W. Robert Thurber

The dopant density and temperature dependence of electron mobility and resistivity in n-type silicon

Abstract Traditional analysis of electron mobility in n -type silicon neglects the effect of electron-electron scattering in the mobility calculations. As a result, theory fails to conform with experiment when dopant density exceeds 2 × 10 16 cm −3 . In this work, an improved theoretical model for computing mobility and resistivity as functions of dopant density and temperature has been developed for n -type silicon. The model has been applied to phosphorus-doped silicon for dopant densities from 10 13 to 10 19 cm −3 , and temperatures between 100 and 500 K. The mobility was calculated analytically by appropriately combining lattice, ionized impurity and neutral impurity scattering contributions. The effect of electron-electron scattering was incorporated empirically for dopant densities greater than 2 × 10 16 cm −3 . Additionally, the anisotropic scattering effect was included in the mobility formulations. Resistivity measurements on seven phosphorus-doped silicon wafers with dopant densities from 1.2 × 10 14 to 2.5 × 10 18 cm −3 were carried out for temperatures from 100 to 500 K. Electron mobility at 300 K was deduced from resistivity and junction C-V measurements for dopant densities from 10 14 to 10 18 cm −3 . Agreement between theoretical calculations and experimental data for both electron mobility and resistivity of phosphorus-doped silicon was within ±7% in the range of dopant densities and temperatures studied.

An Experimental Study of Various Cross Sheet Resistor Test Structures

Newly designed cross sheet resistors are shown to give the same (within 0.5%) measured sheet resistance as conventional van der Pauw structures. Diffused boron and phosphorus layers with sheet resistances near 200 Ω/ were studied with the sampled areas varying from a square 6.4 μm (0.25 mil) on a side to a circle 762 μm (30.0 mils) in diameter. An increase in measured sheet resistance values was observed due to surface leakage currents, and an equivalent circuit model was developed to explain the results. The effect of joule heating on measured sheet resistance values was observed in both large and small cross structures.

A novel method to detect nonexponential transients in deep level transient spectroscopy

In conventional Deep Level Transient Spectroscopy (DLTS) measurements, the analysis of the results is based upon the assumption of an exponential current or capacitance transient. We present experimental and computational results on a novel experimental method for determining when the assumption of exponentiality is not satisfied by the sample under study. The measurement may be performed without any changes in the conventional double‐boxcar DLTS system.

Second indirect band gap in silicon

Abstract We report the first observation of the г 25 → L 1 (second indirect) transition in Si based on optical absorption studies. The energy, (1650 ± 10) meV, measured for this critical point shows that there remains a large discrepancy between theoretical band structure calculations and experimental results for this material.

Measurement of the resistivity of a thin square sample with a square four-probe array

Abstract Geometrical correction factors are evaluated for the measurement of the resistivity of a square conducting sample whose thickness is small compared to the probe spacing of a square four-probe array. The correction factors allow the computation of the resistivity when the probes are not on the periphery of the square sample. The solution is based on the method of images and is written in a compact, easily-evaluated form. The resistivity measurement error encountered with the square sample is presented in graphical form for use in test structure design.

A comparison of measurement techniques for determining phosphorus densities in semiconductor silicon

Phosphorus densities in semiconductor silicon slices cut from 14 single crystal ingots have been determined by two electrical and two analytical techniques. Hall effect measurements were made on specimens from all ingots, and junction capacitance-voltage measurements were made on specimens with densities up to about 5 × 1017 cm−3. Neutron activation analysis was used to measure phosphorus densities from 5 × 1015} to 5 x 1019} cm−3, and a photometric technique was used for densities greater than 1017 cm−3. A systematic discrepancy of about 15% between the photometric and neutron activation data is indicative of the interlaboratory agreement that might be realized in practice with these techniques.

Methods for accurate determination of emission rate and trap concentration with application to platinum‐doped silicon

A procedure for the analysis of junction capacitance was developed which allows one to extract accurate values of emission rate and trap concentration from isothermal transient capacitance measurements. Experiments to demonstrate the procedure were performed on silicon diodes doped with platinum. The capacitance‐ratio method of determining the emission rate was used to remove the nonexponentiality due to large trap concentration from the capacitance transients. Arrhenius plots of scaled emission rate gave activation energies of EC−EA=0.2271±0.0002 eV for the platinum acceptor level in n‐type silicon and EA−Ev=0.3215±0.0012 eV for the platinum donor level in p‐type silicon. A new method for determining the trap concentration is derived and verified by use of simulations and data. This method involves the subtraction of capacitance values obtained from two transients with the same fill voltage, but different reverse voltages. It is much simpler than methods which require iterative solutions of Poisson’s equ...

Composition and carrier-concentration dependence of the electronic structure of InyGa1−yAs1−xNx films with nitrogen mole fraction of less than 0.012

The electronic structure of Si-doped InyGa1−yAs1−xNx films on GaAs substrates, grown by nitrogen-plasma-assisted molecular-beam epitaxy, was examined by photoreflectance (PR) spectroscopy at temperatures between 20 and 300K. The films were approximately 0.5μm thick and had nitrogen mole fraction between x=0.0014 and x=0.012, measured indirectly by a secondary-ion-mass spectrometry calibration; indium mole fraction between y=0.052 and y=0.075, measured by electron-dispersive x-ray spectroscopy; and carrier concentration between 2×1016 and 1.1×1018cm−3, measured by Hall effect. Three critical-point transitions were identified by PR: the fundamental band gap (highest valence band to the lowest conduction band); the spin-orbit split valence band to the lowest conduction band; and the highest valence band to a nitrogen impurity band (above the lowest conduction band). The measured critical-point energies were described by a band anticrossing (BAC) model with the addition of a Burstein-Moss band-filling term. T...

Direct comparison of time-resolved terahertz spectroscopy and Hall Van der Pauw methods for measurement of carrier conductivity and mobility in bulk semiconductors

Charge carrier conductivity and mobility for various semiconductor wafers and crystals were measured by ultrafast above bandgap, optically excited Time-Resolved Terahertz Spectroscopy (TRTS) and Hall Van der Pauw contact methods to directly compare these approaches and validate the use of the non-contact optical approach for future materials and in-situ device analyses. Undoped and doped silicon (Si) wafers with resistances varying over six orders of magnitude were selected as model systems since contact Hall measurements are reliably made on this material. Conductivity and mobility obtained at room temperature by terahertz transmission and TRTS methods yields the sum of electron and hole mobility which agree very well with either directly measured or literature values for corresponding atomic and photo-doping densities. Careful evaluation of the optically-generated TRTS frequency-dependent conductivity also shows it is dominated by induced free-carrier absorption rather than small probe pulse phase shifts, which is commonly ascribed to changes in the complex conductivity from sample morphology and evaluation of carrier mobility by applying Drude scattering models. Thus, in this work, the real-valued, frequency-averaged conductivity was used to extract sample mobility without application of models. Examinations of germanium (Ge), gallium arsenide (GaAs), gallium phosphide (GaP) and zinc telluride (ZnTe) samples were also made to demonstrate the general applicability of the TRTS method, even for materials that do not reliably make good contacts (e.g., GaAs, GaP, ZnTe). For these cases, values for the sum of the electron and hole mobility also compare very favorably to measured or available published data.