The thermoelectric properties of N‐type and P‐type Si‐Ge alloys have been reviewed and detailed calculations for the efficiency of a thermoelectric generator made from a 70% Si‐30% Ge alloy have been made over the temperature range from 300 to 1300 K. A model employing one valence band and two conduction bands has been used. A generator of standard material, optimally doped, and infinitely segmented will have an efficiency of 12.1% operating over this range. If the lattice thermal conductivity can be reduced to its minimum value without upsetting the electrical properties, then the efficiency can be raised to an ultimate maximum of 23.3%. A more modest increase in efficiency to 14.7% could be obtained by a 2.4 volume percent of finely dispersed second‐phase precipitates which would act as phonon scatterers. The utility/futility of GaP additions and grain‐boundary scattering as methods to increase the efficiency is discussed.

The maximum possible conversion efficiency of silicon‐germanium thermoelectric generators

Building on Part I of this paper [Altermatt et al., J. Appl. Phys. 100, 113714 (2006)], the parametrization of the density of states and of incomplete ionization (ii) is extended to arsenic- and boron-doped crystalline silicon. The amount of ii is significantly larger in Si:As than in Si:P. Boron and phosphorus cause a similar amount of ii although the boron energy level has a distinctly different behavior as a function of dopant density than the phosphorus level. This is so because the boron ground state is fourfold degenerate, while the phosphorus ground state is twofold degenerate. Finally, equations of ii are derived that are suitable for implementation in device simulators. Simulations demonstrate that ii increases the current gain of bipolar transistors by up to 25% and that it decreases the open-circuit voltage of thin-film solar cells by up to 10mV. The simulation model therefore improves the predictive capabilities of device modeling of p‐n-junction devices.

A simulation model for the density of states and for incomplete ionization in crystalline silicon. II. Investigation of Si:As and Si:B and usage in device simulation

We report a new microscale Hall effect measurement method for characterization of semiconductor thin films without need for conventional Hall effect geometries and metal contact pads We derive the electrostatic potential resulting from current flow in a conductive filamentary sheet with insulating barriers and with a magnetic field applied normal to the plane of the sheet Based on this potential, analytical expressions for the measured four-point resistance in presence of a magnetic field are derived for several simple sample geometries We show how the sheet resistance and Hall effect contributions may be separated using dual configuration measurements The method differs from conventional van der Pauw measurements since the probe pins are placed in the interior of the sample region, not just on the perimeter We experimentally verify the method by micro-four-point probe measurements on ultrashallow junctions in silicon and germanium On a cleaved silicon ultrashallow junction sample we determine carrier mobility, sheet carrier density, and sheet resistance from micro-four-point probe measurements under various experimental conditions, and show with these conditions reproducibility within less than 15%

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Micro-four-point Probe Hall effect Measurement method

As semiconductor device dimensions continue to decrease, the main challenge in the area of junction formation involves decreasing the junction depth while simultaneously decreasing the sheet resistance. Laser annealing is being investigated as an alternative to rapid thermal annealing to repair the damage from ion implantation and to activate the dopants. With this technique, uniform, box-shaped profiles are obtained, with dopant concentrations that can exceed equilibrium solubility limits at normal processing temperatures. Unfortunately, these super-saturated dopant concentrations exist in a metastable state and deactivate upon further thermal processing. In this article, we describe a comprehensive study of the deactivation kinetics of common dopants (P, B, and Sb) across a range of concentrations and annealing conditions. For comparison, As deactivation data from the literature is also presented. P and As deactivate substantially at temperatures as low as 500 °C, while Sb at moderate concentrations and B remain fully active until 700 to 800 °C. It is proposed that As and P deactivate through the formation of small dopant-defect clusters while B deactivates through precipitation. The proximity to the surface is shown to be a second-order effect.

Thermal stability of dopants in laser annealed silicon

Ultra-low energy implants were used in combination with rapid thermal anneals in the temperature range 900/spl deg/C-1050/spl deg/C to study dopant activation in silicon. First, relatively long time anneals were performed in a conventional tungsten-based RTA to investigate the activation mechanisms. The activation was monitored using Hall measurement, where the rate of electrical activation was considered by measuring the time it takes to reach 50% activation. Using Arrhenius fits, an activation energy was extracted, and it was found that while boron has a mean activation energy for electrical activation of 4.7 eV in agreement with previous studies, arsenic and phosphorus have thermal activation energies of 3.6 eV and 4.1 eV, respectively. The 4.7 eV activation energy for boron is believed to be related to a point defect driven mechanism for electrical activation. Electrical activation of arsenic and phosphorus, however, seems to be related to dopant diffusion. In the second set of experiments, an arc lamp system was utilized to perform ultra-sharp spike anneals. For both dopants, it was found that for a given temperature, there is an optimum ramp-rate that produces the desired dopant activation and junction depth.

A comparative study of dopant activation in boron, BF/sub 2/, arsenic, and phosphorus implanted silicon

The relationship between the Hall mobility and the hole concentration in p-type silicon were experimentally investigated. Boron and gallium were used as dopants; their doping was done by either the ion implantation or the diffusion technique. It was found that the relationships for boron-doped specimens and for gallium-doped specimens for the heavily doped range are considerably different from each other. Both of these relationships are also different from the so-called Irvin curve which is well known as a standard relationship between the mobility of carriers and the impurity concentration, but the relationship for boron doping is almost consistent with that of Thurber et al., if the Hall mobility factor is reasonably taken into account.

K. Itoh

Papers

A new experimental determination of the relationship between the Hall mobility and the hole concentration in heavily doped p-type silicon