Surfaces, Interfaces, and Layered Devices Building blocks for nanodevices! W. Pauli: God made solids, but surfaces were the work of Devil. Surfaces and Interfaces 1
Role of surface effects in mesoscopic objects A / V = 6a 2 / a 3 = 6 / a = 6 V -1/3 t 1. Why are surfaces important in Nanophysics? Are their properties different from bulk? Jonas V = a 3 (2a) 3 = 8 a 3 (5a) 3 = 125 a 3 (10a) 3 = 1000 a 3 Percentage of surface atoms : 100% 100% 78,4% 48,8% Macroscopic: V = (10 8 a) 3 = 10 24 a 3 A = 6 (10 8 a) 2 = 6 10 16 a 2 Percentage of surface atoms: 6 10-6 %!!! (negligible) https://www.chem.wisc.edu Introduction to Nanophysics 2
Progress in miniaturisation By Cmglee - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=16991155 Introduction 3
Interface between a crystal and vacuum: 1D Schematic representation of the potential landscape in a finite crystal, which gets modified close to the surface. Surface states (S) may result, with typical energies inside the gap between the valence band (VB) and the conduction band (CB) t 3. What is the origin of surface states? Where do they come from and where are they located in band structures of semiconductors? Surfaces and Interfaces 4
Tight binding model To find energies and wave functions one should solve the Schrödinger equation in a realistic potential, which often has to be found in a self-consistent way generally difficult! 1D chain of 10 atoms. The surface states are split from other N-2 states, their energies turn out to be larger (or smaller) than those of bulk states Surfaces and Interfaces 5
Tight binding model Overlap integral Transfer integral 5. thow do surface states appear in the tight binding model in crystalvacuum interface? Have they got anything to do with Bloch s theorem solutions with imaginary wave vectors and evanescent waves? Give an example of a surface wave function in one dimension. Surfaces and Interfaces 6
Tight binding model Surfaces and Interfaces 7
Tight binding model t 5. How do surface states appear in the tight binding model in crystalvacuum interface? Have they got anything to do with Bloch s theorem solutions with imaginary wave vectors and evanescent waves? Give an example of a surface wave function in one dimension. Surfaces and Interfaces 8
Tight binding model Energy of surface states in the one-dimensional Shockley model, shown as a function of the lattice constant a. After [ShockleyI939]. At e.g. a 2, both a donor-like and an acceptor-like surface states are present. t 6. Is it possible to have contribution to surface states from different bands? Can they be of different character of doping (n, p)? Maue-Shockley states no modification of the potential Tamm-Goodwin states due to modification of the potential In general more complicated than simple models 3. twhat is the origin of surface states? Where do they come from and where are they located in band structures of semiconductors? Surfaces and Interfaces 9
Nearly free electron model t 7. Can surface states be derived from the nearly-free-electron model? Does the imaginary part of the wave vector play a role there? Does the model of nearly free electrons give qualitatively different results from the tight binding model? Surfaces and Interfaces 10
Nearly free electron model Surfaces and Interfaces 11
Surface states emerge from the conduction and valence band since the total number of states is conserved. Surface states are usually partly filled, so the chemical potential is located within the surface band. Hence, the energy bands get bent and the Fermi level gets pinned utmost important for semiconductor heterostructures. Surface states in real systems are complicated. In particular, one has to allow for: So-called surface reconstruction (change of symmetry) Changes in the surface potential to preserve electrical neutrality Possibilities for surface states to serve as donors and acceptors Surfaces and Interfaces 12
Band bending and Fermi level pinning What happens to the surface states if the material is doped? Usually both donor-like and acceptor-like surface states will appear, and that leads to important complications. Let us consider an example of a n-doped semiconductor. Then the donor electrons in the conduction band will reduce their energy by occupying the acceptor-like surface states. In this way a negative surface charge will be generated, counterbalanced by a positive charge from ionized donors in the depletion layer near the surface. 4. What is the origin of band bending? At what conditions and in what materials does it happen? Is charge redistribution important for this process? Surfaces and Interfaces 13
Illustration: Depleted layer 8. t Can different types (donor-like and acceptorlike) of surface bands be partially filled? What is the charge neutrality level in semiconductors with intrinsic charge carriers? To what energy level are surface states filled in a neutral and a charged surface? Z dep Before equilibration 9. What is surface depletion layer in n-doped semiconductors? How thick is it typically? What is the link between surface and bulk density of states in doped semiconductors? After equilibration: the surface gets charged, an upward band bending results, the Fermi level gets pinned keeping neutrality Surfaces and Interfaces 14
How to find the thickness of the depleted layer? If the donors are fully ionized then the charge density is. Then, the Poisson equation gives the z-dependence of the potential: Then The total surface density,, is still small compared to the integrated density of surface states, so the chemical potential is almost independent of the doping concentration. 10. What is a typical ratio of surface charge density to integrated density of surface states? Does chemical potential at the surface change a lot due to the charge transfer? What is Fermi level pinning by the surface states? 9. What is surface depletion layer in n-doped semiconductors? How thick is it typically? What is the link between surface and bulk density of states in doped semiconductors? Surfaces and Interfaces 15
Semiconductor-metal interfaces Schottky barriers Ohmic contacts Surfaces and Interfaces 16
Band bending In a p-type material the bands bend downwards creating a well for electrons rather than a barrier. n-type semiconductor junction to a metal and a p- type semiconductor junction to a metal Work function in a metal of the at the interface of (a) a low metal and n-type, (b) a low work function metal and a p-type semi conductor, (c)a high work function metal and a n-type semi conductor, (d)a high work function metal and a p-type semi conductor. (Figure adapted from H. Luth's Solid Surfaces, Interfaces, and Thin Films, p. 384 ) Surfaces and Interfaces 17
Interfaces are like surfaces; it is semi-extended functions that have to match at the interface. Most interesting are the situations where the states are located in the conduction band of one component, but in the gap of other one. Most important example the states in the gap of a semiconductor, but in a conduction band of a metal. The extended wave functions in a metal induce evanescent waves in a semiconductor the so-called induced gap states (IGS). These states are similar to the decaying wave function in vacuum. 11. What are induced gap states (ISG) close to a metal-semiconductor interface? Are IGSs semiconductorspecific? What are they built from? Surfaces and Interfaces 18
Band alignment and Schottky barrier Work function Electron affinity Typical energy band alignment between a metal (left) and a semiconductor (right) before charge transfer across the interface is allowed. t 2. What are work function and electron affinity? Why does the latter need to be introduced in semiconductors and insulators? New feature - induced gap interface states (IGS) due to matching of the wave functions. Interface states can be both donor-like and acceptor-like Surfaces and Interfaces 19
Before charge transfer After charge transfer from donors 12. What is the consequence of a charge moving from metal to semiconductor? What is the extent of the formed dipole? What is the Schottky barrier? Does redistribution of dopants in bulk change this picture? What is the scale of dopants redistribution in space? After charge transfer from metal Schottky barrier Surfaces and Interfaces 20
Schottky model Interface states are ignored Schottky barrier 13. How does the Schottky barrier height depend on work function of different metals in contact with the semiconductor? How is the Schottky barrier height calculated? What is its typical value in ev? Positions of the Fermi levels of a metal and a n-doped semiconductor in equilibrium as obtained within the Schottky model. Surfaces and Interfaces 21
Conventional semiconductor interface: p-n junction The regions nearby the p n interfaces lose their neutrality and become charged, forming the space charge region or depletion layer http://en.wikipedia.org/wiki/p%e2%80%93n_junction Surfaces and Interfaces 22
Schottky diode (semiconductor is grounded) 14. What is a Schottky diode and how does it work? Band diagram at positive (a) and negative (b) voltage (semiconductor is grounded) Current-voltage curve Surfaces and Interfaces 23
Variety of Applications. The Schottky diode is used in a wide variety of applications. It can naturally be used as a general-purpose rectifier. However, in terms of RF applications, it is particularly useful because of its high switching speed and high-frequency capability. Schottky diodes are similarly very good as RF detectors as their low capacitance and forward-voltage drop enable them to detect signals which an ordinary PN junction would not see. It has already been mentioned that the Schottky diode has a high-current density and low forward-voltage drop. As a result, Schottky diodes are widely used in power supplies. By using these diodes, less power is wasted, making the supply more efficient. The Schottky diode is used in logic circuits as well as a fundamental building block in a number of other devices Surfaces and Interfaces 24
Ohmic contacts Ohmic contacts can take place when conduction band of both sides overlap InAs - metal Without Schottky barrier 15. Describe how to make Ohmic contact to a semiconductor. With narrow Schottky barrier (heavily doped) Surfaces and Interfaces 25
Semiconductor heterointerfaces Alignment of surface chemical potentials n p Quantum charge is neglected Before charge transfer Equilibration of bulk chemical potentials Surfaces and Interfaces 26
Types of alignment in heterostructures Type I, center Type II, staggered Type II, misaligned 16. What are heterointerfaces? Explain 2 different scales of charge redistribution in p-n heterojunctions. Do induced gap states appear there? What are 3 basic types of band alignments in semiconductor heterointerfaces? What are staggered and misaligned alignments? Surfaces and Interfaces 27
There are many theoretical models for the interface band alignment. However, the agreement between theory and experiments is often hampered by surface defects and imperfections, interface strains, etc. Still, the state-of-art technology can provide close-to-perfect interfaces, which can be considered by modern analytical and numerical models. The simplest (and least accurate) model is, which predicts the band alignment based on the properties of vacuumsemiconductor interfaces (in particular the vacuum ). The main limitation is its neglect of chemical bonding. Surfaces and Interfaces 28
Field effect transistors and quantum wells Si-MOSFET GaAs-HEMT Other devices Jonas Nano FET Surfaces and Interfaces 29
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Si-MOSFET 17. What are MOSFET and HEMT? Which device is based on Si and which on GaAs? Illustrate MOSFET by drawing. How does it differ from a Schottky diode? Does this transistor rely on the electrostatic field effect? p-doped Si Metallic gate Ohmic contacts, n-doped Oxide, SiO 2 Band alignment along the dashed line at V g = 0 Surfaces and Interfaces 33
V g = 0 V g > 0 V g < 0 Inversion (acc. of electr.) Accumulation of holes 18. What is inversion and accumulation in MOSFET? What are ambipolar devices? Ambipolar device: using both EG (gas) and HG. Surfaces and Interfaces 34
Wave functions and eigenenergies: Simple model Splitting of variables Triangular potential approximation Schrödinger equation Dimensionless variable Localization length -z 0 /l F z= l F ( +z 0 /l F ) Airy function p. 241 Building blocks for nanodevices 35
Energy quantization is given by the roots Quasi 2DEG 2DEG Fermi level Each level generates a sub-band in the energy spectrum Building blocks for nanodevices 36
Transverse wave functions in a triangle well z = l F ( +z 0 /l F ) Normalized electron densities Building blocks for nanodevices 37
Quasi-two-dimensional electron gas and Size quantization discrete modes! Quantized levels of transverse motion 19. What are specific properties of the electron gas that is formed at the O S interface in MOSFET (density, spatial extent, possibility of energy quantisation, separation from the ionised donors, impurity scattering, mobility, effective mass, location with respect to interface)? What is two-dimensional electron gas (2DEG)? What is quasi-two-dimensional electron gas? Electron density profile Ions and electrons are separated and Coulomb scattering is relatively weak However, oxide is amorphous and the interface scattering is noticeable Surfaces and Interfaces 38
Energy bands in Ga As and Si GaAs -m e,1 = m e,2 = m e,3 = 0.067m m hh (Si) = 0.54m, m lh (Si) = 0.15m, m hh (GaAs) = 0.51m, and m lh (GaAs) = 0.08m Si -perpendicular to the ΓX direction, m e,t = 0.19m, along the ΓX direction, m e,l = 0.92m. TH Update of solid state physics 39
Usage of Si-MOSFETs for digital electronics according to CMOS-technology, as well as most important circuits for realizing logical operations are briefly discussed in the Sec. 3.4.1.1 of the textbook. 20. Where are Si MOSFET circuits used? What are advantages of Si MOS material systems? What is complementary MOS (CMOS) concept? How can CMOS circuits reduce power consumption? What are NOT and NAND gates? How could NAND gates be used for building a storage cell? Surfaces and Interfaces 40
GaAs-HEMT Typical choice interface Al 0.3 Ga 0.7 As - GaAs, Type I alignment, conduction band of Al 0.3 Ga 0.7 As is 300 mev higher than that one of GaAs. The top of the Al 0.3 Ga 0.7 As valence band is 160 mev below that of GaAs. 21. What is the design of Ga[Al]As high electron mobility transistor (HEMT)? What is the principle of modulation doping? What determines the density of the 2DEG in HEMT? How can it be tuned? In contrast to Si, GaAs remains undoped, and the electrons are provided by the doping layer (Si) inside the Al 0.3 Ga 0.7 As. This is called the modulation doping. Surfaces and Interfaces 41
GaAs-HEMT for RF technology 22. What allows increasing electron mobility and mean free path in HEMT and what is the progress over years? Do these parameters depend on temperature? Surfaces and Interfaces 42
Why d-doping is advantageous? Scattering potential Doping layer 2DEG The scattering matrix elements is W k,k <k V k> 2 Matrix element Backscattering is exponentially suppressed large mobility Building blocks for nanodevices 43
GaAs-HEMT: modulation doping Cross section of a GaAs/AlGaAs/InGaAs phemt equilibrium. of GaAs/AlGaAs -based HEMT, at Surfaces and Interfaces 44
Advantages of GaAs-based systems: Crystalline structure, low interface scattering; Doped layer is rather remote from the two-dimensional electron gas; Very high mobility: the present record is 1440 m 2 /Vs, that corresponds to the mean free path of 120 μm. Possibility to engineer band offsets by varying content of Al. In this way one can make quantum wells. Surfaces and Interfaces 45
Quantum confined vs. bulk carriers Evolution of electron mobility over time, after modulation doping was introduced After L. Pfeiffer et al., 1989. Surfaces and Interfaces 46
Scattering mechanisms in GaAs: 2D Significance of various scattering mechanisms in Ga[Al]As HEMT Dots experimental results for the structure with Each scattering mechanism can be characterized by its contribution to the carrier mobility μ i, which sum up to the total mobility according to the Matthiesen rule, 1/μ = Σ i 1/μ i 2 Surfaces and Interfaces 47
Scattering mechanisms in GaAs: 2D vs 3D 26. What are main scattering mechanisms in HEMT? What is the difference between scattering in quantum well systems and 3D materials? Is further progress in increasing electron mobilities in quantum-well systems expected? Is inter-band scattering important? GaAs 3D bulk GaAs 2DEG The sample contained a donor density of n v = 4.8x10 19 m -3 and an acceptor density of n A = 2.1x10 19 m -3. 2 Update of solid state physics 48
Many technological problems: lattice matching, interface states, possibilities for modulation doping, etc. Doping of a heterostructure implemented in such way that the resulting free electrons are spatially separated from the positive donor ions; as a result scattering of moving electrons on the dopant atoms is avoided; aslo, due to the separation, electrons remain free and mobile even at the very low temperatures 24. What semiconductors can be combined in layered devices? What is the bandgap engineer s map? Give an example of an efficient quantum well system. Are organic FETs possible? The band gap engineer s map. It is shown which compounds can tolerate http://www.rollitup.org/t/astir-growled-panel-project.563118/page-16 Building blocks for nanodevices
Other types of layered devices Quantum wells 25. Are properties of quantum confined carriers different from those in the bulk? Can effective masses of holes be reversed in quantum wells? Is screening different in quantum wells from that in 3D systems? 23. What is a parabolic quantum well and how can it be made? Surfaces and Interfaces 50
Plastic transistors Less expensive Mechanically soft Organic FET pentacene 24. What semiconductors can be combined in layered devices? What is the bandgap engineer s map? Give an example of an efficient quantum well system. Are organic FETs possible? polythiophene OFET-based flexible display At present time such systems are just in the beginning of the way Surfaces and Interfaces 51
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Summary FETs and quantum well, and other layered devices are widely used. They are also promising for future. Interfaces strongly influence the band structure, in particular, dispersion laws, effective masses, etc. Many issues are already understood, but many things have to be done. Organic transistors are in the beginning of their way. Surfaces and Interfaces 53