Bandgap Narrowing Models Research Articles

Influence of Fundamental Model Uncertainties on Silicon Solar Cell Efficiency Simulations

We determine the uncertainties on simulated efficiencies of silicon solar cells due to uncertainties of the fundamental physical models. To determine these, we refit their parameters to the underlying measurement data. Using a metamodeling and Monte Carlo simulation approach, we then deduce how these propagate to the simulated solar cell efficiency. This is evaluated for 150- $\mu \text{m}$ -thick 1 $\Omega $ cm p-type standard and advanced silicon passivated emitter and rear cells (PERC), as well as for an ideal silicon solar cell. When sticking to the best-known set of physical models, we determine resulting efficiency uncertainties as low as 0.06%abs for usual PERC cells and 0.1%abs for an ideal cell. In a variance-based sensitivity analysis, we find the uncertainties of the bandgap and the hole density-of-states effective mass as well as the Auger recombination in the limiting case to dominate the efficiency uncertainty. In addition to these relatively low uncertainties, larger discrepancies may arise when applying different physical models for otherwise fixed device properties. We determine comparably large efficiency discrepancies of up to 0.6%abs for the two most prominent bandgap narrowing (BGN) models, and up to 0.15%abs for the two most recent parameterizations of free carrier absorption. We also show evidence that for the specific case of a strong space charge region being present at a recombining surface, Schenk’s BGN model fails to replicate experiments. Those discrepancies highlight the necessity of further research on those models. Finally, an error of up to 0.08%abs is observed by simplifying diffused regions on textured surfaces to a planar geometry.

Impact of Biosensor Permittivity on a Double-Gate nTFET Ambipolar Current

Biosensors are defined as any device that senses and transmits information about a biological element. The importance of biosensors for health and environment monitoring increase in the past decades, due the global warming, pollution and new biological pathogens. In order to achieve better sensing and to scale down the device dimensions and other advantages (1), the use of field effect transistors (FETs) as biosensors have been studied recently. The goal of this work is to analyze the effect of gate to drain underlapping on n-type Tunnel-FET (nTFET) devices, filled with different dielectric permittivity material (k) in order to simulate the bio element materials. The gate length (LG, where LG = 50nm – LU) was studied changing the underlap (LU) for a range of 0nm (self-aligned) to 15 nm of underlap, with step of 5 nm. The total channel length (LSD, where LSD = 50nm +LU) was evaluated fixing the LG=50 nm and adding the underlap part. In all cases, different dielectric permittivity (k) was considered in these analysis as the bio element. The structure of the Double Gate DG-nTFET biosensor is shown in Fig.1. The parameters used for simulation are: silicon film thickness, tSi = 10 nm, equivalent oxide thickness EOT = 1 nm, channel length LSD = 50 nm, thickness of the bio element tBio = 10 nm and the length of the drain and source regions LD = LS = 100 nm. The gate (Titanium Nitride) work function = 4.7 eV, source doping NA =1.1020 cm-3, drain doping ND= 1.1020 cm-3 and channel doping ND = 1.107 cm-3 . The models used are nonlocal band-to-band tunneling (BTBT), Shockley-Read-Hall (SRH) recombination and band-gap narrowing (BGN) model. The transfer curve of nTFETs with different underlap values are shown in Fig.2. It is observed that with the increment of LU the TFET ambipolar current (drain to channel tunneling) decreases, as already reported in (2). However, if the k values increase, the ambipolar currents increase as can be seen in Fig.3. This effect can be explained in Fig.4, where it is possible to see that the tunneling length becomes thinner when K raise due to improvement of the tunneling between drain and channel. In order to analyze a better configuration for a biosensor device, a sensitivity parameter defined as Sensivity = ID(K=n)/ID(k=1), where n is the value of the corresponding k, was used for comparing all different type of configurations studied in this paper. The sensitivity increases with the k value and with different LU is shown in Fig.5. The best sensitivity is obtained for high K and high underlap region. In the case of the device with LG fixed at 50 nm, the Fig.6 shows that the sensitivity increases with k and the highest sensitivity was obtained for lower underlap (5 nm). It can be explained analyzing the band diagram of the Fig.7, where it is possible to notice that the tunnel length decreases for lower underlap region. An investigation of the impact of biosensor permittivity on a DG-nTFET ambipolar current was done. The bio elements detection using the underlap region showed high sensitivity, of orders of magnitude for different LU and k values. The highest sensitivity for an nTFET biosensor was observed for a Lu = 15 nm (higher Lu), LSD = 50nm (smaller LSD) and higher k bio element, in the range studied in this paper. Figure 1

Band gap narrowing models tested on low recombination phosphorus laser doped silicon

This manuscript discusses bandgap narrowing models for highly phosphorus doped silicon. We simulate the recombination current pre-factor J0,phos in PC1Dmod 6.2 of measured doping profiles and apply the theoretical band gap narrowing model of Schenk [J. Appl. Phys. 84, 3684 (1998)] and an empirical band gap narrowing model of Yan and Cuevas [J. Appl. Phys. 114, 044508 (2013)]. The recombination current pre-factor of unpassivated and passivated samples measured by the photo conductance measurement and simulated J0,phos agrees well, when the band gap narrowing model of Yan and Cuevas is applied. With the band gap narrowing model of Schenk, the simulation cannot reproduce the measured J0,phos. Furthermore, the recombination current pre-factor of our phosphorus laser doped silicon samples are comparable with furnace diffused samples. There is no indication of recombination active defects, thus no laser induced defects in the diffused volume.

Application and comparison of band gap narrowing models for passivated phosphorus doped silicon surfaces

In this work, the recently proposed band-gap narrowing model by Yan and Cuevas [J. Appl. Phys. 114, 044508 (2013)] is evaluated by simulations of the recombination pre-factor J0 of highly phosphorus doped, passivated crystalline silicon surfaces, which are particularly relevant for solar cell applications. The results were fitted to experimental J0 data measured on a large range of samples exhibiting different dopant profiles and passivation coatings, both for planar and textured surfaces. For each sample, the surface recombination velocity parameter Sp was extracted by fitting the simulation results to the experimental data. We show that the Yan and Cuevas' model developed for Fermi-Dirac statistics leads to a smooth and monotonically increasing curve for Sp as a function of the surface dopant concentration Nsurf, for both investigated passivation layers. We provide a parameterization for this relation and compare the findings with those obtained with the widely used model by Schenk [J. Appl. Phys. 84, 3684 (1998)]. On the other hand, we show that the apparent band gap narrowing of Yan and Cuevas developed for use with Boltzmann statistics cannot be used to describe the experimental data, requiring unphysical negative Sp values for high Nsurf.

Nanoscale-RingFET: An Analytical Drain Current Model Including SCEs

In this paper, using a 2-D Poisson equation (in cylindrical coordinates), an analytical drain current model of a nanoscale RingFET architecture has been developed for the first time. Major short-channel effects, such as channel length modulation, velocity scattering, and drain-induced barrier lowering, are taken under consideration while developing the model. A bandgap narrowing model has been employed to investigate the impact of higher channel doping. The modeled results of the surface potential, electric field, threshold voltage ( $V_{\mathrm{ th}}$ ), subthreshold slope, and drain current have been verified by comparing with those of the ATLAS 3-D device simulation. The influence of the drain radius and position of the source/drain regions on the electrical characteristics of the device has also been demonstrated.

Empirical determination of the energy band gap narrowing in p+ silicon heavily doped with boron

In the analysis of highly doped silicon, energy band gap narrowing (BGN) and degeneracy effects may be accounted for separately, as a net BGN in conjunction with Fermi-Dirac statistics, or lumped together in an apparent BGN used with Boltzmann statistics. This paper presents an experimental study of silicon highly doped with boron, with the aim of evaluating the applicability of previously reported BGN models. Different boron diffusions covering a broad range of dopant densities were prepared, and their characteristic recombination current parameters J0 were measured using a contactless photoconductance technique. The BGN was subsequently extracted by matching theoretical simulations of carrier transport and recombination in each of the boron diffused regions and the measured J0 values. An evaluation of two different minority carrier mobility models indicates that their impact on the extraction of the BGN is relatively small. After considering possible uncertainties, it can be concluded that the BGN is slightly larger in p+ silicon than in n+ silicon, in qualitative agreement with theoretical predictions by Schenk. Nevertheless, in quantitative terms that theoretical model is found to slightly underestimate the BGN in p+ silicon. With the two different parameterizations derived in this paper for the BGN in p+ silicon, both statistical approaches, Boltzmann and Fermi-Dirac, provide a good agreement with the experimental data.

Effect of Bandgap Narrowing on Performance of Modern Power Devices

The effect of the bandgap narrowing (BGN) on performance of power devices is investigated in detail in this paper. The analysis reveals that the change in the energy band structure caused by BGN can strongly affect the conductivity modulation of the bipolar devices resulting in a completely different performance. This is due to the modified injection efficiency under high-level injection conditions. Using a comprehensive analysis of the injection efficiency in a p-n junction, an analytical model for this phenomenon is developed. BGN model tuning has been proved to be essential in accurately predicting the performance of a lateral insulated-gate bipolar transistor (IGBT). Other devices such as p-i-n diodes or punch-through IGBTs are significantly affected by the BGN, while others, such as field-stop IGBTs or power MOSFETs, are only marginally affected.

Direct band gap narrowing in highly doped Ge

Direct band gap narrowing in highly doped n-type Ge is observed through photoluminescence measurements by determining the spectrum peak shift. A linear relationship between the direct band gap emission and carrier concentration is observed. We propose a first order phenomenological model for band gap narrowing based on two parameters whose values for Ge are EBGN = 0.013 eV and ΔBGN = 10−21 eV/cm−3. The application of these results to non-invasive determination of the active carrier concentration in submicron areas in n-type Ge structures is demonstrated.

Band gap narrowing of cadmium oxide powder by rare earth praseodymium doping

Abstract

Transparent conducting properties of samarium-doped CdO

Sm-doped CdO thin films (0.4, 1.1, 3, 7.5, and 9.3%) have been prepared by a vacuum evaporation method on glass and Si wafer substrates. The prepared films were characterised by X-ray fluorescence, X-ray diffraction, UV–VIS–NIR absorption spectroscopy, and dc-electrical measurements. Experimental results indicate that Sm 3+ doping creates a slight compressive stress in the CdO crystalline structure and changes (and controls) the optical and electrical properties. The bandgap of CdO was suddenly narrowed by about 17% due to a light (0.4%) doping with Sm 3+ ions. Then, as the Sm doping level was increased, the energygap was slightly increasing reaching a steady state (2.17 eV). This variation was explained by the available bandgap narrowing (BGN) models. The electrical behaviour of Sm-doped CdO films shows that they are degenerate semiconductors of energygaps 1.87–2.17 eV. The 0.4% Sm-doped CdO film shows increase in its mobility by about 6 times, conductivity by 36 times, and carrier concentration by 6 times, relative to undoped CdO film. From transparent-conducting-oxide point of view, Sm is sufficiently effective for CdO doping like other metallic dopants such as In, Sn, Sc, and Y.

Influence of hydrogenation on the electrical and optical properties of CdO:Tl thin films

Electrical and optical properties of Tl-doped CdO films (CdO:Tl) post-annealed in hydrogen atmosphere for different durations (15 min, 30 min, 45 min, and 60 min) were studied. The prepared films were characterised by the X-ray diffraction method and UV–VIS–NIR absorption–reflection spectroscopy. Experimental data indicate that annealing in H 2-atmosphere removes gradually with time the internal structural micro-stress that created as a consequence of Tl doping into CdO structure. The band gap of the hydrogenated Tl-doped CdO samples changes with H 2-annealing time following the changing in the free-electron concentration. These results were found to be in agreement with the available bandgap widening and narrowing models. The optical properties were easily explained within the framework of Hamberg band-to-band transitions and classical Drude theory. It was found that the greatest enhancement of the electrical conduction parameters occurs by annealing of CdO:Tl films in H 2-atmosphere for 30–45 min when the conductivity increased by about 37% and the free-electron concentration increased by about 6%. The results of the present investigation are important for the transparent conducting oxide preparation technique.

Reassessment of the intrinsic carrier density in crystalline silicon in view of band-gap narrowing

The commonly used value of the intrinsic carrier density of crystalline silicon at 300 K is ni=1.00×1010 cm−3. It was experimentally determined by Sproul and Green, J. Appl. Phys. 70, 846 (1991), using specially designed solar cells. In this article, we demonstrate that the Sproul and Green experiment was influenced by band-gap narrowing, even though the dopant density of their samples was low (1014 to 1016 cm−3). We reinterpret their measurements by numerical simulations with a random-phase approximation model for band-gap narrowing, thereby obtaining ni=9.65×109 cm−3 at 300 K. This value is consistent with results obtained by Misiakos and Tsamakis, J. Appl. Phys. 74, 3293 (1993), using capacitance measurements. In this way, long-prevailing inconsistencies between independent measurement techniques for the determination of ni are resolved.

New Coefficients of the Minority Carrier Lifetime and Bandgap Narrowing Models in the Transparent Emitter of Thin Film Silicon Solar Cells

In this study we have determined new coefficients for the physical model describing the band-gap narrowing and the minority carriers lifetime. This was accomplished according to the doping level of the thin emitter. This model allows us to take into account both the effects of the heavy doping and the majority carrier degeneration for the very high level of doping. The results we obtain by the corrected model are in good agreement with those reported in the literature and in different experiments. They show us the possibility of accurately evaluating the performances for then+psilicon solar cell. This model is then used to introduce a new concept for the thin layer emitter, called transparent emitter.

Application of an improved band-gap narrowing model to the numerical simulation of recombination properties of phosphorus-doped silicon emitters

The commonly used band-gap narrowing (BGN) models for crystalline silicon do not describe heavily doped emitters with desirable precision. One of the reasons for this is that the applied BGN models were empirically derived from measurements assuming Boltzmann statistics. We apply a new BGN model derived by Schenk from quantum mechanical principles and demonstrate that carrier degeneracy and the new BGN model both substantially affect the electron–hole product within the emitter region. Simulated saturation current densities of heavily phosphorus-doped emitters, calculated with the new BGN model, are lower than results obtained with the widely used empirical BGN model of del Alamo.

Determination of the density of states in heavily doped regions of silicon solar cells

In highly doped crystalline silicon, the formation of an impurity band substantially changes the density of states (DOS) of electrons. As yet, heavily doped silicon has been modelled using solely the ideal DOS of undoped silicon, regardless of the doping density. Since this approximation influences the position of the Fermi energy, we derive a more realistic silicon DOS model that is suitable for numerical device simulations. Our new model is based on photoluminescence data reported in the literature and a recently published bandgap narrowing model.

New Coefficients of the Minority Carrier Lifetime and Bandgap Narrowing Models in the Transparent Emitter of Thin Film Silicon Solar Cells

In this study we have determined new coefficients for the physical model describing the band‐gap narrowing and the minority carriers lifetime. This was accomplished according to the doping level of the thin emitter. This model allows us to take into account both the effects of the heavy doping and the majority carrier degeneration for the very high level of doping. The results we obtain by the corrected model are in good agreement with those reported in the literature and in different experiments. They show us the possibility of accurately evaluating the performances for the n+p silicon solar cell. This model is then used to introduce a new concept for the thin layer emitter, called transparent emitter.

Study of dopant-dependent band gap narrowing in compound semiconductor devices

Band gap narrowing (BGN) is one of the crucial heavy-doping effects to be considered for bipolar devices. Using a physically-based approach (E.F. Schubert, Doping in III-V Semiconductors, Cambridge University Press, 1993), we suggest a new BGN model which considers the semiconductor material and the dopant species for arbitrary finite temperatures. This unified treatment is especially useful for accurate device simulation. A comparison with experimental data and other existing models is presented and study of BGN in III-V group semiconductors is performed. Finally, as a particular example we investigated with our two-dimensional device simulator MINIMOS-NT (Simlinger et al., Simulation of submicron double-heterojunction high electron mobility transistors with MINIMOS-NT, IEEE Trans. Electron. Devices, Vol. 44, 1997, pp. 700–707), the electrical behavior of a graded composition Si/SiGe HBT using a hydrodynamic transport model.

A model for doping-induced band gap narrowing in 3C-, 4H-, and 6H-SiC

We present an analytical model for doping-induced band edge displacements and band gap narrowing in both n-type and p-type 3C-, 4H-, and 6H-SiC. The model is also applied to Si for comparison. The model takes into account details in the band structure dispersion relations both for electrons and holes. Furthermore, the contribution to band gap narrowing from the minority carrier correlation energy has been evaluated explicitly, applying a two-band model for the dielectric function of a hole gas in the plasmon-pole approximation. The results for band edge displacements and band gap narrowing are expressed as simple functions of doping concentration.

Modeling plasma-induced bandgap narrowing effects for accurate simulation of advanced silicon bipolar transistors

Existing models for plasma-induced bandgap narrowing are briefly reviewed. A simple and more general model for plasma-induced bandgap narrowing in Si devices is proposed. Different issues related to modeling of plasma-induced bandgap narrowing are discussed. Results of numerical simulation of an advanced Si bipolar transistor structure are presented. Results of the simulations are compared with experimental data. It is shown that inclusion of plasma-induced bandgap narrowing model provides a more accurate estimate of the current gain characteristics. It is also shown that this effect becomes more important for simulation at low temperatures. The reasons behind the stronger effect at low temperatures are explained.

An Investigation of the Inconsistency in Barrier Heights for PNP and NPN Polysilicon Emitter Bipolar Transistors Using a New Tunneling Model

A new tunneling model is proposed for polysilicon emitter bipolar transistors in which the interfacial layer is modeled as a wide band-gap semiconductor. This model predicts that potential barriers are formed in both the conduction and valence bands. The shapes and sizes of the barriers are dependent upon the amount of band-bending within the interfacial layer, which is in turn dependent on the amount of dopant segregation in the interfacial layer. Measurements of base current and emitter resistance are made on pnp polysilicon emitter bipolar transistors with deliberately grown interfacial oxide layers. These electrical characteristics are then modeled using the new heterojunction tunneling model, from which values of electron and hole barrier heights are extracted. Specifically, a hole barrier height of 0.31±0.02 eV is obtained, and an electron barrier height of either >0.68±0.08 eV or >0.44±0.06 eV, with the value depending on the band-gap narrowing model used in the calculation. These values of electron and hole barrier height are shown to be different than the values obtained when similar measurements are made on npn devices. The new heterojunction tunneling model is used to model these devices, and it is shown that it is capable of fully explaining this discrepancy between the values of barrier height obtained from measurements on npn and pnp transistors.