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
Interface between a crystal and vacuum 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) Surfaces and Interfaces 2
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 bended and the Fermi level gets pinned utmost important for semiconductor heterostructures. 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 than those of bulk states Surfaces and Interfaces 3
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. Maue-Shockley states no modification of the potential Tamm-Goodwin states due to modification of the potential In general more complicated than simple models Surfaces and Interfaces 4
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 5
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. Surfaces and Interfaces 6
Illustration: Depleted layer Z dep Before equilibration After equilibration: the surface gets charged, an upward band bending results, the Fermi level gets pinned keeping neutrality Surfaces and Interfaces 7
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. Surfaces and Interfaces 8
In a p-type material the bands bend downwards creating a well for electrons rather than a barrier. Surfaces and Interfaces 9
Semiconductor-metal interfaces Schottky barriers Ohmic contacts Surfaces and Interfaces 10
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. Surfaces and Interfaces 11
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. 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 12
Before charge transfer After charge transfer from donors After charge transfer from metal Schottky barrier Since depletion layer is very thin, the step is drawn as sharp Surfaces and Interfaces 13
Schottky model Schottky barrier Interface states are ignored Positions of the Fermi levels of a metal and a n-doped semiconductor in equilibrium as obtained within the Schottky model. Surfaces and Interfaces 14
Schottky diode (semiconductor is grounded) Band diagram at positive (a) and negative (b) voltage (semiconductor is grounded) Current-voltage curve Surfaces and Interfaces 15
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 16
Ohmic contacts Ohmic contacts can take place when conduction band of both sides overlap InAs - metal Without Schottky barrier With narrow Schottky barrier (heavily doped) Surfaces and Interfaces 17
Conventional semiconductor interface: p-n junction Surfaces and Interfaces 18
Semiconductor heterointerfaces Alignment of surface chemical potentials n p IGS IGS Quantum charge is neglected Before charge transfer Equilibration of bulk chemical potentials Surfaces and Interfaces 19
Types of alignment in heterostructures Type I, center Type II, staggered Type II, misaligned Surfaces and Interfaces 20
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. Surfaces and Interfaces 21
Field effect transistors and quantum wells Si-MOSFET GaAs-HEMT Other devices Surfaces and Interfaces 22
Si-MOSFET p-doped Si Metallic gate Ohmic contacts Oxide, SiO 2 Band alignment along the dashed line at V g = 0 Surfaces and Interfaces 23
V g = 0 V g > 0 V g < 0 Inversion (acc. of electr.) Accumulation of holes Ambipolar device Surfaces and Interfaces 24
Wave functions and eigenenergies: Simple model Splitting of variables Triangular potential approximation Schrödinger equation Dimensionless variable Localization length Airy function Building blocks for nanodevices 25
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 26
Transverse wave functions in a triangle well Normalized electron densities Building blocks for nanodevices 27
and Size quantization discrete modes! Quantized levels of transverse motion Electron density profile Quasi-two-dimensional electron gas Ions and electrons are separated and Coulomb scattering is relatively weak However, oxide is amorphous and the interface scattering is noticeable Surfaces and Interfaces 28
Usage of Si-MOSFETs for digital electronics according to CMOStechnology, as well as most important circuits for realizing logical operations are briefly discussed in the Sec. 3.4.1.1 of the textbook. Surfaces and Interfaces 29
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. 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 30
Why δ-doping is advantageous? Scattering potential Doping layer 2DEG Matrix element Backscattering is exponentially suppressed large mobility Building blocks for nanodevices 31
Surfaces and Interfaces 32
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 33
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 34
Significance of various scattering mechanisms in Ga[Al]As HEMT Dots experimental results for the structure with Surfaces and Interfaces 35
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 The band gap engineer s map It is shown which compounds can tolerate Building blocks for nanodevices 36
Other types of layered devices Quantum wells Surfaces and Interfaces 37
Organic FET pentacene Plastic transistors Less expensive Mechanically soft polythiophene At present time such systems are just in the beginning of the way Surfaces and Interfaces 38
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 39