Carrier Generation and Recombination in P-N Junctions and P-N Junction Characteristics
01 Sep 1957-Vol. 45, Iss: 9, pp 1228-1243
TL;DR: In this article, the authors show that the current due to generation and recombination of carriers from generation-recombination centers in the space charge region of a p-n junction accounts for the observed characteristics.
Abstract: For certain p-n junctions, it has been observed that the measured current-voltage characteristics deviate from the ideal case of the diffusion model. It is the purpose of this paper to show that the current due to generation and recombination of carriers from generation-recombination centers in the space charge region of a p-n junction accounts for the observed characteristics. This phenomenon dominates in semiconductors with large energy gap, low lifetimes, and low resistivity. This model not only accounts for the nonsaturable reverse current, but also predicts an apparent exp (qV/nkT) dependence of the forward current in a p-n junction. The relative importance of the diffusion current outside the space charge layer and the recombination current inside the space charge layer also explains the increase of the emitter efficiency of silicon transistors with emitter current. A correlation of the theory with experiment indicates that the energy level of the centers is a few kT from the intrinsic Fermi level.
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TL;DR: In this article, an upper theoretical limit for the efficiency of p−n junction solar energy converters, called the detailed balance limit of efficiency, has been calculated for an ideal case in which the only recombination mechanism of holeelectron pairs is radiative as required by the principle of detailed balance.
Abstract: In order to find an upper theoretical limit for the efficiency of p‐n junction solar energy converters, a limiting efficiency, called the detailed balance limit of efficiency, has been calculated for an ideal case in which the only recombination mechanism of hole‐electron pairs is radiative as required by the principle of detailed balance. The efficiency is also calculated for the case in which radiative recombination is only a fixed fraction fc of the total recombination, the rest being nonradiative. Efficiencies at the matched loads have been calculated with band gap and fc as parameters, the sun and cell being assumed to be blackbodies with temperatures of 6000°K and 300°K, respectively. The maximum efficiency is found to be 30% for an energy gap of 1.1 ev and fc = 1. Actual junctions do not obey the predicted current‐voltage relationship, and reasons for the difference and its relevance to efficiency are discussed.
11,071 citations
Book•
IBM1
TL;DR: In this article, the authors highlight the intricate interdependencies and subtle tradeoffs between various practically important device parameters, and also provide an in-depth discussion of device scaling and scaling limits of CMOS and bipolar devices.
Abstract: Learn the basic properties and designs of modern VLSI devices, as well as the factors affecting performance, with this thoroughly updated second edition. The first edition has been widely adopted as a standard textbook in microelectronics in many major US universities and worldwide. The internationally-renowned authors highlight the intricate interdependencies and subtle tradeoffs between various practically important device parameters, and also provide an in-depth discussion of device scaling and scaling limits of CMOS and bipolar devices. Equations and parameters provided are checked continuously against the reality of silicon data, making the book equally useful in practical transistor design and in the classroom. Every chapter has been updated to include the latest developments, such as MOSFET scale length theory, high-field transport model, and SiGe-base bipolar devices.
2,680 citations
TL;DR: In this article, a new analytical potential fluctuations model for the interpretation of current/voltage and capacitance/voltages measurements on spatially inhomogeneous Schottky contacts is presented.
Abstract: We present a new analytical potential fluctuations model for the interpretation of current/voltage and capacitance/voltage measurements on spatially inhomogeneous Schottky contacts. A new evaluation schema of current and capacitance barriers permits a quantitative analysis of spatially distributed Schottky barriers. In addition, our analysis shows also that the ideality coefficient n of abrupt Schottky contacts reflects the deformation of the barrier distribution under applied bias; a general temperature dependence for the ideality n is predicted. Our model offers a solution for the so‐called T0 problem. Not only our own measurements on PtSi/Si diodes, but also previously published ideality data for Schottky diodes on Si, GaAs, and InP agree with our theory.
1,439 citations
TL;DR: In this paper, a device physics model for radial p-n junction nanorod solar cells was developed, in which densely packed nanorods, each having a pn junction in the radial direction, are oriented with the rod axis parallel to the incident light direction.
Abstract: A device physics model has been developed for radial p-n junction nanorod solar cells, in which densely packed nanorods, each having a p-n junction in the radial direction, are oriented with the rod axis parallel to the incident light direction. High-aspect-ratio (length/diameter) nanorods allow the use of a sufficient thickness of material to obtain good optical absorption while simultaneously providing short collection lengths for excited carriers in a direction normal to the light absorption. The short collection lengths facilitate the efficient collection of photogenerated carriers in materials with low minority-carrier diffusion lengths. The modeling indicates that the design of the radial p-n junction nanorod device should provide large improvements in efficiency relative to a conventional planar geometry p-n junction solar cell, provided that two conditions are satisfied: (1) In a planar solar cell made from the same absorber material, the diffusion length of minority carriers must be too low to allow for extraction of most of the light-generated carriers in the absorber thickness needed to obtain full light absorption. (2) The rate of carrier recombination in the depletion region must not be too large (for silicon this means that the carrier lifetimes in the depletion region must be longer than ~10 ns). If only condition (1) is satisfied, the modeling indicates that the radial cell design will offer only modest improvements in efficiency relative to a conventional planar cell design. Application to Si and GaAs nanorod solar cells is also discussed in detail.
1,397 citations
TL;DR: An electrostatically defined p-n junction in monolayer WSe2 is employed for photodetection, photovoltaic operation and as a light-emitting diode.
Abstract: An electrostatically defined p–n junction in monolayer WSe2 is employed for photodetection, photovoltaic operation and as a light-emitting diode.
1,343 citations
References
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TL;DR: In this article, the statistics of the recombination of holes and electrons in semiconductors were analyzed on the basis of a model in which the recombinations occurred through the mechanism of trapping.
Abstract: The statistics of the recombination of holes and electrons in semiconductors is analyzed on the basis of a model in which the recombination occurs through the mechanism of trapping. A trap is assumed to have an energy level in the energy gap so that its charge may have either of two values differing by one electronic charge. The dependence of lifetime of injected carriers upon initial conductivity and upon injected carrier density is discussed.
5,442 citations
2,366 citations
TL;DR: The theory of potential distribution and rectification for p-n junctions is developed with emphasis on germanium, resulting in an admittance for a simple case varying as (1 + iωτ p )1/2 where τ p is the lifetime of a hole in the n-region.
Abstract: In a single crystal of semiconductor the impurity concentration may vary from p-type to n-type producing a mechanically continuous rectifying junction. The theory of potential distribution and rectification for p-n junctions is developed with emphasis on germanium. The currents across the junction are carried by the diffusion of holes in n-type material and electrons in p-type material, resulting in an admittance for a simple case varying as (1 + iωτ p )1/2 where τ p is the lifetime of a hole in the n-region. Contact potentials across p-n junctions, carrying no current, may develop when hole or electron injection occurs. The principles and theory of a p-n-p transistor are described.
1,844 citations
TL;DR: In this article, the authors measured the electrical conductivity and Hall effect of single-crystal silicon containing arsenic and boron and derived the intrinsic Hall mobility from Hall coefficient and conductivity.
Abstract: Electrical conductivity and Hall effect have been measured from 10\ifmmode^\circ\else\textdegree\fi{} to 1100\ifmmode^\circ\else\textdegree\fi{} Kelvin on single-crystal silicon containing arsenic and boron. Extrinsic carrier concentration is computed from Hall coefficient. Analysis of extrinsic carrier concentration indicates the ionization energy of arsenic donor levels to be 0.049 ev and of boron acceptor levels to be 0.045 ev for low impurity concentrations. Fermi degeneracy is found to occur in the range ${10}^{18}$ to ${10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ impurity concentration. Extrinsic Hall mobility is computed from Hall coefficient and conductivity. Curves of Hall mobility against resistivity at 300\ifmmode^\circ\else\textdegree\fi{}K are computed from theory and compared with experiment. The temperature dependence of lattice-scattering mobility is found from conductivity to be ${T}^{\ensuremath{-}2.6}$ for electrons and ${T}^{\ensuremath{-}2.3}$ for holes. From conductivity mobility and intrinsic conductivity, it is found that carrier concentration at any temperature below 700\ifmmode^\circ\else\textdegree\fi{}K is given by the expression: $np=1.5\ifmmode\times\else\texttimes\fi{}{10}^{33}{T}^{3}\mathrm{exp}(\ensuremath{-}\frac{1.21}{\mathrm{kT}})$. The temperature dependence of the ratio Hall mobility/conductivity mobility is determined for holes and electrons.
801 citations
TL;DR: In this article, an avalanche theory of breakdown at room temperature is proposed for semiconductors based on the assumption of approximately equal ionization rates for electrons and positive holes, and it is shown that this noise represents the unstable onset of breakdown and that all of the current flow in the breakdown region can be attributed to the current carried by the noise pulses.
Abstract: An avalanche theory of breakdown at room temperature is proposed for semiconductors based on the assumption of approximately equal ionization rates for electrons and positive holes. The problem of obtaining ionization rates from data obtained in inhomogeneous fields is solved exactly for two specific field distributions. Ionization rates for silicon thus calculated from experimental data on breakdown voltage and on prebreakdown multiplication for both linear-gradient and step junctions are in good agreement. The temperature coefficient of the ionization rate exhibits a similar internal consistency. It is concluded that internal field emission has not been observed in silicon.Detailed observations are reported of the pulse-type noise associated with breakdown. It is shown that this noise represents the unstable onset of breakdown and that, for the junctions studied, all of the current flow in the breakdown region can be attributed to the current carried by the noise pulses.
403 citations