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J C Campbell - One of the best experts on this subject based on the ideXlab platform.
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multiplication characteristics of al 0 4 ga 0 07 in 0 53 as avalanche photodiodes grown as digital alloys on inp substrates
Device Research Conference, 2020Co-Authors: Stephen C Lee, J C Campbell, S H Kodati, D R Fink, Theodore J Ronningen, Andrew H Jones, M Winslow, C H Grein, Sanjay KrishnaAbstract:Avalanche photodiodes (APDs) are used in short- and mid-wave infrared applications such as optical communication, LIDAR and 3D imaging [1] due to their internal gain, which improves the signal to Noise ratio (SNR). However, the multiplication gain ( M ) gives rise to excess Noise, caused by the stochastic nature of impact ionization, which can significantly degrade the SNR of APDs. The excess Noise is quantitatively measured by excess Noise Factor, F(M) that is expressed by McIntyre’s local field theory [1] , F(M) = kM + (1-k)[2-(1/M)] where k is the ratio of the impact ionization coefficients for electrons and holes. According to the equation above, the low excess Noise Factor in APDs can be attained by a low k value.
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aunassb separate absorption charge and multiplication avalanche photodiodes
IEEE Photonics Conference, 2016Co-Authors: Min Ren, Scott J Maddox, Madison Woodson, Yaojia Chen, Seth R Bank, J C CampbellAbstract:We report Al x In 1−x Asj, Sb 1−y -based separate absorption, charge, and multiplication avalanche photodiodes (APDs) that operate in the short-wavelength infrared spectrum. These APDs exhibit low excess Noise Factor, corresponding to k = 0.01, and low dark current.
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al x in 1 x as y sb 1 y separate absorption charge and multiplication avalanche photodiodes
Device Research Conference, 2016Co-Authors: Min Ren, Scott J Maddox, Madison Woodson, Yaojia Chen, Seth R Bank, Ann Kathryn Rockwell, J C CampbellAbstract:Recently, the rapid growth of optical-fiber communications systems that utilize baud rates up to 25 Gbit/s as represented by 100-Gbit/s Ethernet (100 GbE) has led to a resurgence of research on avalanche photodiodes (APDs) [1]. Two figures of merit for APD optical receivers are the excess Noise Factor and the gain-bandwidth product. Both are linked to the κ Factor, which is the ratio of the electron, α, and hole, β, ionization coefficients. The mean-squared shot-Noise current can be expressed as ≪ AsySb1-y, grown on GaSb [6]. The excess Noise Factor of the Al0.7In0.3As0.3Sb0.7 multiplication region is characterized by a k value of ˜0.01, which is comparable to that of Si. Further, the lattice-matched Al0.4 In0.6As0.6Sb0.4 absorbing region extends the operating wavelength to the short-wavelength infrared (SWIR) spectrum. Gain values as high as 95 have been achieved. These APDs combine the excellent gain/Noise characteristics of Si with the low dark current and high speed of the III-V compound APDs, while operating at the key telecommunications wavelengths of 1.3 and 1.55 μm.
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alinassb separate absorption charge and multiplication avalanche photodiodes
Applied Physics Letters, 2016Co-Authors: Min Ren, Scott J Maddox, Madison Woodson, Yaojia Chen, Seth R Bank, J C CampbellAbstract:We report AlxIn1−xAsySb1−y separate absorption, charge, and multiplication avalanche photodiodes (APDs) that operate in the short-wavelength infrared spectrum. They exhibit excess Noise Factor less or equal to that of Si and the low dark currents typical of III-V compound APDs.
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performance of low dark current 4h sic avalanche photodiodes with thin multiplication layer
IEEE Transactions on Electron Devices, 2006Co-Authors: Xiangyi Guo, J C Campbell, Ning Duan, Ariane L Beck, Zhihong Huang, D Emerson, J J SumakerisAbstract:The authors report on the fabrication and performance of low-dark-current 4H-SiC avalanche photodiodes with a thin 180-nm-thick p - multiplication layer. At a photocurrent gain M of 1000, the dark current of a 100-mum-diameter device was 35 pA (0.44 muA/cm2). The peak unity-gain responsivity was 100 mA/W (external quantum efficiency=46%) at lambda=268 nm, and at high gain, a responsivity greater than 107 A/W was achieved. The excess Noise Factor corresponds to k=0.12. Time-domain pulse measurements indicate an RC-limited unity-gain bandwidth of 300 MHz
Malvin C Teich - One of the best experts on this subject based on the ideXlab platform.
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boundary effects on multiplication Noise in thin heterostructure avalanche photodiodes theory and experiment al sub 0 6 ga sub 0 4 as gaas
IEEE Transactions on Electron Devices, 2002Co-Authors: Majeed M Hayat, Bahaa E A Saleh, J C Campbell, Ohhyun Kwon, Shuling Wang, Malvin C TeichAbstract:The history-dependent recurrence theory for multiplication Noise in avalanche photodiodes (APDs), developed by Hayat et al., is generalized to include inter-layer boundary effects in heterostructure APDs with multilayer multiplication regions. These boundary effects include the initial energy of injected carriers as well as bandgap-transition effects within a multilayer multiplication region. It is shown that the excess Noise Factor can be significantly reduced if the avalanche process is initiated with an energetic carrier, in which case the initial energy serves to reduce the initial dead space associated with the injected carrier. An excess Noise Factor reduction up to 40% below the traditional thin-APD limit is predicted for GaAs, depending on the operational gain and the multiplication-region's width. The generalized model also thoroughly characterizes the behavior of dead space as a function of position across layers. This simultaneously captures the effect of the nonuniform electric field as well as the anticipatory nature of inter-layer bandgap-boundary effects.
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impact ionization and Noise characteristics of thin iii v avalanche photodiodes
IEEE Transactions on Electron Devices, 2001Co-Authors: M A Saleh, Bahaa E A Saleh, Majeed M Hayat, P Sotirelis, A L Holmes, J C Campbell, Malvin C TeichAbstract:It is, by now, well known that McIntyre's localized carrier-multiplication theory cannot explain the suppression of excess Noise Factor observed in avalanche photodiodes (APDs) that make use of thin multiplication regions. We demonstrate that a carrier multiplication model that incorporates the effects of dead space, as developed earlier by Hayat et al. provides excellent agreement with the impact-ionization and Noise characteristics of thin InP, In/sub 0.52/Al/sub 0.48/As, GaAs, and Al/sub 0.2/Ga/sub 0.8/As APDs, with multiplication regions of different widths. We outline a general technique that facilitates the calculation of ionization coefficients for carriers that have traveled a distance exceeding the dead space (enabled carriers), directly from experimental excess-Noise-Factor data. These coefficients depend on the electric field in exponential fashion and are independent of multiplication width, as expected on physical grounds. The procedure for obtaining the ionization coefficients is used in conjunction with the dead-space-multiplication theory (DSMT) to predict excess Noise Factor versus mean-gain curves that are in excellent accord with experimental data for thin III-V APDs, for all multiplication-region widths.
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dead space based theory correctly predicts excess Noise Factor for thin gaas and algaas avalanche photodiodes
IEEE Transactions on Electron Devices, 2000Co-Authors: M A Saleh, Bahaa E A Saleh, Majeed M Hayat, Malvin C TeichAbstract:The conventional McIntyre carrier multiplication theory for avalanche photodiodes (APDs) does not adequately describe the experimental results obtained from APDs with thin multiplication-regions. Using published data for thin GaAs and Al/sub 0.2/Ga/sub 0.8/As APDs, collected from multiplication-regions of different widths, we show that incorporating dead-space in the model resolves the discrepancy. The ionization coefficients of enabled carriers that have traveled the dead space are determined as functions of the electric field, within the confines of a single exponential model for each device, independent of multiplication-region width. The model parameters are determined directly from experimental data. The use of these physically based ionization coefficients in the dead-space multiplication theory, developed earlier by Hayat et al. provide excess Noise Factor versus mean gain curves that accord very closely with those measured for each device, regardless of multiplication-region width. It is verified that the ratio of the dead-space to the multiplication-region width increases, for a fixed mean gain, as the width is reduced. This behavior, too, is in accord with the reduction of the excess Noise Factor predicted by the dead-space multiplication theory.
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effect of dead space on gain and Noise of double carrier multiplication avalanche photodiodes
IEEE Transactions on Electron Devices, 1992Co-Authors: Majeed M Hayat, Bahaa E A Saleh, Malvin C TeichAbstract:The effect of dead space on the statistics of the gain in a double-carrier-multiplication avalanche photodiode (APD) is determined using a recurrence method. The dead space is the minimum distance that a newly generated carrier must travel in order to acquire sufficient energy to become capable of causing an impact ionization. Recurrence equations are derived for the first moment, the second moment, and the probability distribution function of two random variables that are related, in a deterministic way, to the random gain of the APD. These equations are solved numerically to produce the mean gain and the excess Noise Factor. The presence of dead space reduces both the mean gain and the excess Noise Factor of the device. This may have a beneficial effect on the performance of the detector when used in optical receivers with photon Noise and circuit Noise. >
Majeed M Hayat - One of the best experts on this subject based on the ideXlab platform.
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exact analytical formula for the excess Noise Factor for mixed carrier injection avalanche photodiodes
Journal of Lightwave Technology, 2019Co-Authors: Md Mottaleb Hossain, J P R David, Majeed M HayatAbstract:The well-known analytical formula for the excess Noise Factor associated with avalanche photodiodes (APDs), developed by R. J. McIntyre in 1966, assumes the injection of either an electron or a hole at the edge of the APD's avalanche region. This formula is based on the statistics of the probabilities of carriers gaining and losing energy subject to high electric fields. However, this analytical formula, is not applicable in cases when photons are absorbed inside the avalanche region (even though the physics of the high field transport remains the same), and its use may severely underestimate or overestimate the actual excess Noise Factor depending on the absorption profile and the hole-to-electron ionization coefficient ratio, k . Here, an easy-to-use exact analytical formula is derived for the excess Noise Factor of APDs while taking into account a mixed-carrier initiated avalanche multiplication process, which is triggered by a parent electron-hole pair at an arbitrarily specified location within the multiplication region. The derivation relies on analytically solving a special case of a previously reported recursive integral equations [Hayat et al. , IEEE Trans. Electron Devices, vol. 39, no. 3, pp. 546–552, Mar. 1992.], and the result matches the formula reported by McIntyre in 1999 using a different and limited technique. In addition, an expression for the excess Noise Factor is presented in the case when the location of the parent electron-hole pair within the multiplication region obeys an arbitrary exponential distribution. The results show that in contrast to the case of edge parent-electron injection, when mixed injection is allowed even a small level of hole ionization (e.g., small k ∼ 0.0001) causes the excess Noise Factor to increase dramatically, depending on the absorption profile as it ranges from narrow to flat within the multiplication region. The theoretical results are validated against experimental results for Si APDs.
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improved dual carrier high gain impact ionization engineered avalanche photodiode
Device Research Conference, 2012Co-Authors: Jun Huang, Koushik Banerjee, Siddhartha Ghosh, Majeed M HayatAbstract:Avalanche photodiodes (APDs), which have light detection and amplification combined in a single stage, are crucial for infrared detection. They operate at a relatively high reverse bias to enable avalanche multiplication from impact ionization of electrons and holes. However, avalanche multiplication process can contribute to excess Noise, which results from the non-uniformity of ionization of individual carriers. Based on McIntyre's Theory [1], one important key to minimize excess Noise is to make impact ionization coefficient ratio, k, zero or infinity, which is pure electron or hole multiplication. Based on previous work [2], multiple novel dual carrier multiplication structures are simulated for the study of gain and excess Noise Factor. Such structures can achieve much higher gain compared to conventional APDs while minimizing excess Noise Factor through localization of impact ionization in thin multiplication layers.
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boundary effects on multiplication Noise in thin heterostructure avalanche photodiodes theory and experiment al sub 0 6 ga sub 0 4 as gaas
IEEE Transactions on Electron Devices, 2002Co-Authors: Majeed M Hayat, Bahaa E A Saleh, J C Campbell, Ohhyun Kwon, Shuling Wang, Malvin C TeichAbstract:The history-dependent recurrence theory for multiplication Noise in avalanche photodiodes (APDs), developed by Hayat et al., is generalized to include inter-layer boundary effects in heterostructure APDs with multilayer multiplication regions. These boundary effects include the initial energy of injected carriers as well as bandgap-transition effects within a multilayer multiplication region. It is shown that the excess Noise Factor can be significantly reduced if the avalanche process is initiated with an energetic carrier, in which case the initial energy serves to reduce the initial dead space associated with the injected carrier. An excess Noise Factor reduction up to 40% below the traditional thin-APD limit is predicted for GaAs, depending on the operational gain and the multiplication-region's width. The generalized model also thoroughly characterizes the behavior of dead space as a function of position across layers. This simultaneously captures the effect of the nonuniform electric field as well as the anticipatory nature of inter-layer bandgap-boundary effects.
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impact ionization and Noise characteristics of thin iii v avalanche photodiodes
IEEE Transactions on Electron Devices, 2001Co-Authors: M A Saleh, Bahaa E A Saleh, Majeed M Hayat, P Sotirelis, A L Holmes, J C Campbell, Malvin C TeichAbstract:It is, by now, well known that McIntyre's localized carrier-multiplication theory cannot explain the suppression of excess Noise Factor observed in avalanche photodiodes (APDs) that make use of thin multiplication regions. We demonstrate that a carrier multiplication model that incorporates the effects of dead space, as developed earlier by Hayat et al. provides excellent agreement with the impact-ionization and Noise characteristics of thin InP, In/sub 0.52/Al/sub 0.48/As, GaAs, and Al/sub 0.2/Ga/sub 0.8/As APDs, with multiplication regions of different widths. We outline a general technique that facilitates the calculation of ionization coefficients for carriers that have traveled a distance exceeding the dead space (enabled carriers), directly from experimental excess-Noise-Factor data. These coefficients depend on the electric field in exponential fashion and are independent of multiplication width, as expected on physical grounds. The procedure for obtaining the ionization coefficients is used in conjunction with the dead-space-multiplication theory (DSMT) to predict excess Noise Factor versus mean-gain curves that are in excellent accord with experimental data for thin III-V APDs, for all multiplication-region widths.
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dead space based theory correctly predicts excess Noise Factor for thin gaas and algaas avalanche photodiodes
IEEE Transactions on Electron Devices, 2000Co-Authors: M A Saleh, Bahaa E A Saleh, Majeed M Hayat, Malvin C TeichAbstract:The conventional McIntyre carrier multiplication theory for avalanche photodiodes (APDs) does not adequately describe the experimental results obtained from APDs with thin multiplication-regions. Using published data for thin GaAs and Al/sub 0.2/Ga/sub 0.8/As APDs, collected from multiplication-regions of different widths, we show that incorporating dead-space in the model resolves the discrepancy. The ionization coefficients of enabled carriers that have traveled the dead space are determined as functions of the electric field, within the confines of a single exponential model for each device, independent of multiplication-region width. The model parameters are determined directly from experimental data. The use of these physically based ionization coefficients in the dead-space multiplication theory, developed earlier by Hayat et al. provide excess Noise Factor versus mean gain curves that accord very closely with those measured for each device, regardless of multiplication-region width. It is verified that the ratio of the dead-space to the multiplication-region width increases, for a fixed mean gain, as the width is reduced. This behavior, too, is in accord with the reduction of the excess Noise Factor predicted by the dead-space multiplication theory.
P.n. Robson - One of the best experts on this subject based on the ideXlab platform.
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full band monte carlo modeling of impact ionization avalanche multiplication and Noise in submicron gaas p i n diodes
Journal of Applied Physics, 2000Co-Authors: D S Ong, G J Rees, S.a. Plimmer, J P R David, P.n. RobsonAbstract:A full-band Monte Carlo model is used to investigate the probability distribution functions of impact ionization path length and impact ionization energy for electrons and holes in GaAs. The simulations show that the soft ionization threshold energy in GaAs allows impact ionization to occur at energies much higher than the band gap. As a result, secondary carriers have a shorter dead space than newly injected carriers. The ionization path length distributions narrow at higher fields, producing a more deterministic impact ionization process in thin devices. The model is also used to simulate avalanche multiplication and Noise in submicron homojunction GaAs p+-i-n+ diodes. The predicted mean multiplication, 〈M〉 and excess Noise Factor, F are in quantitative agreement with the experimental results, in which F decreases as the length of multiplication region is reduced.
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low avalanche Noise characteristics in thin inp p sup i n sup diodes with electron initiated multiplication
IEEE Photonics Technology Letters, 1999Co-Authors: S.a. Plimmer, G J Rees, P.n. Robson, J P R David, R C Tozer, C C Button, Jenny ClarkAbstract:We have performed electron initiated avalanche Noise measurements on a range of homojunction InP p/sup +/-i-n/sup +/ diodes with "i" region widths, w ranging from 2.40 to 0.24 /spl mu/m. 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 /spl alpha/, the electron ionization coefficient being less than /spl beta/, the hole ionization coefficient. In the w=0.24 /spl mu/m structure an effective /spl beta///spl alpha/ 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.
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avalanche multiplication Noise characteristics in thin gaas p sup i n sup diodes
IEEE Transactions on Electron Devices, 1998Co-Authors: D S Ong, G J Rees, P.n. Robson, J P R David, R C Tozer, R GreyAbstract:Avalanche Noise measurements have been performed on a range of homojunction GaAs p/sup +/-i-n/sup +/ and n/sup +/-i-p/sup +/ diodes with "i" region widths, /spl omega/ from 2.61 to 0.05 /spl mu/m. The results show that for /spl omega//spl les/1 /spl mu/m the dependence of excess Noise Factor F on multiplication does not follow the well-established continuous Noise theory of McIntyre [1966]. Instead, a decreasing Noise Factor is observed as /spl omega/ decreases for a constant multiplication. This reduction in F occurs for both electron and hole initiated multiplication in the thinner /spl omega/ structures even though the ionization coefficient ratio is close to unity. The dead-space, the minimum distance a carrier must travel to gain the ionization threshold energy, becomes increasingly important in these thinner structures and largely accounts for the reduction in Noise.
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a monte carlo investigation of multiplication Noise in thin p sup i n sup gaas avalanche photodiodes
IEEE Transactions on Electron Devices, 1998Co-Authors: D S Ong, G J Rees, J P R David, G M Dunn, P.n. RobsonAbstract:A Monte Carlo (MC) model has been used to estimate the excess Noise Factor in thin p/sup +/-i-n/sup +/ 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.
J P R David - One of the best experts on this subject based on the ideXlab platform.
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exact analytical formula for the excess Noise Factor for mixed carrier injection avalanche photodiodes
Journal of Lightwave Technology, 2019Co-Authors: Md Mottaleb Hossain, J P R David, Majeed M HayatAbstract:The well-known analytical formula for the excess Noise Factor associated with avalanche photodiodes (APDs), developed by R. J. McIntyre in 1966, assumes the injection of either an electron or a hole at the edge of the APD's avalanche region. This formula is based on the statistics of the probabilities of carriers gaining and losing energy subject to high electric fields. However, this analytical formula, is not applicable in cases when photons are absorbed inside the avalanche region (even though the physics of the high field transport remains the same), and its use may severely underestimate or overestimate the actual excess Noise Factor depending on the absorption profile and the hole-to-electron ionization coefficient ratio, k . Here, an easy-to-use exact analytical formula is derived for the excess Noise Factor of APDs while taking into account a mixed-carrier initiated avalanche multiplication process, which is triggered by a parent electron-hole pair at an arbitrarily specified location within the multiplication region. The derivation relies on analytically solving a special case of a previously reported recursive integral equations [Hayat et al. , IEEE Trans. Electron Devices, vol. 39, no. 3, pp. 546–552, Mar. 1992.], and the result matches the formula reported by McIntyre in 1999 using a different and limited technique. In addition, an expression for the excess Noise Factor is presented in the case when the location of the parent electron-hole pair within the multiplication region obeys an arbitrary exponential distribution. The results show that in contrast to the case of edge parent-electron injection, when mixed injection is allowed even a small level of hole ionization (e.g., small k ∼ 0.0001) causes the excess Noise Factor to increase dramatically, depending on the absorption profile as it ranges from narrow to flat within the multiplication region. The theoretical results are validated against experimental results for Si APDs.
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avalanche Noise characteristics in submicron inp diodes
IEEE Journal of Quantum Electronics, 2008Co-Authors: L J J Tan, Chee Hing Tan, J P R DavidAbstract:We report excess Noise Factors measured on a series of InP diodes with varying avalanche region thickness, covering a wide electric field range from 180 to 850 kV/cm. The increased significance of dead space in diodes with thin avalanche region thickness decreases the excess Noise. An excess Noise Factor of F = 3.5 at multiplication Factor M = 10 was measured, the lowest value reported so far for InP. The electric field dependence of impact ionization coefficients and threshold energies in InP have been determined using a non-local model to take into account the dead space effects. This work suggests that further optimization of InP separate absorption multiplication avalanche photodiodes (SAM APDs) could result in a Noise performance comparable to InAlAs SAM APDs.
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full band monte carlo modeling of impact ionization avalanche multiplication and Noise in submicron gaas p i n diodes
Journal of Applied Physics, 2000Co-Authors: D S Ong, G J Rees, S.a. Plimmer, J P R David, P.n. RobsonAbstract:A full-band Monte Carlo model is used to investigate the probability distribution functions of impact ionization path length and impact ionization energy for electrons and holes in GaAs. The simulations show that the soft ionization threshold energy in GaAs allows impact ionization to occur at energies much higher than the band gap. As a result, secondary carriers have a shorter dead space than newly injected carriers. The ionization path length distributions narrow at higher fields, producing a more deterministic impact ionization process in thin devices. The model is also used to simulate avalanche multiplication and Noise in submicron homojunction GaAs p+-i-n+ diodes. The predicted mean multiplication, 〈M〉 and excess Noise Factor, F are in quantitative agreement with the experimental results, in which F decreases as the length of multiplication region is reduced.
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low avalanche Noise characteristics in thin inp p sup i n sup diodes with electron initiated multiplication
IEEE Photonics Technology Letters, 1999Co-Authors: S.a. Plimmer, G J Rees, P.n. Robson, J P R David, R C Tozer, C C Button, Jenny ClarkAbstract:We have performed electron initiated avalanche Noise measurements on a range of homojunction InP p/sup +/-i-n/sup +/ diodes with "i" region widths, w ranging from 2.40 to 0.24 /spl mu/m. 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 /spl alpha/, the electron ionization coefficient being less than /spl beta/, the hole ionization coefficient. In the w=0.24 /spl mu/m structure an effective /spl beta///spl alpha/ 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.
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avalanche multiplication Noise characteristics in thin gaas p sup i n sup diodes
IEEE Transactions on Electron Devices, 1998Co-Authors: D S Ong, G J Rees, P.n. Robson, J P R David, R C Tozer, R GreyAbstract:Avalanche Noise measurements have been performed on a range of homojunction GaAs p/sup +/-i-n/sup +/ and n/sup +/-i-p/sup +/ diodes with "i" region widths, /spl omega/ from 2.61 to 0.05 /spl mu/m. The results show that for /spl omega//spl les/1 /spl mu/m the dependence of excess Noise Factor F on multiplication does not follow the well-established continuous Noise theory of McIntyre [1966]. Instead, a decreasing Noise Factor is observed as /spl omega/ decreases for a constant multiplication. This reduction in F occurs for both electron and hole initiated multiplication in the thinner /spl omega/ structures even though the ionization coefficient ratio is close to unity. The dead-space, the minimum distance a carrier must travel to gain the ionization threshold energy, becomes increasingly important in these thinner structures and largely accounts for the reduction in Noise.
