used靶材为纯度9999%的镍和纯度9999%的氮化硼(h-BN)

used靶材为纯度9999%的镍和纯度9999%的氮化硼(h-BN) Novel quantum real-space transfer in semiconductor heterostructures 1,21*2*Chuan Jin, Zhenqiang Chen, Jianxin Chen 1 (College of Science and Engineering, Jinan University, Guangzhou 510632, China 2Key Laboratory of Infrared Imaging Material and Detectors Shanghai Institute of Technical Physics, Chinese Academy of Sciences Shanghai 200083, China) ABSTRACT Real-space transfer (RST) has many excellent characteristics, such as high speed, high frequency and negative differential resistance(NDR). RST has drawn a lot of attention since it was proposed by Z.S.Gribnikov in 1972. However, most of the researches about RST were restricted to the classical regime with the hot electron theory. Quantum real-space transfer (QRST) which relies solely on the wave nature of electrons has not been given sufficient attention. In this work, the quantum real-space transfer was deeply investigated. AlInAs/GaAsSb/AlInAs alternative symmetry 0.480.520.510.490.480.52 quantum-well structures was designed, and each thickness of the layer(is 10 nm, 12 nm, 10nm. We carried out theoretical calculations on the wave-function module and the electrons confinement probability as the function of the in-plane wave-vector. According to our calculations，a sharp electron transfer occurs in the wave-vector range of 663.42×10-7.6×10 /cm. Therefore, it’s feasible to achieve a quantum real-space transfer. We also compared the results to that of the previous quantum structures. At last we propose the optimization to realize quantum real-space transfer (QRST) and discuss the potential applications of the quantum real-space transfer. Keywords: real-space transfer, quantum effect 1. INTRODUCTION 1-2The repeated pulses of microwave current have been observed in the n-type GaAs and InP substrates by Gunn in 1966. For the scattering of electron in different energy valley inducing the phenomenon, we called these transfer as electron effect or Gunn effect. The Gunn effect happens in the momentum space. 1972, Z.S. Gribnikov gave the concept of the 3electron real-space transfer effect. This effect is different from the Gunn effect , because it happens in different heterostructures, not in the momentum space. Different from the Gunn effect, RST has many unique excellent characteristics, such as negative differential resistance(NDR), high speed, the response time in pico-seconds(ps). Soon, 4-6RST found applications in some three-terminal devices, i.e. field-effect transistors and charge-injection transistors. Scientists also expanded the applications of RST, and developed a few of new devices, such as logic devices, microwave 7-9sources, lasers , luminescent devices and so on. RST has many different forms in the thickness of the material layer from the heterostructure, band discontinuities and structural parameters. In accordance with the difference in forms, the RST has different theoretical descriptions. Conditionally the different forms and descriptions differed in two opposite sides : classic RST and quantum RST. The classic RST has been studied and reviewed in great detail. As is shown above, in these devices, the RST is restricted to classic RST, which is based on the hot electron theory, and assumes sufficient sizes of the layers forming the heterostructure. Due to the heating effect of a parallel electric field, electrons have enough kinetic energy and momentum to cross the barrier of the heterostructure. So achieving the classic RST usually needs a high electrical field, which may cause some problems in heating and reliability in devices applications. On the contrast, quantum RST, originates solely from wave nature of electrons in small sizes of the heterostructure layers. QRST depends on the spatial distribution of wave function with the longitudinal momentum of electrons, so QRST can avoid the problem due to heating of electron scattering. In this paper, we presents a novel QRST heterostructrue, then we calculates the structural parameters. Form the calculations, we got the wave-function module square with the in-plane wave vector and the confinement probability of electrons in different layers as the function of in-plane wave vector, the wave-vector range of sharp electron transfers. At last, we give the feasibility of the experiment which verify the QRST. 2. STRUCTURE 10The concept of QRST has been proposed in the late 1990s. The structure of Yang’s QRST is the step quantum well structure as show in Fig. 1. Figure 1: Schematic illustration of a step quantum well comprising layers 1 and 2 with the conduction band edge offset δ(k) TLayers 1and 2 are made of two semiconductors with different effective masses, and a small conduction band edge offset δ(k). With different effective masses, the different QWs have different energy-momentum dispersion relations, so the T dispersion relations will intersect in special wave-vector, then the spatial distribution of the wave-function in different layers changes with the changing of longitudinal wave-vector. From figure 1, the electrons has been confined in layer 1 when k is small, However when the longitudinal wave-vector k is larger than the k ,the electron wave-function shifts to T layer 2. That is the process of the quantum real-space transfer (QRST). We propose that a novel AlInAs/ GaAsSb/ AlInAs alternative quantum well structure is based on the 0.480.520.510.490.480.52 model of Yang. This QW structure is sandwiches between the wide band gap semiconductor in order to conform to the wave-guide structure, at the same time the outside layer is made of a material having a potential barrier large enough to 11-13confine the electron in the quantum well structure as show in Fig.2. Figure 2: The schematic diagram of energy band-edge lineup of AlInAs/GaAsSb/AlInAs heterostructure 0.480.520.510.490.480.52The structure has a large difference effective masses between these materials, m(GaAsSb) =0.052 m; me 0.510.490e [14]15(AlInAs) =0.075 m; m(AlAsSb) =0.125 m，where m is the free-electron mass. The conduction band 0.480.520e 0.560.4400 offset between AlInAs and GaAsSb is ?E=0.05 eV. we assume that when there is no parallel electric field, 0.480.520.510.49c the electrons confine in GaAsSblayer , however the electrons will transfer to AlInAs layer with increase the 0.510.49 0.480.52 electric field. The thickness of QW structure is 120 Å GaAsSb and 100 Å AlInAs. The alternative QW 0.510.490.480.52structure is symmetry and is first be purposed. 3. THEORETICAL COMPUTATION As a novel QRST quantum well structure, the theoretical calculations of QRST is obvious different from the classic RST. The calculation of the classic RST involves the scattering mechanism, such as the alloy scattering, the phonon scattering, the LO scattering, then simulation the process through the Monte Carlo method. However QRST solve the problem by the eigen wave-function of electrons. The effective mass m, the thickness W of layer and the confinement potential V is e show in Fig. 3. Figure 3: Schematic potential and effective mass of alternative QW rThe eigen wave-function ,()rcorresponding to the electron’s total energy E is determined by the Schrodinger equation: 2rrrh1 (1)-蜒yyyrVxrEr+=(())()()()m2e The m and V change spatially along the x direction. Considering the electron wave-function propagating along the z e direction, so we write the wave-function as r,,()()exp()rxikz, (2) The k is mode propagation constant. The Schrodinger equation change to 2222hhkd,z (3),，,,()()()VxEx,,a222mdxmaa 2222hhkd,z (4),，,,()()()VxEx,,b222mdxmbb Where Va and Vare the potential energy in the GaAsSb and AlInAs layers, respectively, k is the b 0.510.490.480.52z longitudinal wave-vector in the propagation direction, because of the translation symmetry, the wave-vector is the same for different layers. The above equation is the standard eigenvalue equation for electron wave-function. The egienvalue for equation in ground state is shown mkWbxatan()'kk, (5)x2ma mmVVmm2(),,222bbbbaakkk，,,' (6)xz2mmhaa 222 (7)kmEVk,,,2()/hxaaz 222 (8)kmVEk'2()/,,，hbbz 22From the above equations, we can get the egienenergy in the x direction depends on the Ekm,h/2xxa mmlongitudinal wave-vector k as we expected. So the eigen wave-function ,()xalso depends on the k. If the <, zzab the electron wave-function shifts from GaAsSblayer primarily to AlInAs layer, when the longitudinal 0.510.49 0.480.52wave-vector k increases. After substituting the structures parameters into the equations, we have the wave-function z distribution and the confinement probability of electron in different layers as the function of longitudinal wave-vector k. z They are shown in Fig.4 and 5. Figure 4: The wave-function module square with three values of longitudinal wave-vector (in units of inverse Bohr radius a), Bthe dashed lines indicate the positions of heterointerfaces As show in Fig.4, it give the electron wave-function module square with the different longitudinal wave-vector k, the zresult of the calculation is self-consistent due to the sum is 1. The figure clearly give that when the wave-vector is 0, the 6wave-function confined in the GaAsSb layer, but when the wave-vector is 5.76×10 /cm, the wave-function 0.510.49 confined in the AlInAs layer. We can learn that the process is the electron of the GaAsSb layer transfering 0.480.520.510.49into the AlInAs layer. 0.480.52 Figure 5: The confinement probability of electrons in each layer as the function of longitudinal wave-vector ( in units of inverse Bohr radius a), the dashed lines indicate the sharp transfers. BIt can be seen that the confinement probability of electrons in different layers vary with the k. When the kincreases, the zzconfinement probability of electrons in GaAsSb layer vary from 0.9 to 0, opposite to the probability in 0.510.4966AlInAs layer vary from 0.1 to 0.9. Except the above, there is a sharp variety in the range of 3.42×10-7.6×10 /cm, 0.480.52 we can consider the electron has a sharp transfer. [10] Through the theory model of the Yang, we got the critical wave-vector equation keF,,/h (9)c For typical value of the scattering time of 1 ps and a reasonable electric field of 5 kV/cm, we can get the calculation of 6the kis 7.6×10 /cm. It’s feasible to achieve quantum real-space transfer. c Compared with the above alternative QW and the step QW, the sharp transfer is obviously different. The sharp wave-vector of the alternative QW is much smaller than step QW. In other words, the electron has a sharp transfer in alternative QW that only needs a smaller electric field in theory than the step QW. However the wave-vector of the alternative QW has a larger span, thus it can cause some other problems such as the scattering of electron when the electric field increases. From the calculation of the QRST, it is clear that the QRST is solely on the wave nature of electrons. It can help us to understand the QRST profoundly. However there are also some problems with QRST since we don’t consider the scattering effect in QRST structure. Because the scattering of electron reduces the quantum effect, we need much higher quantum efficiency of structures to verify the QRST in real experiment. The QRST has many excellent characteristics due to the quantum mechanism, it has many prospects of application in many areas .For example, the QRST is sensitive to the magnitude of the band-edge offsets, so it can measure the small band-edge offsets. Except that, we can use it to make a switch to control the electron transport. At last, for the response [16]time in ps, there are many applications in microwave source, e. g. the THz oscillation generator. 4. SUMMURY We propose a novel quantum real-space transfer alternative quantum well structure, then calculates the structure. 66According to the calculation, there is a sharp transfer in the wave-vector range of 3.42×10-7.6×10 /cm. We analyze the feasibility of QRST in the experiment. Through comparing the structures with the pervious structure, we give the problem which we need to solve. For next step, we will demonstration the QRST effect experimently. REFERENCES 1. J.B.Gunn. 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