Mobility of Holes and Electrons in High Electric Fields
TL;DR: In this paper, the field dependence of mobility has been determined for electrons and holes in both germanium and silicon, and the observed critical field at 298\ifmmode^\circ\else\textdegree\fi{}K beyond which $\ensuremath{\mu}$ varies as ${E}^{-}\frac{1}{2}}$.
Abstract: The field dependence of mobility has been determined for electrons and holes in both germanium and silicon. The observed critical field at 298\ifmmode^\circ\else\textdegree\fi{}K beyond which $\ensuremath{\mu}$ varies as ${E}^{\ensuremath{-}\frac{1}{2}}$ is 900 volts/cm for $n$-type germanium, 1400 volts/cm for $p$-type germanium, 2500 volts/cm for $n$-type silicon, and 7500 volts/cm for $p$-type silicon. These values of critical field are between two to four times those calculated on the basis of spherical constant energy surfaces in the Brillouin zone. A saturation drift velocity of ${6(10)}^{6}$ cm/sec is observed in germanium which is in good agreement with predictions based on scattering by the optical modes. Data on $n$-type germanium at 20\ifmmode^\circ\else\textdegree\fi{}K show a range over which impurity scattering decreases and the mobility increases with field until lattice scattering dominates as at the higher temperatures.
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TL;DR: In this paper, it was shown that the observed falloff in the f T of a transistor at high currents is due to the spreading of the neutral base layer into the collector region of the device at high current densities.
Abstract: It is shown that the observed falloff in the f T of a transistor at high currents is due to the spreading of the neutral base layer into the collector region of the device at high current densities. The base layer spreading mechanism derives from an analysis of the effect of the current-dependent buildup of the mobile-carrier space-charge density in the collector transition layer. Calculations show that at sufficiently high collector current levels, the mobile space-charge density in the collector transition layer cannot be considered negligible in comparison to the fixed charge density of that region. The over-all effect of taking the mobile space charge into account in analyzing the collector transition region is that, at high current densities, the transition region boundary adjacent to the neutral base layer is displaced toward the collector metal contact with increasing collector current. The attendant widening of the neutral base layer results in the observed, high-current falloff in f T . The application of this theory to transistor structures of both the alloy and mesa variety yields, in each case, calculated curves of f T vs I c which are in reasonably good agreement with experiment.
569 citations
TL;DR: The electron current in a semiconductor at uniform lattice temperature, with a nonuniform electric field distribution (e.g., a barrier layer), consists of terms arising from conduction, diffusion, and thermal diffusion as discussed by the authors.
Abstract: The electron current in a semiconductor at uniform lattice temperature ${T}_{0}$, with a nonuniform electric field distribution (e.g., a barrier layer), consists of terms arising from conduction, diffusion, and thermal diffusion. The first two terms involve the mobility and diffusion coefficient which are functions of the electron temperature $T$ or, more generally, depend on certain averages over the nonequilibrium, field-dependent electron energy distribution function. The third term is due to the electron temperature gradient and is analogous to conventional thermal diffusion of a gas in a temperature gradient. In conventional theory, which neglects electron heating or cooling, the mobility and diffusion coefficient are material constants and thermal diffusion is absent. Contrary to the case of uniform fields, $T$ is not a unique function of the local field; it also depends on the current and can only be determined by a simultaneous solution of the equations for current flow and conservation of energy with boundary conditions for a particular structure. As an example, a one carrier metal-semiconductor contact rectifer has been analyzed in detail including a discussion of the Peltier effect. In the barrier region $T$ is greater than ${T}_{0}$ (i.e., hot electrons) for a reverse bias but less than ${T}_{0}$ (i.e., cold electrons) for a forward bias. Computer solutions have been obtained for a Schottky barrier and electron scattering due to acoustic phonons only.
472 citations
01 Jan 1965
TL;DR: In this article, a simple analysis showed that the ultimate performance limits of a transistor are set by the product Ev_{s}/2\pi, where E is the semiconductor's dielectric breakdown strength and v is its minority carrier saturated drift velocity.
Abstract: A simple analysis shows that the ultimate performance limits of a transistor are set by the product Ev_{s}/2\pi , where E is the semiconductor's dielectric breakdown strength and v_{s} is its minority carrier saturated drift velocity. This product, having a value of about 2 \times 10^{11} volts/ second for silicon, emphasizes that a semiconductor material has a maximum capability for energizing the electric charges that process a signal. If the device operating frequency is high, the frequency time period is short and only a small amount of energy can be given to a charge carrier. Consequently, the power and power amplification must be relatively low. At low frequencies the inverse is true. That is, device physics demands an inverse relation between frequency and power parameters that is independent of the thermal dissipation arguments commonly given to explain the trade-off between these parameters. The analysis leads to an effective means for making comparisons between existing devices. This is illustrated.
460 citations
TL;DR: Semiconductor photodiodes were developed in the early 'Forties approximately at the time when the photomultiplier tube became a commercial product (RCA 1939) as mentioned in this paper.
Abstract: Semiconductor photodiodes were developed in the early `Forties approximately at the time when the photomultiplier tube became a commercial product (RCA 1939) Only in recent years, with the invention of the Geiger-mode avalanche photodiodes, have the semiconductor photo detectors reached sensitivity comparable to that of photomultiplier tubes The evolution started in the `Sixties with the p-i-n (PIN) photodiode, a very successful device, which is still used in many detectors for high energy physics and a large number of other applications like radiation detection and medical imaging The next step was the development of the avalanche photodiode (APD) leading to a substantial reduction of noise but not yet achieving single photon response The weakest light flashes that can be detected by the PIN diode need to contain several hundreds of photons An improvement of the sensitivity by 2 orders of magnitude was achieved by the development of the avalanche photodiode, a device with internal gain At the end of the millennium, the semiconductor detectors evolved with the Geiger-mode avalanche photodiode into highly sensitive devices, which have an internal gain comparable to the gain of photomultiplier tubes and a response to single photons A review of the semiconductor photo detector design and development, the properties and problems, some applications and a speculative outlook on the future evolution will be presented
385 citations
TL;DR: In this paper, it was shown that α and β remain constant over a practical range of multiplied photocurrents, and that α does not reduce the device bandwidth as long as the dc multiplication M 0 is less than α/β.
Abstract: The short‐circuit photocurrent from an avalanche photodiode is calculated using an exact solution of the differential transport equations for the multiplication region. The dcelectric field and the hole and electron velocities are assumed constant in the avalanche region into which photoelectrons are injected. It is shown that the electron‐ and hole‐ionization coefficients α and β remain constant over a practical range of multiplied photocurrents. Computer studies of the solution show that avalanche multiplication does not reduce the device bandwidth as long as the dc multiplication M 0 is less than the ratio of α and β, i.e., as long as M0 α/β. The previously unspecified ``effective'' transit time, τ1, in this equation is approximately τ1 = N(β/α)τ, where N is a number varying slowly from ⅓ to 2 as β/α varies from 1 to 10−3, and τ is the multiplication‐region transit time. The complete solution of this problem thus shows that the widely different results previously obtained for β/α = 0 and β/α = 1 are continuously joined, and provides a simple criterion for judging the ranges of validity of the two limiting cases. The results emphasize the practical importance of obtaining the required multiplication at fields such that M 0<α/β where the multiplication does not affect the bandwidth. This also leads to minimum excess avalanche‐region noise, and hence to the closest possible solid‐state analog to the vacuum‐tube photomultiplier.
291 citations