Mott-Schottky Theory Research Articles

Ionic Mott-Schottky formalism allows the assessment of mobile ion concentrations in Li+-conducting solid electrolytes

• Classical Mott-Schottky theory can be transferred from semiconductors to solid electrolytes. • With few adaptions, it can describe the ionic space-charge capacitances in blocking electrodes. • From impedance spectra and a physical equivalent circuit, the mobile charge carrier concentration can be calculated. • The analysis reveal that only a fraction of the stoichiometric Li-ions take part in the conduction process. Li + -conducting solid electrolytes have been in the focus of researchers for the last decade thanks to the recent efforts to develop efficient all-solid-state batteries. While material scientists discovered new compounds with unprecedented Li + conductivities, surprisingly often, a fundamental question remains: What fraction of the total lithium-ions inside the solid electrolyte is mobile and thus contributes to the conductivity? In this work, we propose an approach, which can be considered as a Mott-Schottky-based analysis applied to an ionically conducting system, to calculate the concentration of mobile Li + in a lithium-conducting glass–ceramic. We use the space charge layer (SCL) capacitances obtained from the electrochemical impedance data recorded at different bias potentials and temperatures as the input. We demonstrate that the space charge layer in the ionic conductors can be formally described similarly to the SCLs formed in semiconductors in contact with, e.g., liquid electrolytes. This analysis makes it possible to provide deeper insights into the mechanisms of conductivity and its temperature dependencies in the SCL in ion conductors and, in general, help to uncover the nature of the mobility of Li-ions in various Li + -conducting electrolytes.

S-scheme SrTiO3/porous ZnO derived by pyrolysis of ZIF-8 composite with efficient photocatalytic activity for pollutant degradation

Semiconductor catalyst with high photocatalytic activity can be exploited via heterojunction. In this study, a new S-scheme SrTiO3/porous ZnO composite was rationally devised, successfully prepared by utilizing a two-step pyrolysis of SrTiO3/ZIF-8, and analyzed by various characterization technologies including XRD, SEM, TEM, BET, XPS, PL, UV–vis DRS, and photoelectrochemical and DFT theoretical calculations. A porous structure, tight contact, and a heterojunction formed between SrTiO3 and porous ZnO (ZnOT) can be observed by SEM and TEM images. BET testing indicates that the SrTiO3/porous ZnO composite (S3ZT) shows the highest specific surface area (30.37 m2/g). The band gap values (Eg) of SrTiO3 and ZnOT are around 3.17 and 2.95 eV, which agree with those obtained from DFT calculations. Compared to other samples, the SrTiO3/porous ZnO composite (S3ZT) shows higher light absorption and lower transfer resistance as demonstrated by UV–vis DRS and EIS results. S3ZT presents a superior photocatalytic efficiency of 48.8% in degrading 5 mg/L methyl orange (MO) irradiated by 1 h UV–vis light, which are 7- and 1.5-fold higher than pristine SrTiO3 and ZnOT, respectively. Moreover, based on Mott-Schottky theory, active species trapping experiments, XPS determination, and DFT calculations (energy band gap and work function), it was shown to be reasonable to utilize the S-scheme charge migration process for an explanation regarding the better photocatalytic activity of SrTiO3/porous ZnO composite. Overall, this work will provide an effective protocol for devising and preparing semiconductor photocatalysts with S-scheme heterojunction by utilizing the superior characteristics of MOFs.

(Invited) Relationship between the Resistivity Profiles Obtained from the Power Law Model and the Physico-Chemical Properties of Passive Films

Passive film (PF) could be considered a particular nanomaterial with its growth, chemical composition, microstructure, performance and evolution of its performance. The understanding of the film construction, its maintenance and its resistance is the result of a total complementarity between characterization from enhanced physico-chemical analysis techniques, especially those developed by P. Marcus and his group[1], and electrochemical measurements, mainly the electrochemical impedance spectroscopy (EIS).EIS gives access to the capacitive and resistive properties of the passive film. The first, complemented by the Mott-Schottky theory, allows a quantitative approach of electronic properties (semi-conductivity) and the maintenance process of passive films. The second involves the corrosion resistance of the film. Nevertheless, it is important to make a rigorous adjustment of the parameters resulting from the impedance diagrams. An adjustment that takes into account the physical meaning of parameters, especially for the analysis of the constant phase elements (CPE) used in the treatment of the diagrams that present one depressed semicircle [2]. The knowledge of the oxi-hydroxide character of the PF, evidenced from physicochemical characterizations, allows considerations of the spatial distribution of the heterogeneities (3D) within the thickness of the PF from the variation of its resistivity obtained from the Power Law Model (PLM)[3,4]. In fine, the resistivity profiles give information about interface reactivity and distribution of species along the thickness of the passive layer.The use of the PLM requires the assessment of several parameters, especially a and Q defining the CPE or the thickness of the PF, which is generally assessed by physicochemical measurements. Most of them can be determined by advanced graphical analysis of impedance diagrams[5,6]. It can then be used to guide the adjustment of the diagrams by inputting known parameters into the model.To exemplify the interdependency between physicochemical analysis and electrochemical impedance measurements, two studies illustrate the contribution of in-depth analyses of the resistivity profiles for two passive materials. That will be the opportunity to highlight which information can be drawn and finally, to propose reaction mechanism.First of all, the passivity of the Ni-20Cr alloy has been studied in different solutions[7]. In this work, the electrochemical impedance diagrams have been successively performed under applied potential in passive region. From PLM analysis, it was observed that the evolution of the resistivity at the Ni-20Cr/PF interface explains the evolution of the current density during polarization. The resistivity profiles obtained for increasing applied potentials on the passive plateau showed a decrease of the resistivity plateau at the substrate/PF interface and an increase of the resistivity at the PF/electrolyte interface, highlighting the modification of the passive film according to the anodic polarization.The second example concerns 316L stainless steel immersed in a 0.02M sodium sulphate solution and under proton irradiation[8]. It was shown that the impedance diagrams obtained before and after irradiation were almost superimposed, suggesting that the system was reversible. However, the resistivity profiles showed that under irradiation, the resistivity at the PF/electrolyte interface decreased and reached its initial value after irradiation. On the other hand, the length of the plateau at 316L/PF interface disappeared during irradiation and was reduced after irradiation by comparison with before irradiation.The case studies presented show that the advances proposed in the analysis of impedance diagrams, combined with physicochemical analyses, provide a global knowledge of passivation mechanisms. Maurice, P. Marcus, Current opinion in solid state & material science, 22 (2018) 156-167.Tribollet, V. Vivier, M.E. Orazem, in Encyclopedia of Interfacial Chemistry (2018), Ed. Elsevier, 93-107.B Hirschorn, M. E. Orazem, B. Tribollet, V. Vivier, I. Frateur, M. Musiani, Journal of the Electrochemical Society 157 (2010) C452-C457.B Hirschorn, M. E. Orazem, B. Tribollet, V. Vivier, I. Frateur, M. Musiani, Journal of the Electrochemical Society 157 (2010) C458-C463.E. Orazem, N. Pébère, B. Tribollet, Journal of the Electrochemical Society 153 (2006) B129-B136.Benoit, C. Bataillon, B. Gwinner, F. Miserque, M. E. Orazem, C. M. Sánchez-Sánchez, B. Tribollet, V. Vivier, Electrochimica Acta 201 (2016) 340-347.Zhang, B. Ter-Ovanessian, S. Marcelin, B. Normand, submitted to Electrochimica Acta.Normand, N. Bererd, P. Martinet, S. Marcelin, M. Moine, J. Ferreira, D. Baux, T. Sauvage, N. Moncoffre, submitted to Corrosion Science.

Semiconducting properties of passive films and corrosion layers on weathering steel

Anodic films were grown on Weathering Steel by potentiostatic polarization in slightly alkaline solution. The photoelectrochemical results reveal that they are n-type iron oxide with Eg = 2.0 eV. Rust layer grown by atmospheric corrosion are n-type semiconductors with a band gap higher than that estimated for the anodic film attributed to the formation of γ-lepidocrocite. The electrochemical impedance spectra allow to evidence that rust layers have a higher conductivity with respect to anodic films due to the presence of highly doped iron oxide layers. The use of Mott-Schottky theory to model the dependence of oxide capacitance as function of potential is critically discussed.

Characterization of the Passive Film Formed on Iron in Phosphoric Acid Solution: On the Use of a Double Modulation Technique

The interpretation of the response of an electrochemical system is usually based on the assumption that the current flowing through the electrode is the sum of two independent processes: the faradic current corresponding to the electrochemical processes and the capacitive current corresponding to the response of the interfacial capacitance. However, the separation of faradaic and capacitive currents is questionable in many different cases such as experiments performed in low-concentrated supporting electrolyte or the specific adsorption of diluted reactants. It was also shown that a charge injection to an ideal polarizable electrode results in two relaxations of the double layer corresponding to the charge neutralization on the electrode in the higher frequency domain and the charge rearrangement in the diffuse layer in a lower frequency range[1-3]. Passive layer and thin oxide films formed at a metal surface usually provide a natural protection of the metal resulting in an additional capacitive response in series with the electrical double layer. In the case of the contribution of such superficial phase, 2D- or 3D-film growth, the dielectric-like response of the interface can no longer be neglected. When these phases are kinetically involved in charge transfers, the decoupling can become particularly arbitrary. The modulation of the interfacial capacitance transfer function (MICTF) which was devised by Antaño-Lopez et al. for studying the influence of the ac and dc current on the interface capacitance [4] provides a unique way to overcome this difficulty. The MICTF provides the capacitive response of the interface at a frequency Ω when it is simultaneously scanned at a second frequency ω with the impedance spectrum. That is performed by a proper signal processing of the system response to a two- frequency, ω and Ω, composite measuring signal. It was used to study the double layer relaxation and specific adsorption of halide ions on mercury electrode [5] or to gather information on electron dynamics in TiO2 dye-sensitized solar-cells [6]. In this work, we report on the response of the oxide film formed on iron in phosphoric acid solution using this double modulation technique. A specific attention will be paid on the capacitive response of the electrode as a function of the potential so as to be able to provide a detailed analysis of both the EIS and the capacity responses with the MICTF technique compared with other data interpretation such as the Mott-Schottky theory. [1] F.C. Anson, R.F. Martin, C. Yarnitzky, Creation of nonequilibrium diffuse double layers and studies of their relaxation, J. Phys. Chem., 73 (1969) 1835-1842. [2] C. Yarnitzky, F.C. Anson, Mechanism of charging and discharging ionic double layers at electrodes, J. Phys. Chem., 74 (1970) 3123-3130. [3] S.W. Feldberg, Theory of relaxation of the diffuse double layer following coulostatic charge injection, J. Phys. Chem., 74 (1970) 87-90. [4] R. Antaño-Lopez, M. Keddam, H. Takenouti, A new experimental approach to the time-constants of electrochemical impedance: frequency response of the double layer capacitance, Electrochim. Acta, 46 (2001) 3611-3617. [5] E.R. Larios-Duran, R. Antaño-Lopez, M. Keddam, Y. Meas, H. Takenouti, V. Vivier, Dynamics of double-layer by AC Modulation of the Interfacial Capacitance and Associated Transfer Functions, Electrochim. Acta, 55 (2010) 6292-6298. [6] H. Cachet, M. Keddam, H. Takenouti, R. Antaño-Lopez, T. Stergiopoulos, P. Falaras, Capacitance probe of the electron displacement in a dye sensitized solar cell by an intermodulation technique: a quantitative model, Electrochim. Acta, 49 (2004) 2541-2549.

Valence-Mending Passivation of Si(100) Surface: Principle, Practice and Application

Surface states have hindered and degraded many semiconductor devices since the Bardeen era. Surface states originate from dangling bonds on the surface. This paper discusses a generic solution to surface states, i.e. valence-mending passivation. For the Si (100) surface, a single atomic layer of valence-mending sulfur, selenium or tellurium can terminate ~99% of the dangling bonds, while group VII fluorine or chlorine can terminate the remaining 1%. Valence-mending passivation of Si (100) has been demonstrated using CVD, MBE and solution passivation. The keys to valence-mending passivation include an atomically-clean Si (100) surface for passivation and precisely one monolayer of valence-mending atoms on the surface. The passivated surface exhibits unprecedented properties. Electronically the Schottky barrier height between various metals and valence-mended Si (100) now follows more closely the Mott-Schottky theory. With metals of extreme workfunctions, new records for low and high Schottky barriers are created on Si (100). The highest barrier so far is 1.14 eV, i.e. a larger-than-bandgap barrier, and the lowest barrier is below 0.08 eV and potentially negative. Chemically silicidation between metal and valence-mended Si (100) is suppressed up to 500 °C, and the thermally-stable record Schottky barriers enable their applications in nanoelectronic, optoelectronic and photovoltaic devices. Another application is transition metal dichalcogenides. Valence-mended Si (100) is an ideal starting surface for growth of dichalcogenides, as it provides only van der Waals bonding to the dichalcogenide.

Preparation of Nickel Tungstate (NiWO4) Nanoparticles and Characterization with Electrochemical Methods in Combination with Mott-Schottky Theory

Nickel tungstate is an interesting semiconductor for application in solar cell owing to its low band gap1, high mechanical stability and abundant oxygen sites (4 oxygen/Ni-W) for dye molecule absorption. Nanoparticle nickel tungstate has been synthesized with different methods including solid state2, direct mechanical rout3 and standard ceramic rout4. In current study nickel tungstate has been synthesized with different particle size distribution using co-precipitation5 method (N1) and in microemulsion medium in presence of cetyltrimethylammonium bromide (CTAB) as surfactant (N2). Synthesized samples were examined using XRD, TEM and DRS methods. Electrochemical impedance spectroscopy method in combination with mott-schottky theory has been applied for determination of electronic specification of all samples. Furthermore, light transformation efficiency of samples for application in solar cell has been studied using gratzel two-electrode cell. Figure 1

Quantitative investigation on the effect of hydrogenation on the performance of MnO2/H-TiO2 composite electrodes for supercapacitors

Based on the Mott–Schottky theory, the electron concentration of the as-synthesized nanostructures can be calculated by M–S plot.

The electrochemical behaviour of nanocrystalline nickel: A comparison with polycrystalline nickel under the same experimental condition

The main objective of this work was to study the effect of nanocrystalline (nc) grain size on the electrochemical behaviour of solid-state and interfacial processes in the Ni | oxide film | electrolyte system inside the potential region between hydrogen and oxygen evolutions. Nc–Ni thin films were deposited by magnetron sputtering onto alumina ceramic substrates. The study was performed in a pH 8.4 borate buffer solution by using the following in situ techniques: voltammetry, electrochemical impedance spectroscopy (EIS), and electrochemical quartz crystal nanobalance (EQCN) methods. Both the significant increase in the charge storage ability during anodic polarization inside the potential region of Ni(OH) 2 formation and a shift of the onset potential for hydrogen evolution to the positive potentials due to the small grain size and the high volume fraction of grain boundaries in comparison to polycrystalline Ni have been observed. The oxide film properties were discussed in terms of the point defect model and the Mott–Schottky theory. The passive film behaves as a p-type semiconductor.

Properties of passive film formed on 316L / 2205 stainless steel by Mott-Schottky theory and constant current polarization method

Semiconductor properties of the passive films formed on 316L and 2205 stainless steel were studied by Electrochemical Impedance Spectroscopy (EIS) in the high-temperature acetic acid. The results showed that the corrosion resistance of 2205 was higher than that of 316L, and the passive films formed on 316L and 2205 stainless steel showed p-type and n-type semiconductor behavior, respectively. Destruction and self-repairing of passive films were studied by using the constant current polarization method. The results showed that for 316L, the self-repairing process would occur when the destruction was lower than the critical extent or it would not do; for 2205, the self-repairing process only happened in a short time when the destruction was in the same extent as 316L.

Semiconductor Properties of Anodic Oxide Film Formed on Aluminum

The semiconductor properties of anodic oxide film formed on commercial pure aluminum were analyzed using Mott-Schottky theory and point defect model (PDM). The donor density, oxygen vacancy diffusion coefficient and flat-band potential were measured for the oxide films sealed by boiling water and K2Cr2O7, respectively. The results indicated that the anodic oxide films showed the n-type semiconductor property and the donor density decreased exponentially with the voltage elevating. The value of oxygen vacancy diffusion coefficient is about (1.12-5.53)×10-14 cm-2·s-1. The flat-band potential of anodic oxide film declined after sealing.

Electrochemical behaviors of TiO 2− x films synthesized by plasma-based ion implantation and deposition in fibrinogen containing PBS solution

TiO 2− x films were synthesized on carbon by plasma-based ion implantation and deposition (PBII-D). Electrochemical behaviors of the prepared films were investigated in phosphate buffer solution (PBS) and fibrinogen containing PBS solution (PBS(Fn)), to probe charge transfer phenomena between TiO 2− x film and fibrinogen. Electrochemical impedance spectroscopy (EIS) as well as simulated values of equivalent circuit units including reaction resistance and electric double layer has been obtained, indicating different charge transfer rate occurred across the interfaces. The shape of Mott-Schottky spectroscopy around the rest-open potential indicates that TiO 2− x films are typical n-type semiconductor. Donor density results calculated by Mott-Schottky theory show that TiO 2− x films exhibit higher donor density in PBS(Fn) than in PBS, indicating charge transfer from fibrinogen to TiO 2− x films, and the space charge layers bend lower.

Semiconductor electrochemistry approach to passivity and passivity breakdown of metals and metallic alloys

A critical appraisal of the use of the theory of semiconductors in characterising passive films on metals and alloys is provided, with special emphasis on the use of Mott-Schottky theory for the location of characteristic energy levels of the passive film-electrolyte junction. Some inconsistencies between theory and experimental results in the case of thin passive films are discussed together with possible alternative ways for overcoming such problems. The role of semiconducting properties in determining the pitting behaviour of passive films on W in solutions containing halide is presented and discussed. The validity of a recently proposed correlation between the solid state properties of passive films and the pitting potential is critically reviewed.

Polarization currents in varistors

The time, voltage, and temperature dependencies of transient polarization currents are reported for two types of varistors (i.e., ZnO and a SiC composite). The current transients exhibit a power-law time response to a step change in voltage (i.e., I≊I0/tm, where m is slightly less than unity) that persists over a time scale exceeding 10−8–104 s. The polarization current increases linearly with low applied voltage, but at more than a linear rate for higher voltage. The temperature dependence of the polarization current in medium voltage ZnO varistors is described by an Arrhenius plot with a change of slope near 200 K, which suggests thermal activation energies of about 160 and 10 meV. The time dependence of the polarization currents is confirmed and extended to short times by the ac admittance measured as a function of frequency. Transient changes in the ac admittance accompany the transient polarization currents, and exhibit time and temperature dependencies that reveal their close relationship to the polarization currents. By comparing transient admittance data to predictions of the Mott–Schottky theory of a barrier, it is concluded that the theory gives an inadequate account of the ac conductance, even though the voltage dependence of the capacitance is predicted well. Theoretical explanations of the polarization currents that are based upon a distribution of exponential relaxation times are examined. A reasonable account of the polarization current is provided, but the origin of the distribution is uncertain. Possible origins are a distribution of thermal activation energies or electron hopping among randomly distributed donors.

TiO 2 rectifying barriers

Measurements of the current-voltage characteristics, barrier capacitance, and distributions of the donor density within the potential barriers (as determined from the barrier capacitance) are presented for both gold-ceramic rutile rectifiers and gold-single crystal rutile rectifiers. The sample barriers have a thin insulating layer within the rectifying barrier between the gold contact and a semiconducting rutile substrate. Over a moderate range of applied voltage, the barriers on ceramic substrates follow the Mott-Schottky theory, but the forward current with large applied voltage is space-charge-limited.

Theory of Conductivity of Semiconductors

The author's older theory of conduction in polarizable media is generalized in such a way as to include rectification. An electronic component (positive holes or electrons) and an ionic component (negative or positive ions) are taken into account. The former are subjected to the boundary conditions of the MottSchottky theory, the latter to the boundary conditions of the author's theory of polarization. Significant deviations from the Mott-Schottky theory are caused by the ionic component.In Sec. I the fundamental equations are established in a general way and the boundary conditions are discussed. In the remainder of the present paper only the limiting case is treated where all impurity centers are either completely associated or completely dissociated. In Sec. II(a) the general procedure for treating the time-dependent equations is sketched, and subsequently the special case of simple ac is treated in detail. An expression for the current is obtained without the omission of any terms [Eq. (21)]; however, its evaluation requires the introduction of a simplified "zero solution." Then the complete expression for the frequency dependence of the equivalent susceptance and conductance is established (Sec. II(b)). Finally, in Sec. III, the theory is compared with the results of ac measurements performed in this laboratory on locally manufactured selenium disks. The theory explains the frequency dependence of capacitance and conductance over the range from about 2000 to 200,000 cps, if the presence of two species of ions of different mobilities is assumed. From this agreement ionic data, i.e. the concentrations of the carriers, their mobilities, diffusivities, and the thickness of the depletion layer, are derived and discussed.

Physical Principles Involved in Transistor Action

The transistor in the form described herein consists of two point-contact electrodes, called emitter and collector, placed in close proximity on the upper face of a small block of germanium. The base electrode, the third element of the triode, is a large area, low resistance contact on the lower face. Each point contact has characteristics similar to those of the high back-voltage rectifier. When suitable d.c. bias potentials are applied, the device may be used to amplify a.c. signals. A signal introduced between the emitter and base appears in amplified form between collector and base. The emitter is biased in the positive direction, which is that of easy flow. A larger negative or reverse voltage is applied to the collector. Transistor action depends on the fact that electrons in semiconductors can carry current in two different ways: by excess or conduction electrons and by defect "electrons" or holes. The germanium used is $n$-type, i.e., the carriers are conduction electrons. Current from the emitter is composed in large part of holes, i.e., of carriers of opposite sign to those normally in excess in the body of the block. The holes are attracted by the field of the collector current, so that a large part of the emitter current, introduced at low impedance, flows into the collector circuit and through a high impedance load. There is a voltage gain and a power gain of an input signal. There may be current amplification as well.The influence of the emitter current, ${I}_{e}$, on collector current, ${I}_{c}$, is expressed in terms of a current multiplication factor, $\ensuremath{\alpha}$, which gives the rate of change of ${I}_{c}$ with respect to ${I}_{e}$ at constant collector voltage. Values of $\ensuremath{\alpha}$ in typical units range from about 1 to 3. It is shown in a general way how $\ensuremath{\alpha}$ depends on bias voltages, frequency, temperature, and electrode spacing. There is an influence of collector current on emitter current in the nature of a positive feedback which under some operating conditions may lead to instability.The way the concentrations and mobilities of electrons and holes in germanium depend on impurities and on temperature is described briefly. The theory of germanium point contact rectifiers is discussed in terms of the Mott-Schottky theory. The barrier layer is such as to raise the levels of the filled band to a position close to the Fermi level at the surface, giving an inversion layer of $p$-type or defect conductivity. There is considerable evidence that the barrier layer is intrinsic and occurs at the free surface, independent of a metal contact. Potential probe tests on some surfaces indicate considerable surface conductivity which is attributed to the $p$-type layer. All surfaces tested show an excess conductivity in the vicinity of the point contact which increases with forward current and is attributed to a flow of holes into the body of the germanium, the space charge of the holes being compensated by electrons. It is shown why such a flow is to be expected for the type of barrier layer which exists in germanium, and that this flow accounts for the large currents observed in the forward direction. In the transistor, holes may flow from the emitter to the collector either in the surface layer or through the body of the germanium. Estimates are made of the field produced by the collector current, of the transit time for holes, of the space charge produced by holes flowing into the collector, and of the feedback resistance which gives the influence of collector current on emitter current. These calculations confirm the general picture given of transistor action.

Physical Principles Involved in Transistor Action*

The transitor in the form described herein consists of two-point contact electrodes, called emitter and collector, placed in close proximity on the upper face of a small block of germanium. The base electrode, the third element of the triode, is a large area low resistance contact on the lower face. Each point contact has characteristics similar to those of the high-back-voltage rectifier. When suitable d-c. bias potentials are applied, the device may be used to amplify a-c. signals. A signal introduced between the emitter and base appears in amplified form between collector and base. The emitter is biased in the positive direction, which is that of easy flow. A larger negative or reverse voltage is applied to the collector. Transistor action depends on the fact that electrons in semi-conductors can carry current in two different ways: by excess or conduction electrons and by defect “electrons” or holes. The germanium used is n-type, i.e. the carriers are conduction electrons. Current from the emitter is composed in large part of holes, i.e. of carriers of opposite sign to those normally in excess in the body of the block. The holes are attracted by the field of the collector current, so that a large part of the emitter current, introduced at low impedance, flows into the collector circuit and through a high-impedance load. There is a voltage gain and a power gain of an input signal. There may be current amplification as well. The influence of the emitter current, I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</inf> , on collector current, I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</inf> , is expressed in terms of a current multiplication factor, α, which gives the rate of change of I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</inf> with respect to I <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</inf> at constant collector voltage. Values of α in typical units range from about 1 to 3. It is shown in a general way how α depends on bias voltages, frequency, temperature, and electrode spacing. There is an influence of collector current on emitter current in the nature of a positive feedback which, under some operating conditions, may lead to instability. The way the concentrations and mobilities of electrons and holes in germanium depend on impurities and on temperature is described briefly. The theory of germanium point contact rectifiers is discussed in terms of the Mott-Schottky theory. The barrier layer is such as to raise the levels of the filled band to a position close to the Fermi level at the surface, giving an inversion layer of p-type or defect conductivity. There is considerable evidence that the barrier layer is intrinsic and occurs at the free surface, independent of a metal contact. Potential probe tests on some surfaces indicate considerable surface conductivity which is attributed to the p-type layer. All surfaces tested show an excess conductivity in the vicinity of the point contact which increases with forward current and is attributed to a flow of holes into the body of the germanium, the space charge of the holes being compensated by electrons. It is shown why such a flow is to be expected for the type of barrier layer which exists in germanium, and that this flow accounts for the large currents observed in the forward direction. In the transistor, holes may flow from the emitter to the collector either in the surface layer or through the body of the germanium. Estimates are made of the field produced by the collector current, of the transit time for holes, of the space charge produced by holes flowing into the collector, and of the feedback resistance which gives the influence of collector current on emitter current. These calculations confirm tie general picture given of transistor action.