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Abstract
Stimulation of 700 and 900 nm optical emissions in a two junction monolithically integrated circuit silicon avalanche mode Si light emitting device have been achieved, based on some first iteration modelling and realization of first iteration experimental results. Previously only stimulation of 600 nm emission intensities had been realized. The current devices are of micron dimension and were realized using a standard Si integrated circuit design in a 0.35-micron RF design process. Evidence has been obtained that 700 nm and 900 nm in Si AM LEDs occur primarily through direct intra-band exited electron and exited hole relaxation phenomena and short-range phonon assisted inter-band transitions. Indications have been obtained that this occurs when energetic electrons relax in a high impurity density charge scattering environment. The devices operate at 8–10 V, 1 mA–10 mA regimes. Emission intensities of up to 1000 nW·µm−2 at the point of source have been derived. The developed technologies can find diverse new applications for on-chip electro-optic applications, particularly for coupling optical radiation laterally in silicon nitride-based waveguides in silicon integrated circuitry.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Several researchers have hypothesized about the realization of light emitting devices in standard silicon integrated circuitry [1–9]. Through earlier research, light emission from silicon devices has been realized in various reverse-biased p-n avalanche structures, later nomenclated silicon light emitting diodes that operate in the reverse breakdown avalanche mode (Si AM LEDs) [10–14]. It has been postulated that the light emission occurs from these structures through phonon assisted intra-band and inter-band recombination phenomena [12–14]. Kramer et al [15], and Snyman et al [16,17] was the first to realize a series of practical and utilizable light emitting devices (Si LEDs) in standard CMOS technology. They used novel surface engineering and current density engineering techniques and utilized standard CMOS process design and manufacturing procedures.
Snyman, Du Plessis et al subsequently realized devices that showed increased light emission when additional carriers are injected into avalanching Si n + p light emitting junctions [18,19]. The emission intensities ranged from 0.1 to about 1 nW/um2. Du Plessis et al and Xu et al have subsequently realized a series of first iteration CMOS integrated LED devices, with third terminal gated control [20,21]. Dutta, Schmitz et al have more recently analyzed the temperature, carrier density and electric field aspects as encountered in Si LEDs operating in the avalanche mode. The same group also suggested operation of gated Si LED operating in the forward bias mode and emitting in the 1100 nm region [22,23].
Because of the reverse bias configuration of Si AM LEDs, the devices offer an inherent high modulation speed ranging into the GHz range. This is a major advantage as associated with Si AM LEDs [24]. Other advantages are the ease of integration into silicon integrated circuit technology, particularly for these types of devices show great potential to be integrated into RF based and CMOS based optical interconnect, hybrid optical RF systems, and on-chip micro-photonic systems.
Snyman, Ogudo, et al have recently realized first iteration on-chip optical links, where optical pulses were transmitted up to 10 GHz over distances of 50 micron using novel Si Av LED design and waveguide technology in a RF bipolar process [25].
Major progresses have recently been obtained in increasing the emission intensities from Si AM LEDs in the 650 nm emission regime (Snyman et al, Xu et al), where, for the first time, evidence has been obtained that enhanced emission can be obtained from Si CMOS based LEDs by up to two orders of magnitude by using enhanced impurity scattering and novel extended E-field profiling in the device [26–29] . Evidence is provided in these paper that the emission intensity has been increased from 1 nW per µm2 to 100 nW per µm2 . This can be regarded as a major progress with regard to increasing the emission intensities by our group as associated with Si AMLEDs.
In this paper, we report on further progresses that have been made with regard to the design and realization of micro- and nano-dimensioned silicon LEDs that emit specifically in the 700 to 900 nm regime. 700 to 900 nm optical emissions have particularly potential to be applied in next generation Silicon Photonics integrated circuitry where longer wavelengths can be propagated with lesser loss in silicon integrated circuit waveguides [30,31]. Previous increases in emission intensity was realized only for the 550 to 650 nm regime [29], where losses in silicon nitrides are about 10 fold higher, approximately at 5 dB cm−1 [30].
Furthermore, we illustrate in this paper that SiAM LEDs can quite effectively couple optical radiation into adjacently positioned silicon nitride-based waveguides while the propagated radiation can still be detected effectively by standard Silicon pin detectors. This can be regarded as a major progress with regard to future and viable technological application of Si AM LEDs.
2. Hypothesis for enhancing 700–900 nm optical emissions through carrier energy and momentum engineering
Snyman and Bellotti, have performed theoretical simulations of carrier energies and momentums in the silicon band structure as a function of prevailing electric field in the silicon crystal [28]. The main results are presented again here in Fig. 1 for further analyses purposes. It was observed that the energy distribution of the electrons in the conduction band for this excitation field of 300 kV·cm−1 range from 1.1 to 1.7 eV, while quite a wide momentum scattering is observed for electrons at this excitation level. Similar tendencies were observed for holes, but the spread in both energy and momentum is much less due to the heavier effective mass of holes in silicon. The momentum scattering for holes are observed to be much more directional.
Fig. 1. (a) Electron energy distributions of carriers in k-space and energy in Silicon for an applied field of 300 kV·cm−1 as obtained from a Monte Carlo simulation study. (b) and (c): Electron and hole momentum distributions in k-space in the first Brillouin Zone (After Ref. [28]).
It was argued that transitions of the Type A as in Fig. 2, could be stimulated on purpose by designing specific device that could promote these transitions. Firstly, energetic electrons in large densities had to be excited to around 1.8 eV up in the electron energy band. Simultaneously, a density of holes had to be created with low excited energy in the valence band and in a specific device zone where the energetic electrons and low energy holes could intermix. If the zone also promoted enhanced scattering of the electrons through some defect interaction mechanism or impurity scattering mechanisms, the transition of photonic transitions Type A could be further enhanced. The expected transition probability for these transitions is assumed to be a function of both the excited electron density as well as the hole density according to the relationship:
where n’ is energized electron density as exiting the avalanching junction, Δp’ is the injected hole carrier density, and C is a recombination constant. The transition probability may indeed grow exponentially with increase in hole injection density and the optical emission could increase orders of magnitude. Particular evidences of this phenomenon have recently been realized and published by us, illustrating this effect, by designing a specific device to stimulate this type of transitions and photonic emissions [29]. Particularly the 650 nm emission in silicon integrated circuitry could, in total, be enhanced by about two orders of magnitude.Fig. 2. Energy distribution of populations of electrons and holes in the conduction band and valence band of silicon for various excitation conditions, momentum changes, and possible subsequent photonic transitions (after Ref. [28]).
It has recently been argued by us that 700–900 nm emissions can also be stimulated in Si AM LEDs. If electrons gain enough energies and momentums to high up in both the first and second conduction band to about 1.8 eV, the electron ionization threshold for electrons in silicon, direct intra-band relaxation transitions of the Type C as in Fig. 2 could be favored, yielding about 1.8 eV emissions or 700 nm wavelength optical emissions. Correspondingly, if holes are excited in the valence bands due to impact ionization processes to energies of up to 1.5 eV, transitions of Type D as in Fig. 2 could be favored, leading to transitions of about 1.5 eV and 800 nm emissions.
A further current hypothesis is that these processes can be enhanced if a short-range momentum change is introduced in the diffusing electron carriers, for example, by populated concentrations of impurities or structural defects in the device region. This could then enable transitions over a wider range of the respective bands, and lead to wider spreads in the wavelengths of the emitted radiation. Subsequently, mathematical modelling can be effectively utilized in further modeling and device design of Si AM LEDs for stimulation of 750 and 850 nm emissions. Using Maxwell’s equation in which the particles are the sources for current and charge distribution, the exact field at the position of the particle can be obtained from a self-consistent calculation. Consequently, the kinetic equation becomes
In general, the existence of radiative elastic collisions (Bremsstrahlung) is the scattering of an electron by an external field, accompanied by the emission of a photon. Considering charge-charge or charge-neutral elastic collisions, the collision frequency is calculated as follows. The collision time is the time for a charge to experience a significant deflection (i.e., change in momentum). The equation of conversion of momentum for the species α is obtained by multiplying Eq. (1) by mvα and then integrating over vα. The collision term for momentum transfer can be evaluated for drifting Maxwell distribution functions, and it is found that
During the scattering processes, it can be assumed that carriers maintain mainly energies up the threshold energy necessary for ionization of host atoms. This is about 1.8 eV, the threshold energy required for ionization of host silicon atoms by electrons; and about 2.4 eV, the threshold energy for ionization of host silicon atoms by diffusing holes. Further parameters that may particularly influence the global scattering and energy loss mechanisms are neutral and ionized impurity centers, if the specific crystal region where diffusion occurs is screened by opposing free charge carriers. For example, when an energetic electron is injected into an n- region where a high concentration of other free electrons exists. In such case, the ionized donor atoms of positive localized charge are screened by surrounding negative free charges and the scattering processes.
However, when a specific crystal region is depleted of free carriers, ionized donor atoms with positive charges are exposed and diffusing energetic electrons may experience enhanced scattering due to the large capturing cross-sections as seen by the electrons, now unscreened by an electron cloud. Moreover, if ionized acceptor atoms are also present, large negative opposing or reflecting scattering cross-sections may be seen and the scattering process may be greatly further enhanced. The momentum changes as experienced during such interactions may greatly impact on and stimulate the transition possibilities as elucidated above. This was primarily the mechanism that we implemented in this study in order to specifically stimulate 750 - 850 nm direct intra-band transitions of the Type C and D in Fig. 2.
3. Device designs and device operating conditions to stimulate 750 nm and 850 nm optical emissions and effectively couple into Si3N4 on-chip waveguides
A specific p + nn + p+ two junction device was purposefully designed in order to stimulate optical emissions in the 750 to 850 nm regime. This device is schematically presented in Fig. 3(a). We used a 0.35-micron Si bi-polar process with a high frequency RF application capability to realize this device. The process enabled “elongated pillar” of columnar structures to be etched out on a broad lower lying silicon semi-insulating p-substrate.
Fig. 3. Device design: (a) Lateral cross-section of the p + nn + p+ Si Avalanche Si LED, (b) electric field distribution through the device during active bias conditions, and, (c), conduction cross-section of the device and coupling of optical radiation into an adjacently lying silicon nitride-based waveguide.
These structures could hence effectively confine the lateral carrier diffusion and maximized the diffusing carrier density along the structures (Fig. 3(a)). A thin p + nn+ region was defined in the center region of two adjacently lying p+ and n+ regions separated by 1 micron.
The purpose of the device was to create a thin lowly doped n region which was edged by respective highly doped p+ and n+ regions, containing a high density of impurity scattering centers. On applying voltage bias, the lowly doped n region could sustain a high electric field, and act as an excitation region to energize electrons and holes. The ionization potential for electrons are about ten times higher than for holes on the onset of breakdown [32], hence predominantly electrons will initially be excited, and injected into the high scattering n+ environment. Excited holes that result during the excitation processes will diffuse in opposite direction and be injected into the high scattering p+ environment As the bias voltage is increased the E field in the n region is increased and result in more even excitation of electrons and holes. At low excitation conditions, holes could be injected from an adjacently lying p+ region and injected into the energetic diffusing electron region, and the effect of this could be investigated. This could then increase the density of excited holes in the excitation zone and that will enhance emission intensities ion the 850 nm regime, when these holes dissipate their energy in the p+ region. Not all the doping regions in the elevated pillar structures had the same doping implantation depths. Subsequently, the n+ region in the center device zone limits the diffusion cross-section and enhances the diffusion density of the carriers near to the surface of the device. The dimensions of each block of the columnar structure were of about one-micron cube each. The total device cross-sectional conduction area was about 0.3 um2. Appropriate contacts were positioned at the respective highly doped regions.
It should also be noted that the particular pillar and pedestal nature of the device above the substrate plane, allow the formation of waveguide structures containing oxides and silicon nitrides adjacently to the predicted light emitting zones. The light emitting zones then laterally couple light directly into these waveguides. Aspects of this design strategy has been published elsewhere [25].
4. Experimentally observed results
The processed devices were inspected with an ultra-high-resolution optical microscope (Leica Model DMI 8) with advanced image processing facilities. The optical spectrum was measured with an optical fiber Aristo MS9710B Spectrum Analyzer with a lensed-probe optical fiber. In each case the lensed optical probe was placed directly vertically above the device and the lensed probe was electronically micro manipulated to within 0.2 mm of the light emitting device. A HP network analyzer was used to monitor the output from the spectrum analyzer and to record the spectra in I-V and P-I format. Separate photomicrographs were taken from the spectrum analyzer screen in order to record results separately in macro format. These were later used as correlation tracking when analyzed the data recorded results as recorded with the HP network analyzer.
Figure 4 shows high-resolution optical micrographs of the realized device and observed performance as of the type of as demonstrated in Fig. 3 at 6 V and 1 mA. Figure 4(a) shows the I-V characteristics of the device as measured with discrete current monitoring device. Figure 4(b) shows a bright field micrograph of the device showing layout, dimensions and connections.
Fig. 4. Figure composition showing characteristics and optical emissions of the device as in Fig. 3. (a) and (b): (a) I-V curve of the device as measured (b) Low magnification images showing a bright field image of the device.
Figure 5(a) shows the device under active bias conditions under dark field observation conditions at 0.2 mA. Figure 5(b) show a micrograph of the same area taken with the color CCD camera of the microscope. Figure 5(c) shows the device under higher bias conditions of about 1 mA. A monochrome CCD camera, which is largely sensitive to infrared radiation was used in this case.
Fig. 5. (a): Monochrome CCD high resolution image of the p + nn+ device region. At 0.2 mA (b) Color CCD image of the similar area under lower magnification, and (c) monochrome CCD image of the same area as in (a) at 1 mA operating current.
Hence, at low voltage bias and current conditions, very clear light emission zones are shown throughout the high field excitation region. The optical microscopy at these high-resolution conditions, furthermore, clearly reveal two white bright light emission lines at the edges of the excitation region. Particularly, noticeable is the reddish glow observed in the excitation region in the regions between the lower doped (high E -Field) n- region between the n+ and p+ regions, as well as the “whitish color” nature of the individual “brighter emission spots” as located in between. With increasing bias and current conditions, the emission at the n+ side becomes much brighter. At still higher bias conditions, distinct bright emission “spots” appear at the peripheries showing clear brighter emissions.
Figure 6 shows the specific set-up used during measurement and the projected optical paths from the optical source, assumed to be located slightly subsurface, is shown in Fig. 5(a). It should be noted that due to the high refractive index of Silicon (n = 3.5) and the high refractive index difference going from silicon to silicon oxide, the escape angle (critical angle for internal reflection) is only 17 degrees. This implies that only 8% of the energy of the optical source is emitted into the silicon oxide vertically upwards. The combined critical angle (internal refection angle) for radiation going from silicon oxide to air was calculated as 43 degrees, implying that only a further 47% of the radiation in the silicon oxide layer is emitted into air. The numerical aperture of the fiber lens is 0.45, implying that only 25% of the radiation as emitted into air reaches the fiber probe. In total, this imply that the intensity or optical power emitted at the optical source are approximately 103 higher than detected at the probe. This implies that the optical power at the source could indeed be of the order of hundreds of nano-watts. The measured optical power spectra as externally observed are hence a minute sample of the internal phenomena.
Fig. 6. (a) Optical output measuring and optical power distribution in the device. (b) Optical output versus current (L-I curve) for the device as in Fig. 3.
The specific optical output versus current as measured with the optical fiber probe is shown in Fig. 6(b).
Figure 7, subsequently, shows samples of the observed optical emission spectra that were observed on the spectral photometer and analyzer for the device, as the current through the device was systematically increased. Since the device operated in avalanche mode, with a sharp breakdown behavior all the spectra voltages were observed at near 5 V. A low excitation and low avalanche condition at 0.2 mA, a clear small growth of emission peaks is observed at about 780 and 870 nm wavelength as shown in Fig. 7(a), and as derived from the original spectra as observed on the spectrometer. A averaging algorithm was applied in order to determine the exact position of the peaks and also to derive the exact power intensity as shown in Fig. 7(b).
Fig. 7. (a) Spectral characteristics as observed for the device as in Fig. 3 on the Optical Probe Spectrometer and derived peaks using an averaging algorithm at 8 V and 0.5 mA. (b) Derivation of detail power amplitude and position of the peaks after an averaging algorithm was applied to the spectrum data.
Upon further higher voltage bias at about 1 mA, a clear secondary emission peaks at 700 nm, and also at 750 nm also emerges as illustrated in Fig. 8(a) and (b). Upon further higher bias conditions, at about 3 mA of current, a growth of a 600 nm emission peak was observed to the left of the spectrum, however, not exceeding the peaks of the 770 nm and 870 nm.s.
Fig. 8. (a) Spectral characteristics as observed for the device as in Fig. 3 on the Optical Probe Spectrometer and derived peaks using an averaging algorithm at 8 V and 2 mA. (b) Derivation of detail power amplitudes and position of the peaks after an averaging algorithm was applied to the spectrum data.
5. Discussion of the results
The distribution of emission regions as observed under high resolution optical microscopy in Fig. 5, may indeed correlate with the modelled energy loss and momentum loss mechanisms as modelled in Section 2. The scattering by energetic carriers by opposing ionized and localized charge centers will offer the highest scattering scenarios and lead to specific momentum changes of the diffusing and injected carriers. This phenomenon seems to dominate, and a high continuous low background emission is observed, particularly as a reddish glow in Fig. 5(b).
The 770 nm and 870nm emissions observed in the spectral characteristics as observed in Fig. 7(a) and (b) may correlate with Transitions of Type C and Type D in Fig. 2. When the transition energies as associated with these transitions are calculated (750nmm and 850 nm, respectively), it compares very favorably with the experimentally observed values. Presumably, the exited and energized holes in the excitation region, as a result of impact ionizations by electrons, are injected into the p+ high impurity region, undergoes more dominant scattering as a result of their heavier effective mass. Hence, this emission is observed at very low current levels. This may correspond with the observed spatial characteristics as observed in Fig. 5(a) where a clear low reddish background illumination is observed in the high E field n region between the n+ and p+ regions. Furthermore, very interestingly in these investigations, is the higher intensities observed at the edges of the n excitation region, that is at the edges of the p+ and n+ regions. This observed phenomenon may indeed correlate with scenarios where the energized carrier’s loose energy or relaxes to lower energies due to scattering of carriers in more neutral, but heavily impurity doped regions in the silicon, and the dopant atoms less ionized.
The growth of the 700 and 750 nm peak at higher operating current as observed in Fig. 8(b), may relate with the higher multiplication rate as associated with electrons in silicon [32] at higher operating current levels, and the subsequent higher density of exited electrons that diffuses through the excitation region, and then injected into the n+- region where they again relax their energies through scattering processes. This is again clearly confirmed by the observation of clear distinctive line of higher intensity of light emission at the n+ side of the n excitation region.
The higher emission at the p + n junction at higher current may correlate with the higher electric field at this junction causing higher ionization of carriers and subsequent both relaxation and recombination mechanisms according to Type A and Type B, in Fig. 2. At further higher bias voltages, interesting brighter and “whiter” emission spots are observed in the images of Fig. 5(b) to (c). It can be anticipated that both electron and holes densities may occur and interaction between these energetic carriers occur. Evidence of a small peak around 600 nm is indeed evident in Fig. 8(a). . Hence the appearance and stimulation of 600-nm peak spectral characteristics for devices operating at higher operating currents and tailor designed for this purpose, as published earlier in [29], is also evident in this study.
A further confirmation of the above derivations lies in the shape of the emission peaks as observed in Fig. 5(c) and (d) as well as in the movement of the peaks towards lower wavelength values with increase voltage bias. At low excitation and at higher excitation values the peaks in Fig. 7(b) and Fig. 8(b) clearly reveal a long tail-off towards the longer wavelength values. This may correlate with the relaxation of carriers in the first and second conduction and hole bands in the Si band structure according to the mechanisms of transition Type C and Type D as in Fig. 2. Both these bands have a convergence to lower energy transitions (longer wavelengths) with increase in k- momentum values, and with higher E transitions (shorter wavelengths) and shorter k values. It hense seems as if these particular transitions are reflected in the peak shape of the emitted radiation in Fig. 7(a) and Fig. 8(b).
Also, we observe a general shift of the emission peaks towards shorter wavelengths with increase in voltage bias. This phenomenon may correlate with the energy excitation of carriers into the respective hole and electron conduction bands, leading to a shift towards lower wavelength emissions with increase in bias voltage.
Of technological application significance, it has been established that 700- 900 nm light will propagate with almost tenfold lower loss than 600 nm wavelength in Silicon Nitride PECVD type waveguides as realized in silicon integrated circuitry [30]. The loss of at 600 nm propagation in these waveguides has been measured as at 4.3 dBcm−1 at 530 nm, while only 1 dBcm−1 at 650 nm and only 0.1 dBcm−1 loss at 750 nm for silicon nitride waveguides as fabricated with a silicon integrated circuit process [30]. This wavelength emission may be particularly utilized to design many new diverse and further optimized devices. Particularly, new novel device applications at the micro- and Nano-device applications, can couple longer wavelength light directly into adjacently lying optically transparent device zones and wave-guiding structures.
It should also be noted that the coupling of light from the emission spots into the adjacently lying Silicon Nitride region is also extremely favorable. The refractive index change from Silicon (n = 3.5) to Silicon Nitride (n = 2.2) at 750 nm wavelength is only 2.3, which imply a acceptance angle of 0.34 for the waveguide inside the silicon, and which imply that up to 35% or 0.35 of the emitted light may be coupled into the waveguide and subsequently propagated in the waveguide at low loss.
The observed optical emissions at the optical fiber probe imply that the emission intensity at the point of origin at the optical source position is about 1000 nW at a operating current of 2 mA and 8V operating current. This is comparable or even exceeds previous emission intensities that was observed by our previous determinations at 550 to 650 nm emissions [30].
6. Conclusions
The following important conclusions can hence be derived from the work as presented:
- 1. It is clearly illustrated in this work that by applying specific device engineering design, and utilization of knowledge of carriers about energy and momentum at specific electric field excitation conditions, light emitting devices (Si LEDs) having nanometer and micrometer dimensions and emitting predominantly at 700 nm to 800 nm emission regime at quite low device operating currents, may indeed be generated in Silicon integrated circuitry.
- 2. Further evidence has been obtained that the introduction of high density of impurity centers or structural defect densities (as at surface interfaces) increases the total light emission from Si AM LEDs. This observation clearly confirms the earlier recent hypotheses by Xu [25] and by Snyman et el [26] that impurity scattering is a profound mechanism for light emission in Si Avalanche Mode LEDs, is hence again strengthened here.
- 3. This work particularly further indicate that by applying specific dedicated device design and device structures with SiAM LEDs, particular wavelength emission in the 700 - 900 wavelength regimes can be stimulated. In previous realizations in [29], we stimulated 600nm regime emissions (Transitions of Type A in Fig. 2), while, seemingly for the first time here, we demonstrate in this article a stimulation of 700 - 900 nm emissions (Transitions of Type C and D in Fig. 2) and increasing their emission intensities with about 100 fold..
- 4. Furthermore, it has been established that these higher optical emissions can be effectively coupled at coupling factors of about 0.35 into Si Nitride type waveguides which can be realized in o.35 micron RF bipolar technology, and propagate in these waveguides at lesser losses of about 10 fold.
- 5. The fact that Si AMLEDs emitting at 700- 900 nm wavelength can be integrated in standard silicon integrated circuitry may hence indeed open some interesting and diverse new applications in standard silicon integrated circuitry. Such applications could range from diverse sensor-on-chip and to various on-chip optical waveguiding applications. The high frequency optical modulation characteristics of these devices may also be exploited.
Funding
National Research Foundation (IFR2011033100025); Key International Collaboration Grant (KICG) (KSC69798); National Natural Science Foundation of China (61704019, 61674001).
Acknowledgments
The RF and Opto-electronics Laboratory at ESIEE, France, is specially thanked for supporting device design, experimental analyses as well and facilitating the spectroscopic analytical work and high-resolution optical microcopy as presented in this article. Particularly, Mr K. Ogudo is also thanked for providing technical assistance. The intellectual property aspects as associated with this work have been protected at both a national as well as internationally [33–35]. The work as presented in this article particularly forms the subject of further provisional RSA Patent Application of November 2016 [36].
Disclosures
The authors declare no conflicts of interest.
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30. A. Gorin, A. Jaouad, E. Grondin, V. Aimez, and P. Charette, “Fabrication of silicon nitride waveguides for visible-light using PECVD: a study of the effect of plasma frequency on optical properties,” Opt. Express 16(18), 13509–13516 (2008). [CrossRef]
31. M. Beals, J. Micheal, F. J. Liu, D. H. Ahn, D. Sparacin, R. Sun, C. Y. Hong, and L. C. Kimerling, “Process flow innovations for photonic device integration in CMOS,” Proc. SPIE 6898, 689804 (2008). [CrossRef]
32. S. M. Sze, “Carrier transport phenomenon: high field effects,” in Physics of Semiconductor Devices, 2nd ed. (Wiley, 1981), chap. 2, p. 67.
33. S. M. Sze, “Saturation current and voltage breakdown in bipolar devices,” in Physics of Semiconductor Devices, 2nd ed. (Wiley, 1981), chap. 4, p. 103.
34. “Opto-electronic device with separately controllable carrier injection means,” by L.W. Snyman. H. Aharoni, M. Du Plessis, USA Patent of 30 November 1999 (Priority date: 4 March 1996). by Republic of South African Patent No 96/2528 of 4 March 1996. Granted: SA (96/2528) (Assigned to University of Pretoria . Granted: USA Patent 6,111,27, (Assigned to University of Pretoria).
35. L. W. Snyman, “Wavelength specific silicon light emitting structure,” WO Patent WO/2011/038422 of 31 March 2011, U.S. Patent Application 2010819669 of European Patent EPO Application . 1020127000895 of 25 April 2012 and of Korean Patent 1020127000895 of 27 December 2013 (assigned to the Tshwane University of Technology).
36. L. W. Snyman, J.-L. Polleux, and K. Xu, “Optimised 650 nm Impurity assisted injection controlled Si Av LED,” Provisional submitted S.A Patent of September 2016 (assigned to the University of South Africa)
