Impact Ionization and Carrier Multiplication

The “Li-drifted germanium detector” (http://en. wikipedia. org/wrki/Germanium_ detector#Germanium_detector.) is an elegant commercially available solid-state

Impact Ionization and Carrier Multiplication Подпись: (8.1)

device to measure the energy of a single high-energy gamma ray photon. A pure single crystal of germanium is treated in a special way with lithium, so that the mean free paths of electrons and holes are larger than the dimensions of the device. Metallic electrodes apply a small bias voltage across the germanium, and a sensitive detector of the charge flow in the circuit is provided. The germanium is pure and is also cooled to 77 K, the temperature of liquid nitrogen, so that the numbers of thermally generated free electrons and free holes is low, and only a small background current flows. A gamma ray, that is, a photon of high energy (MeV) Ey = hf ^ Eg, is absorbed, creating initially an electron in the conduction band and a hole in the valence band, whose kinetic energies add up to hf — Eg. The final result from the single absorbed gamma ray photon, an outcome of internal processes in the germanium, is n electrons and n holes flowing in opposite direction across the crystal and into an external charge meter, such that the total measured charge

From this relation, the gamma ray energy hf is deduced from the measured charge Q and the known value of Eg, according to

Подпись:Ey = (Q/2e)Eg.

Подпись: Figure8.5 Exampleofintermediate band solar cell [104] based on quantum dots. Here, “ARC” represents “antireflection coating” and “S-doping” means a pure deposit, in this case of Si. The indicated quantum dots are InAs, which have also been used to lower the threshold

current in versions of GaAs heterojunction lasers. The authors [104] found extra photocurrent in this structure arising from lower energy photons, substantiating an aspect ofthe model depicted in Figures 8.2-8.4.

The carrier multiplication process that occurs within the extremely pure semiconductor creates n = (hf/Eg) electron-hole pairs from the initial high-energy electron-hole pair. The high-energy carriers reduce their kinetic energy by colli­sions creating additional electron-hole pairs of lower energy, and in this process loss of energy to lattice vibrations (phonons) apparently is not an important effect.

A similar process would be beneficial in the efficiency of solar cells, to capture energy from the portion of the solar spectrum in the range hf > Eg. This process in a solar cell could multiply the conversion efficiency by a large factor.

The idea of a quantum dot was given in connection with Equations 2.11-2.16, and later in section 3.3.1 of Chapter 3. The wavefunction Equation 2.16 and energy level Equation 2.11 of a single electron in a confining potential of width L is given in Chapter 2 and generalized to three dimensions in Chapter 3, see Equation 3.15.

In the present context, quantum dots are 3D structures introduced locally in a junction device such as a solar cell or junction laser.

A quantum dot may be called an “artificial atom,” characterized by discrete sharp electron energy states, and sharp absorption and emission wavelengths for photons.

Transmission electron microscope (TEM) images of such nanocrystals, which may contain only 50 000 atoms, reveal perfect crystals having the bulk crystal structure and bulk lattice constant. Quantitative analysis ofthe light emission process in QDs suggests that the bandgap, effective masses of electrons and holes, and other microscopic material properties are very close to their values in large crystals of the same material. The light emission comes from radiative recombination of an electron and a hole, created initially by the shorter wavelength illumination.

The energy Er released in the recombination is given entirely to a photon (the quantum unit of light), according to the relation Er = hv — hc/l. Here, v and l are, respectively, the frequency and wavelength of the emitted light, c is the speed of light 3 x 108m/s, and his Planck’s constant h = 6.63 x 10~34 J s = 4.136 x 10~15 eVs. The color of the emitted light is controlled by the choice of L, since Er = Eg + Ee + Eh, where Eg is the semiconductor bandgap, and the electron and hole confinement energies, Ee and Eh, respectively, become larger with decreasing L as h2/8mL2.

These confinement (blueshift) energies are proportional to 1/L2. Since these terms increase the energy of the emitted photon, they act to shorten the wavelength of the light relative to that emitted by the bulk semiconductor, an effect referred to as the “blueshift” of light from the quantum dot. These nanocrystals are used in biological research as markers for particular kinds of cells, as observed under an optical microscope with background ultraviolet light (UV) illumination.

In these applications, the basic semiconductor QD crystal is coated with a thin layer to make it impervious to (and soluble in) the aqueous biological environment. Another coating may then be applied that allows the QD to preferentially bond to a specific biological cell or cell component of interest. The biological researcher may, for example, see the outer cell surface illuminated in green while the surface of the inner cell nucleus may be illuminated in red, all under illumination of the whole field with light of a single shorter wavelength.

8.2.1

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