Uncompensated Silicon Research Articles

1/f Noise Reduction in Cryogenic Highly Compensated Silicon Thermistors

The thermal sensitivity and Low Frequency Noise (LFN) of compensation doped Silicon-On-Insulator (SOI) resistors are studied experimentally, down to the cryogenic regime. A high compensation nominal ratio K = N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</sub> of 0.82 is compared with uncompensated and partially compensated configurations, using Phosphorus and Boron as dopant species. The Temperature Coefficient of Resistance (TCR) reaches -2.7%/K at 80 K, for an effective compensation ratio close to 0.98 considering incomplete dopant ionization. The measurements reveal a low LFN with a nearly frequency-independent spectrum, far from the classical 1/f trend observed in uncompensated silicon. The mean value of the Hooge constant on the highly compensated silicon sample equals 3.15 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> at 300 K and 4.50 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> at 80 K. The normalized LFN at 80 K does not depend on the resistor length and thereby seems independent of the volume. Such high performance thermistors represent an attractive, mature and affordable solution for high performance thermal sensing.

On the defect responsible for the carrier injection-induced degradation of uncompensated n-type Czochralski silicon

It is generally taken for granted that the bulk minority carrier lifetime in uncompensated phosphorus-doped silicon (Si) wafers is stable under illumination. In contradiction with this long-time belief, we report on a fast and significant lifetime degradation under light soaking for Czochralski wafers sampled from the top ingot end. We demonstrate that defect formation also proceeds during carrier injection by forward biasing Si heterojunction solar cells made from such wafers, suggesting a carrier-induced degradation rather than merely light-induced. The involved bulk defect is shown to preferentially form at the wafer center, where double Thermal Donors are in high concentration. The role of Thermal Donors is investigated further and the obtained preliminary results support their involvement in the reported carrier-induced degradation.

Carrier mobility reduction and model in n-type compensated silicon

Research on electrical properties of the compensated silicon is very crucial for understanding the doping layer and compensated substrates of solar cells. Regarding the fact that there are still inadequate experimental data of carrier mobility on the n-type compensated silicon, hence in this paper, both majority electron and minority hole mobilities measured on the n-type compensated solar-grade silicon substrates are presented. Prediction models of carrier mobility are essential for material characterization and device (e.g. solar cells) simulation. However, as prediction models of carrier mobility are commonly established based on the uncompensated silicon, large deviations of carrier mobility have been observed on the compensated silicon. In this work, the standard Klaassen’s model and optimized model for the compensated silicon by Schindler et al. are reviewed and compared to measured carrier mobilities. Moreover, the factors that lead to deviations of Klaassen’s model on the n-type compensated silicon are critically discussed, and then we propose an optimized model for prediction of carrier mobility in the compensated silicon. This model can also be extended to both majority and minority carrier mobilities in p- and n-type compensated silicon and fits well with previous published data as well as carrier mobility data presented here. In addition, evolutions of majority electron and minority hole mobilities as crystal grows are also simulated for n-type compensated Czochralski silicon which agrees well with our measured results.

N-type compensated silicon: resistivity, crystal growth, carrier lifetime, and relevant application for HIT solar cells

N-type compensated silicon shows unusual distribution of resistivity as crystal grows compared to the n-type uncompensated silicon. In this paper, evolutions of resistivities with varied concentrations of boron and varied starting resistivities of the n-type silicon are intensively calculated. Moreover, reduction of carrier mobility is taken into account by Schindler’s modified model of carrier mobility for the calculation of resistivity of the compensated silicon. As for substrates of solar cells, optimized starting resistivity and corresponding concentration of boron are suggested for better uniformity of resistivity and higher yield (fraction with ) of the n-type compensated Cz crystal rod. A two-step growth method is investigated to obtain better uniformity of resistivity of crystal rod, and this method is very practical especially for the n-type compensated silicon. Regarding the carrier lifetime, the recombination by shallow energy-level dopants is taken into account for the compensated silicon, and evolution of carrier lifetime is simulated by considering all main recombination centers which agrees well with our measured carrier lifetimes as crystal grows. The n-type compensated silicon shows a larger reduction of carrier lifetime compared to the uncompensated silicon at the beginning of crystal growth, and recombination with a oxygen-related deep defect is sufficient to describe the reduction of degraded lifetime. Finally, standard heterojunction with intrinsic thin-layer (HIT) solar cells are made with substrates from the n-type compensated silicon rod, and a high efficiency of 22.1% is obtained with a high concentration () of boron in the n-type compensated silicon feedstock. However, experimental efficiencies of HIT solar cells based on the n-type compensated silicon show an average reduction of 4% along with the crystal length compared to the uncompensated silicon. The obtained results enrich our knowledge on the n-type compensated silicon and contribute to the development of n-type compensated silicon-based solar cells for commercial application.

A Unified Parameterization of the Formation of Boron Oxygen Defects and their Electrical Activity

The magnitude of light-induced degradation of solar cells based on Czochralski grown silicon strongly depends on material properties. We have performed experiments to describe the activation and recombination activity of boron oxygen defects in boron compensated n-type silicon. Compensated n-type material enables flexible assessment of charge carrier influences on the defect that cannot be distinguished on p-type material. The results can be generalized to p-type material and thus provide valuable insights to the defect. Our measurements demonstrate the two-level defect nature of the slow-formed boron oxygen defect component and allow the study of the dopant dependency of the defect concentrations. Our findings strongly support a revision of the existing model of the defect composition.Based on the experimental results and literature data we have created a parameterization of the lifetime limitation in silicon due to BO defects. Established findings from literature for uncompensated p-type silicon are taken into account and ensure general validity. The parameterization is useful to discuss BO defect influences and can serve to predict material properties after LID.

Effect of Dopant Compensation on the Behavior of Dissolved Iron and Iron-Boron Related Complexes in Silicon

The behavior of iron, iron-boron (FeB) pairs, and iron-boron-phosphorus (FeB-P) complexes has been studied in B-doped Czochralski silicon with phosphorus (P) compensation and compared with that in uncompensated material. The interstitial iron concentration has been measured at temperatures from 50 to 270°C. The apparent binding energy (Eb) of FeB in compensated silicon is (0.25 ± 0.03) eV, significantly lower than the (0.53 ± 0.02) eV in uncompensated silicon. Possible reasons for this reduction in binding energy are discussed by experimental and calculation methods. The results are important for understanding and controlling the behavior of Fe in compensated silicon.

Towards a unified low-field model for carrier mobilities in crystalline silicon

The electrical properties of crystalline silicon crucially depend on the mobility of minority and majority charge carriers. As parameters like the conductivity and the diffusion length are directly connected to carrier mobility, its exact prediction is essential for device simulation and material characterization. While generally accepted mobility models exist for uncompensated silicon, strong deviations have been observed in compensated silicon depending on the compensation level. Different approaches have been suggested for modeling majority carrier mobility correcting for compensation. In this work, the controversially discussed physical reasons for mobility reductions in compensated silicon are critically reviewed and we present a unified description of mobility in silicon. Based on the approach suggested by Schindler et al. [Solar Energy Materials and Solar Cells 106 (2012) 31–36], which describes the modeling of majority carrier mobilities in p-type compensated silicon at room temperature, the model is extended to both majority and minority carrier mobilities in p- and n-type compensated silicon at room temperature and a description for the temperature dependence is suggested. Fit parameters are obtained based on a wide range of published and new carrier mobility data presented here. Additionally, a new parameterization for scattering of holes by phonons is presented and included in the model.

Turnover Temperature Point in Extensional-Mode Highly Doped Silicon Microresonators

This paper demonstrates the existence of a local zero temperature coefficient of frequency (i.e., turnover point) in extensional-mode silicon microresonators, fabricated on highly n-type-doped substrates and aligned to the [100] crystalline orientation. It is shown through both theoretical analysis and finite-element simulation that the turnover point in thin-film piezoelectric-on-silicon (TPoS) resonators is a function of doping concentration and orientation. Moreover, the turnover point can be adjusted by changing the thickness ratio of Si and the piezoelectric film (e.g., AlN) in the resonant structure. In order to experimentally validate this result, similar resonators are fabricated on silicon-on-insulator substrates, and the temperature variation of frequency is measured. An overall temperature-induced frequency variation of less than 245 ppm is measured over the range of -40 °C-85 °C for an ~ 25-MHz TPoS resonator aligned to the [100] plane. This is more than a 15-times reduction with respect to the uncompensated conventional silicon resonators reported before. This work is a significant step toward strengthening silicon's position as an alternative resonator technology in the quartz-dominated stable oscillator market.

Modeling majority carrier mobility in compensated crystalline silicon for solar cells

Carrier mobility in silicon plays a crucial role for photovoltaic applications. While the influence of doping on mobility in standard monocrystalline silicon is well understood, recent research has been focused on the effects of crystal defects in multicrystalline (mc) silicon and of the presence of both acceptors and donors in compensated silicon, both introducing additional scattering centers influencing carrier mobility. In this work measurements of the majority carrier mobility have been carried out in two blocks of compensated multicrystalline silicon. Confirming existing results we come to the conclusion that with increasing compensation level mobilities may be significantly lower than predicted by Klaassen's mobility model, which is basically suited for the description of mobilities in compensated silicon as it accounts for scattering on both acceptors and donors. However, as this model is based on mobility data from uncompensated silicon, a compensation-related reduction of screening is not taken into account sufficiently. To describe mobilities in compensated silicon, a modification of Klaassen's mobility model based on published mobility data in compensated silicon is suggested.

Hard breakdown mechanisms of compensated p-type and n-type single-crystalline silicon solar cells

The hard breakdown behaviors of boron–phosphorus compensated p-type and n-type Czochralski silicon solar cells were studied as functions of the type of conductivity, the net doping concentration and the temperature. We showed as expected from previous studies that the hard breakdown was governed by avalanche mechanisms (impact ionization) and that for a given net doping concentration the hard breakdown voltage was almost the same for both p-type and n-type solar cells, despite the different reported values for the electron and hole impact ionization coefficients. The studied compensated materials offered the opportunity to determine the hard breakdown voltages for samples with the same net doping concentration but different total amount of doping species. However no major effects of the dopant compensation were observed, the experimental data being described by the empirical expressions used for uncompensated silicon samples.

Impact of incomplete ionization of dopants on the electrical properties of compensated p-type silicon

This paper investigates the importance of incomplete ionization of dopants in compensated p-type Si and its impact on the majority-carrier density and mobility and thus on the resistivity. Both theoretical calculations and temperature-dependent Hall-effect measurements demonstrate that the carrier density is more strongly affected by incomplete ionization in compensated Si than in uncompensated Si with the same net doping. The previously suggested existence of a compensation-specific scattering mechanism to explain the reduction of mobility in compensated Si is shown not to be consistent with the T-dependence of the measured carrier mobility. The experiment also shows that, in the vicinity of 300 K, the resistivity of compensated Si has a much weaker dependence on temperature than that of uncompensated silicon.

Light-induced degradation in compensated p- and n-type Czochralski silicon wafers

Light-induced degradation (LID) due to boron-oxygen complex formation seriously diminishes the minority carrier lifetime of p-type Czochralski-grown (Cz) wafers. Depending linearly on the boron concentration NA in uncompensated silicon, the boron-oxygen defect density was suggested to depend on the net doping concentration p0 = NA − ND in compensated p-type samples, containing similar amounts of boron and phosphorus [D. Macdonald, F. Rougieux, A. Cuevas, et al., Journal of Applied Physics 105, 093704 (2009)]. However, this dependency contradicts observations of LID in compensated n-type silicon wafers [T. Schutz-Kuchly, J. Veirman, S. Dubois, et al., Applied Physics Letters 96, 1 (2010)], which are confirmed in this study by investigating the boron-oxygen complex formation on a large variety of compensated p- and n-type samples. In spite of their high boron content, compensated n-type samples may show a less pronounced LID than p-type samples containing less boron. Our experiments indicate that in compensated silicon, the defect concentration is only a function of the compensation ratio RC = (NA + ND)/(NA – ND).

Silicon Resonator Based 3.2 $\mu$W Real Time Clock With $\pm$10 ppm Frequency Accuracy

This paper presents an ultra-low power generic compensation scheme that is used to implement a real time clock based on an AlN-driven 1 MHz uncompensated silicon resonator achieving 3.2 μW power dissipation at 1 V and ±10 ppm frequency accuracy over a 0-50°C temperature range. It relies on the combination of fractional division and frequency interpolation for coarse and fine tuning respectively. By proper calibration and application of temperature dependent corrections, any frequency below that of the uncompensated resonator can be generated yielding programmability, resonator fabrication tolerances and temperature drift compensation without requiring a PLL. To minimize the IC area, a dual oscillator temperature measurement concept based on a ring oscillator/resistor thermal sensor was implemented yielding a resolution of 0.04°C. The IC was fabricated on a 0.18 μm 1P6M CMOS technology.

Dynamic calibration technique for thermal shear-stress sensors with mean flow

This paper presents the development of a dynamic calibration technique for thermal shear-stress sensors using acoustic plane wave excitation. The technique permits the independent variation in the mean and fluctuating shear stresses. The theoretical development and the practical implementation of the technique are presented. The studied configuration has the capability to dynamically calibrate shear-stress sensors up to 20 kHz. An illustrative application of this technique to an uncompensated silicon micromachined thermal shear-stress sensor operated in constant current mode is discussed. Specifically, the sensor has been statically calibrated over a range of wall shear stress from 7 to 80 mPa. A dynamic calibration of the sensor over a range of 2–12 mPa has been performed up to 7 kHz.

Conductivity via impurities in low‐doped uncompensated silicon

AbstractIt was found that in low‐doped silicon crystals (2 × 1016 &lt; N &lt; 1017 cm–3) with compensation rate decrease (10–5 &lt; K &lt; 10–2) the experimental results differ from the theoretical ones. At low electric fields (E) this concerns the values of the activation energy (ε3) and the dependence of ε3 on N and K. The results are explained by the influence of neutral impurity interaction on the density of states. With increasing E a previously unknown conductivity (σM) appears. The dependence of σM on N, K, E, magnetic field (H), and temperature (T) is quite different from the dependence that is usual for σ3 conductivity. The results are explained by the appearance of conductivity via H?‐like states of impurities, which are concentrated in the vicinity of edge dislocations.

Electrodynamics of a Coulomb glass in n-type silicon.

Measurements of the complex frequency dependent conductivity of uncompensated n-type silicon are reported. The experiments are done in the quantum limit, variant Planck's over 2pi omega>k(B)T, across a broad doping range on the insulating side of the metal-insulator transition. The low energy linear frequency dependence is consistent with theories of a Coulomb glass, but discrepancies exist in the relative magnitudes of the complex components. At higher energies we observe a crossover to a quadratic frequency dependence that is sharper than expected. The concentration dependence gives evidence that the Coulomb interaction energy is the energy scale that determines this crossover.

Magnetic field effects on the nonohmic impurity conduction of uncompensated crystalline silicon

The impurity conduction of a series of crystalline silicon samples with the concentration of major impurity N ≈ 3 × 1016 cm−3 and with a varied, but very small, compensation K was measured as a function of the electric field E in various magnetic fields H-σ(H, E). It was found that, at K 1 (negative magnetoresistance). With increasing E, these inequalities are simultaneously reversed (positive nonohmicity and positive magnetoresistance). It is suggested that both negative and positive nonohmicities are due to electron transitions in electric fields from impurity ground states to states in the Mott-Hubbard gap.

Hysteresis of conduction via impurities in uncompensated crystalline silicon in strong crossed electric and magnetic fields

It was observed that in uncompensated silicon in sufficiently strong crossed electric (E) and magnetic (H) fields the conductivity σ exhibits hysteresis as a function of E with H=const and as a function of H with Econst. For the same values of E and H the conductivity can differ by a factor of 105. Weak pulses of a field E transfer the conductivity from one branch of the hysteresis loop to another. Very low-intensity background radiation radically changes the form of this loop. The results can be attributed to an insulator-metal transition stimulated in the D− band of silicon by a strong electric field.

Nature of conduction via impurities in uncompensated silicon

The static conductivity σ(E) and photoconductivity (PC) at radiation frequencies ħω=10 and 15 meV in Si doped with shallow impurities (density N=1016−6×1016 cm−3, ionization energy e1≃45 meV) with compensation K=10−4−10−5 in electric fields E=10–250 V/cm are measured at liquid-helium temperatures T. Special measures are taken to prevent the high-frequency part of the background radiation (ħω>16 meV) from striking the sample. It is found that the conductivity σ(E) is due to carrier motion along the D− band, which is filled with carriers under the influence of the field E. In fields E Eq carriers drift along localized D− states with energy e∞e1−10 meV. An explanation is proposed for the threshold behavior of the field dependence of the photo-and static conductivities.

Appearance of a band of delocalized D − states in uncompensated silicon in an electric field

The impurity photoconductivity spectra of uncompensated silicon at liquid-helium temperatures under conditions of strongly suppressed background radiation (background) are studied in different electric fields E. It is established that the delocalization arising in the D− band as E increases is not associated with any changes of the fluctuation potential and is due to the direct action of the field E. A delocalization band of finite width appears abruptly at a critical value E c (∼100 V/cm) of E. The critical field E c increases with the density of charged centers in the sample.