Murray A. Lampert

Use of a Schottky barrier to measure impact ionization coefficients in semiconductors

Abstract The use of a Schottky barrier to determine the impact ionization coefficients of electrons and holes in semiconductors has been studied analytically and also evaluated experimentally by comparing the results for silicon with those already available in the literature. The Schottky barrier offers several advantages over a diffused p-n junction in such measurements. Pure electron initiation and pure hole initiation can be separately achieved. The abrupt barrier provides an accurately known electric field, and the linearity of the field distribution simplifies the problem of extracting the ionization coefficients from the multiplication data. We present a general solution of the charge multiplication equation and derive expressions for the ionization coefficients for the particularly simple conditions that can be achieved in a Schottky-barrier junction. Our results for silicon in the range 2 × 105 α = α ∞ exp ( −b n E ) for electrons and β = β ∞ exp ( −b p E ) for holes, with α∞ = 9·2 × 105 cm−1, β∞ = 2·4 × 105 cm−1, bn = 1·45 × 106 V/cm and bb = 1·64 × 106 V/cm.

Model for the bleaching of WO3 electrochromic films by an electric field

Measurements have been made of the current flow in amorphous WO3 films containing electrons and mobile cations. In a configuration in which electrons are extracted at one contact and cations at the other, the current decays as t−3/4 over many decades of time. By using space‐charge current flow ideas, we develop a theory that gives the correct time dependence and magnitude of the current for this double‐extraction phenomenon.

High‐field transport in SiO2 on silicon induced by corona charging of the unmetallized surface

A study has been made of high‐field electronic transport in thermally grown SiO2 in which the injection and transport of carriers were induced by charging the exposed surface of the insulator with ions extracted from a corona discharge. This technique totally avoids destructive breakdown through weak spots in the insulator. Auxiliary developments included a comparison technique for measuring the steady‐state potential difference across the unmetallized insulator and a p‐n junction method for determining the sign of the principal charge carrier in the oxide. Using a corona discharge in dry air, breakdown fields of approximately 6.5 and 13.5 MV/cm were obtained for charging with positive and negative ions, respectively. Electrons were identified as the current carriers for both polarities of applied field. Measurements of the discharge of the samples, made with a Kelvin probe, yield results that are consistent with Fowler‐Nordheim tunneling of electrons from the silicon into the oxide, with an electron effe...

Hydrogenation and dehydrogenation of amorphous and crystalline silicon

The dehydrogenation of amorphous silicon leaves dangling bonds which can be rehydrogenated by exposure to atomic H, but not to undissociated H2. The hydrogenation of dangling bonds in crystalline Si was monitored via the I (V) characteristics of a p‐n junction.

Determination of the sign of carrier transported across SiO2 films on Si

A technique has been developed for determination of the sign of charge carrier transported across an insulating film on a semiconductor substrate, utilizing the charge‐carrier separation properties of a shallow p‐n junction diffused into the semiconductor. For thermally grown SiO2, unmetallized and contacted by a corona discharge in dry air, electrons are found to carry the current for both polarities of surface potential. Also demonstrated is electron‐hole pair production in the Si by electrons entering from the oxide.

Simplified Theory of One‐Carrier Currents with Field‐Dependent Mobilities

A general method is presented for the calculation of steady‐state, one‐carrier currents in nonmetallic solids where the mobility is field dependent. The analysis includes the effects of space charge and trapping. The essential mathematical step is the representation of the electric‐field intensity as a polynomial in the drift velocity. Detailed applications are made to semiconductor and insulator problems. A new mobility function of convenient mathematical form is proposed for the case that the carrier has a constant mean free path. Some very general properties of the current flow are established by geometric analysis.

Theory of One‐Carrier, Space‐Charge‐Limited Currents Including Diffusion and Trapping

The theoretical problem of one‐carrier, space‐charge‐limited current flow is beyond the reach of analytical solutions when trapping and diffusion are included in the analysis. Nonetheless, the problem for the semiinfinite solid very generally lends itself to rather simple numerical solution on a digital computer. An interesting feature of the machine solution is that it is based on a universal geometric property of the one dimensional, planar current flow. Detailed solutions are obtained for several special cases of the trap‐filled insulator problem which plays a fundamental role in the space‐charge‐limited current measurement of trap densities in insulators. A comparison of these exact solutions with the analytical solutions neglecting diffusion indicates that an error of a factor of two might be made in a trap density determination for the typical case which is completely studied. A brief discussion of the problem of extending the technique to the finite solid with an anode constraint is given. Also a f...

Measurement of the steady−state potential difference across a thin insulating film in a corona discharge

A comparison method has been developed for measurement of the potential difference across a thin insulating film under steady−state charging conditions in a corona discharge. The method is based on the dynamics of charged particles (ions or electrons) when drifting under collision−dominated conditions: their trajectories follow, to a close approximation, the electrostatic field lines. The method is simple, accurate, and reliable, and it is particularly valuable where the surface potential, following cessation of charging, decays too rapidly to permit use of the conventional Kelvin probe techniques. The method has been applied successfully to the study of the electrical behavior of thermally grown SiO2 films on Si and thermoplastic materials.

Electron trapping in aluminum−implanted silicon dioxide films on silicon

Photoelectric and MOS capacitance−voltage techniques were used to study electron trapping in 1400−A dry−grown silicon dioxide films that were implanted with aluminum ions at 20 keV to a fluence of 1014 cm−2. The photoinjection of electrons into the implanted oxides resulted in the buildup of negative space charge. Data analysis indicated that all injected electrons had been trapped and that the observed transient responses of the photocurrent and flatband voltage were governed by the electric−field dependence of the photoinjected current. The negative space charge could be annealed either optically by photons of energy exceeding 4 eV or thermally at 350 °C. A 600 °C anneal for 30 min considerably reduced the concentration of electron traps. From this it is concluded that a substantial fraction of the traps were associated with displacement damage created by the ion implantation.

Second-breakdown phenomena in avalanching silicon-on-sapphire diodes

A new experimental technique, based on local temperature-induced changes in optical absorption, is used to study second breakdown in avalanching reverse-biased silicon-on-sapphire diodes. The technique allows spatial resolution down to 1 µm and temperature resolution of a few degrees Celsius. Further, used stroboscopically, the technique allows time resolution on the order of nanoseconds. The technique, in conjunction with special constant-current bias circuits and light-emission studies, has been used to elucidate the physical mechanisms underlying second breakdown in avalanching diodes. It is found that second breakdown occurs when the thermally generated leakage current becomes large enough at some localized region of the junction to quench the avalanche there. Under pulse biases, the product of the average pulse power times the square root of the delay time τD was essentially constant for τD as short as 1½ ns. However, the junction temperature at τD increased as τD decreased, and for very short τD the heating was highly nonuniform.