surfaces, interfaces, and layered devices -...

Surfaces and Interfaces 1

Surfaces, Interfaces, and Layered Devices

Building blocks for nanodevices!

W. Pauli: “God made solids, but surfaces were the work of Devil.”


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)

Interface between a crystal and vacuum


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


Energy of surface states in the one-dimensional Shockley model, shown as a function of the lattice constant a. After [ShockleyI939].

At e.g. a2, 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


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


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.


Before equilibration

After equilibration: the surface gets charged, an upward band bending results, the Fermi level gets pinned keeping neutrality

Illustration:

Zdep

Depleted layer


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.


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


Semiconductor-metal interfaces

Schottky barriers Ohmic contacts


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.


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.

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

Work function


Before charge transfer After charge transfer from donors

After charge transfer from metal

Since depletion layer is very thin, the step is drawn as sharp

Schottky barrier


Positions of the Fermi levels of a metal and a n-doped semiconductor in equilibrium as obtained within the Schottky model.

Interface states are ignored

Schottky model Schottky barrier


Schottky diode

Current-voltage curve

(semiconductor is grounded)

Band diagram at positive (a) and negative (b) voltage (semiconductor is grounded)


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


Ohmic contacts

Without Schottky barrier

Ohmic contacts can take place when conduction band of both sides overlap

With narrow Schottky barrier (heavily doped)

InAs - metal


Conventional semiconductor interface: p-n junction


Semiconductor heterointerfaces

n p

Before charge transfer

Equilibration of bulk chemical potentials

IGS

Alignment of surface chemical potentials

IGS

“Quantum charge” is neglected


Types of alignment in heterostructures

Type I, center

Type II, staggered

Type II, misaligned


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.


Field effect transistors and quantum wells

Si-MOSFET GaAs-HEMT

Other devices


Si-MOSFET

p-doped Si

Ohmic contacts

Oxide, SiO2

Metallic gate

Band alignment along the dashed line at Vg= 0


Vg = 0

Vg > 0

Inversion (acc. of electr.) Vg < 0

Accumulation of holes

Ambipolar device

Building blocks for nanodevices 25

Wave functions and eigenenergies: Simple model

Triangular potential approximation

Schrödinger equation

Splitting of variables

Dimensionless variable

Localization length

Airy function


Energy quantization is given by the roots

Each level generates a sub-band in the energy spectrum

Fermi level

2DEG

Quasi 2DEG


Transverse wave functions in a triangle well

Normalized electron densities


and Size quantization – discrete modes!

Quantized levels of transverse motion

Electron density profile

Quasi-two-dimensional electron gas

However, oxide is amorphous and the interface scattering is noticeable

Ions and electrons are separated and Coulomb scattering is relatively weak


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.


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 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 Al0.3Ga0.7As. This is called the modulation doping.


2DEG

Doping layer

Why δ-doping is advantageous?

Scattering potential

Matrix element

Backscattering is exponentially suppressed

large mobility


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.


Evolution of electron mobility over time, after modulation doping was introduced After L. Pfeiffer et al., 1989.

Quantum confined vs. bulk carriers


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


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. 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


Other types of layered devices

Quantum wells


Organic FET

pentacene

polythiophene

“Plastic” transistors • Less expensive

• Mechanically soft

At present time such systems are just in the beginning of the way


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.

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