and the defects present in practical samples cannot be easily modeled. So, a question arises as to whether the phonon-limited ZT can represent the thermoelectric potential of the material. In this work, we demonstrate that the exclusion of defect scattering could provide ZT close to the actual values in single crystal by analyses of the ZT involved parameters. This is also illustrated in the case of SnSe by performing first-principles calculations of phonon-limited ZT compared with available experimental data. The calculated ZT can reproduce the measured values, indicating that the calculations possess predictive capability. On the basis, strong and anisotropic thermoelectric enhancement of SnSe induced by pressure is found. The pressure significantly increases the thermoelectric power factor of n-type SnSe along its a crystallographic axis and that of p-type SnSe along the b axis, while the increase of lattice thermal conductivity is relatively small. As a result, a large enhancement of ZT is obtained. By applying pressure up to 3.2 GPa, at room temperature, the a-axis ZT of n-type SnSe is as high as 1.2, while the b-axis ZT of p-type SnSe reaches up to 0.8, which are more than twice larger than the values at ambient pressure. This study provides strong confidence and support for the application of first-principles calculations to search high-performance thermoelectric materials and thus would be an important reference for future researches.
EPIq: An open-source software for the calculation of electron-phonon interaction related properties
2024, Computer Physics Communications
epiq (Electron-Phonon wannier Interpolation over k and q-points) is an open-source software for the calculation of electron-phonon interaction related properties from first principles. Acting as a post-processing tool for a density-functional perturbation theory code (Quantum ESPRESSO) and wannier90, epiq exploits the localization of the deformation potential in the Wannier function basis and the stationary properties of a force-constant functional with respect to the first-order perturbation of the electronic charge density to calculate many electron-phonon related properties with high accuracy and free from convergence issues related to Brillouin zone sampling. epiq features include: the adiabatic and non-adiabatic phonon dispersion, superconducting properties (including the superconducting band gap in the Migdal-Eliashberg formulation), double-resonant Raman spectra and lifetime of excited carriers. The possibility to customize most of its input makes epiq a versatile and interoperable tool. Particularly relevant is the interaction with the Stochastic Self-Consistent Harmonic Approximation (SSCHA) allowing anharmonic effects to be included in the calculation of electron-properties. The scalability offered by the Wannier representation combined with a straightforward workflow and easy-to-read input and output files make epiq accessible to the wide condensed matter and material science communities.
Program Title: epiq
CPC Library link to program files: https://doi.org/10.17632/f2syws66d7.1
Developer's repository link: https://gitlab.com/the-epiq-team/epiq
Licensing provisions: GPLv3
Programming language: FORTRAN95
External routines: BLAS (http://www/netlib.org/blas), LAPACK (http://www.netlib.org/lapack), Quantum ESPRESSO (https://www.quantum-espresso.org/), wannier90 (https://wannier.org/)
Nature of problem: Direct first principles calculation of quantities obtained via linear response methods in solid-state systems, such as the deformation potential, can be computationally demanding, hindering proper convergence.
Solution method: An interpolation scheme exploiting the localization of the deformation potential in the Wannier function basis and the stationary properties of a force-constant functional with respect to the first-order perturbation of the electronic charge density is implemented in epiq. Within this approach it is possible to calculate many electron-phonon related properties with high accuracy and a low computational effort.
Defining specifications for accurate Metal/TCO specific contact resistivity measurements by TLM in silicon heterojunction devices
2024, Solar Energy Materials and Solar Cells
Measuring specific contact resistivity ( $ρ_{c}$ ) in test vehicles representative of the final solar cell is critical for interface engineering in high efficiency devices such as silicon heterojunction (SHJ) solar cell. The Transfer Length Method (TLM) is commonly used for layer sheet resistance ( $R_{s h e e t}$ ) and $ρ_{c}$ evaluation and is valid for samples with charge transport confined in one conductive layer only. For metal/Transparent Conductive Oxide (TCO) interface $ρ_{c}$ evaluation from SHJ cells precursors, there is a need to prevent any contribution from the conductive c-Si. In this work, we investigated by simulation and experimental approach the parameters restricting the current confinement inside the TCO. The first one is the mid-gap trap density $(D_{i t})$ at the a-Si:H/c-Si interface which has no strong impact on current confinement on simulated TLM test structures. The second one is the variation of the activation energy $(E_{a} = E_{c} - E_{F})$ of the a-Si:H contact layers. Both simulated and experimental results have demonstrated that three current distribution regimes are possible in the TLM test structure depending on the $E_{a}$ value with only one regime, for $E_{a}$ between 0.6 and 1.4 eV, enabling to isolate the metal/TCO interface. This condition is mandatory to maintain a sufficiently high potential barrier for electrons at the interfaces a-Si:H(p)/a-Si:H(i)/c-Si(n) and thus lateral current in the TCO layer to apply TLM on SHJ devices.
Simulation of DAMPE silicon microstrip detectors in the Allpix<sup>2</sup> framework
2023, Nuclear Instruments and Methods in Physics Research, Section A: Accelerators, Spectrometers, Detectors and Associated Equipment
Silicon strip detectors have been widely utilized in space experiments for gamma-ray and cosmic-ray detections thanks to their high spatial resolution and stable performance. For a silicon micro-strip detector, the Monte Carlo simulation is recognized as a practical and cost-effective approach to verify the detector performance. In this study, a technique for the simulation of the silicon micro-strip detector with the Allpix $^{2}$ framework is developed. By incorporating the electric field into the particle transport simulation based on Geant4, this framework could precisely emulate the carrier drift in the silicon micro-strip detector. The simulation results are validated using the beam test data as well as the flight data of the DAMPE experiment, which suggests that the Allpix $^{2}$ framework is a powerful tool to obtain the performance of the silicon micro-strip detector.
ElecTra code: Full-band electronic transport properties of materials
2023, Computer Physics Communications
This paper introduces ElecTra, an open-source code which solves the linearized Boltzmann transport equation in the relaxation time approximation for charge carriers in a full-band electronic structure of arbitrary complexity, including their energy, momentum, and band-index dependence. ElecTra stands for ‘ELECtronic TRAnsport’ and computes the electronic and thermoelectric transport coefficients electrical conductivity, Seebeck coefficient, electronic thermal conductivity, and mobility, for semiconductor materials, for both unipolar and bipolar (small bandgap) materials. The code uses computed full-bands and relevant scattering parameters as inputs and considers single crystal materials in 3D and 2D. The present version of the code (v1) considers: i) elastic scattering with acoustic phonons and inelastic scattering with non-polar optical phonons in the deformation potential approximation, ii) inelastic scattering with polar phonons, iii) scattering with ionized dopants, and iv) alloy scattering. The user is given the option of intra- and inter-band scattering considerations. The simulation output also includes relevant relaxation times and mean-free-paths. The transport quantities are computed as a function of Fermi level position, doping density, and temperature. ElecTra can interface with any DFT code which saves the electronic structure in the ‘.bxsf’ format. In this paper ElecTra is validated against ideal electronic transport situations of known analytical solutions, existing codes employing the constant relaxation time approximation, as well as experimentally well-assessed materials such as Si, Ge, SiGe, and GaAs.
Program title: ElecTra – Electronic Transport simulation lab
CPC Library link to program files: https://doi.org/10.17632/ycgx2fjzb6.1
Licensing provisions: GPLv3
Programming Language: MATLAB®
Nature of the problem: computing the electronic and thermoelectric charge transport coefficients of materials with arbitrary complex full-band electronic structures, considering the carrier energy-, momentum-, and band-dependence of the scattering rates.
Solution method: Semiclassical Linearized Boltzmann transport equation, with electronic structures (DFT or analytical) as input, formed into constant-energy surfaces, with scattering rates evaluated using Fermi's Golden Rule.
Additional comments including restrictions and unusual features:
- •
  Programming interface: any DFT code which saves data in the ‘.bxsf’ format.
- •
  RAM: a case study for a half-Heusler bandstructure on a $51 \times 51 \times 51$ k-mesh, 2 Gb per processor is needed
- •
  Running time: for the example above, depending on the number and complexity of the scattering mechanisms and the number of simulated Fermi levels and temperatures considered, the time needed varies from ∼ 1 hour on a desktop PC or laptop (light simulations), to 5-10 hours on an HPC with 30-45 cores (heavy simulations). Using the constant relaxation time and constant mean-free-path approximations on a desktop PC or laptop, the running time is of the order of minutes.

View all citing articles on Scopus

^☆: Partially supported by Consiglio Nazionale delle Ricerche, Italy.

View full text

A review of some charge transport properties of silicon☆

Abstract

J. Phys. Chem. Solids

J. Phys. Chem. Solids

J. Phys. Chem. Solids

J. Phys. Chem. Solids

IEEE Trans. Electron Devices

IEEE Trans. Electron Devices

Solid-St. Electron.

Electron. Lett.

Phys. Rev.

Lett. Nuovo Cimento

Solid-St. Commun.

Phys. Rev. Lett.

Phys. Rev.

Phys. Letters

Phys. Stat. Solidi

Solid-St. Electron.

Phys. Rev.

Solid-St. Electron.

J. Appl. Phys.

J. Phys. Soc. Japan

Semiconductors

Electrons in Crystalline Solids

Electrons in Crystalline Solids

Phys. Rev.

Phys. Rev.

Phys. Rev.

Phys. Rev.

J. Phys. Chem. Solids

Phys. Rev.

J. Phys. C: Solid State Physics

J. Phys. C: Solid State Physics

Phys. Rev.

Phys. Rev.

Phys. Rev.

Bell. System Tech. J.

Phys. Rev.

J. Phys. Chem. Solids

Phys. Rev.

J. Appl. Phys.

J. Phys. Chem. Solids

Phys. Rev.

J. Phys. Chem. Solids

Appl. Phys. Lett.

Appl. Phys. Lett.