Ionized Impurity Scattering Research Articles

Electron and Hole Mobility of SnO2 from Full-Band Electron–Phonon and Ionized Impurity Scattering Computations

Mobility is a key parameter for SnO2, which is extensively studied as a practical transparent oxide n-type semiconductor. In experiments, the mobility of electrons in bulk SnO2 single crystals varies from 70 to 260 cm2V−1s−1 at room temperature. Here, we calculate the mobility as limited by electron–phonon and ionized impurity scattering by coupling the Boltzmann transport equation with density functional theory electronic structures. The linearized Boltzmann transport equation is solved numerically beyond the commonly employed constant relaxation-time approximation by taking into account all energy and momentum dependencies of the scattering rates. Acoustic deformation potential and polar optical phonons are considered for electron–phonon scattering, where polar optical phonon scattering is found to be the main factor which determines the mobility of both electrons and holes at room temperature. The calculated phonon-limited electron mobility is found to be 265 cm2V−1s−1, whereas that of holes is found to be 7.6 cm2V−1s−1. We present the mobility as a function of the carrier concentration, which shows the upper mobility limit. The large difference between the mobilities of n-type and p-type SnO2 is a result of the different effective masses between electrons and holes.

Enhancing Thermoelectric Performance of Yb0.3Co4Sb12 by Synergistically Optimized Carrier Concentration and Ionized Impurity Scattering.

Previous results indicated that acceptor doping was considered an effective clue to substantially suppress electronic thermal conductivity and in the meanwhile hold a rather low lattice thermal conductivity in high Yb-filled skutterudites. However, the strength of ionized impurity scattering needs to be regulated elaborately to balance the enhanced Seebeck coefficient and the deteriorated carrier mobility. In this work, Ge doping not only synergistically modulates the Fermi energy level and strength of ionized impurity scattering to an optimal range and attains a benign power factor but also offers a valuable opportunity to further suppress κe and κ in the classic Yb0.3Co4Sb12 alloy. Since the Yb0.3Co4Sb11.75Ge0.25 sample is endowed with the most highlighted ZT value in the device application temperature range, a promising average ZT value of 1.00 across the 300-823 K is achieved, reaching up to the level of a typical triple-filled skutterudite, which is highly desirable for achieving a satisfactory theoretical conversion efficiency of ∼14.5%. Our work corroborates that the ionized impurity strength is an extremely critical benchmark to obtain desirable thermoelectric performance in the high Yb-filled skutterudites.

The Effect of Doping in Split-Well Direct-Phonon THz Quantum-Cascade Laser Structures

We have studied the effect of doping on the temperature performance of a split-well (SW) direct-phonon (DP) terahertz (THz) quantum-cascade laser (QCL) scheme supporting a clean three-level system. Achieving a system that is as close as possible to a clean n-level system proved to be the strategy that led to the best temperature performance in THz-QCLs. We expected to obtain a similar improvement to that observed in resonant-phonon (RP) schemes after increasing the carrier concentration from 3 × 1010 cm−2 to 6 × 1010 cm−2. Our goal was to improve the temperature performance by increasing the doping, ideally the results should have improved. To our surprise, in the devices we checked, the results show the contrary. Although an increase in doping had previously shown a positive effect in RP schemes, our results indicated that this does not happen with SW–DP devices. However, we observed a significant increase in gain broadening and a reduction in the dephasing time as the doping and temperature increased. We attribute these effects to enhanced ionized-impurity scattering (IIS). The observation and study of effects related to dephasing included in our experimental work have previously only been possible via simulation.

Simulation of the Impact of Ionized Impurity Scattering on the Total Mobility in Si Nanowire Transistors.

Nanowire transistors (NWTs) are being considered as possible candidates for replacing FinFETs, especially for CMOS scaling beyond the 5-nm node, due to their better electrostatic integrity. Hence, there is an urgent need to develop reliable simulation methods to provide deeper insight into NWTs’ physics and operation, and unlock the devices’ technological potential. One simulation approach that delivers reliable mobility values at low-field near-equilibrium conditions is the combination of the quantum confinement effects with the semi-classical Boltzmann transport equation, solved within the relaxation time approximation adopting the Kubo–Greenwood (KG) formalism, as implemented in this work. We consider the most relevant scattering mechanisms governing intraband and multi-subband transitions in NWTs, including phonon, surface roughness and ionized impurity scattering, whose rates have been calculated directly from the Fermi’s Golden rule. In this paper, we couple multi-slice Poisson–Schrödinger solutions to the KG method to analyze the impact of various scattering mechanisms on the mobility of small diameter nanowire transistors. As demonstrated here, phonon and surface roughness scattering are strong mobility-limiting mechanisms in NWTs. However, scattering from ionized impurities has proved to be another important mobility-limiting mechanism, being mandatory for inclusion when simulating realistic and doped nanostructures, due to the short range Coulomb interaction with the carriers. We also illustrate the impact of the nanowire geometry, highlighting the advantage of using circular over square cross section shapes.

Effects of GaN interlayer on the transport properties of lattice-matched AlInN/AlN/GaN heterostructures

We study the effects of GaN interlayer on the transport properties of two-dimensional electron gases confined in lattice-matched AlInN/AlN/GaN heterostructures. It is found that the Hall mobility is evidently enhanced when an additional ultrathin GaN interlayer is introduced between AlInN and AlN layers. The enhancement of the Hall mobility is especially remarkable at low temperature. The high Hall mobility results in a low sheet resistance of 23 Ω/◻ at 2 K. Meanwhile, Shubnikov-de Haas oscillations (SdH) are also remarkably enhanced due to the existence of GaN interlayer. The enhancement of the SdH oscillations is related to the larger quantum mobility μq owing to the suppression of the interface roughness, alloy disorder, and ionized impurity scatterings by the GaN interlayer.

Electron transport in ZnMgO/ZnO heterostructures

We numerically calculate the wave function of two-dimensional electron gas (2DEG) for use in 2DEG transport theory and study the electron transport in ZnMgO/ZnO heterostructures. For strongly confined 2DEG, the temperature dependence of the electron mobility is satisfactorily explained using 2DEG transport theory. The interface roughness and ionized impurity scatterings play important roles in the electron transport at low and moderate temperatures. At room temperatures polar optical phonon scattering is the most important scattering mechanism. For heterostructures having two parallel conduction paths in the 2DEG at the ZnMgO/ZnO interface and in the ZnO thick layer, the electron transport is contributed by the two paths. We calculate the mobility for the respective conduction paths, and then combine the two mobility components to fit the experimental data. The theoretical calculations are in good agreement with the experimental data.

The effect of nanostructuring on thermoelectric transport properties of p-type higher manganese silicide MnSi1.73

Higher manganese silicide (HMS) alloys have a complex band structure with multiple valleys close to the conduction and valence band edges, which complicates the analysis of their electronic transport properties. We present a semi-classical two-band model that can describe the charge carrier and phonon transport properties of p-type HMS in crystalline and bulk nanostructured forms. The effect of grain boundaries is modeled with an interface potential scattering for charge carriers and diffusive and refractive scattering for phonons. A unique set of effective masses and acoustic phonon deformation potentials are introduced that can explain both electrical and thermal transport properties versus temperature. The acoustic phonon and ionized impurity scatterings for charge carriers and phonon-phonon, point defect, and electronphonon scattering mechanisms for phonons are included in the model. The simplicity of the presented model would be valuable especially for practical purposes. The thermoelectric transport properties of nanostructured HMS were calculated versus grain size and it was shown that even though bulk nanostructuring of HMS enhances thermoelectric performance, it is not sufficient to enhance considerably the figure-of-merit.

High electron mobility of indium oxide grown on yttria-stabilized zirconia

In 2 O 3 heteroepitaxial layers of improved surface morphology and mobility were obtained by pulsed-laser-deposition method supplying proper oxygen to indium ratio on the growing surface, combined with the suppression of thermal decomposition of In2O3 layers. In situ monitoring of reflection high-energy electron diffraction patterns and ex situ monitoring of growth rate of the epilayers grown under different oxygen pressures and growth temperatures revealed that thermal decomposition occurred during the high-temperature growth and the use of significant oxygen pressure could suppress decomposition allowing for an increase in obtainable growth temperatures. As a result of the decomposition control and growth optimization, undoped In2O3 epilayers exhibited atomically flat surfaces, improved Hall mobility of 110cm2∕Vs, and carrier density of 6.6×1018cm−3. The influences of growth and postgrowth conditions on the electrical properties of epilayers were investigated based on charged and neutral impurity scattering models. The origins of the scattering centers of electrons were considered to be the same for both epilayers grown under different growth conditions (oxygen pressure and growth temperature) and annealed in reduced atmosphere after growths, and ionized impurity scatterings such as oxygen vacancy are the most probable candidates; however, postgrowth annealing process under 1atm oxygen was considered to generate another scattering center, leading to the decrease in both mobility and carrier density.

Hot-Phonon Effects on Millimeter and Submillimeter Wave Response of Two-Dimensional Hot Electrons in GaAs Quantum Wells

Small-signal ac transport of degenerate two-dimensional hot electrons in GaAs quantum wells is studied for lattice temperatures of 77 and 300 K including deformation potential, acoustic, polar optical and ionized impurity scatterings. The consideration of nonequilibrium optical phonons or hot phonons is found to enhance considerably the 3 dB cut-off frequency (f 3dB ), where the ac mobility μ ac falls to 0.707 of its low-frequency value. f 3dB is shown here to decrease with increasing channel width, and to initially decrease and then rise slowly with increasing carrier concentration.

Ionized Impurity Scattering of Charge Carriers in Crystalline Semiconductors

Within first order perturbation theory the time of electron–ion interaction is assumed to be equal to the time of an electron passing through the crystal region related to one impurity ion. In terms of the relaxation time approximation for nondegenerate semiconductors the mobility μi, limited by elastic ion scattering, is shown to be proportional to T/N2/3; the Hall factor is equal to 1.4. Calculated for various temperatures T the majority carrier mobility dependences on the doping impurity concentration N are in good agreement with known experimental data. It is shown that the Brooks-Herring formula for μBH ∝ T3/2/N overestimates the value of mobility. Comparison of mobility calculation in degenerate crystals with experiments also yields μi < μBH.

Ionized-Impurity Scattering of Majority Electrons in Silicon

The Brooks–Herring approach to ionized-impurity scattering overestimates the low-field mobility of electrons in doped semiconductors. It relies on a static single-site description of the carrier-impurity interaction and on the first Born approximation. We present a consistent ionized-impurity scattering model which accounts for degenerate statistics, dispersive screening and two-ion scattering. The dielectric function is accurately approximated by a rational function. From the Schwinger scattering amplitude a correction to the first Born amplitude is derived. Plasmon scattering as another concentration dependent mechanism is included. Despite the various physical effects taken into consideration the scattering model can be used in Monte Carlo transport calculations without any significant increase in computation time. Monte Carlo calculations of majority electron mobility in silicon are discussed, and good agreement with experimental data is found in the doping range [10 14, 10 20]cm −3.

An Improved Ionized Impurity Scattering Model forMonte Carlo Calculations

The well known Brooks‐Herring (BH) formula for charged‐impurity (CI) scattering overestimates the mobility of electrons in highly doped semiconductors. The BH approach relies on a static, single‐site description of the carrier‐impurity interactions neglecting many‐particle effects. We propose a physically based charged‐impurity scattering model including Fermi‐ Dirac statistics, dispersive screening, and two‐ion scattering. An approximation for the dielectric function is made to avoid numerical integrations. The resulting scattering rate formulas are analytical. Monte Carlo calculations were performed for majority electrons in bulk silicon at 300 K with impurity concentrations from 1015 cm3 to 1021 cm3.

Ionized Impurity Scattering in Isotopically Engineered, Compensated Ge:Ga,As

Ionized Impurity Scattering in Isotopically Engineered, Compensated Ge:Ga,As

Efficient Evaluation of Ionized-Impurity Scattering in Monte Carlo Transport Calculations

Carrier scattering by ionized impurities is strongly anisotropic, and events with small scattering angles are highly preferred. On the Monte Carlo technique applied to semiconductor device modeling this behavior imposes several problems which are discussed. We present a method which reduces the amount of low-angle scattering very effectively. Instead of the anisotropic scattering mechanism an equivalent isotropic mechanism is defined which gives the same momentum relaxation time. Depending on doping concentration and carrier energy the equivalent scattering rate is up to four orders of magnitude lower. By analyzing the Boltzmann transport equation a condition is derived on which the use of the equivalent scattering model is justified. The equivalence of the anisotropic and the isotropic scattering models is also demonstrated empirically by means of Monte Carlo calculations. The plain Brooks-Herring model is employed as well as an improved model including momentum-dependent screening and coherent multi-potential scattering. An empirical correction to attenuate the peak of the scattering rate at low energies is presented, and the statistical screening model of Ridley is critically discussed.

Calculations of high-frequency response of two-dimensional hot electrons in GaAs quantum wells

Small-signal ac mobility of two-dimensional (2D) degenerate hot electrons in a GaAs square quantum well is studied on a heated drifted Fermi–Dirac distribution function for the carriers. Carrier energy loss via longitudinal optic (LO) phonons, and the momenta losses via LO, acoustic and ionized impurity scatterings are considered. The ac mobility is found to drop off with frequency beyond 100 GHz although the drift velocity starts to lag behind the applied field at a lower frequency. The ac mobility μac and the phase angle φ increase with the rise of the channel width and the 2D carrier concentration. However, the 3-dB cut-off frequency f3 dB is found to decrease with increasing channel width. The values of μac and f3dB are higher but those of φ are lower at 300 K than that at 77 K.

Hall effect and impurity levels in lead doped indium selenide

Hall effect and deep hole level studies in indium selenide single crystal doped with lead are reported. The temperature dependence of the hole mobility can be interpreted by combining the homopolar optical phonon and the ionized impurity scatterings. Electrical properties above 180 K are dominated by an acceptor center at 0.48 eV from the valence band. Moreover, two hole traps of 0.49 and 0.63 eV depths have been evidenced by deep-level transient spectroscopy measurements. These centers are probably associated with defects or defect complexes due to lead atoms precipitated in the interlayers of the crystal.

Hall effect and deep level transient spectroscopy measurements in indium selenide doped with chlorine

Abstract The temperature dependence of the Hall effect has been studied on InSe single crystals doped with Cl. The electron mobility can be explained by combining the homopolar optical-phonon and the ionized impurity scatterings. Moreover, two electron traps of depths 0.66 and 0.30 eV have been investigated by deep-level transient-capacitance spectroscopy measurements (DLTS). The first level is present in both pure and doped samples, while the second level only appears in doped samples.

Investigation of the electrical properties of Cd-doped indium selenide

Resistivity, Hall-effect, and deep-level transient spectroscopy measurements have been performed on Cd-doped InSe single crystals grown by the Bridgman–Stockbarger method. The temperature dependence of the hole mobility can be explained by combining the optical phonon and the ionized impurity scatterings. Two hole-trapping levels have been detected at 0.42 and 0.48 eV above the valence band with a capture cross section of about 10−17 cm2. Finally, we have found the latter trap to be a deep acceptor level, which is very probably associated with defects or defect complexes formed by the dopant atoms.

Quantum limit cyclotron resonance in semiconductors

The electron scattering behaviour in semiconductors is explored at the quantum limit for Ge, GaAs and InSb, making use of the FIR cyclotron resonance. The inverse relaxation time, or the scattering rate, has been obtained for acoustical deformation potential phonon scattering in Ge, neutral impurity scattering in GaAs, ionized impurity scattering in Ge and InSb, and electron-carrier scattering in GaAs and InSb. It is found that the inverse relaxation time shows a TB 1 2 dependence for phonon scattering, NT 0B − 1 2 dependence for neutral and ionized impurity scatterings and a linear concentration dependence for electron-carrier scattering. Ionized impurity scattering has a stronger rate than neutral impurity scattering, nearly by an order of magnitude, although the dependence on the physical parameter is of the same form for these two scattering types. The dramatic difference in size between electron-neutral donor and electron-neutral acceptor scatterings observed in classical cyclotron resonance is carried over to the quantum limit. All in all, the scattering rate is simply proportional to the density of scatterers.

The Effect of Scattering Mechanisms on Transverse Magnetoresistance in Piezoelectric Semiconductors

The transverse magnetoresistance in nondegenerate piezoelectric semiconductors has been investigated according to the acoustic phonon scattering, the piezoelectric scattering, and the ionized-impurity scattering. The energy band of carriers in semiconductors is assumed to be nonparabolic. Results show that the transverse magnetoresistance for these three types of scattering depends strongly on the dc magnetic field and temperature. It is found that the effect of the piezoelectric and ionized-impurity scatterings on the transverse magnetoresistance is much smaller than that of the acoustic phonon scattering in the lower magnetic field region. However, in the high-magnetic field region, the effect of the piezoelectric scattering becomes comparable to the effect of the acoustic phonon scattering, while the effect of the ionized-impurity scattering is still insignificant.