Carrier Density Distribution Research Articles

Thermomagnetic effect with two temperature theory for photothermal process under hydrostatic initial stress

A novel technique is used to investigate the influence of magnetic field for a two dimensional deformations on a two temperature problem at the free surface of a semi-infinite medium. The investigation is carried out under the effects of both mechanical force and hydrostatic initial stress during a photothermal excitation theory. The equations of elastic waves, heat conduction equation, quasi-static electric field, carrier density, two temperature coefficient, ratios, and constitutive relationships for the thermo-magnetic-electric medium are obtained using the Harmonic Wave Method (HWM) technique. The effects of thermoelastic, thermoelectric and two temperature parameters of the applied force on the displacement component, force stress, carrier density and temperature distribution has been depicted graphically.

Picosecond charge transport in rutile at high carrier densities studied by transient terahertz spectroscopy

We study terahertz photoconductivity of a rutile single crystal between 10 and 300 K under strong photoexcitation by femtosecond pulses at 266 nm. A marked dependence of the carrier mobility on the carrier density is observed leading to highly complex transport phenomena on a picosecond time scale. We develop a general model of carrier photoconductive response in the case of time dependent inhomogeneous distribution of carrier density and mobility. This allows us to assess an important role of both electrons and holes in the response of photoexcited rutile. At low temperatures, the carrier mobility is initially reduced due to the electron-hole scattering and increases by one order of magnitude upon ambipolar diffusion of the carriers into deeper regions of the sample. At room temperature, contributions of transient hot optical phonons and/or of midinfrared polaron excitations with charge-density-dependent dielectric strength emerge in the photoconductivity spectra.

Two-temperature plane strain problem in a semiconducting medium under photothermal theory

In this investigation, we study the two-temperature problem with two-dimensional (2-D) deformations for a semi-infinite semiconducting medium at the free surface with the influence of mechanical force through a photothermal process. The harmonic wave method (Normal Mode analysis) has been used to get the exact expression of normal displacement, normal force stress, carrier density, and temperature distribution, and also the two-temperature coefficients ratios has been obtained analytically. The effects of several parameters as thermoelastic and thermoelectric coupling parameters and two-temperature parameter of this force on the displacement component, force stress, carrier density, and temperature distribution have been depicted graphically.

Mobility anisotropy in monolayer black phosphorus due to scattering by charged impurities

We study the charged impurity limited mobility in black phosphorus, a highly anisotropic layered material. We compute the mobility within the Boltzmann transport equation under detailed balance condition, and taking into account the anisotropy in transport and electronic structure. For carrier densities accessible in experiments, we obtained an anisotropy ratio of 3 ~ 4 at zero temperature, two-folds larger than that observed in experiments on multilayers samples. We discuss also how the anisotropy depends on carrier density and impurity distribution.

(Invited) 2D Transport and Velocity Modulation in Black Phosphorus Field Effect Transistors

Black phosphorus (bP) is an elemental allotrope with a layered crystal structure of puckered honeycombs that can be mechanically exfoliated down to atomic layer thickness. First synthesized over a century ago, bP has been previously studied as a bulk semiconductor [1,2] and is subject to a resurgence of interest as a 2D semiconductor with properties complementary to the 2D semi-metal graphene [3]. bP is the most thermodynamically stable allotrope of phosphorus but is nonetheless subject to photo-oxidation in the presence of water, oxygen and visible light with a reaction rate that increases as bP layer thickness decreases [4]. We have fabricated bP quantum wells in both back-gated and dual-gated field effect transistor (FET) geometries with bP thicknesses ranging from 6±1 nm to 47±1 nm. Stability under ambient conditions was achieved in back-gated FETs by encapsulation with a layer of poly methyl methacrylate (PMMA), while dual-gated FETs were additionaly protected by a combination of Al2O3 deposited by atomic layer deposition and optically opaque gold metallization. Charge transport measurements reveal ambipolar conduction, field effect mobilities of up to 900 cm2/Vs for holes at low temperatures ( T< 100 K ), current saturation as expected of a bona fide semiconductor, and on/off current ratios exceeding 105 at room temperature [5]. Shubnikov-de Haas (SdH) oscillations were observed in bP FETs at 300 mK to 30 K and magnetic fields of up to 35 T. Lifshitz-Kosevich analysis of the SdH oscillations indicates the presence of a 2-D hole gas with Schrödinger fermion character in an accumulation layer at the bP surface. A simple Schrödinger-Poisson analysis predicts accumulation of holes in a single 2-D sub-band at 300 mK over the range of applied electric fields used in our experiments. Analysis of the thermal activation of SdH oscillations yields a hole effective mass of m*=0.36±0.03m0. Improvements to bP device quality by the independent Y. Zhang group has led to the observation of the quantum Hall effect [6].The top gate of dual-gate bP FETs was found to be effective at modulating both carrier mobility and contact resistance [7]. The mobility modulation effect enables operation of the dual-gate bP FET as a velocity modulated transistor (VMT), first proposed by Sakaki [8] to overcome the limitation on transistor switching frequency imposed by the channel transit time of charge carriers. The mobility of charge carriers within an assymetric bP FET structure is dependent upon the charge carrier density distribution, and is thereby dependent upon the externally applied electric field of the top gate. A two-fold mobility modulation and a two-fold contact resistance modulation leads to a four-fold modulation of transconductance at a fixed hole density. The observation of mobility modulation effects in dual-gate bP FETs demonstrates the capacity for bP to function as a room temperature VMT. Charge density distribution plays an important role in the charge transport properties of 2D atomic crystals, where the exposed surfaces of naked quantum well structures can lead to a strong spatial dependence of charge carrier scattering rates. The recent observation in angle resolved photo-emission spectroscopy of bandgap tuning and a semiconductor to semi-metal transition in K-doped bP via a giant Stark effect [9] suggests the possibility of electric field tuning of bP bandgap in bP FETs. Further work is required to improve the quality of bP/dielectric interfaces and to increase the applied electric field strength to access electric field tunable bandgap devices with bP.

Percolative switching in transition metal dichalcogenide field-effect transistors at room temperature

We have addressed the microscopic transport mechanism at the switching or ‘on–off’ transition in transition metal dichalcogenide (TMDC) field-effect transistors (FETs), which has been a controversial topic in TMDC electronics, especially at room temperature. With simultaneous measurement of channel conductivity and its slow time-dependent fluctuation (or noise) in ultrathin WSe2 and MoS2 FETs on insulating SiO2 substrates where noise arises from McWhorter-type carrier number fluctuations, we establish that the switching in conventional backgated TMDC FETs is a classical percolation transition in a medium of inhomogeneous carrier density distribution. From the experimentally observed exponents in the scaling of noise magnitude with conductivity, we observe unambiguous signatures of percolation in a random resistor network, particularly, in WSe2 FETs close to switching, which crosses over to continuum percolation at a higher doping level. We demonstrate a powerful experimental probe to the microscopic nature of near-threshold electrical transport in TMDC FETs, irrespective of the material detail, device geometry, or carrier mobility, which can be extended to other classes of 2D material-based devices as well.

Magnetic field dependence of energy levels in biased bilayer graphene quantum dots

Using the tight-binding approach, we study the influence of a perpendicular magnetic field on the energy levels of hexagonal, triangular, and circular bilayer graphene (BLG) quantum dots (QDs) with zigzag and armchair edges. We obtain the energy levels for AB (Bernal)-stacked BLG QDs in both the absence and the presence of a perpendicular electric field (i.e., biased BLG QDs). We find different regions in the spectrum of biased QDs with respect to the crossing point between the lowest-electron and -hole Landau levels of a biased BLG sheet. Those different regions correspond to electron states that are localized at the center, edge, or corner of the BLG QD. Quantum Hall corner states are found to be absent in circular BLG QDs. The spatial symmetry of the carrier density distribution is related to the symmetry of the confinement potential, the position of zigzag edges, and the presence or absence of interlayer inversion symmetry.

Wavelength-dependent femtosecond pulse amplification in wideband tapered-waveguide quantum well semiconductor optical amplifiers.

In this paper, we study the wavelength-dependent amplification in three different wideband quantum well semiconductor optical amplifiers (QWAs) having conventional, exponentially tapered, and linearly tapered active region waveguide structures. A new theoretical model for tapered-waveguide QWAs considering the effect of lateral carrier density distribution and the strain effect in the quantum well is established based on a quantum well transmission line modeling method. The temporal and spectral characteristics of amplified femtosecond pulse are analyzed for each structure. It was found that, for the amplification of a single femtosecond pulse, the tapered-waveguide QWA provides higher saturation gain, and the output spectra of the amplified pulse in all three structures exhibit an apparent redshift and bandwidth narrowing due to the reduction of carrier density; however, the output spectrum in the tapered-waveguide amplifier is less distorted and exhibits smaller bandwidth narrowing. For the simultaneous amplification of two femtosecond pulses with different central frequencies, in all the three structures, two peaks appear in the output spectra while the peak at the frequency closer to the peak frequency of the QWA gain spectrum receives higher amplification due to the frequency (wavelength) dependence of the QWA gain. At a low peak power level of the input pulse, the bandwidth of each window in the tapered structure is larger than that of the conventional waveguide structure, which aggravates the spectrum alias in the amplification of femtosecond pulses with different central frequencies. As the peak powers of the two pulses increase, the spectrum alias in the conventional waveguide becomes more serious while there are small changes in the tapered structures. Also, we have found that in the amplification of a femtosecond pulse train, the linear-tapered QWAs exhibit the fastest gain recovery as compared with the conventional and exponentially tapered QWAs.

Two-Photon Absorption Induced Single-Event Effects: Correlation Between Experiment and Simulation

Carrier-density distributions generated via two-photon absorption from pulsed laser excitation are simulated using nonlinear-optical beam propagation software. These simulated carrier-density distributions are used to calculate depth profiles of the integrated collected charge using a rectangular-parallel-piped approach for two silicon diodes of different structure. Using a set of proposed correlation metrics, the resulting simulated charge collection profiles are found to exhibit good agreement with measured transient charge-collection data for most, but not all of the metrics. The physical phenomena underlying the correlation metrics are discussed in detail. The remaining discrepancies that exist between the simulated and experimental results are addressed and their potential causes are detailed.

Charge carrier density dependent transport in disordered organic photovoltaic devices

Charge carrier transport via drift-diffusion model has been investigated in organic bulk-heterojunction solar cells. With the Pasveer's mobility model, the distributions of charge carrier mobilities in organic active layer change obviously (more than one order of magnitude, according to our simulations), due to the effect of carrier density. The dissociation rate of electron–hole pair, recombination, and net generation rate in the organic bulk are determined simultaneously by the electron and hole concentrations. The distribution of carrier density directly affects the charge transport and extraction efficiency.

Carrier density distribution in silicon nanowires investigated by scanning thermal microscopy and Kelvin probe force microscopy

The use of scanning thermal microscopy (SThM) and Kelvin probe force microscopy (KPFM) to investigate silicon nanowires (SiNWs) is presented. SThM allows imaging of temperature distribution at the nanoscale, while KPFM images the potential distribution with AFM-related ultra-high spatial resolution. Both techniques are therefore suitable for imaging the resistance distribution. We show results of experimental examination of dual channel n-type SiNWs with channel width of 100nm, while the channel was open and current was flowing through the SiNW. To investigate the carrier distribution in the SiNWs we performed SThM and KPFM scans. The SThM results showed non-symmetrical temperature distribution along the SiNWs with temperature maximum shifted towards the contact of higher potential. These results corresponded to those expressed by the distribution of potential gradient along the SiNWs, obtained using the KPFM method. Consequently, non-uniform distribution of resistance was shown, being a result of non-uniform carrier density distribution in the structure and showing the pinch-off effect. Last but not least, the results were also compared with results of finite-element method modeling.

Simulation of Laser-Based Two-Photon Absorption Induced Charge Carrier Generation in Silicon

Numerical simulation software is used to calculate quantitatively the two-photon absorption-induced carrier-density distributions generated under conditions that are experimentally relevant for single-event effects studies. The results provide valuable insight into how the magnitudes and shapes of the charge carrier distributions evolve over a large range of experimental conditions and the impacts this has for different device geometries. Furthermore, values of integrated charge are determined that can be more directly correlated with experimental observables.

Development of the plasma channel of a plasma dipole antenna created by the radiation of a transmitter

Characteristics of the plasma layer (a plasma antenna of dipole type), excited by the radiation of a transmitter such as the carrier density distribution over the radius of the dielectric tube (near the boundary) and the growth rate of the plasma region along the tube length are considered. It is shown that it is possible to distinguish such typical dimensions as the radius of the dielectric tube, the radius of the plasma column, and the thickness of the skin layer, and, depending on relationships between these dimensions, consider the influence of the transition layer on excitation of the surface wave in the plane or cylindrical symmetry.

Modeling and understanding of the frequency dependent HPM upset susceptibility of the CMOS inverter

In this paper, we interpret and, for the first time, model a frequency dependent high-power mi-crowave (HPM) upset susceptibility. We constructed the analytical models of the total amount of injected charges Ninj, the excess carrier density distribution in P-Substrate, and the frequency dependent HPM upset susceptibility level. The models are validated by simulated results and experimental data, respectively. Results reveal that Ninj is proportional to f α while the exponent α should be adjusted to-0.525. The excess carrier density distribution behaves the frequency dependence as well; the dependence is attributable to the fact that the AC field within the CMOS inverter varies too rapidly for the carriers to follow at high frequency. Meanwhile, the HPM upset susceptibility level is a decreasing function of f . The f dependent HPM upset susceptibility model is verified to be reliable and able to quickly estimate the susceptibility level of CMOS inverter considering IC technology, layout parameters, pulse properties, and operating environment simultaneously. Besides, the empirical formula P = A · f α is proposed to provide instant estimation to the HPM upset power threshold. In conclusion, by aid of the analytical model, we acquired the influence of the layout parameter L B on the HPM susceptibility and demonstrated that the CMOS inverter with minor L B is more susceptible to HPM.

Longitudinal spatial hole burning, its impact on laser operation, and suppression

Longitudinal spatial hole burning (LSHB) is a common effect that appears in lasers with standing-wave cavities, especially in edge-emitting semiconductor laser diodes. The standing-wave pattern introduces a non-uniform distribution of the photon density along the laser cavity. Due to the anti-correlationship between the carrier and photon densities (as the stimulated emission depletes carriers where photons exist), the carrier density distribution becomes non-uniform as well, which further causes the nonuniformity of the optical gain of the active region and the refractive index of the waveguide along the cavity. As such, the lasing condition, determined by the gain and refractive index (through the amplitude and phase condition, respectively), is jeopardized. While distributed feedback (DFB) lasers [1, 2] become the only viable solution now in many applications where the single-mode operation is indispensable, LSHB turns out to be a serious issue that deteriorates a number of DFB laser characteristics. It may cause lasing instability [3], linewidth broadening [4], and increased susceptibility to external feedback, to name just a few. Severe LSHB shakes the fundamental lasing condition and even results in coherent collapse [5]. Actually, LSHB is one of the major limiting factors that cause the relative low yield of DFB lasers in their mass productions, especially for the DFB laser having high coupling factor and/or long cavity design for achieving high side-mode-suppression ratio (SMSR) as required. In 100 Gbps and beyond coherent fiber-optic communication systems, lasers with linewidth in several tens of kHz are usually demanded [6] as the light source or local oscillator. It is mainly LSHB that prevents normal DFB lasers from achieving this goal, as otherwise the linewidth reduction can readily be realized by extending the cavity length. For directly modulated DFB lasers, any external feedback (from, e.g., the fiber-pigtail, or splitter/combiner, or filter, or wavelength multiplexer/demultiplexer) may lead to the lasing wavelength shift, or optical power fluctuation, or even coherent collapse, and lasing termination. Although an optical isolator can be co-packaged with the DFB laser to solve this problem, it is certainly not cost-effective. Chen’s group has been working on the sampled gratingbased DFB lasers and has made many significant contributions on multiple wavelength laser sources and tunable laser sources [7, 8]. Their recent work on LSHB suppression by introducing a pair of phase shifts in the basic sampled grating DFB structure [9] has shed light on solving the aforementioned issue through a viable approach. Comparing with the existing methods [10], not only this approach appears to be more effective, but it also bears the unique feature of fabrication readiness and easiness. This work is also comprehensively and coherently presented with the design concept and working principle clearly explained, and with the simulation and experimental results shown consistently. Therefore, it deserves the great attention of researchers in the relevant area.

Modeling and analysis of the HPM pulse-width upset effect on CMOS inverter**Project supported by the National Natural Science Foundation of China (No. 60776034) and the State Key Development Program for Basic Research of China (No. 2014CB339900).

We derive analytical models of the excess carrier density distribution and the HPM (high-power microwave) upset susceptibility with dependence of pulse-width, which are validated by the simulated results and experimental data. Mechanism analysis and model derivation verify that the excess carriers dominate the current amplification process of the latch-up. Our results reveal that the excess carrier density distribution in P-substrate behaves as pulse-width dependence. The HPM upset voltage threshold Vp decreases with the incremental pulse-width, while there is an inflection point which is caused because the excess carrier accumulation in the P-substrate will be suppressed over time. For the first time, the physical essence of the HPM pulse-width upset effect is proposed to be the excess carrier accumulation effect. Validation concludes that the Vp model is capable of giving a reliable and accurate prediction to the HPM upset susceptibility of a CMOS inverter, which simultaneously considers technology information, ambient temperature, and layout parameters. From the model, the layout parameter LB has been demonstrated to have a significant impact on the pulse-width upset effect: a CMOS inverter with minor LB is more susceptible to HPM, which enables us to put forward hardening measures for inverters that are immune from the HPM upset.

Computational model of 2DEG mobility in AlGaN/GaN heterostructures

AbstractThe computational scheme of multiscale modeling of semiconductor heterostructures is presented. Three scale levels are taken into account. On the atomic level the system is described using crystallographic information and quantum‐mechanical model. Ab initio modeling allows to determine the electronic structure, define polarization effects and calculate charge densities on the interfaces between layers. Obtained information is used in the nanoscale level model for the calculation of the charge carrier distribution in the heterostructure. At this level mathematical model contains the system of conjugated Schrödinger and Poisson equations. The carrier density distributions over the lateral direction of the multilayered structure and 2DEG localization are of the most interest at this point. This data is used in the next scale level model where electron mobility is calculated. A wide range of electron scattering mechanisms are taken into account during this calculation. This approach was applied to model 2DEG in AlGaN/AlN/GaN heterostructures. The good agreement between calculated values of interface charge density, 2DEG electron concentration, electron mobility and known experimental data was achieved. (© 2015 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Cross‐sectional mapping of hole concentrations as a function of copper treatment in CdTe photo‐voltaic devices

AbstractThe carrier density and carrier density distribution within CdTe solar cells were studied with scanning capacitance microscopy (SCM). The CdTe solar cells were studied after every process step and as a function of varying copper treatment conditions. It was found that the CdTe film is practically undoped after deposition and after CdCl2 treatment, while after the copper step the carrier density distribution is non‐uniform with a mixture of p‐type and intrinsic grains in the CdTe film. These SCM observations were also confirmed with device performance data as well as capacitance–voltage measurements and Van der Pauw Hall measurements. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Influence of Carrier Transport on Diffraction Efficiency of Steady-State Photocarrier Grating

A two-dimensional theoretical model of a diffractive steady-state photocarrier grating (SSPCG) has been developed. The carrier diffusion equation with a spatially periodic excitation source was solved, and an analytical expression of the carrier density distribution was obtained. Based on the band-filling theory and the Kramers–Kronig relation, the carrier-induced refractive index change of SSPCG was estimated, and the refractive index profile was determined. The diffraction efficiency of the SSPCG was calculated by multilevel rigorous coupled-wave analysis. Simulations were carried out to investigate the influence of the carrier transport properties on the diffraction efficiency of the SSPCG. The results show that a semiconductor material with a longer lifetime and a smaller diffusivity will have a higher diffraction efficiency. The spatial amplitude of the carrier density and the grating strength of the SSPCG are closely related to the grating period. For an InP-based SSPCG, the diffraction efficiency of the $$+1\mathrm{st}$$ transmitted wave reaches its maximum value (25 %) when the grating provides a $$\pi $$ phase shift. The theoretical analysis and conclusions are helpful for material selection and experimental parameter determination of a diffractive SSPCG.

Ground state of graphene heterostructures in the presence of random charged impurities

We study the effect of long-range disorder created by charge impurities on the carrier density distribution of graphene-based heterostructures. We consider heterostructures formed by two graphenic sheets [either single-layer graphene (SLG) or bilayer graphene (BLG)] separated by a dielectric film. We present results for symmetric heterostructures SLG-SLG and BLG-BLG, and hybrid ones BLG-SLG. As for isolated layers, we find that the presence of charged impurities induces strong carrier density inhomogeneities, especially at low dopings where the density landscape breaks up in electron-hole puddles. We provide quantitative results for the strength of the carrier density inhomogeneities and for the screened disorder potential for a large range of experimentally relevant conditions. For heterostructures in which BLG is present, we also present results for the band gap induced by the perpendicular electric field generated self-consistently by the disorder potential and by the distribution of charges in the heterostructure. For SLG-SLG heterostructures, we discuss the relevance of our results for the understanding of the recently observed metal-insulator transition in each of the graphene layers forming the heterostructure. Moreover, we calculate the correlation between the density profiles in the two graphenic layers and show that for standard experimental conditions, the two profiles are well correlated.