Surfaces, Interfaces, and Layered Devices

1. Surfaces, Interfaces, and Layered Devices Building blocks for nanodevices! W. Pauli: “God made solids, but surfaces were the work of Devil.” Surfaces and Interfaces TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAA

2. Interface between a crystal and vacuum Surface states (S) may result, with typical energies inside the gap between the valence band (VB) and the conduction band (CB) Schematic representation of the potential landscape in a finite crystal, which gets modified close to the surface. Surfaces and Interfaces

3. 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-2states, their energies turn out to be larger than those of bulk states Surfaces and Interfaces

4. At e.g. a2, both a donor-like and an acceptor-like surface states are present. Energy of surface states in the one-dimensional Shockley model, shown as a function of the lattice constant a. After [ShockleyI939]. 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

5. 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

6. 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

7. After equilibration: the surface gets charged, an upward band bending results, the Fermi level gets pinned keeping neutrality Depleted layer Illustration: Zdep Before equilibration Surfaces and Interfaces

8. The total surface density, , is still small comparing to the integrated density of surface states, so the chemical potential is almost independent of the doping concentration. 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 Surfaces and Interfaces

9. In a p-type material the bands bend downwards creating a well for electrons rather than a barrier. Surfaces and Interfaces

10. Semiconductor-metal interfaces Schottky barriers Ohmic contacts Surfaces and Interfaces

11. Interfaces are like surfaces; it is semi-extendedfunctions that have to match at the interface. Most interesting are the situations where the states are located in the conductionbandof one component, but in the gapof other one. Most important example – the states in the gap of a semiconductor, but in a conduction band of a metal. Theextendedwave functions in a metal induce evanescentwaves in a semiconductor – the so-called induced gap states (IGS). These states are similar to the decaying wave function in vacuum. Surfaces and Interfaces

12. Work function Electron affinity New feature - induced gap interface states (IGS) due to matching of the wave functions. Interface states can be both donor-like and acceptor-like Band alignment and Schottky barrier Typical energy band alignment between a metal (left)and a semiconductor(right)before charge transfer across the interface is allowed. Surfaces and Interfaces

13. After charge transfer from donors Before charge transfer After charge transfer from metal Schottky barrier Since depletion layer is very thin, the step is drawn as sharp Surfaces and Interfaces

14. Schottky barrier Schottky model 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

15. Current-voltage curve Schottky diode (semiconductor is grounded) Band diagram at positive (a) and negative (b) voltage (semiconductor is grounded) Surfaces and Interfaces

16. 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

17. With narrow Schottky barrier (heavily doped) Ohmic contacts Ohmic contacts can take place when conduction band of both sides overlap Without Schottky barrier Surfaces and Interfaces

18. Alignment of surface chemical potentials Equilibration of bulk chemical potentials Semiconductor heterointerfaces n p IGS Before charge transfer Surfaces and Interfaces

19. Type II, misaligned Type II, staggered Types of alignment in heterostructures Type I, center Surfaces and Interfaces

20. Field effect transistors and quantum wells Si-MOSFET GaAs-HEMT Other devices Surfaces and Interfaces

21. p-doped Si Ohmic contacts Metallic gate Oxide, SiO2 Band alignment along the dashed line at Vg= 0 Si-MOSFET Surfaces and Interfaces

22. Vg > 0 Inversion (acc. of electr.) Vg < 0 Accumulation of holes Vg = 0 Ambipolar device Surfaces and Interfaces

23. Wave functions and eigenenergies: Simple model Splitting of variables Triangular potential approximation Schrödinger equation Dimensionless variable Localization length Airy function Building blocks for nanodevices

24. Each level generates a sub-band in the energy spectrum Energy quantization is given by the roots Quasi 2DEG 2DEG Fermi level Building blocks for nanodevices

25. Transverse wave functions in a triangle well Normalized electron densities Building blocks for nanodevices

26. and Quantized levels of transverse motion Electron density profile Ions and electrons are separated and Coulomb scattering is relatively weak However, oxide is amorphous and the interface scattering is noticeable Size quantization – discrete modes! Quasi-two-dimensional electron gas Surfaces and Interfaces

27. GaAs-HEMT Typical choice – interface Al0.3Ga0.7As - GaAs, Type I alignment, conduction band of Al0.3Ga0.7As is 300 meV higher than that one of GaAs. The top of the Al0.3Ga0.7As is 160 meV below that one of GaAs. In contrast to Si, GaAs remains undoped, and the electrons are provided by the doping layer (Si) inside the Al0.3Ga0.7As. This is called the modulation doping. Surfaces and Interfaces

28. Why d-doping is advantageous? Scattering potential Doping layer 2DEG Matrix element Backscattering is exponentially suppressed large mobility Building blocks for nanodevices

29. Surfaces and Interfaces

30. 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 m2/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

31. 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

32. Significance of various scattering mechanisms in Ga[Al]As HEMT Dots – experimental results for the structure with Surfaces and Interfaces

33. 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 Many technological problems: lattice matching, interface states, possibilities for modulation doping, etc. Building blocks for nanodevices

34. Other types of layered devices Quantum wells Surfaces and Interfaces

35. pentacene polythiophene Organic FET • “Plastic” transistors • Less expensive • Mechanically soft At present time such systems are just in the beginning of the way Surfaces and Interfaces

36. 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