Band bending in semiconductor
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The depletion width associated with the Schottky barrier depends upon the doping level of the semiconductor, and is generally far too large to allow tunneling to occur. At these boundaries, the electronic structure of the materials must align, creating the phenomenon known as band bending. Glatzel et al.164 performed KPFM under both dark and illuminated conditions necessary to extract locally resolved SPV for conjugated polymer/fullerene organic solar cells, as shown in Figure 2.8d.
Understanding band bending is fundamental to designing and optimizing contemporary microelectronics.
Understanding Energy Levels in Solids
In solid materials, electrons are not free to possess any amount of energy but are instead confined to specific ranges called energy bands. This approach exploits a natural characteristic of the interface, and avoids the use of a discrete barrier layer and the accompanying problems with pinholes and thickness uniformity.
This barrier is due to the difference in work functions between the metal and the semiconductor. By understanding how band bending is affected by various factors, such as temperature, radiation, and mechanical stress, engineers can identify potential failure modes and develop mitigation strategies.
7. KPFM has also been extensively applied to map variations in SPV, i.e., the change in the work function with illumination (Φilluminated − Φdark).
Also, it is expected that the charge trapping in the metal-organic dye interface is responsible for this high value of Rs. By increasing the dye concentration, the no of charge carriers are increased which in turn increase the device performance.
In the modern world of solid-state electronics, nearly every digital technology relies on the precise interaction of different materials brought together at an interface.
The conduction band is the next-highest energy range, where electrons are free to move throughout the material, readily carrying an electric current. This separation prevents the charge carriers from recombining and drives them toward external contacts, where they can be collected as an electric current.
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This method discretizes the semiconductor into a grid of points, and approximates the derivatives in Poisson’s equation using finite differences.4.2.2 Finite Element Method
Another popular numerical method is the finite element method.
This charge transfer leads to the redistribution of charges near the interface, resulting in a bending of the energy bands.
Band bending is crucial for several reasons:
- It affects the electrical properties of the device, such as the barrier height and the depletion width.
- It influences carrier transport and recombination processes.
- It plays a significant role in the operation of semiconductor devices, including diodes, transistors, and solar cells.
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The samples showed a typical granular topographic structure, and by comparing with KPFM potential captured under dark/light conditions, it was possible to deduce a reduced surface band bending upon illumination. This geometric representation of the energy change is what is referred to as band bending, and its shape dictates the electrical properties of the interface.
How Band Bending Controls Electronic Devices
The curvature of the energy bands near an interface controls the movement of charge carriers, which is the operational basis for nearly all semiconductor devices.
Fundamentals of Band Bending
To understand band bending calculation from potential, it is essential to grasp the basics of semiconductor physics, including energy bands, Fermi levels, and the concept of charge neutrality.
2.1 Energy Bands and Fermi Levels
In a semiconductor, the energy bands are divided into the valence band and the conduction band, separated by a forbidden gap.
These simulations solve Poisson’s equation numerically, taking into account the full charge density distribution.
4.2.1 Finite Difference Method
One common numerical method is the finite difference method. The band bending effect for the migration of charge carriers produce a potential barrier near interfaces.
When a metal is brought into contact with a semiconductor, charge transfer occurs to align the Fermi levels of the two materials. These junctions, often involving a semiconductor, a metal, or an insulator, are the functional heart of devices that process and store information. This behavior is a consequence of quantum mechanics, where the closely packed atoms in a crystal lattice cause the discrete energy levels of individual atoms to merge into these continuous bands.
They demonstrated mapping of the SPV (or open circuit potential) on hybrid organic/inorganic perovskite films at an imaging rate of ~16 frames/second.
Electrical Spin Injection and Transport in Semiconductors
Published in Evgeny Y. Tsymbal, Igor Žutić, Spintronics Handbook: Spin Transport and Magnetism, Second Edition, 2019
Berend T.
Jonker
One avenue is to take advantage of the band bending which occurs at the metal/semiconductor interface. But due to the disorder of the organic material, presence of traps, recombination of carriers at the metal-semiconductor interface, the current flow through the device is very low. So the carriers will not come out from the electrode and the current, as well as the mobility of the charge carriers, becomes very low.
For example, in n-GaAs, the depletion width is on the order of 100 nm for n ∼ 1017 cm−3, and 40 nm for n ∼ 1018 cm−3 [102]. These states can trap charge carriers, modifying the space charge region and the barrier height.
5.4 External Fields and Biases
External fields and biases, such as applied voltages or temperature gradients, can also influence band bending.