J. Semicond. > 2014, Volume 35 > Issue 2 > 021001, doi: 10.1088/1674-4926/35/2/021001

INVITED REVIEW PAPERS

Solid State Physics View of Liquid State Chemistry Ⅱ. Electrical Capacitance of Pure and Impure Water

Binbin Jie1, and Chihtang Sah1, 2

+ Author Affiliations

 Corresponding author: Jie Binbinbb_jie@msn.com; Sah Chihtang tom_sah@msn.com

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Abstract: More than 80 years of theories and experiments on water suggested to us, described in our first water-physics report, that pure water's "abnormally" high electrical conductivity is due to transport of positive and negative quasi-protons, p+ and p-, between the neutral proton traps V0 ≡ (H2O)0 in the extended water, [(H2O)N→∞]0±, converting it respectively to positively and negatively charged proton traps, V+ ≡ (H3O)1+ and V- ≡ (HO)1-. In this second report, we present the theoretical charge control capacitances of pure and impure water as a function of the DC electric potential applied to water.

Key words: solid state physics, liquid state chemistry, pure and impure water, positive and negative quasi-protons, proton vacancies, water capacitance



[1]
Sah Chihtang and Jie Binbin, "Semiconductor Physics View of Liquid State Chemistry, " Invited Paper at the Special Session, the Sah Pen-Tung 111th Anniversary Symposium, of the 2013 National Fall-Meeting of the Chinese Physical Society, August 13-15, 2013, Xiamen University, Xiamen, Fujian, China.
[2]
Jie Binbin and Sah Chihtang, "Solid State Physics View of Liquid State Chemistry-Electrical conduction in pure water, " Journal of Semiconductors 34(12) 121001-121001-8, December 2013.
[3]
J. D. Bernal and R. H. Fowler (Cambridge), "A theory of water and ionic solution, with particular reference to hydrogen and hydroxyl ions, " J. Chem. Phys. 1(8), 515-548, August, 1933. Received April 29, 1933. (University of Cambridge, England. )
[4]
Linus Pauling (Caltech), "The structure and entropy of ice and other crystals with some randomness of atomic arrangement, " J. Amer. Chem. Soc. 57(12), 2680-2684, December 1935. Received September 24, 1935. (Gates Chemical Laboratory, Caltech, Pasadena. )
[5]
W. F. Giauque and H. L. Hohnston (UC Berkeley), "Symmetrical and Antisymmetrical Hydrogen and the Third Law of Thermodynamics. Thermal Equilibrium and the Triple Point Pressure", J. Amer. Chem. Soc. 50, 3221-3228, 1928; J. O. Clayton and W. F. Giauque, "The Heat Capacity and Entropy of Carbon Monoxide. Heat of Vaporation. Vapor Pressures of Solid and Liquid. Free Energy To 5000°K. From Spectroscopic Data", J. Amer. Chem. Soc. 54, 2610-2626, 1932; W. W. Blue and W. F. Giauque, "The Heat Capacity and Vapor Pressure of Solid and Liquid Nitrous Oxide. The Entropy from its Band Spectrum", J. Amer. Chem. Soc. 57, 991-997, 1935. Quoted by Pauling in [2].
[6]
N. H. Fletcher (University of New England University), The Chemical Physics of Ice (Cambridge Monographs on Physics), Cambridge University Press. 1970. Digital version 2009. Made in the U. S. A. Lexington, KY, 03 September 2013. 271pp.
[7]
N. H. Fletcher, "Structural aspects of the ice-water system, " Report Progress Physics, 34, 913-994, 1971.
[8]
Peter V. Hobbs (University of Washington, Seattle), Ice Physics, Oxford Classic Texts in the Physical Sciences, Oxford University Press, Oxford, 1974. Paperback 2010. 837 pp. A detailed description of the Pauling's zero-point entropy calculation[4] for the 1h hexagonal ice crystal is given in section 1. 2. 2 on p. 25-33, including the 1964 analytical solution of Hollins that took into account of the correlated motion of the smallest hexagonal ring structure containing the six H2O molecules ring, and the interference between rings described by DiMarzio and Sillinger in 1964 which was extended by Nagle in 1966 giving S0=Rloge[(3/2)×(1+1/729)2+0. 002732]=3. 4103 J/mol-degree almost in exact agreement with the experimental value of 3. 41, obtained from constant pressure heat capacity measurements made by Giauque and Stout in 1936, and lower temperature measurement in 1960 made by Simon, and further extended to nearly 0°K in 1966 by Flubacher and co-authors, giving a residual experimental value of 3. 41 calculated by Eisenberg and Kauzmann in 1969, as indicated in Fig. 5. 7 on p 363 and Table 5. 4 on p. 364. These ascertained the position of the two protons in the 1h hexagonal ice, which is more than 70% of ice.
[9]
Chih-Tang Sah and William Shockley, "Electron-hole recombination statistics in semiconductors through flaws with many charge conditions, " Physical Review, v109, 1103-1115, 15 February 1958
[10]
Chih-Tang Sah, "The equivalent circuit model in solid-state electronics, I. The single level defect centers, " Proc. IEEE, v55, 654-672, May 1967. "The equivalent circuit model in solid-state electronics, Ⅱ. The multiple level impurity centers, " Proc. IEEE, v55, 673-685, May 1967. "The equivalent circuit model in solid-state electronics, Ⅲ. Conduction and displacement currents, " Solid-State Electronics, v13, 1547-1575, December 1970. "Equivalent circuit models in semiconductor transport for thermal, optical, Auger-impact and tunneling recombination-generation-trapping processes, " Physica Status Solidi, (a)v7, 541-559, 16 October 1971.
[11]
Jie Binbin and Sah Chihtang, "MOS Capacitance-Voltage Characteristics from Electron-Trapping at Dopant Donor Impurity," Journal of Semiconductors, 32(4), 041001-1-9, April 2011. "MOS Capacitance-Voltage Characteristics: Ⅱ. Sensitivity of Electronic Trapping at Dopant Impurity from Parameter Variations," Journal of Semiconductors, 32(12), 121001-1-11, December 2011. "MOS Capacitance-Voltage Characteristics: Ⅲ. Trapping Capacitance from 2-Charge-State Impurities," Journal of Semiconductors, 32(12), 121002-1-16, December 2011. "MOS Capacitance-Voltage Characteristics: IV. Trapping Capacitance from 3-Charge-State Impurities," Journal of Semiconductors, 33(1), 011001-1-19, January 2012. "MOS Capacitance-Voltage Characteristics: V. Methods to Enhance the Trapping Capacitance," Journal of Semiconductors, 33(2), 011001-1-19, February 2012.
[12]
William L. Marshall and E. U. Franck, "Ion Product of Water Substance, 0-1000C, 1-10000 bars - New International Formulation and Its Background", J. Phys. Chem. Ref. Data, vol. 10, No. 2, pp. 295-304, 1981.
Fig. 1.  Theoretical charge control capacitances of Metal-Gate/Insulator/pure-Water capacitors (MIWC's) at T = 0 ℃, 25 ℃ and 50 ℃. The two proton trap energies are at EV±-E± = ± 128 meV from two edges of the one-proton energy gap with an energy gap of E+-E-(meV)= 578.3 (0 ℃), 575.7 (25 ℃) and 574.6 (50 ℃). See Appendix for data sources.

Insulator capacitance CIN = large. (a) Mobile proton storage capacitances, Cp+ and Cp-, trapped proton storage capacitances, CV+, CV- and trapping-limited mobile impurity ion storage capacitance CB+ as a function of surface potential VS at the water surface. (b) Total mobile proton storage capacitance Cp+ + Cp- versus VS. (c) CV+ + CV-+CB+ versus VS. (d) Water capacitance CS versus VS.
Insulator capacitance CIN = 25.9 μF/cm2. (e) Cp+, Cp-, CV+, CV- and CB+, as a function of the DC voltage applied to the metal gate relative to the body, VGB, shifted by the flatband voltage VFB (VS = 0). (f) Gate capacitance Cg versus VGB-VFB.
Notice the symmetry of all curves with respect to the flatband. This is expected from the identical experimental trapping energy, 128 meV, determined by few data, of the positive and negative conduction protons of the amphoteric protonic water. Such closeness is also anticipated from the neutral proton trap of the positive and negative protons.


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Fig. 2.  Theoretical charge control capacitances of Metal-Gate/Insulator/impure-Water capacitors (MIWC's) at T = 0 ℃, 25 ℃ and 50 ℃, with 10℃ acid impurity HA (H1+A1-) such as injecting a HCl drop into a beaker of H2O. When equilibrium is reached, we have HCl + H2O↔H1++ Cl1-+ (H3O)1+ + p-+ (H2O)0± + p+ + (HO)1-≡ p+ + Cl1-+ V1+ + p-+ V0± + p+ + V1-. Therefore, V1+ ≡ (H3O)1+ also serves as an attractive Coulomb trap for the migrating Cl1- which is limited by the low energy oxygen-phonon scattering and higher energy [(MH2O/MH1→H2)1/2 = (18/1)1/2 = 4.24 to (18/2)1/2 = 3.00 times higher] protonic-phonon trapping at V1+, in competition with p-, thus, CA-≡ CCl-. We assume EA--Ei = 0.000 meV = midgap or a Cl-like impurity with trapping energy of about 300 meV. 1 meV = 23.1 Cal/mole = 96.5 J/mole.

Insulator capacitance CIN = large. (a) Mobile proton storage capacitances, Cp+ and Cp-, trapped proton storage capacitances, CV+, CV- and trapping-limited mobile impurity ion storage capacitance CB+ as a function of surface potential VS at the water surface. (b) Total mobile proton storage capacitance Cp+ + Cp- versus VS. (c) CV+ + CV-+CB+ versus VS. (d) Water capacitance CS versus VS.
Insulator capacitance CIN = 25.9 μF/cm2. (e) Cp+, Cp-, CV+, CV- and CB+, as a function of the DC voltage applied to the metal gate relative to the body, VGB, shifted by the flatband voltage VFB (VS = 0). (f) Gate capacitance Cg versus VGB-VFB.


DownLoad: Full-Size Img PowerPoint
Fig. 3.  Theoretical charge control capacitances of Metal-Gate/Insulator/impure-Water capacitors (MIWC's) at T = 0 ℃, 25 ℃ and 50 ℃, with 10℃ base BOH [B1+(OH)1-] such as NaOH. When equilibrium is reached, we have NaOH + H2O↔Na1++ (OH)1-+ (H3O)1+ + p-+ (H2O)0± + p+ + (HO)1-≡ Na1+ + V1-+ V1+ + p-+ V0± + p+ + V1-. Therefore, V1- ≡(HO)1- also serves as an attractive negative Coulomb trap for the migrating Na1+ which is limited by the low energy oxygen-phonon scattering and higher energy [(MH2O/MH1↔H2)1/2 = (18/1)1/2 = 4.24 to (18/2)1/2 = 3.00 times higher] protonic-phonon trapping at V1-, in competition with p+, thus, CB+ ≡ CNa+. We assume EB+-Ei = 0.000 meV = midgap or ～ 300 meV trap.

Insulator capacitance CIN = large. (a) Mobile proton storage capacitances, Cp+ and Cp-, trapped proton storage capacitances, CV+, CV- and trapping-limited mobile impurity ion storage capacitance CB+ as a function of surface potential VS at the water surface. (b) Total mobile proton storage capacitance Cp+ + Cp- versus VS. (c) CV+ + CV-+CB+ versus VS. (d) Water capacitance CS versus VS.
Insulator capacitance CIN = 25.9 μF/cm2. (e) Cp+, Cp-, CV+, CV- and CB+, as a function of the DC voltage applied to the metal gate relative to the body, VGB, shifted by the flatband voltage VFB (VS = 0). (f) Gate capacitance Cg versus VGB-VFB.


DownLoad: Full-Size Img PowerPoint
Fig. 4.  Theoretical charge control capacitances of Metal-Gate/Insulator/impure-Water capacitors (MIWC's) with 20℃ acid impurity at T = 25 ℃. Energy levels of the acid impurity are: (EA--Ei) =-200, -100, 0.0, +100, +200 meV, corresponding to trapping energies of ～100, 200, 300, 400, and 500 meV (if E+ -E- = 600 meV). 1 meV = 23.1 Cal/mol = 96.5 J/mol.

Insulator capacitance CIN = large. (a) Mobile proton storage capacitances, Cp+ and Cp-, trapped proton storage capacitances, CV+, CV- and trapping-limited mobile impurity ion storage capacitance CB+ as a function of surface potential VS at the water surface. (b) Total mobile proton storage capacitance Cp+ + Cp- versus VS. (c) CV+ + CV-+CB+ versus VS. (d) Water capacitance CS versus VS.
Insulator capacitance CIN = 25.9 μF/cm2. (e) Cp+, Cp-, CV+, CV- and CB+, as a function of the DC voltage applied to the metal gate relative to the body, VGB, shifted by the flatband voltage VFB (VS = 0). (f) Gate capacitance Cg versus VGB-VFB.


DownLoad: Full-Size Img PowerPoint
Fig. 5.  Theoretical charge control capacitances of Metal-Gate/Insulator/impure-Water capacitors (MIWC's) with 20% base impurity at T =25 ℃. Energy levels of the base impurity are: (EB+-Ei) =-200, -100, 0.0, +100 and +200 meV, or trapping energies of ～100, 200, 300, 400 and 500 meV (if E+-E- = 600 meV). 1 meV = 23.1 Cal/mol = 96.5 J/mol.

Insulator capacitance CIN = large. (a) Mobile proton storage capacitances, Cp+ and Cp-, trapped proton storage capacitances, CV+, CV- and trapping-limited mobile impurity ion storage capacitance CB+ as a function of surface potential VS at the water surface. (b) Total mobile proton storage capacitance Cp+ + Cp- versus VS. (c) CV+ + CV-+CB+ versus VS. (d) Water capacitance CS versus VS.
Insulator capacitance CIN = 25.9 μF/cm2. (e) Cp+, Cp-, CV+, CV- and CB+, as a function of the DC voltage applied to the metal gate relative to the body, VGB, shifted by the flatband voltage VFB (VS = 0). (f) Gate capacitance Cg versus VGB-VFB.


DownLoad: Full-Size Img PowerPoint
Fig. 6.  Theoretical charge control capacitances of Metal-Gate/Insulator/impure-Water capacitors (MIWC's) with acid impurity energy level at midgap. T = 25 ℃. The acid impurity concentrations are: 10%, 20%, 40%, 80% and 100%.

Insulator capacitance CIN = large. (a) Mobile proton storage capacitances, Cp+ and Cp-, trapped proton storage capacitances, CV+, CV- and trapping-limited mobile impurity ion storage capacitance CB+ as a function of surface potential VS at the water surface. (b) Total mobile proton storage capacitance Cp+ + Cp- versus VS. (c) CV+ + CV-+CB+ versus VS. (d) Water capacitance CS versus VS.
Insulator capacitance CIN = 25.9 μF/cm2. (e) Cp+, Cp-, CV+, CV- and CB+, as a function of the DC voltage applied to the metal gate relative to the body, VGB, shifted by the flatband voltage VFB (VS = 0). (f) Gate capacitance Cg versus VGB-VFB.


DownLoad: Full-Size Img PowerPoint
Fig. 7.  Theoretical charge control capacitances of Metal-Gate/Insulator/impure-Water capacitors (MIWC's) with base impurity energy level at midgap. T = 25 ℃. The base impurity concentrations are: 10%, 20%, 40%, 80% and 100%.

Insulator capacitance CIN = large. (a) Mobile proton storage capacitances, Cp+ and Cp-, trapped proton storage capacitances, CV+, CV- and trapping-limited mobile impurity ion storage capacitance CB+ as a function of surface potential VS at the water surface. (b) Total mobile proton storage capacitance Cp+ + Cp- versus VS. (c) CV+ + CV-+CB+ versus VS. (d) Water capacitance CS versus VS.
Insulator capacitance CIN = 25.9 μF/cm2. (e) Cp+, Cp-, CV+, CV- and CB+, as a function of the DC voltage applied to the metal gate relative to the body, VGB, shifted by the flatband voltage VFB (VS = 0). (f) Gate capacitance Cg versus VGB-VFB.


DownLoad: Full-Size Img PowerPoint
Fig. 8.  Theoretical charge control capacitances of Metal-Gate/Insulator/impure-Water capacitors (MIWC's) at T = 25 ℃ containing a salt impurity B+A-, at the assumed model impurity ion trapping energy levels of EB+-Ei= 0 (Trapping Energy of Cl1- = 287.85 meV.) and EB+-Ei=-0.187 eV (Trapping Energy of Na1+ = 100.7 meV.) and impurity concentrations of 10%, 20%, 40%, 80% and 100% of water.

Insulator capacitance CIN = large. (a) Mobile proton storage capacitances, Cp+ and Cp-, trapped proton storage capacitances, CV+, CV- and trapping-limited mobile impurity ion storage capacitance CB+ as a function of surface potential VS at the water surface. (b) Total mobile proton storage capacitance Cp+ + Cp- versus VS. (c) CV+ + CV-+CB+ versus VS. (d) Water capacitance CS versus VS.
Insulator capacitance CIN = 25.9 μF/cm2. (e) Cp+, Cp-, CV+, CV- and CB+, as a function of the DC voltage applied to the metal gate relative to the body, VGB, shifted by the flatband voltage VFB (VS = 0). (f) Gate capacitance Cg versus VGB-VFB.


DownLoad: Full-Size Img PowerPoint
Fig. 9.  Theoretical charge control capacitances of Metal-Gate/Insulator/impure-Water capacitors (MIWC's) at T = 25 ℃ containing a salt impurity B+A-, at the assumed model impurity ion trapping energy levels of EB+-Ei= 0 (Trapping Energy of Cl1- = 287.85 meV.) and EB+-Ei=-0.187 eV (Trapping Energy of Na1+ = 100.7 meV.) and impurity concentrations of 10%, 20%, 40%, 80% and 100% of water.

Insulator capacitance CIN = large. (a) Mobile proton storage capacitances, Cp+ and Cp-, trapped proton storage capacitances, CV+, CV- and trapping-limited mobile impurity ion storage capacitance CB+ as a function of surface potential VS at the water surface. (b) Total mobile proton storage capacitance Cp+ + Cp- versus VS. (c) CV+ + CV-+CB+ versus VS. (d) Water capacitance CS versus VS.
Insulator capacitance CIN = 25.9 μF/cm2. (e) Cp+, Cp-, CV+, CV- and CB+, as a function of the DC voltage applied to the metal gate relative to the body, VGB, shifted by the flatband voltage VFB (VS = 0). (f) Gate capacitance Cg versus VGB-VFB.


DownLoad: Full-Size Img PowerPoint
Fig. 10.  Theoretical charge control capacitances of Metal-Gate/Insulator/impure-Water capacitors (MIWC's) with acid impurity energy level at midgap. T = 25 ℃. The acid impurity concentrations are: 10%, 40%, 100%, 150% and 200% on showing acid impurity solubility limitation in water.

Insulator capacitance CIN = large. (a) Mobile proton storage capacitances, Cp+ and Cp-, trapped proton storage capacitances, CV+, CV- and trapping-limited mobile impurity ion storage capacitance CB+ as a function of surface potential VS at the water surface. (b) Total mobile proton storage capacitance Cp+ + Cp- versus VS. (c) CV+ + CV- + CB+ versus VS. (d) Water capacitance CS versus VS.
Insulator capacitance CIN = 25.9 μF/cm2. (e) Cp+, Cp-, CV+, CV- and CB+, as a function of the DC voltage applied to the metal gate relative to the body, VGB, shifted by the flatband voltage VFB (VS=0). (f) Gate capacitance Cg versus VGB-VFB.


DownLoad: Full-Size Img PowerPoint
Fig. 11.  Theoretical charge control capacitances of Metal-Gate/Insulator/impure-Water capacitors (MIWC's) with base impurity energy level at midgap. T = 25 ℃. The base impurity concentrations are: 10%, 40%, 100%, 150% and 200% on showing base impurity solubility limitation in water.

Insulator capacitance CIN = large. (a) Mobile proton storage capacitances, Cp+ and Cp-, trapped proton storage capacitances, CV+, CV- and trapping-limited mobile impurity ion storage capacitance CB+ as a function of surface potential VS at the water surface. (b) Total mobile proton storage capacitance Cp+ + Cp- versus VS. (c) CV+ + CV- + CB+ versus VS. (d) Water capacitance CS versus VS.
Insulator capacitance CIN = 25.9 μF/cm2. (e) Cp+, Cp-, CV+, CV- and CB+, as a function of the DC voltage applied to the metal gate relative to the body, VGB, shifted by the flatband voltage VFB (VS=0). (f) Gate capacitance Cg versus VGB-VFB.


DownLoad: Full-Size Img PowerPoint
[1]
Sah Chihtang and Jie Binbin, "Semiconductor Physics View of Liquid State Chemistry, " Invited Paper at the Special Session, the Sah Pen-Tung 111th Anniversary Symposium, of the 2013 National Fall-Meeting of the Chinese Physical Society, August 13-15, 2013, Xiamen University, Xiamen, Fujian, China.
[2]
Jie Binbin and Sah Chihtang, "Solid State Physics View of Liquid State Chemistry-Electrical conduction in pure water, " Journal of Semiconductors 34(12) 121001-121001-8, December 2013.
[3]
J. D. Bernal and R. H. Fowler (Cambridge), "A theory of water and ionic solution, with particular reference to hydrogen and hydroxyl ions, " J. Chem. Phys. 1(8), 515-548, August, 1933. Received April 29, 1933. (University of Cambridge, England. )
[4]
Linus Pauling (Caltech), "The structure and entropy of ice and other crystals with some randomness of atomic arrangement, " J. Amer. Chem. Soc. 57(12), 2680-2684, December 1935. Received September 24, 1935. (Gates Chemical Laboratory, Caltech, Pasadena. )
[5]
W. F. Giauque and H. L. Hohnston (UC Berkeley), "Symmetrical and Antisymmetrical Hydrogen and the Third Law of Thermodynamics. Thermal Equilibrium and the Triple Point Pressure", J. Amer. Chem. Soc. 50, 3221-3228, 1928; J. O. Clayton and W. F. Giauque, "The Heat Capacity and Entropy of Carbon Monoxide. Heat of Vaporation. Vapor Pressures of Solid and Liquid. Free Energy To 5000°K. From Spectroscopic Data", J. Amer. Chem. Soc. 54, 2610-2626, 1932; W. W. Blue and W. F. Giauque, "The Heat Capacity and Vapor Pressure of Solid and Liquid Nitrous Oxide. The Entropy from its Band Spectrum", J. Amer. Chem. Soc. 57, 991-997, 1935. Quoted by Pauling in [2].
[6]
N. H. Fletcher (University of New England University), The Chemical Physics of Ice (Cambridge Monographs on Physics), Cambridge University Press. 1970. Digital version 2009. Made in the U. S. A. Lexington, KY, 03 September 2013. 271pp.
[7]
N. H. Fletcher, "Structural aspects of the ice-water system, " Report Progress Physics, 34, 913-994, 1971.
[8]
Peter V. Hobbs (University of Washington, Seattle), Ice Physics, Oxford Classic Texts in the Physical Sciences, Oxford University Press, Oxford, 1974. Paperback 2010. 837 pp. A detailed description of the Pauling's zero-point entropy calculation[4] for the 1h hexagonal ice crystal is given in section 1. 2. 2 on p. 25-33, including the 1964 analytical solution of Hollins that took into account of the correlated motion of the smallest hexagonal ring structure containing the six H2O molecules ring, and the interference between rings described by DiMarzio and Sillinger in 1964 which was extended by Nagle in 1966 giving S0=Rloge[(3/2)×(1+1/729)2+0. 002732]=3. 4103 J/mol-degree almost in exact agreement with the experimental value of 3. 41, obtained from constant pressure heat capacity measurements made by Giauque and Stout in 1936, and lower temperature measurement in 1960 made by Simon, and further extended to nearly 0°K in 1966 by Flubacher and co-authors, giving a residual experimental value of 3. 41 calculated by Eisenberg and Kauzmann in 1969, as indicated in Fig. 5. 7 on p 363 and Table 5. 4 on p. 364. These ascertained the position of the two protons in the 1h hexagonal ice, which is more than 70% of ice.
[9]
Chih-Tang Sah and William Shockley, "Electron-hole recombination statistics in semiconductors through flaws with many charge conditions, " Physical Review, v109, 1103-1115, 15 February 1958
[10]
Chih-Tang Sah, "The equivalent circuit model in solid-state electronics, I. The single level defect centers, " Proc. IEEE, v55, 654-672, May 1967. "The equivalent circuit model in solid-state electronics, Ⅱ. The multiple level impurity centers, " Proc. IEEE, v55, 673-685, May 1967. "The equivalent circuit model in solid-state electronics, Ⅲ. Conduction and displacement currents, " Solid-State Electronics, v13, 1547-1575, December 1970. "Equivalent circuit models in semiconductor transport for thermal, optical, Auger-impact and tunneling recombination-generation-trapping processes, " Physica Status Solidi, (a)v7, 541-559, 16 October 1971.
[11]
Jie Binbin and Sah Chihtang, "MOS Capacitance-Voltage Characteristics from Electron-Trapping at Dopant Donor Impurity," Journal of Semiconductors, 32(4), 041001-1-9, April 2011. "MOS Capacitance-Voltage Characteristics: Ⅱ. Sensitivity of Electronic Trapping at Dopant Impurity from Parameter Variations," Journal of Semiconductors, 32(12), 121001-1-11, December 2011. "MOS Capacitance-Voltage Characteristics: Ⅲ. Trapping Capacitance from 2-Charge-State Impurities," Journal of Semiconductors, 32(12), 121002-1-16, December 2011. "MOS Capacitance-Voltage Characteristics: IV. Trapping Capacitance from 3-Charge-State Impurities," Journal of Semiconductors, 33(1), 011001-1-19, January 2012. "MOS Capacitance-Voltage Characteristics: V. Methods to Enhance the Trapping Capacitance," Journal of Semiconductors, 33(2), 011001-1-19, February 2012.
[12]
William L. Marshall and E. U. Franck, "Ion Product of Water Substance, 0-1000C, 1-10000 bars - New International Formulation and Its Background", J. Phys. Chem. Ref. Data, vol. 10, No. 2, pp. 295-304, 1981.

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    Received: 23 December 2013 Revised: 10 January 2014 Online: Published: 01 February 2014

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      Article Navigation >  Journal of Semiconductors  > 2014  >  35(2): 021001
      Binbin Jie, Chihtang Sah. Solid State Physics View of Liquid State Chemistry Ⅱ. Electrical Capacitance of Pure and Impure Water[J]. Journal of Semiconductors, 2014, 35(2): 021001. doi: 10.1088/1674-4926/35/2/021001 B B Jie, C T Sah. Solid State Physics View of Liquid State Chemistry Ⅱ. Electrical Capacitance of Pure and Impure Water. J. Semicond., 2014, 35(2): 021001. doi:  10.1088/1674-4926/35/2/021001.Export: BibTex EndNote
      Citation:
      Binbin Jie, Chihtang Sah. Solid State Physics View of Liquid State Chemistry Ⅱ. Electrical Capacitance of Pure and Impure Water[J]. Journal of Semiconductors, 2014, 35(2): 021001. doi: 10.1088/1674-4926/35/2/021001

      B B Jie, C T Sah. Solid State Physics View of Liquid State Chemistry Ⅱ. Electrical Capacitance of Pure and Impure Water. J. Semicond., 2014, 35(2): 021001. doi:  10.1088/1674-4926/35/2/021001.
      Export: BibTex EndNote
      shu

      Solid State Physics View of Liquid State Chemistry Ⅱ. Electrical Capacitance of Pure and Impure Water

      doi: 10.1088/1674-4926/35/2/021001
      • 1.

        Department of Physics, Xiamen University, Xiamen 351005, China

      • 2.

        Chinese Academy of Sciences, Beijing 100864, China

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      • Corresponding author: Jie Binbinbb_jie@msn.com; Sah Chihtang tom_sah@msn.com
      • Received Date: 2013-12-23
      • Revised Date: 2014-01-10
      • Published Date: 2014-02-01

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