Semiconductors carriers

Electric current is conducted either by these excited electrons in the conduction band or by holes remaining in place of excited electrons in the original valence energy band. These holes have a positive effective charge. If an electron from a neighbouring atom jumps over into a free site (hole), then this process is equivalent to movement of the hole in the opposite direction. In the valence band, the electric current is thus conducted by these positive charge carriers. Semiconductors are divided into intrinsic semiconductors, where electrons are thermally excited to the conduction band, and semiconductors with intentionally introduced impurities, called doped semiconductors, where the traces of impurities account for most of the conductivity. 

This always holds when the semiconductor is clean, without any added impurities. Such semiconductors are called intrinsic. The balance (4.126) can be changed by adding impurities that can selectively ionize to release electrons into the conduction band or holes into the valence band. Consider, for example, an arsenic impurity (with five valence electrons) in gennanium (four valence electrons). The arsenic impurity acts as an electron donor and tends to release an electron into the system conduction band. Similarly, a gallium impurity (three valence electrons) acts as an acceptor, and tends to take an electron out of the valence band. The overall system remains neutral, however now n p and the difference is balanced by the immobile ionized impurity centers that are randomly distributed in the system. We refer to the resulting systems as doped or extrinsic semiconductors and to the added impurities as dopants. Extrinsic semiconductors with excess electrons are called n-type. In these systems the negatively charged electrons constitute the majority carrier. Semiconductors in which holes are the majority carriers are calledp-type. 

Consider condition 2 when (4.46) is satisfied. From the generation-recombination theorem for a two-carrier semiconductor without minority carrier trapping [4.17],... 

We want to derive in a general way the shot-noise-like expression for generation-recombination (gr) noise used in (4.12) in Subsection 4.1.3. The usual expression for the gr noise current in a two-carrier semiconductor [4.17,18] can be written as... 

Free-electron lasers have long enabled the generation of extremely intense, sub-picosecond TFlz pulses that have been used to characterize a wide variety of materials and ultrafast processes [43]. Due to their massive size and great expense, however, only a few research groups have been able to operate them. Other approaches to the generation of sub-picosecond TFlz pulses have therefore been sought, and one of the earliest and most successfid involved semiconducting materials. In a photoconductive semiconductor, carriers (for n-type material, electrons)... 

Figure Bl.22.4. Differential IR absorption spectra from a metal-oxide silicon field-effect transistor (MOSFET) as a fiinction of gate voltage (or inversion layer density, n, which is the parameter reported in the figure). Clear peaks are seen in these spectra for the 0-1, 0-2 and 0-3 inter-electric-field subband transitions that develop for charge carriers when confined to a narrow (<100 A) region near the oxide-semiconductor interface. The inset shows a schematic representation of the attenuated total reflection (ATR) arrangement used in these experiments. These data provide an example of the use of ATR IR spectroscopy for the probing of electronic states in semiconductor surfaces [44]-...

In an extrinsic semiconductor, tlie conductivity is dominated by tlie e (or h ) in tlie CB (or VB) provided by shallow donors (or acceptors). If tlie dominant charge carriers are negative (electrons), tlie material is called n type. If tlie conduction is dominated by holes (positive charge carriers), tlie material is called p type. 

The application of a small external electric field A to a semiconductor results in a net average velocity component of the carriers (electrons or holes) called the drift velocity, v. The coefficient of proportionality between E and is known as the carrier mobility p. At higher fields, where the drift velocity becomes comparable to the thennal... 

In tenns of the carrier mobility, the electrical conductivity c of an n type semiconductor can be written as... 

Most of our ideas about carrier transport in semiconductors are based on tire assumption of diffusive motion. Wlren tire electron concentration in a semiconductor is not unifonn, tire electrons move diffuse) under tire influence of concentration gradients, giving rise to an additional contribution to tire current. In tliis motion, electrons also undergo collisions and tlieir temporal and spatial distributions are described by the diffusion equation. The... 

In n type semiconductors, electrons are tire majority carriers. Holes will also be present tlirough accidental incoriioration of acceptor impurities or, more importantly, tlirough tlie intentional creation of electron-hole pairs. Holes in n type and electrons in p type semiconductors are minority carriers. 

There are many ways of increasing tlie equilibrium carrier population of a semiconductor. Most often tliis is done by generating electron-hole pairs as, for instance, in tlie process of absorjition of a photon witli h E. Under reasonable levels of illumination and doping, tlie generation of electron-hole pairs affects primarily the minority carrier density. However, tlie excess population of minority carriers is not stable it gradually disappears tlirough a variety of recombination processes in which an electron in tlie CB fills a hole in a VB. The excess energy E is released as a photon or phonons. The foniier case corresponds to a radiative recombination process, tlie latter to a non-radiative one. The radiative processes only rarely involve direct recombination across tlie gap. Usually, tliis type of process is assisted by shallow defects (impurities). Non-radiative recombination involves a defect-related deep level at which a carrier is trapped first, and a second transition is needed to complete tlie process. 

Radiative recombination of minority carriers is tlie most likely process in direct gap semiconductors. Since tlie carriers at tlie CB minimum and tlie VB maximum have tlie same momentum, very fast recombination can occur. The radiative recombination lifetimes in direct semiconductors are tlius very short, of tlie order of tlie ns. The presence of deep-level defects opens up a non-radiative recombination patli and furtlier shortens tlie carrier lifetime. 

The situation is very different in indirect gap materials where phonons must be involved to conserve momentum. Radiative recombination is inefficient, resulting in long lifetimes. The minority carrier lifetimes in Si reach many ms, again in tire absence of defects. It should be noted tliat long minority carrier lifetimes imply long diffusion lengtlis. Minority carrier lifetime can be used as a convenient quality benchmark of a semiconductor. 

Light is generated in semiconductors in the process of radiative recombination. In a direct semiconductor, minority carrier population created by injection in a forward biased p-n junction can recombine radiatively, generating photons with energy about equal to E. The recombination process is spontaneous, individual electron-hole recombination events are random and not related to each other. This process is the basis of LEDs [36]. 

The light emitted in the spontaneous recombination process can leave tire semiconductor, be absorbed or cause additional transitions by stimulating electrons in tire CB to make a transition to tire VB. In tliis stimulated recombination process anotlier photon is emitted. The rate of stimulated emission is governed by a detailed balance between absorjDtion, and spontaneous and stimulated emission rates. Stimulated emission occurs when tire probability of a photon causing a transition of an electron from tire CB to VB witli tire emission of anotlier photon is greater tlian that for tire upward transition of an electron from tire VB to tire CB upon absorjDtion of tire photon. These rates are commonly described in tenns of Einstein s H and 5 coefficients [8, 43]. For semiconductors, tliere is a simple condition describing tire carrier density necessary for stimulated emission, or lasing. This carrier density is known as... 

A logical consequence of this trend is a quantum w ell laser in which tire active region is reduced furtlier, to less tlian 10 nm. The 2D carrier confinement in tire wells (fonned by tire CB and VB discontinuities) changes many basic semiconductor parameters, in particular tire density of states in tire CB and VB, which is greatly reduced in quantum well lasers. This makes it easier to achieve population inversion and results in a significant reduction in tire tlireshold carrier density. Indeed, quantum well lasers are characterized by tlireshold current densities lower tlian 100 A cm . ... 

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