Time and frequency response of avalanche photodiodes with arbitrarystructure

A method is developed for solving the coupled transport equations that describe the electron and hole currents in a double-carrier multiplication (DCM) avalanche photodiode (APD) of arbitrary structure. This solution makes it possible to determine the time and frequency response of the device. The injection can be localized to one or both ends of the multiplication region, or distributed throughout an extended region where multiplication can occur concurrently. The results are applied to conventional APDs with position-dependent carrier ionization rates (e.g., a separate-absorption-grading-multiplication APD) as well as to superlattice multiquantum-well (MQW) structures where the ionizations are localized to bandgap transition regions. The analysis may also be used to determine the dark current and include the carrier trapping at the heterojunction interfaces. The results indicate that previous time-dependent theories only account for the tail of the time response under high-gain conditions and are inaccurate for high-speed devices     

Time and frequency response of the conventional avalanche photodiode

An analytical expression for the time course of the average impulse response function for a conventional avalanche photodiode is derived. Delta-function absorption of a single photocarrier and single-carrier-initiated/single-carrier multiplication conditions are assumed. The result is obtained as a limiting case of a previously derived equation for the staircase avalanche photodiode. The initial exponential growth of the curves is shown to represent electron and hole contributions arising from multiplication in the avalanche region whereas the subsequent exponential decay arises from residual holes transiting backward across the multiplication region. The associated frequency response function is obtained by Fourier transformation. The analytical results are shown to be in good accord with average impulse response functions obtained by Riad and Hayes by means of simulation from the transport equations. The results should also apply to the channeling avalanche photodiode and to related structures in which the carriers are spatially separated and the multiplication is essentially single-carrier like.     

An analytical expression for the multiplication factor M in semiconductors with equal ionization coefficients

An analytical approximation of the multiplication factorMis derived for linear and abrupt junctions for the case of equal electron and hole ionization rates. The results are compared with the exact multiplication curve for different abrupt and linear GaAs junctions and the relative errors are plotted.     

Two-carrier conduction in MOS tunnel oxides—1 Experimental results

A novel device structure incorporating a p-channel MOSFET with a metal/tunnel-oxide/n-silicon device is proposed as a tool for separating electron and hole tunneling currents in ultra-thin silicon dioxide films. With this structure, the electron and hole tunneling currents can be independently measured at the substrate and source terminals, respectively. Furthermore, the injected minority carrier (hole) current which is supplied by the p-MOSFET can be varied independently of the tunnel-oxide bias. As expected, the injected hole current modulates the electron current and “current multiplication” was observed. By correlating experimental results for 22.5 Å SiO₂ films with theoretical calculations, the electron and hole barrier heights were determined to be 3.2 and 3.6 eV, respectively, where a trapezoidal tunneling barrier was assumed and a carrier effective mass of 0.5 m₀ was used.The tunnel-oxide quality and uniformity was evaluated by measuring I–V and C-V curves on two-terminal MOS capacitors of various areas. The results suggest that the oxide films are extremely uniform in thickness, and the measured interface trap density was determined to be less than 10¹¹ cm^?2eV^?1. For the reverse-biased tunnel-oxide, the electron/hole current ratio was found to be less than unity except for the condition when the injected hole current was very small compared to the electron current without any hole injection. In addition, this ratio was found to decrease rapidly with increasing oxide thickness and/or increasing hole injection level.     

Particle conservation in the hot‐carrier solar cell

In conventional p–n junction solar cells, carrier multiplication by impact ionisation, is negligible, owing to the low temperature of the electron–hole pairs. This leads to particle conservation between the net number of absorbed photons and the number of electron–hole pairs withdrawn from the cell. In hot‐carrier solar cells, in which electrons are at a high temperature by assuming suppression of electron–phonon scattering, such particle conservation leads to peculiar results. Numerical calculations show that entire current–voltage characteristics with meaningful values of temperature and chemical potential do not exist. If the energy at which electron–hole pairs are extracted is smaller than the average energy of absorbed photons, the temperature of the electrons and holes becomes much larger than the tem perature of the sun. When the extraction energy is larger than the average energy of the absorbed photons, an entire current–voltage curve cannot always be obtained. It follows that impact ionisation and Auger recombination cannot be neglected when the thermal energy of the electron–hole pairs is comparable to the bandgap of the absorber. Accounting for these processes results in current–voltage characteristics that are well behaved. Copyright © 2005 John Wiley & Sons, Ltd.     

A Monte Carlo investigation of multiplication noise in thin p+-i-n+ GaAs avalanche photodiodes

A Monte Carlo (MC) model has been used to estimate the excess noise factor in thin p⁺-i-n⁺ GaAs avalanche photodiodes (APD's). Multiplication initiated both by pure electron and hole injection is studied for different lengths of multiplication region and for a range of electric fields. In each ease a reduction in excess noise factor is observed as the multiplication length decreases, in good agreement with recent experimental measurements. This low noise behavior results from the higher operating electric field needed in short devices, which causes the probability distribution function for both electron and hole ionization path lengths to change from the conventionally assumed exponential shape and to exhibit a strong dead space effect. In turn this reduces the probability of higher order ionization events and narrows the probability distribution for multiplication. In addition, our simulations suggest that fur a given overall multiplication, electron initiated multiplication in short devices has inherently reduced noise, despite the higher feedback from hole ionization, compared to long devices     

Temperature dependence of impact ionization in GaAs

The temperature dependence of electron and hole impact ionization in gallium arsenide (GaAs) has been determined from photomultiplication measurements at temperatures between 20 K and 500 K. It is found that impact ionization is suppressed by increasing temperature because of the increase in phonon scattering. Temperature variations in avalanche multiplication are shown to decrease with decreasing avalanching region width, and the effect is interpreted in terms of the reduced phonon scattering in the correspondingly reduced ionization path length. Effective electron and hole ionization coefficients are derived and are shown to predict accurately multiplication characteristics and breakdown voltage as a function of temperature in p/sup +/in/sup +/ diodes with i-regions as thin as 0.5 /spl mu/m.     

Performance degradation of APD-optical receivers due to darkcurrent generated within the multiplication region

General expressions for the effective gain and effective excess noise factor associated with dark current generated within the high-field region of an avalanche photodiode (APD) are given. The influence of this background current on the performance of a uniformly multiplying APD receiver is evaluated and compared with that due to a dark current component generated outside the multiplication region (diffusion current). The results indicate clearly that the former dark current component has less effect on receiver performance than the latter, especially when hole and electron ionization rates are very different     

Extremely Low Excess Noise in InAs Electron Avalanche Photodiodes

Measurements of the avalanche multiplication noise in InAs p-i-n and n-i-p diodes at room temperature demonstrate unambiguously that the avalanche multiplication process is dominated by impact ionization of electrons. This results in the excess noise factor for electron initiated multiplication asymptotically approaching a maximum value just less than two and becoming virtually gain-independent for higher gains. Measurements for predominantly hole initiated multiplication show corresponding high excess noise factors suggesting the electron to hole ionization coefficient ratios are comparable to those reported for $hbox{Hg}_{1-{x}}hbox{Cd}_{x}hbox{Te}$ electron avalanche photodiodes.      

Avalanche multiplication properties of GaAs calculated from spatially transient ionisation coefficients

In this paper the high field phenomenon of avalanche multiplication in a GaAs p-i-n infrared detector is studied using a Monte-Carlo simulation. The Lucky-Drift model of impact ionization is used to give the characteristic lengths for transport through the device. The transport is then modelled by generating motion consistent with the probability functions derived from the mean free paths. This produces a spatially transient ionization coefficient for each carrier and allows the realistic statistical simulation of avalanche multiplication. Properties such as mean gain, multiplication noise and the transient response to a photonic pulse have been calculated and explained for a length of i-GaAs, with an emphasis on short active region phenomena. The effect on the ionization coefficients of a periodic field change has been investigated. It has been found that the effective carrier deadspace is approx. 1.35 times the absolute deadspace. The transient current calculations indicate the narrow bandwidth of this type of device. The presence of a periodic field change, caused by periodic δ-doping, was found to increase both electron and hole ionization coefficients by different proportions.     

Hg0.56 Cd0.44 Te 1.6- to 2.5-μm avalanchephotodiode and noise study far from resonant impact ionization

An investigation was made on the avalanche multiplication and impact ionization processes in p-n^--n⁺ junctions formed in Hg_0.56Cd_0.44Te solid solutions. Photocurrent multiplication was determined at 300 K in planar p-n^- -n⁺ structures characterized by a breakdown voltage of 30 V. The experimental results were used to calculate the electron, α, and hole, β, ionization coefficients. It was found that α is greater than β because Δ, the spin-orbit splitting energy, is higher than the bandgap energy. These experimental results were in satisfactory agreement with multiplication noise measurements using separate electron and hole injection     

Hot-hole-induced negative oxide charges in n-MOSFETs

We investigate the generation of electron traps by hole injection during hot-carrier stressing of n-MOSFETs. These generated electron traps are filled by an electron injection following the primary hole stress. The effect is proven and quantified by monitoring the detrapping kinetics in the multiplication factor and the charge pumping current. The traps are located in the oxide within the first few nanometers to the interface. An interaction of those traps with interface states is found in that charged electron traps inhibit charging or uncharging of interface states. The kinetics of hot-carrier-induced fixed negative charges in n- and p-channel MOSFET's are compared showing significant differences in the properties of the two species of traps. Hole-induced electron traps are located much closer to the interface and their energetic level is deeper. Finally, a method is presented that allows the quantification of the effect for reliability purposes. We conclude that under digital and analog operation conditions in which hole effects cannot completely be ruled out, this effect has to be considered.<>     

Measurement of collector-base junction avalanche multiplicationeffects in advanced UHV/CVD SiGe HBT's

This paper presents measurements of the avalanche multiplication factor (M-1) in SiGe HBTs using a new technique capable of separating the avalanche multiplication and Early effect contributions to the increase of collector current with collector-base bias, as well as allowing safe measurements at practical current densities. The impact of collector doping, current density, Ge profile, and operation temperature are reported for the first time using measured and simulated results from a production quality UHV/CVD SiGe HBT technology. Limitations of the technique in the presence of significant self-heating are discussed. By turning on the secondary hole impact ionization, we revealed the difference in impact ionization between strained SiGe and Si in the presence of the “dead space” effect. Despite its smaller bandgap, the compressively strained SiGe layer shows an apparent decrease in the secondary hole impact ionization rate compared to Si     

Low avalanche noise characteristics in thin InP p+-i-n+ diodes with electron initiated multiplication

We have performed electron initiated avalanche noise measurements on a range of homojunction InP p⁺-i-n⁺ diodes with “i” region widths, w ranging from 2.40 to 0.24 μm. In contrast to McIntyre's noise model a significant reduction in the excess noise factor is observed with decreasing w at a constant multiplication in spite of α, the electron ionization coefficient being less than β, the hole ionization coefficient. In the w=0.24 μm structure an effective β/α ratio of approximately 0.4 is deduced from the excess noise factor even when electrons initiate multiplication, suggesting that hole initiated multiplication is not always necessary for the lowest avalanche noise in InP-based avalanche photodiodes     

The frequency response of avalanching photodiodes

The Townsend equations for avalanche breakdown in back biased p-n junctions may be derived from the transport equations for semiconductors. Integral solutions of the time independent equations are well known. An integral solution of the time dependent equations is given for multiplication by one carrier only. An exact solution is given for multiplication by two carriers with equal ionization coefficients in a constant junction field. The Townsend equations are nonlinear because of space charge effects. It is shown, however, that the nonlinearity, which imposes an upper limit on the current multiplication possible, is not important until the total multiplied current approaches the space charge limited current for the junction. Assuming multiplication is due to one carrier, frequency response curves are calculated for constant and linear junction fields and for a generation rate, due to photon absorption, which is either uniform or given by a delta function at the junction boundary. The curves indicate a relatively slight dependence of the frequency response on multiplication. Frequency response curves are also given for multiplication by both carriers with equal ionization coefficients when the junction field is constant. In this case the frequency response decreases continuously as the multiplication is increased. For multiplication by two carriers with unequal ionization coefficients, the frequency response is independent of multiplication until the product of the multiplication and the ratio of the ionization coefficients approaches one. Thereafter the frequency response decreases with multiplication.     

Multiplication factors and breakdown voltages of n+?p and p+?n abrupt junctions

It is shown that, in complementary n+p and p+n abrupt junctions for pure electron or hole multiplication, four different multiplication factors and two breakdown voltages can be defined. As an example, the four multiplication curves for a doping of 1016 cm?3, and the breakdown voltages of p+ n and n+ p abrupt Si junctions, are reported, using the multiplication data of Lee et al. and Van Overstraeten and De Man.     

场引晶体管理论:XI.双极电化电流（薄及厚、纯及不纯基体,单及双MOS栅极）

场引晶体管本质双极,包括电子和空穴表面和体积沟道和电流,一或多个外加横向控制电场．自1952年Shockley发明,55年来它被认为单极场引晶体管,因电子电流理论用多余内部和边界条件,不可避免忽略空穴电流．多余条件,诸如电中性和常空穴电化电势,导致仅用电子电流算内部和终端电学特性的错误解．当忽略的空穴电流与电子电流可比,可在亚阈值区和强反型区,错误解有巨大误差．本文描述普适理论,含有电子和空穴沟道和电流．用z轴宽度方向均匀的直角平行六面体（x,y,z）晶体管,薄或厚、纯或杂基体,一或二块MOS栅极,描述两维效应及电势、电子空穴电化电势的正确内部和边界条件．没用多余条件,导出四种常用MOS晶体管,直流电流电压特性完备解析方程：半无限厚不纯基上一块栅极（传统的Bulk MOSFET）,与体硅以氧化物绝缘的不纯硅薄层上一块栅极（SOI）,在沉积到绝缘玻璃的不纯硅薄层上一块栅极（SOI TFT）,和薄纯基上两块栅极（FinFETs）．     

场引晶体管理论:Ⅺ.双极电化电流(薄及厚、纯及不纯基体,单及双MOS栅极)

场引晶体管本质双极,包括电子和空穴表面和体积沟道和电流,一或多个外加横向控制电场.自1952年Shockley发明,55年来它被认为单极场引晶体管,因电子电流理论用多余内部和边界条件,不可避免忽略空穴电流.多余条件,诸如电中性和常空穴电化电势,导致仅用电子电流算内部和终端电学特性的错误解.当忽略的空穴电流与电子电流可比,可在亚阈值区和强反型区,错误解有巨大误差.本文描述普适理论,含有电子和空穴沟道和电流.用z轴宽度方向均匀的直角平行六面体(x,Y,z)晶体管,薄或厚、纯或杂基体,一或二块MOS栅极,描述两维效应及电势、电子空穴电化电势的正确内部和边界条件.没用多余条件,导出四种常用MOS晶体管,直流电流电压特性完备解析方程:半无限厚不纯基上一块栅极(传统的Bulk MOSFET),与体硅以氧化物绝缘的不纯硅薄层上一块栅极(SOI),在沉积到绝缘玻璃的不纯硅薄层上一块栅极(SOI TFT),和薄纯基上两块栅极(FinFETs).     

Characterization of current transport in MNOS structures with complementary tunneling emitter bipolar transistors

We have extended the work of previous investigators and studied current transport in thin- (10-20 Å) and thick-(80 Å) oxide MNOS structures with complementary tunneling emitter bipolar transistors. These devices are fabricated with ion-implanted p-n and n-p junctions to distinguish the dominant carrier species in the insulator. The dominant species in thin-oxide devices is hole transport, comprising about 99 percent of the emitter current. The hole transport is suppressed in the thick-oxide structures, where the dominant carriers are electrons. Electron impact ionization multiplication is observed in thick-oxide structures.     

Avalanche multiplication characteristics ofAl0.8Ga0.2As diodes

The avalanche multiplication characteristics of Al_0.8Ga _0.2As have been investigated in a series of p-i-n and n-i-p diodes with i-region widths, w, varying from 1 μm to 0.025 μm. The electron ionization coefficient, α, is found to be consistently higher than the hole ionization coefficient, β, over the entire range of electric fields investigated. By contrast with Al_xGa _1-xAs (x⩽0.6) a significant difference between the electron and hole initiated multiplication characteristics of very thin Al_0.8Ga_0.2As diodes (w=0.025 μm) was observed. Dead space effects in the diodes with w⩽0.1 μm were found to reduce the multiplication at low bias below the values predicted from bulk ionization coefficients. Effective α and β that are independent of w have been deduced from measurements and are able to reproduce accurately the multiplication characteristics of diodes with w⩾0.1 μm and breakdown voltages of all diodes with good accuracy. By performing a simple correction for the dead space, the multiplication characteristics of even thinner diodes were also predicted with reasonable accuracy