The dopant density and temperature dependence of hole mobility and resistivity in boron doped silicon

Theoretical expressions for computing resistivity and conductivity mobility of holes as functions of dopant density and temperature have been derived for boron-doped silicon. The model is applicable for dopant densities from 10¹³ to 3 × 10¹⁸ cm^?3 and temperatures between 100 and 400 K.Using a 3-band [i.e. heavy-hole, light-hole and the spin-orbit splitting (SO) band] model, the hole mobility was calculated by properly combining the contributions from scattering by lattice phonons, ionized impurities and neutral impurities. In addition, the effects of hole-hole (h-h) scattering and nonparabolicity of valence bands were taken into account in the mobility formulation.To verify our theoretical calculations, resistivity measurements on nine boron-doped silicon slices with dopant densities from 4.5 × 10¹⁴ to 3.2 × 10¹⁸ cm^?3 were performed for 100 ≤ T ≤ 400 K, using planar square-array test structure. Agreement between our calculated and measured resistivity values was within 6 percent over the entire range of dopant density and temperature studied here. Excellent agreement (within ±5%) between our calculated hole mobility values and those of Wagner [9] was obtained for N_A ≤ 10¹⁷ cm^?3 for boron-doped silicon, while discrepancies were found for boron densities greater than 10¹⁷ cm^?3. This discrepancy is attributed to neglecting the effect of deionization of boron impurities at higher dopant densities by Wagner (i.e. assuming hole density is equal to the total boron density).     

Mobility of majority carriers in doped noncompensated silicon

A unique theoretical model of mobility calculation of majority carriers in n-type doped noncompensated silicon at T = 300 K is given. Starting with the Fermi statistics and spherical but non-parabolic equienergetic surfaces, a procedure to calculate mobility is proposed which allows to take complex dependence between the density of states and energy in heavily doped semiconductors under consideration. The following types of scattering are observed; scattering by ionized impurities, acoustic-mode scattering and intervalley scattering. Besides, electron-electron scattering influence is also taken under consideration. Based on the suggested model the calculation of mobility in a phosphorous doped silicon in the impurity concentration range from 10¹⁵ to 10²⁰ cm^?3, and the comparison with the experiment were done.     

Effects of Rapid Thermal Annealing on Electrical Transport in Heavily Doped ZnO Thin Films Deposited at Different Substrate Temperatures

In this work, heavily doped ZnO thin films with carrier concentrations of 1.7 × 10²⁰–1.1 × 10²¹ cm^?3 were prepared on glass substrates using direct current magnetron sputtering combined with rapid thermal annealing (RTA). The effects of RTA on the electrical transport properties of the thin films were investigated. Results showed that the resistivities of the thin films deposited at low temperatures were markedly improved due to the increased mobilities and/or carrier concentrations. Temperature-dependent Hall measurements and theoretical calculations suggested that the influence of grain boundary scattering was negligible for all the samples and the mobility was mainly determined by ionized impurity scattering. The influence of crystallographic defects on the mobility could be effectively reduced via RTA when the carrier concentration was above 4.0 × 10²⁰ cm^?3, resulting in a mobility and resistivity close to the ionized impurity scattering theoretical estimation. The highest mobility of 46 cm² V^?1 s^?1 at the resistivity of 2.8 × 10^?4 Ω cm and the lowest resistivity of 2.6 × 10^?4 Ω cm were achieved for the RTA-treated 1 wt.% Al-doped ZnO and 5 wt.% Ga-doped ZnO thin films, respectively.     

Temperature dependence of resistivity and hole conductivity mobility in p-type silicon

A new method is employed to determine the temperature dependence of the resistivity and hole conductivity mobility of p-type silicon. This method involves the use of an aluminum-on-p-Si ohmic diode and a magnesium on p-Si Schottky barrier diode on the same silicon chip. The resistivity is determined from the Al/p-Si ohmic diode. The hole concentration is evaluated from the C-V data of the Mg/p-Si Schottky barrier diode. The conductivity mobility is then computed from the resistivity and hole concentration data. The following ranges are covered: 77–300 K, 0.4–100 ohm-cm and 5 × 10¹⁶?2 × 10¹⁴ holes/cm³ at room temperature.     

The mechanisms of hole scattering in p-Hg0.8Cd0.2Te crystals at low temperatures

The resistivity and Hall effect were investigated in p-Hg_0.8Cd_0.2Te crystals that contained from 1.5×10¹⁵ to 1.7×10¹⁸ cm^?3 Cu atoms. The measurements were carried out in the temperature range of 4.2–100 K. It is demonstrated that, in order to correctly determine the Hall mobility of holes at low temperatures, one should exclude the contribution of hopping charge transfer. It was found that heavy holes are scattered at 77 K by each other, by impurity ions, by composition fluctuations, and by lattice vibrations. In compensated crystals, holes are scattered only by lattice vibrations at low temperatures. For uncompensated crystals, when calculating the mobility, it is necessary to make allowance for the hole scattering by positively charged centers formed due to trapping of excess holes by acceptors.     

The effects of incomplete annealing on the temperature dependence of sheet resistance and gage factor in aluminum and phosphorus implanted silicon on sapphire

The temperature coefficient of resistivity (TCR) of ion implanted silicon can be significantly reduced by partially annealing the crystal damage produced during implantation. The extent to which this method can be used to temperature compensate the resistivity and the gage factor has been determined for 300 ohm-cm silicon on sapphire implanted with either 100 keV Al²⁷ or P³¹ ions. The implantations were made at room temperature parallel to the 〈100〉 axis and in four fluences ranging from 1 × 10¹³cm^?2 to 1·25 × 10¹⁵ cm^?2. Sheet resistance, Hall coefficient, and effective mobility were measured from ?150°C to 150°C for various anneal temperatures. It was possible to obtain very low temperature dependences of sheet resistance at 300°K for all dopant fluences by appropriate partial annealing. On samples having the lowest temperature dependence of sheet resistance, the gage factor was measured from ?75°C to 75°C. The measurements were made along the 〈100〉 direction for phosphorus doped samples, and along the 〈110〉 direction for aluminum doped samples for all four fluences. The gage factor and its temperature dependence for these crystal orientations are not drastically affected by the crystal damage. These results are interpreted in terms of a model previously developed to explain the effect of electron damage on the temperature dependence of the resistivity and the piezoresistance of silicon.     

Edge-photoluminescence concentration dependence in semi-insulating undoped GaAs

Dependences of the spectral peak position of edge photoluminescence, its half-width, resistivity, charge carrier mobility in crystals of semi-insulating undoped GaAs on the carbon concentration N _C at 77 K (3.0×10¹⁵ cm^?3≤N _C≤4.3×10¹⁶ cm^?3) were studied. The dependences observed are explained by the interaction of charge carriers with ionized impurity atoms and with structural defects.     

Theoretical analysis of hall factor and hall mobility in p-type silicon

Using a two-band (i.e. heavy-hole and light-hole band) model and the relaxation time approximation, the Hall factor was calculated for the case of silicon doped with boron. Contributions from scattering by acoustical and optical phonons and by ionized and neutral impurities were considered. In addition, the effects of hole-hole scattering, as well as valence band nonparabolicity and anistropy were also taken into account. The scattering and anistropy factors were separately evaluated to emphasize their individual contributions to the Hall factor. Theoretical values of the Hall factor at 300 K vary between 0.882 and 0.714 over the dopant density ranges 10¹⁴ ≦ N_A ≦ 3 × 10¹⁸ cm^?3. Hall mobilities for p-type silicon were calculated and compared with published data 100 ≤ T ≤ 400 K and 10¹⁴ ≦ N_A ≦ 3 × 10¹⁸ cm^?3. The present model is limited to the case of uncompensated material and for the weak field in which μ_HB ? 1.     

Microwave Annealing of High Dose Al<Superscript>+</Superscript>-implanted 4H-SiC: Towards Device Fabrication

High-purity semi-insulating 8° off-axis 〈0001〉 4H-SiC was implanted with Al⁺ at different doses and energies to obtain a dopant concentration in the range of 5 × 10¹⁹–5 × 10²⁰ cm^?3. A custom-made microwave heating system was employed for post-implantation annealing at 2,000 °C for 30 s. Sheet resistance and Hall-effect measurements were performed in the temperature range of 150–700 K. At room temperature, for the highest Al concentration, a minimum resistivity of 3 × 10^?2 Ω cm was obtained, whereas for the lowest Al concentration, the measured resistivity value was 4 × 10^?1 Ω cm. The onset of impurity band conduction was observed at around room temperature for the samples implanted with Al concentrations ≥3 × 10²⁰ cm^?3. Vertical p ⁺-i-n diodes whose anodes were made by 1.5 × 10²⁰ cm^?3 Al⁺ implantation and 2,000 °C/30 s microwave annealing showed exponential forward current–voltage characteristics with two different ideality factors under low current injection. A crossover point of the temperature coefficient of the diode resistance, from negative to positive values, was observed when the forward current entered the ohmic regime.     

Electrical properties of uncontaminated PbTe films on mica substrates prepared by molecular beam deposition

Uncontaminated PbTe films were prepared by molecular beam deposition under clean conditions in a uhv environment and the film properties were measured in situ. The carrier concentration was found to be determined by source conditions and values between 10¹⁶ cm^?3 (intrinsic level) and n = 5 × 10¹⁸cm^?3 could be obtained in a controllable manner. A low temperature anneal enabled bulk value Hall mobilities (1750 cm² V^?1 sec^?1 at 300 K) to be obtained at room temperature and above which indicated that surface scattering in the films was predominantly specular. The mobility at low temperatures (down to 100 K) was limited by small potential barriers located at the double-positioned grain boundaries which were present in the film. Field effect measurements indicated the potential barriers arose from a continuous distribution of band gap states situated in the grain boundaries. These states had a fairly uniform density (? 10¹²cm^?2 (kT)^?1) but there was some increase towards the conduction band edge. They also limited the field effect mobility (μ_FE) to ?0.5 bulk value, giving μ_FE ? 800cm² (volt sec)^?1 for films with carr concentrations above 5 × 10¹⁷ cm^?3. By exposure to low pressures of oxygen the carrier concentrations in annealed n-type films could be reduced to near intrinsic values with no associated degradation in the electrical properties. This indicated that the films were not compensated with the native p-type defect.     

Mobility of holes in p-type silicon determined by the self-consistent method

The mobility of majority carriers is calculated in p-type silicon in the impurity concentration range from 10¹⁶ to 10²⁰ cm^?3. Taking into account the complexity of the band structure of holes and using the self-consistent model development earlier for electrons, the value of the Fermi energy and the screening length is determined. The following scattering types are considered: scattering by acoustical phonons, scattering by non-polar optical phonon and scattering by ionized impurities. The influence of interband transition of heavy and light holes on the total relaxation time is analysed. It is shown that it does not lead to essential changes in mobility. The obtained results are compared with experimental results and satisfactory agreement is found.     

The role of intercarrier scattering in excited silicon

We have used laser and electron-beam excitation to investigate the influence of intercarrier scattering upon several properties of high-purity silicon, viz. the drift and Hall mobilities, the ambiopolar diffusion coefficient, the optical absorption cross section (at 10.6 μm) and Verdet coefficient (at 1.06 μm), covering the carrier density range n = 10¹⁵ ? 4 · 10¹⁸ cm^?3. The mobility data obtained are in accordance with theoretical models that take both lattice scattering and electron-hole (e-h) scattering into account as the main scattering mechanisms. In the region above n ≈ 10¹⁷ cm^?3 the additional effects of electron-electron and hole-hole scattering must be considered as well. For the other parameters studied, however, lattice scattering alone is found to be quite dominant. Finally, the Caughey-Thomas formula for the mobilities in doped silicon has been modified to be applicable to the present case of a light-induced e-h plasma.     

Iodine Doping of CdTe and CdMgTe for Photovoltaic Applications

Iodine-doped CdTe and Cd_1?x Mg _x Te layers were grown by molecular beam epitaxy. Secondary ion mass spectrometry characterization was used to measure dopant concentration, while Hall measurement was used for determining carrier concentration. Photoluminescence intensity and time-resolved photoluminescence techniques were used for optical characterization. Maximum n-type carrier concentrations of 7.4 × 10¹⁸ cm^?3 for CdTe and 3 × 10¹⁷ cm^?3 for Cd_0.65Mg_0.35Te were achieved. Studies suggest that electrically active doping with iodine is limited with dopant concentration much above these values. Dopant activation of about 80% was observed in most of the CdTe samples. The estimated activation energy is about 6 meV for CdTe and the value for Cd_0.65Mg_0.35Te is about 58 meV. Iodine-doped samples exhibit long lifetimes with no evidence of photoluminescence degradation with doping as high as 2 × 10¹⁸ cm^?3, while indium shows substantial non-radiative recombination at carrier concentrations above 5 × 10¹⁶ cm^?3. Iodine was shown to be thermally stable in CdTe at temperatures up to 600°C. Results suggest iodine may be a preferred n-type dopant compared to indium in achieving heavily doped n-type CdTe.     

Methods for the doping of silicon layers in growth by sublimation MBE

Epitaxial layers doped with various impurities were grown by sublimation MBE on Si (100) substrates. Doping with phosphorus was controlled at electron densities ranging from 2×10¹³ to 10¹⁹ cm^?3. A high dopant concentration of ～10²⁰ cm^?3 was obtained from the evaporation of partly molten Si sources. It shown that the type and concentration of an impurity in the sublimation MBE process can be controlled by the fabrication of multilayer p ⁺?n ⁺ structures.     

The electrical properties of zinc diffused indium phosphide

The electrical properties of p-type layers of InP, formed by the diffusion of zinc into n-type material, are studied. A wide range of diffusion conditions are used and both homogeneously doped specimens and those containing a zinc atom concentration gradient are produced. The impurity atom distribution of the diffused crystals is characterised by radiotracer analysis. p?n junction measurements on non-homogeneously doped specimens indicate that the number of zinc atoms in a diffused layer is much greater than the number of shallow acceptors. This non-correspondence of atom and carrier concentrations is confirmed by four point resistivity, Hall effect and capacitance-voltage measurements. The first two of these techniques are used to produce carrier concentration profiles which are compared with corresponding radio-tracer profiles. The carrier profiles are achieved by both serial sectioning and multiple specimen techniques. A gold probe point contacting procedure is developed for the Hall Effect measurements from which a plot of carrier mobility versus carrier concentration, in the range 5 × 10¹⁸ – 5 × 10¹⁹cm^?3, is produced for p-type InP.     

Small-signal analysis of punch-through injection microwave devices

A theoretical small-signal analysis of punch-through injection microwave devices is given. A numerical study of a silicon p⁺?n?p⁺ structure is performed, which shows good agreement with experimental measurements by Snapp and Weissglas for a diode with a doping density of 1·2 × 10¹⁵/cm³. Negative resistance is also calculated for diodes with doping densities of 0·6 × 10¹⁵/cm³ and 5 × 10¹⁵/cm³. A partially analytical mode, including the lowfield region, is developed and compared with the numerical calculation. Ohmic losses for devices with low impurity concentrations and diffusion for devices with high impurity concentrations are shown to be significant factors.The noise spectrum is calculated numerically from the assumption of two noise sources, injection noise and diffusion noise. The noise measure is determined and shown to be in good agreement with experiments by Björkman and Snapp.     

Characterization of <Emphasis Type="Italic">n</Emphasis>-Type and <Emphasis Type="Italic">p</Emphasis>-Type Long-Wave InAs/InAsSb Superlattices

The influence of dopant concentration on both in-plane mobility and minority carrier lifetime in long-wave infrared InAs/InAsSb superlattices (SLs) was investigated. Unintentially doped (n-type) and various concentrations of Be-doped (p-type) SLs were characterized using variable-field Hall and photoconductive decay techniques. Minority carrier lifetimes in p-type InAs/InAsSb SLs are observed to decrease with increasing carrier concentration, with the longest lifetime at 77 K determined to be 437 ns, corresponding to a measured carrier concentration of p ₀ = 4.1 × 10¹⁵ cm^?3. Variable-field Hall technique enabled the extraction of in-plane hole, electron, and surface electron transport properties as a function of temperature. In-plane hole mobility is not observed to change with doping level and increases with reducing temperature, reaching a maximum at the lowest temperature measured of 30 K. An activation energy of the Be-dopant is determined to be 3.5 meV from Arrhenius analysis of hole concentration. Minority carrier electrons populations are suppressed at the highest Be-doping levels, but mobility and concentration values are resolved in lower-doped samples. An average surface electron conductivity of 3.54 × 10^?4 S at 30 K is determined from the analysis of p-type samples. Effects of passivation treatments on surface conductivity will be presented.     

Mechanism of local amorphization of a heavily doped Ti1 − x V x CoSb intermetallic semiconductor

Structural and electron transport characteristics of a TiCoSb intermetallic semiconductor heavily doped with the V donor impurity (dopant concentration ～9.5 × 10¹⁹ ? 1.9 × 10²¹ cm^?3, temperatures 80–380 K) have been investigated and the distribution of the electron density of states in this material has been calculated. Different occupancies have been established for Co and (Ti, V) atomic positions in the Ti_{1 ? x} V _x CoSb lattice; this difference is equivalent to introduction of two types of acceptors into the semiconductor. Suppression of the metallic conductivity in the n-type semiconductor with an increase in the donor concentration has been found, which is explained by simultaneous generation of acceptors. It is shown that the methods of numerical calculation adequately describe the physical processes if the occupancy of unit-cell positions is taken into account in construction of the Wigner-Seitz lattice. The results obtained are discussed within the model of a heavily doped and compensated Shklovskii-Efros semiconductor.     

Electrical properties of silicon layers implanted with ytterbium ions

It is ascertained that implantation of 1-MeV ytterbium ions with a dose of 10¹³ cm^?2 into silicon with subsequent annealing at temperatures of 600–1100°C gives rise to donor centers. The donor-center concentration is higher in the samples implanted additionally with oxygen ions. The results show that at least two types of donor centers are formed; these centers contain either ytterbium or oxygen impurity atoms. The dependence of electron mobility on the concentration of electrically active centers in the silicon layers implanted with the ytterbium rare-earth ions is determined in the concentration range of 7×10¹⁵–10¹⁷ cm^?3.     

The hall mobility and its relationship with persistent photoconductivity of undoped GaN

Temperature-variable Hall effect measurements have been used to investigate the electrical properties of undoped GaN, which have the electron densities on the order of mid-10¹⁶ cm⁻³ and a Hall mobility varying from <50 cm²/sV to >500 cm²/sV. We found that very strong ionized impurity scattering limits the Hall mobility of GaN. Illumination even at 77 K has very little effect on the electron density but can lead to a noticeable persistent increase of the Hall mobility. The induced persistent photoconductivity (PPC) effect is therefore related to the Hall mobility through intrinsic electrically active defects. The properties of those defects were further investigated by monitoring a transient change of resistivity after removal of illumination at different temperatures. It reveals that the recapturing process of excited electrons into illumination-neutralized defects is the mechanism responsible for the PPC effect of undoped GaN.