Electron inelastic mean free paths in solids: A theoretical approach

In the present paper, the inelastic mean free path (IMFP) of incident electrons is calculated as a function of energy for silicon (Si), oxides of silicon (SiO2 ), SiO, and Al2O3 in bulk form by employing atomic/molecular inelastic cross sections derived by using a semi-empirical quantum mechanical method developed earlier. A general agreement of the present results is found with most of the available data. It is of great importance that we have been able to estimate the minimum IMFP, which corresponds to the peak of inelastic interactions of incident electrons in each solid investigated. New results are presented for SiO, for which no comparison is available. The present work is important in view of the lack of experimental data on the IMFP in solids.     

Determination of the inelastic mean free path of electrons in GaAs and InP after surface cleaning by ion bombardment using elastic peak electron spectroscopy

The inelastic mean free path (IMFP) of electrons is an important material parameter needed for quantitative AES, EELS and non-destructive depth profiling. The distinction between the terms for IMFP and the attenuation length (AL) has been established by ASTM standards. A practical experimental method for determining values of the IMFP is elastic peak electron spectroscopy (EPES). In this method, experimentally determined ratios of elastically backscattered electrons from test surfaces and from a Ni reference standard are compared with the values evaluated theoretically.The present paper reports systematic measurements of the IMFP by EPES for GaAs and InP. They are carried out in two laboratories using two different electron spectrometers: a CMA in Budapest and DCMA in Warsaw. Prior to measurements, the samples were amorphized by high-energy Ar⁺ ions (100–400 keV), and the surface composition was determined by quantitative XPS. Argon cleaning produces enrichment of samples in the surface layer in Ga (80%) and In (70%), respectively. The experiments refer to a such modified sample surface that was considered in Monte Carlo calculations. The experimental data were analyzed using calibration curves from Monte Carlo calculations which account for multiple elastic scattering events. This approach has been used previously for elemental solids and is now extended to amorphized binary compounds. The experimental values of IMFP obtained in both laboratories exhibited a reasonable agreement with the available literature data in the 0.1–3.0 keV energy range. With respect to the information depth of EPES, the experimental results refer to the bulk composition within a reasonable extent.     

B与N掺杂对单层石墨纳米带自旋极化输运的影响

通过第一性原理计算研究了具有锯齿状边沿并且具有反铁磁构型的单层石墨纳米带的自旋极化输运.研究发现,在中心散射区同一位置掺入单个B和N原子,尽管对整个体系磁矩的影响完全相同,但对两个自旋分量电流的影响却完全相反.掺B时,自旋向上的电流显著大于自旋向下的电流;而掺N时,自旋向下的电流显著大于自旋向上的电流.这是由于不管掺B还是掺N都将打破自旋简并,使得导带和价带中自旋向上的能级比自旋向下的能级更高.掺B引入空穴,使完全占据的价带变为部分占据,从而自旋向上的能级正好处于费米能级,使得电子透射能力更强、电流更大,而自旋向下的能级则离费米能级较远使电子透射的能力较弱.掺N则引入电子,使得原来全空的导带变为部分占据,从而费米能级穿过导带中自旋向下的能级,使得自旋向下的电子比自旋向上的电子透射能力更强. 关键词： 自旋极化输运 单层石墨纳米带 第一性原理 非平衡格林函数     

Rashba spin-orbit effect on dwell time of electrons tunneling through semiconductor barrier

A study on characteristics of electrons tunneling through semiconductor barrier is evaluated, in which we take into account the effects of Rashba spin-orbit interaction. Our numerical results show that Rashba spin-orbit effect originating from the inversion asymmetry can give rise to the spin polarization. The spin polarization does not increase linearly but shows obvious resonant features as the strength of Rashba spin-orbit coupling increases, and the amplitudes of spin polarization can reach the highest around the first resonant energy level. Furthermore, it is found that electrons with different spin orientations will spend quite different time through the same heterostructures. The difference of the dwell time between spin-up and spin-down electrons arise from the Rashba spin-orbit coupling. And it is also found that the dwell time will reach its maximum at the first resonant energy level. It can be concluded that, in the time domain, the tunneling processes of the spin-up and spin-down electrons can be separated by modulating the strength of Rashba spin-orbit coupling. Study results indicate that Rashba spin-orbit effect can cause a nature spin filter mechanism in the time domain.     

Inelastic mean free path, surface excitation parameter, and differential surface excitation parameter in Au for 300-3000 eV electrons

An analytical approach for simultaneously determining an inelastic mean free path (IMFP), a surface excitation parameter (SEP) and a differential SEP (DSEP) with absolute units was applied for the analysis of absolutely measured reflection electron energy loss spectra for Au. The IMFP, SEP and DSEP in Au for 300-3000 eV electrons are successfully obtained. The obtained DSEPs show a reasonable agreement with those theoretically calculated. The present SEPs were compared with those calculated by several empirical equations, revealing that the present SEPs are close to those calculated using the Oswald's equation. The IMFPs for Au determined by the present analysis were compared with those calculated by the TPP-2M predictive equation, revealing that the present IMFPs are in fairly good agreement with those calculated by the TPP-2M equation. The results confirmed that the present approach is effective for experimentally determining the SEP, DSEP, and IMFP for electrons in solids.     

蒙特卡洛方法计算材料表面激发参数

电子非弹性散射平均自由程（IMFP）是用表面电子能谱进行表面化学定量分析时极为重要的一个参数,它可以用测量的弹性峰电子能谱分析以及蒙特卡洛模拟来确定.为了更加精确地确定电子非弹性散射平均自由程,必须对弹性峰电子能谱中的表面激发效应进行修正,通常使用介电响应理论方法计算得到的表面激发参数.然而,通过理论计算得到的表面激发参数不能包含电子在材料内部输运过程中弹性散射的影响,进而影响所测的电子非弹性散射平均自由程的准确度.在这个工作中,我们采用蒙特卡洛方法来确定包含弹性散射效应时的表面激发参数.所得到的表面激发参数在不同能量、角度情况下,尤其是在弹性散射效应显著的60°以上的大角度入射、出射情况下,都与实验测量值符合得非常好.基于这些新确定的表面激发参数,可以在弹性峰电子能谱测量中获得更为准确的电子非弹性散射平均自由程数据.     

Possibility of new effects in quantum wells coupled by Coulomb interaction

The hamiltonian for two 2-dimensional layers of electrons (neglecting spin), is similar to that of a free electron gas with the role of spin-up and spin-down electrons being played by electrons in two layers. An anomalous ground state analogous to the spiral spin density wave (SSDW) state presents intriguing possibilities.     

Spin-tunneling time in a hybrid semimagnetic/semiconductor heterostructure with a single paramagnetic layer

We investigate spin-dependent tunneling times in a hybrid semimagnetic/semiconductor heterostructure with a single paramagnetic layer under the influence of both electric and magnetic fields. We find that the tunneling times for electrons strongly depend on the incident energy, the magnitude of the external fields, and on their spin orientation. The results indicate that the tunneling time for spin-up electrons can be longer than that for spin-down ones by up to several orders of magnitude. This implies that tunneling for spin-up and spin-down electrons are separated in time within the same heterostructure.     

Surface sensitivity of Auger-electron spectroscopy and X-ray photoelectron spectroscopy

A convenient measure of surface sensitivity in Auger-electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS) is the mean escape depth (MED). If the effects of elastic-electron scattering are neglected, the MED is equal to the electron inelastic mean free path (IMFP) multiplied by the cosine of the emission angle with respect to the surface normal, and depends on the material and electron energy of interest. An overview is given here of recent calculations of IMFPs for 50–2000 eV electrons in a range of materials. This work has led to the development of a predictive formula based on the Bethe equation for inelastic electron scattering in matter from which IMFPs can be determined. Estimates show, however, that elastic-electron scattering can significantly modify the MED. Thus, for AES, the MED will be reduced by up to about 35%. For XPS, however, the MED can be changed by up to ±30% for common measurement conditions although it can be much larger (by up to a factor of 2) for near-grazing emission angles. Ratios of MED values, calculated with elastic scattering considered and neglected for XPS from the 3s, 3p, and 3d subshells of silver with Mg Kα X-rays are approximately constant (to about 10%) over a range of emission angles that varies from 40° to 60° depending on the subshell and the angle of X-ray incidence. Recommendations are given on how to determine the optimum range of emission angles for satisfactory analysis of angle-resolved XPS (ARXPS) data. Definitions are included of three terms often used for describing surface sensitivity (IMFP, MED, and effective attenuation length (EAL)), and examples are given of the varying magnitudes of these quantities for different analytical conditions.     

Zero-field spin splitting in a two-dimensional electron gas with the spin-orbit interaction revisited

We consider a two-dimensional electron gas (2DEG) with the Rashba spin-orbit interaction (SOI) in the presence of a perpendicular magnetic field. We derive analytical expressions of the density of states (DOS) of a 2DEG with the Rashba SOI in the presence of a magnetic field by using the Green's function technique. The DOS allows us to obtain the analytical expressions of the magnetoconductivities for spin-up and spin-down electrons. The conductivities for spin-up and spin-down electrons oscillate with different frequencies and give rise to the beating patterns in the amplitude of the Shubnikov-de Haas (SdH) oscillations. We find a simple equation which determines the zero-field spin splitting energy if the magnetic field corresponding to any beat node is known from the experiment. Our analytical results reproduce well the experimentally observed non-periodic beating patterns, number of oscillations between two successive nodes and the measured zero-field spin splitting energy.     

Spin-polarized transmission through a mesoscopic ring with a magnetic impurity

Based on one-dimensional quantum waveguide theory we study the symmetry of the spin-polarized transmission through an Aharonov–Bohm ring with a magnetic impurity, in which the spin-exchange interaction between an incident electron and the magnetic impurity leads to spin–flip scattering. It shows that for some special Fermi energies, both spin-up and spin-down transmission coefficients are symmetric under the flux reversal in the spin–flip scattering process and the spin-polarized conductance also is symmetric. In above case, AB oscillations of spin-down transmission and reflection are perfectly identical. The effect of the exchange interaction strength and Fermi wave vector on transmission behavior of spin-state electrons is examined.     

Probing collective modes of correlated states of few electrons in semiconductor quantum dots

Low-lying collective excitations above highly correlated ground states of few interacting electrons confined in GaAs semiconductor quantum dots are probed by resonant inelastic light scattering. We highlight that separate studies of the changes in the spin and charge degrees of freedom offer unique access to the fundamental interactions. The case of quantum dots with four electrons is found to be determined by a competition between triplet and singlet ground states that is uncovered in the rich light scattering spectra of spin excitations. These light scattering results are described within a configuration-interaction framework that captures the role of electron correlation with quantitative accuracy. Recent light scattering results that reveal the impact of anisotropic confining potentials in laterally coupled quantum dots are also reviewed. In these studies, inelastic light scattering methods emerge as powerful probes of collective phenomena and spin configurations in quantum dots with few electrons.     

High-efficiency spin filtering in salophen-based molecular junctions modulated with different transition metal atoms

Based on the density functional theory and nonequilibrium Green's function methods, we investigate the spin transport properties of the molecular junctions constructed by a homologous series of 3d transition metal(II) salophens (TM-salophens, TM = Co, Fe, Ni and Mn) sandwiched between two gold electrodes. It is found that among the four molecular junctions only Co-salophen junction can act as an efficient spin filter distinctively. The conductance through Co-salophen molecular junction is dominated by spin-down electrons. The mechanism is proposed for these phenomena.     

Low-temperature spin coulomb drag in a two-dimensional electron gas

The phenomenon of low-temperature spin Coulomb drag in a two-dimensional electron gas is investigated. The spin transresistivity coefficient is essentially enhanced in the diffusive regime, as compared to conventional predictions. The origin of this enhancement is the quantum coherence of spin-up and spin-down electrons propagating in the same random impurity potential and coupled via the Coulomb interaction. A comprehensive analysis of spin and interlayer Coulomb drag effects is presented.     

自旋轨道耦合和磁场对准一维铁磁/半导体/铁磁系统中电子输运性质的影响

利用传递矩阵方法，我们计算了自旋轨道耦合和磁场对准一维铁磁/半导体/铁磁系统中电子输运性质的影响。计算结果发现，透射系数的振幅随磁场增加而增大。在反铁磁排列时，即使在磁场作用下，上、下自旋电子具有相同的透射系数。与不加磁场时的情况相反，在一定的磁场和耦合强度时，铁磁排列中，上自旋电子的透射系数大于下自旋电子的，而且出现了自旋反转。     

Ⅱ-Ⅵ族稀磁半导体多层结构中的自旋极化隧穿

采用转移矩阵法和Airy函数,研究了ZnSe/ZnMnSe/ZnSe/ZnBeSe/ZnSe/ZnBeSe/ZnSe异质结构的自旋极化输运。在外加偏压和磁场对电子透射系数和自旋极化率的影响方面,所得到的结论显现出复杂而有趣的特性。磁场对自旋向上和向下电子隧穿的影响是不同的:对于自旋向上情况,出现双共振向单共振转换现象。     

Electron-phonon interaction in an impure metal

On the basis of the existing theory of ultrasonic attenuation, a model Hamiltonian is derived which has to replace the Fröhlich Hamiltonian, at least in an impure metal. Whilst the imaginary part of the phonon self-energy is easily connected with the ultrasonic attenuation constant, the same quantity of the electrons allows no conclusion on inelastic collisions in this case. Therefore, from the linear response function, a kinetic equation for the electrons is derived. It is found that the time between inelastic collisions with phonons increases if impurities are added to the metal.     

Opposite spin asymmetry of elastic and inelastic scattering of nonequilibrium holes injected into a ferromagnet

The spin asymmetry of elastic and inelastic scattering of nonequilibrium holes injected into Co thin films is examined using a p-type magnetic tunnel transistor. Spin-dependent transmission yields a positive or negative magnetocurrent depending on Co thickness and hole energy. Up to a critical thickness of about 3 nm, (quasi)elastic scattering dominates with a short attenuation length (<1 nm) and preferential attenuation of holes in the majority spin bands, consistent with spin-wave emission. At a larger Co thickness, inelastic scattering dominates with a larger attenuation length ( approximately 4 nm) and opposite spin asymmetry.     

Spin Polarization and Andreev Conductance through a Diluted Magnetic Semiconductor Quantum Wire with Spin--Orbit Interaction

Spin-dependent Andreev reflection and spin polarization through a diluted magnetic semiconductor quantum wire coupled to normal metallic and superconductor electrodes are investigated using scattering theory. When the spin-orbit coupling is considered, more Andreev conductance steps appear at the same Fermi energy. Magnetic semiconductor quantum wire separates the spin-up and spin-down electrons. The Fermi energy, at which different- spin-state electrons begin to separate, becomes lower due to the effect of the spin-orbit interaction. The spin filter effect can be measured more easily by investigating the Andreev conductance than by investigating the normal conductance.     

Relative electron inelastic mean free paths for diamond and graphite at 8 keV and intrinsic contributions to the energy-loss

We used hard X-ray photoelectron spectroscopy (HAXPES) with 8 keV X-rays to investigate the 1s emission of carbon. We recorded spectra extending from the peak of the C 1s electrons (“elastic” line) to electrons with up to 110 eV energy-loss. Using two samples side by side, we could compare the inelastic mean free paths (IMFPs) of the electrons of almost 8 keV in diamond and graphite and find them to be practically identical despite about 50% difference in densities. Published extrapolations of their IMFP calculations at lower energies are in good agreement with this result. We show that information from the almost structureless region of overlapping multiple extrinsic energy-losses can be used to quantify the fraction of photoelectrons experiencing intrinsic energy-losses (those due to the sudden creation of the hole). We find that this fraction is 58% of the primary excited C 1s electrons for diamond and is practically the same for graphite. This is at first sight an unexpected result since hole-screening should differ in a semimetal from that in an insulator. The observation can be accounted for by dynamic screening in contrast to static screening.