Majority Carrier Density Research Articles

A Quasi-One-Dimensional Model of the Potential Barrier and Carrier Density in the Channel of Si and 4H-SiC BSITs

An original model of the potential barrier in the channel of bipolar static induction transistors (BSITs) is presented. The model allows us to evaluate the potential barrier height for an arbitrary gate topology and to accurately predict the minority and majority carrier densities at the middle of the channel for a generic gate bias. The validity of the model is verified by comparison with numerical simulations of BSIT structures reported by other authors and with original simulations carried out on silicon (Si) and silicon carbide (SiC) junction field-effect transistors.

Free-to-bound recombination in near stoichiometric Cu2ZnSnS4single crystals

Cu${}_{2}$ZnSnS${}_{4}$ single crystals prepared by the chemical vapor transport technique were investigated by x-ray diffraction, chemical microprobe analysis, and Raman and photoluminescence spectroscopies. Single-crystal x-ray measurements show that Cu${}_{2}$ZnSnS${}_{4}$ crystallizes in the kesterite structure with the space group $I\overline{4}$ and unit cell parameters a = 5.4174(2) and c = 10.7903(7) $\AA{}$ at 150 K. Photoluminescence measurements show one broad asymmetric band peaked at 1.29 eV at low temperature. Temperature and excitation intensity dependencies of the luminescence band indicate that the transition is due to a free-to-bound recombination with an activation energy of 140 meV. We attribute this activation energy to the intrinsic acceptor-type Cu${}_{\mathrm{Zn}}$ antisite defect in close agreement with results from density-functional theory. It is shown that by a detailed analysis of the temperature dependence of the free-to-bound luminescence transition the majority carrier density can be deduced, which in our case is estimated at $\mathrm{p}\ensuremath{\approx}{10}^{16}$ cm${}^{\ensuremath{-}3}$.

Temperature‐dependent Hall‐effect measurements of p‐type multicrystalline compensated solar grade silicon

ABSTRACTIn this study, we have investigated the Hall majority carrier mobility of p‐type, compensated multicrystalline solar grade silicon (SoG‐Si) wafers for solar cells in the temperature range 70–373 K. At low temperature (~70 K) the difference in the mobilities measured for the compensated and the uncompensated reference samples is the highest, and the measured mobility shows dependence on the compensation ratio. Mobilities decrease with increasing temperature, and towards room temperature, the mobilities of the different samples are in the same range. The measurements show that, for these samples, the contribution from lattice scattering is dominating over ionized impurity scattering at room temperature. In the range of interest for silicon solar cells (above room temperature), the trend in carrier mobility is similar for all the samples, and the measured value for the sample with low compensation ratio and low doping density is comparable to the uncompensated references. A comparison of resistivity and majority carrier density measured by the Hall setup at room temperature and by four‐point probe and glow discharge mass spectroscopy, respectively, is reported as well. Copyright © 2012 John Wiley & Sons, Ltd.

3D modelling of magnetic field and light concentration effects on a bifacial silicon solar cell illuminated by its rear side

According to their installation places, the solar cells are often under the effect of the electro-magnetic field coming from outside sources as telecommunication antennas, radio antennas… These magnetic fields have a big influence on the distribution and mobility of charge carriers in the base of the solar cell and therefore on its efficiency. This work presents a tree-dimensional study of bifacial silicon solar cell under intense light concentration (more than 50 suns) and under a constant magnetic field. This approach is based on the resolution of the minority continuity equation, taking into account the distribution of the electric field in the bulk evaluated as a function of both majority and minority carrier densities. In this approach new analytical expression of carrier's density is established for rear side illumination. The effects of light concentration and magnetic field on excess minority carriers distribution, photocurrent and photovoltage in solar cell base are analysed.

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.

Local charge neutrality condition, Fermi level and majority carrier density of a semiconductor with multiple localized multi-level intrinsic/impurity defects

For semiconductors with localized intrinsic/impurity defects, intentionally doped or unintentionally incorporated, that have multiple transition energy levels among charge states, the general formulation of the local charge neutrality condition is given for the determination of the Fermi level and the majority carrier density. A graphical method is used to illustrate the solution of the problem. Relations among the transition energy levels of the multi-level defect are derived using the graphical method. Numerical examples are given for p-doping of the CdTe thin film used in solar panels and semi-insulating Si to illustrate the relevance and importance of the issues discussed in this work.

Simultaneous measurement of carrier density and mobility of organic semiconductors using capacitance techniques

We present a method to measure both the majority carrier density and mobility in organic semiconductors from the voltage and frequency dependence of capacitance ( C– V– f). Poly(3-hexylthiophene) (P3HT) is used as the prototypical material. The carrier density, and its spatial distribution in a planar device structure, is obtained from a subset of the C– V– f data by conventional capacitance–voltage analysis. We show that the validity of the carrier density extraction depends critically on the measurement frequency. Namely, one should make sure that the measurement frequency is lower than the modified dielectric relaxation frequency, which is characteristically low in organic semiconductors due to their low carrier mobility. Our method further exploits the voltage dependence of the modified dielectric relaxation frequency to measure the conductivity and carrier mobility. This mobility extraction method requires no complex fitting or simulation. Nor does it assume any particular dispersive model of mobility a priori. The carrier density, mobility, and conductivity of P3HT all increase with temperature from 250 to 300 K. The activation energies of mobility and conductivity are 0.15 ± 0.01 and 0.24 ± 0.03 eV, respectively.

Influence of microstructure and composition on hydrogenated silicon thin film properties for uncooled microbolometer applications

Doped n- and p-type hydrogenated silicon (Si:H) thin films prepared by plasma enhanced chemical vapor deposition have been investigated for uncooled microbolometer applications. The material microstructure has been studied by in situ real time spectroscopic ellipsometry collected during thin film deposition or ex situ spectroscopic ellipsometry measurements on a static sample with a multiple sample analysis technique. The key electrical properties of interest, including film resistivity (ρ), temperature coefficient of resistance (TCR), and 1/f noise, have been measured as a function of deposition conditions for p-type amorphous hydrogenated silicon (a-Si:H) films and microcrystalline content for n-type amorphous (a), microcrystalline (µc), and mixed-phase amorphous + microcrystalline (a + µc) Si:H films. The TCR and 1/f noise values were compared for p- and n-type a-Si:H samples in the resistivity range of 100 < ρ < 3000 Ω cm and show that for a given resistivity, amorphous p-type films exhibit a lower 1/f noise, which might be expected due to a larger density of majority carriers.

Approximate graphical method of solving Fermi level and majority carrier density of semiconductors with multiple donors and multiple acceptors

We present a generic approximate graphical method for determining the equilibrium Fermi level and majority carrier density of a semiconductor with multiple donors and multiple acceptors compensating each other. Simple and easy-to-follow procedures of the graphical method are described. By graphically plotting two wrapping step functions facing each other, one for the positive hole-ionized donor and one for the negative electron-ionized acceptor, we have the crossing point that renders the Fermi level and majority carrier density. Using the graphical method, new equations are derived, such as the carrier compensation proportional to NA/ND, not the widely quoted NA — ND. Visual insight is offered to view not only the result of graphic determination of Fermi level and majority carrier density but also the dominant and critical pair of donors and acceptors in compensation. The graphical method presented in this work will help to guide the design, adjustment, and improvement of the multiply doped semiconductors. Comparison of this approximate graphical method with previous work on compensation, and with some experimental results, is made. Future work in the field is proposed.

Modulation of 1.5 μm dislocation-related luminescence emitted from a direct silicon bonded interface by external bias

Interfacial dislocation networks were formed in silicon by direct bonding technology. Cathodoluminescence and deep level transient spectroscopy measurements verified that the D1 luminescence at 1.5 μm is associated with carrier transitions via a dislocation-related deep level at 0.35 eV. Both the experiment and theoretical calculations demonstrate that application of an external bias voltage on the bonding interface increases the majority carrier density at this deep level, thereby enhancing the local dislocation-related luminescence. However, beyond a critical voltage, corresponding to saturation of the majority carrier occupancy, the luminescence intensity decreases, due to the reduction in minority carrier density.

Bandgap changes in excited intrinsic (heavily doped) Si and Ge semiconductors

Our results for the bandgap changes in highly excited intrinsic (heavily doped-HD) Si (Ge) for any majority-carrier density N and temperature T have been investigated and expressed in terms of (i) the bandgap narrowing (BGN>0) due to many-body carrier–carrier interactions and screening effect on carrier-impurity (or electron–hole) potential energies, (ii) the bandgap widening (BGW<0) due to the effects of Fermi Dirac statistics, and (iii) the apparent BGN defined by ABGN≡BGN+BGW<BGN. Since those ABGN and BGN can be extracted from respective electical-and-optical measurements, this relation thus suggests a conjunction between electrical-and-optical bandgaps (EBG-and-OBG). Then, our results for BGN, ABGN, OBG, and EBG have been computed and also compared with other theoretical and experimental ones, giving rise to a satisfactory description of both electrical-and-optical data in those materials. Furthermore, in the p-type HD base of Si 1− x Ge x hetero bipolar transistors for x≤0.3, using a same assumption taken by Eberhardt and Kasper (EK) [Mater. Sci. Eng. B 89 (2002) 93–96], we have obtained the results for ABGN and EBG, which are found to be in good accordance with the respective EK-ones.

Precursors' order effect on the properties of sulfurized Cu2ZnSnS4 thin films

A dc magnetron sputtering-based method to grow high-quality Cu2ZnSnS4 (CZTS) thin films, to be used as an absorber layer in solar cells, is being developed. This method combines dc sputtering of metallic precursors with sulfurization in S vapour and with post-growth KCN treatment for removal of possible undesired Cu2−xS phases. In this work, we report the results of a study of the effects of changing the precursors' deposition order on the final CZTS films' morphological and structural properties. The effect of KCN treatment on the optical properties was also analysed through diffuse reflectance measurements. Morphological, compositional and structural analyses of the various stages of the growth have been performed using stylus profilometry, SEM/EDS analysis, XRD and Raman Spectroscopy. Diffuse reflectance studies have been done in order to estimate the band gap energy of the CZTS films. We tested two different deposition orders for the copper precursor, namely Mo/Zn/Cu/Sn and Mo/Zn/Sn/Cu. The stylus profilometry analysis shows high average surface roughness in the ranges 300–550 nm and 230–250 nm before and after KCN treatment, respectively. All XRD spectra show preferential growth orientation along (1 1 2) at 28.45°. Raman spectroscopy shows main peaks at 338 cm−1 and 287 cm−1 which are attributed to Cu2ZnSnS4. These measurements also confirm the effectiveness of KCN treatment in removing Cu2-xS phases. From the analysis of the diffuse reflectance measurements the band gap energy for both precursors' sequences is estimated to be close to 1.43 eV. The KCN-treated films show a better defined absorption edge; however, the band gap values are not significantly affected. Hot point probe measurements confirmed that CZTS had p-type semiconductor behaviour and C–V analysis was used to estimate the majority carrier density giving a value of 3.3 × 1018 cm−3.

Thermoelectric and Magnetothermoelectric Transport Measurements of Graphene

The conductance and thermoelectric power (TEP) of graphene is simultaneously measured using a microfabricated heater and thermometer electrodes. The sign of the TEP changes across the charge neutrality point as the majority carrier density switches from electron to hole. The gate dependent conductance and TEP exhibit a quantitative agreement with the semiclassical Mott relation. In the quantum Hall regime at a high magnetic field, quantized thermopower and Nernst signals are observed and are also in agreement with the generalized Mott relation, except for strong deviations near the charge neutrality point.

3D Study of Bifacial Silicon Solar Cell under Intense Light Concentration and Under External Constant Magnetic Field

This work presents a three-dimensional study of bifacial silicon solar cell under intense light concentration and under constant magnetic field. This approach is based on the resolution of the minority continuity equation, taking into account the distribution of the electric field in the bulk evaluated as a function of both majority and minority carrier densities. In this approach, new analytical expressions of diffusion length, diffusion coefficient and excess minority carrier density was established for front illumination. The effect of magnetic field on excess minority carrier generation, carriers mobility, carriers density and electric parameters profile are then analysed.

Analysis of the Space Charge Capacitance of Bipolar Semiconductor Passive Films

In this paper,the space charge capacitance of a bipolar semiconductor passive film was considered to be equivalent to a series connection of a capacitance at the passive film/solution interface and an np-junction capacitance at the outer layer film/inner layer film interface. Based on a uniform expression established in our previous work,a non-linear method was used to fit the Mott-Schottky(M-S) plots of bipolar semiconductor passive films. We then investigated the semiconductor characteristics of passive films formed on the surface of the nickel base alloy G3 after environmental corrosion at high temperatures and high partial pressures of H2S/CO2 using this method. Fitting results of measured M-S plots indicated that the majority carrier density of the p type semiconductor outer layer of the bipolar passive film obviously increased as the temperature increased while the majority carrier density of the n type semiconductor inner layer was almost unchanged. The fitting results show that the non-linear fitting method can produce multiple semiconductor characteristic parameters of the inner/outer layer of bipolar passive films. From these fitting results a mechanism for the formation and breakdown of passive films was established. A variable mechanism for the passive film structure and the role of the np-junction in the corrosion inhibition process were discussed by considering X-ray photoelectron spectroscopy(XPS) results as well.

Analysis of the Space Charge Capacitance of Bipolar Semiconductor Passive Films (II)

In this paper,the space charge capacitance of a bipolar semiconductor passive film was considered to be equivalent to a series connection of a capacitance at the passive film/solution interface and an np-junction capacitance at the outer layer film/inner layer film interface. Based on a uniform expression established in our previous work,a non-linear method was used to fit the Mott-Schottky(M-S) plots of bipolar semiconductor passive films. We then investigated the semiconductor characteristics of passive films formed on the surface of the nickel base alloy G3 after environmental corrosion at high temperatures and high partial pressures of H2S/CO2 using this method. Fitting results of measured M-S plots indicated that the majority carrier density of the p type semiconductor outer layer of the bipolar passive film obviously increased as the temperature increased while the majority carrier density of the n type semiconductor inner layer was almost unchanged. The fitting results show that the non-linear fitting method can produce multiple semiconductor characteristic parameters of the inner/outer layer of bipolar passive films. From these fitting results a mechanism for the formation and breakdown of passive films was established. A variable mechanism for the passive film structure and the role of the np-junction in the corrosion inhibition process were discussed by considering X-ray photoelectron spectroscopy(XPS) results as well.

Minority carrier lifetimes in HgCdTe alloys

We present the results of full band structure calculations of Fermi levels, intrinsic carrier densities, and one-photon absorption coefficients in undoped HgCdTe alloys. The full band structure is used in the calculation of majority and minority carrier densities and the minority carrier lifetimes limited by radiative, Auger-1, and Auger-7 mechanisms in both n- and p-doped alloys. The lifetimes we predicted differ substantially from those calculated with widely used analytical expressions, except in cases where the hole density is small. This difference originates from the significantly non-parabolic and anisotropic valence bands, which are of increasing significance as the hole density increases. From a comparison of the calculated and measured lifetimes, we deduce that the lifetimes at low temperatures are limited by the Shockley-Read-Hall (SRH) recombination. We have generalized the SRH expression to include Fermi-Dirac statistics, but we still treat the density, energy level, and cross section as adjustable parameters. We find that the calculated radiative and Auger recombination lifetimes, as well as SRH lifetimes, can fit the measured lifetimes using traps located (a) near the conduction band edge in n-HgCdTe and (b) near the valence band edge for p-HgCdTe. In addition, the movement of Fermi level with respect to the trap level explains the observed temperature-dependence of the lifetimes. We conclude that there is considerable room for improvement in HgCdTe material quality.

Trapping artifacts in quasi-steady-state photoluminescence and photoconductance lifetime measurements on silicon wafers

Photoluminescence and photoconductance lifetime measurements on multicrystalline silicon wafers are presented. It is demonstrated experimentally that the large overestimation of the lifetime at low carrier concentrations due to trapping that is observed in photoconductance measurements is not found in photoluminescence data. This is explained theoretically by the dependence of photoluminescence and photoconductance on the product and the sum, respectively, of the minority and majority carrier densities. Based on this analysis, it is shown that photoluminescence lifetime measurements are not significantly affected by minority carrier trapping in most practical cases while implied current-voltage curves obtained from photoluminescence are completely unaffected.

Gettering impurities from crystalline silicon by aluminum diffusion using a porous silicon layer

In this paper, we report a study on the possibility of gettering transition metal impurities from solar grade crystalline silicon (Si). Porous silicon layers were formed by the stain-etching method on both sides of the Si wafer. Aluminum diffusion was done throughout the PS layer in an infrared furnace under a (N2/O2) controlled atmosphere. This enables to getter eventual metal impurities towards the PS layer. The gettering effect was evaluated by measuring the majority carrier density and mobility and the minority carrier diffusion length (Ld) of the Si substrate. For this purpose, Wander Pauw and Hall Effect measurements together with the Light Beam Induced Current (LBIC) technique were used. We noticed that the best gettering corresponds to a heat treatment at 850 °C for 30 min; in that case an evident decrease of the majority carrier density and an enhancement of the mobility were observed. After gettering, we found an apparent improvement of the minority carrier diffusion length. These results give evidence of the effectiveness of external gettering treatments by combining (Al-PS) layer for an efficient gettering effect in solar grade monocrystalline Si. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Observation of two distinct magnetic states in [formula omitted] via the dHvA effect under pressure

We have found an anomaly in magnetic field dependence of the de Haas-van Alphen (dHvA) frequency of ZrZn 2 . Pressure dependence of this anomaly suggests an existence of two distinct ferromagnetic states and then a “nested” phase diagram similar to that of UGe 2 . The Stoner exchange parameter and the exchange splitting energy are 400 and 66 meV, respectively, which are derived from comparing the field dependence of the dHvA frequency difference with the magnetization. The two parameters do not change in both the low and slightly higher average moment states, suggesting that the phase transition between these states is ascribed to the change in the difference of majority and minority spin carrier densities.