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  • c1ue
    replied
    Re: led paper sought

    Originally posted by astonas
    Clue, I really hate doing this to you. But you keep insisting that you know about things you don't, and appealing to the authority of your experience to overwhelm perfectly reasonable concerns and corrections:
    Sorry, you can flaunt all you want, but I both have direct experience working with silicon semiconductors (i.e. digital design) and work directly with individuals who design the machines that create gallium arsenide chips.

    Originally posted by astonas
    At the very least, you are significantly over-representing your expertise in this field (GaN LEDs), in which you consistently demonstrate such a profound lack of understanding.
    All is clear now. You seem to think that my comments are directly exclusively to GaN LEDs, when all I'm noting is that there are shared physics based constraints between LEDs and semiconductors. And to be specific, semiconductors used for analog and digital design.

    Yet I have specifically noted that there are fundamental differences between designs intended to perform analog/digital calculations vs. designs intended to generate light:

    This is different than standard semiconductors where electrons are primarily used as electrical current.

    Sure, LEDs do also use electrons to generate electrical current, but this is secondary to what they are intended to do: generate light.
    So, to return to the question:

    Are hot electrons only what you describe:

    Originally posted by astonas
    A hot electron is just one that has high momentum (is traveling rapidly in the semiconductor).
    The answer is NO. For a physicist, this would be true, but in real life the cause and the effect are related.

    A physicist might say that a car driving off a cliff is one event, and the car landing on someone underneath is a separate one, but engineers understand that one doesn't occur without the other.

    Originally posted by astonas
    I received my B.S. in Engineering Physics from UC Berkeley, and my Ph.D. in Electrical Engineering from the UC Santa Barbara, which was then, as it is now, ranked the #1 school in the world in the fields of optoelectronic semiconductor materials, and GaN in particular. I held 1 full academic scholarship as an undergraduate, and 2 fellowships as a graduate student. My work at UCSB resulted in numerous conference presentations, as well as authorships and co-authorships on 10 peer-reviewed archival journal articles, all involving the material system GaN, that is the subject of the paper you cited. One of my papers was co-authored with James Speck, the UCSB professor interviewed in the article you posted, in which he describes his own recent publication on Auger recombination.

    I have designed and created gallium nitride LEDs (with my own hands) in lab, growing the material epitaxially using MOCVD, processing it in a cleanroom, testing it using a very wide range of characterization tools, analyzing the results, and publishing these. I have also worked on teams that made and published results from quite a few other GaN-based devices, some of which had never before been created by anyone, anywhere in the world. Other teams I worked on had, at the time, world-record performance. I have even (alone) created for the first time a new class of optoelectronic GaN devices, never constructed before my work, which was enabled by my work, spawning research efforts at other universities that sought to extend it. I invented and patented some of the new tools that allowed me to do this. One of these patents has been licensed by a major player in the LED industry.
    This is all fine and interesting, but I fail to see how your LED expertise leads you to be able to categorize all hot electrons.

    If you're trying to say that hot electrons in GaN LEDs are fundamentally different than in silicon or GaAs semiconductors - I'd be happy to say that you should know GaN LEDs better.

    I, however, have worked for years on hot electron (as well as other related) fields in both silicon and GaAs designs, so know your comments are not correct for all instances. Equally, to be sure, I checked with several of my friends who create the machines which in turn create both GaN and GaAs products. They also have fancy schmancy degrees and what not, but more importantly design, field, and maintain the multi-million dollar machinery which has to do the industrial work of producing LEDs, solar panels, and what not. They too have dozens of patents. They validated what I said: hot electrons for high voltage designs primarily affect performance - to be specific they trigger discharges earlier than expected. Given that there are probably charge pumps and what not involved in building up voltages, I can see how this would affect LED overall output. However, hot electrons for smaller/lower voltage devices primarily affect behavior through structural damage exactly as I noted above.

    But ultimately the issue is: you think you know all there is to know about hot electrons.

    You don't.

    If you said you know everything there is to know about hot electrons in GaN LEDs, then I would bow to that - although I don't how much you necessarily know about hot electrons in the non-light generating aspect of the LED (i.e. the control and setup circuitry).

    Leave a comment:


  • metalman
    replied
    Re: led paper sought





























    Leave a comment:


  • astonas
    replied
    Re: led paper sought

    *sigh*


    Clue, I really hate doing this to you. But you keep insisting that you know about things you don't, and appealing to the authority of your experience to overwhelm perfectly reasonable concerns and corrections:

    Originally posted by c1ue View Post
    You have a lot of knowledge in certain areas, but don't assume you have greater knowledge of semiconductors. This is what I did for a long time.
    and
    Originally posted by c1ue View Post
    So you can talk all you want - but I actually worked in this field and do understand the differences as opposed to theory.
    The reader should be warned. I'm sorry, but you are bluffing. At the very least, you are significantly over-representing your expertise in this field (GaN LEDs), in which you consistently demonstrate such a profound lack of understanding.

    Instead, you seem to have a cursory and outdated understanding of several concepts very relevant to silicon transistors, and this shallow knowledge is misleading you into believing that they are also relevant here, in gallium nitride optoelectronics. They are not.

    The differences between silicon transistor physics and the physics of optoelectronic devices are very significant, and you clearly do not understand the science of either at a level fundamental enough to appreciate that fact.

    These fields diverge due to differences in material quality (point and threading dislocation density differences), dispersion relation (eg. direct vs. indirect bandgap), crystal structure (hexagonal wurtzite vs. cubic diamond lattice), ionic bond character (GaN's bonding more ionic, silicon's symmetric) and bandgap (3.4 eV vs. 1.1 eV). These differences are what make your understanding non-transferrable. They affect ideality and scattering mechanisms, hot electron dynamics, and more, thus limiting the applicability of more superficial and general semiconductor theory to this system.

    If you really understood the subject of semiconductor device physics the way you claim, you would know that already. This isn't a "secret sauce." It's taught to undergraduates.

    Instead you continue to trot out one irrelevant concept or outdated theory after another, and simply pound harder on the table that you should be believed, because of your "experience."


    Very well.


    I generally try never to bring up credentials in a debate. They should not carry any weight; if the logic and information itself is sound, an uncredentialed person should be able to have their arguments evaluated based on the facts and arguments presented, regardless of "rank" or "experience." Civilized discussions are based on the information, not the person or position.

    However, since you have tried to cite your qualifications to overwhelm reasonable arguments here, with me and with Polish_Silver, I have no choice but to offer a brief summary of my own credentials in my defense.

    Whatever you think I may or may not know about other subjects discussed on this site, those are my hobbies, which draw comparatively little of my mental energy, or focus. My profession is optoelectronic device physics, and I was trained principally in gallium nitride. I will happily admit that there are some things I do well, and some things I don't. But there is nothing I do better than (applied) optoelectronic device physics. Allow me to support that assertion.

    I received my B.S. in Engineering Physics from UC Berkeley, and my Ph.D. in Electrical Engineering from the UC Santa Barbara, which was then, as it is now, ranked the #1 school in the world in the fields of optoelectronic semiconductor materials, and GaN in particular. I held 1 full academic scholarship as an undergraduate, and 2 fellowships as a graduate student. My work at UCSB resulted in numerous conference presentations, as well as authorships and co-authorships on 10 peer-reviewed archival journal articles, all involving the material system GaN, that is the subject of the paper you cited. One of my papers was co-authored with James Speck, the UCSB professor interviewed in the article you posted, in which he describes his own recent publication on Auger recombination.

    I have designed and created gallium nitride LEDs (with my own hands) in lab, growing the material epitaxially using MOCVD, processing it in a cleanroom, testing it using a very wide range of characterization tools, analyzing the results, and publishing these. I have also worked on teams that made and published results from quite a few other GaN-based devices, some of which had never before been created by anyone, anywhere in the world. Other teams I worked on had, at the time, world-record performance. I have even (alone) created for the first time a new class of optoelectronic GaN devices, never constructed before my work, which was enabled by my work, spawning research efforts at other universities that sought to extend it. I invented and patented some of the new tools that allowed me to do this. One of these patents has been licensed by a major player in the LED industry.


    I have continued working in the optoelectronic semiconductor industry since graduate school, first at a fortune-500 R&D facility, and then at a startup where I created and grew a new business unit using grant funding, all of it directly related to advancing the state-of-the-art in applied semiconductor device physics. One grant that I wrote and served as principal investigator for (a $1.5M DOE grant) even relied on precisely the transformation of hot carriers into excitons using impact ionization (multiexciton generation) mechanisms, to exceed the Schockley-Quiesser efficiency limit of solar cells. This effect was observed in samples made in my lab, which would not have been possible to do if hot electrons were correctly understood in the way you simplistically describe them.

    I have started and still run a company which seeks to apply similar device physics understanding to novel applications. This requires me to remain current with the literature, which I do. I also hold a concurrent adjunct faculty position at a major tier-1 research university, where I perform my own research, and help guide undergraduate and graduate students doing publishable research in the field.

    The unique path of my career has moved from novel research in GaN, to the impact ionization of hot carriers. Because these fields, by their nature, very seldom overlap, the fact that I have meaningful personal experience with both is very unique. To the best of my knowledge, there is no other scientist in the world who has done research in both the fields that this discussion is bridging. One might even say that I am uniquely qualified to assess your points. I would certainly be happy to compare CVs with another asserting to be better qualified.

    I'm sure that your own semiconductor industry experience is far more relevant to the behavior of Auger electrons in Gallium Nitride, and will easily overwhelm all of my own qualifications. I look forward to hearing what that might be. Until then, let's review what you've learned from your extensive semiconductor experience:

    You seem to repeatedly mix up usage of "semiconductor" with "silicon" or even "transistor" (thus neglecting categorically the many crucial differences between the three terms which would imply potentially different dynamics and scattering of hot electrons).

    You talk of analog and digital function, when it is obvious that an LED is exclusively an analog device, and digital speeds are irrelevant.

    The confusion of "hot electrons" with phonons (you use the term "heat") is equally bizarre and wrong, as is your (thereby implied) confusion of recombination with scattering.

    You appear not to comprehend even the most basic consequences (taught in 1st term undergraduate device physics courses!) of the difference between direct- and indirect-band-gap semiconductors.

    Your assertion that recombination always generates heat is similarly wrong in a direct bandgap semiconductor.

    Stating that an electron "gets" charged by an LED (when all electrons have a single, fixed charge of q=-1.602176565 10−19 C) is as well. Middle school children know that an electron has a definitive, constant charge.

    You even, through your sentence structure, imply that LEDs are not made of semiconductors (and go on to lie about this being implied in a subsequent post)!

    I'll repeat the quote here for reference (emphasis added):
    Originally posted by c1ue View Post
    In semiconductors - the desired behavior is movement while in LEDs the desired behavior is the emission of a photon.
    The use of the word "while" implies different but comparable objects.

    When challenged, you link to a website describing silicon transistors, which contains not a single statement relevant to gallium nitride optoelectronic devices at all. It is even called siliconfareast.

    The gap between the understanding claimed, and the understanding demonstrated, is irreconcilable to me, given what can only be described as the clear demonstration of a sub-remedial level of understanding concerning the physical picture of what mechanisms occur in optoelectronic devices. Anyone who claims to understand "semiconductors" but doesn't even know how semiconductor materials differ from one another can only possess a very superficial level of understanding.

    If, as you imply, semiconductors is the field on which one should find you most credible, I am afraid that to me, you no longer have any credibility left at all. I am sure that you will be able to find a witty reply, come-back, justification, explanation, or expression of outrage for each of your exceedingly basic errors, but you needn't bother. I will not be reading your reply, nor will I be reading any of your future posts. It isn't worth the time.


    [ignore]


    Pulling rank is bad, though on rare occasions forgivable or necessary.


    Pulling rank specifically to hide one's own deep-seated ignorance or incompetence, or to cow others into submission when one oneself is found to be wrong, is never acceptable. It is a form of bullying, that seeks to assert a lie by force, rather than seek truth with evidence. When I am in the very rare position to be able to identify it first-hand (as I am now) I treat it as such -- unambiguously.


    p.s. My apologies to all others who read this, for sinking to the level of my debate partner, and comparing qualifications rather than arguments. I do not intend to make a habit of it.

    Leave a comment:


  • c1ue
    replied
    Re: led paper sought

    Originally posted by astonas
    Clue, you haven't seen all the conversations in the select section (and hence, some of the background and skill that Polish_Silver and others display there) so I'll just give a bit of friendly advice.

    This is the time to admit that you don't understand the science, apologize for the debate "tactic" of trying to bluff your way through by referring to your semiconductor experience, and move on.
    Sorry, but I am not bluffing.

    HCI and hot electrons are similar for high voltage/analog, but they're different for digital.

    For high voltage/analog, the primary effect is malfunctioning of the device.

    For digital, it is damage - exactly as noted above.

    So you can talk all you want - but I actually worked in this field and do understand the differences as opposed to theory.

    If you want to actually get a better idea of how it all fits together, then this is a good example - though of course very generic:

    http://www.siliconfareast.com/hotcarriers.htm

    For LEDs - it isn't absolutely clear the high voltage is the issue, as the devices are both very large and not very high voltage given their size. However, the energy levels are high thus it might be. Certainly the effect (loss in efficiency) would seem to point towards device characteristic breakdown.

    However, the original point was that hot electrons were an issue in both LEDs and semiconductors. This is still true no matter how you attempt to slice it.

    Equally the reality is that 'hot electrons' can and do have ways of creating damage via heat - and via the exact mechanism I described.

    EDIT:

    To put some scale into the differences between high V analog and digital, digital cutting edge today is 28 nm. That's about 300 atoms across. In contrast a high V analog is multiple microns or 3+ orders of magnitude larger. The damage I'm referring to occurs in analog high V as well, but doesn't really make any significant difference to performance of the device except possibly for very, very long time frames, but it matters a very great deal for digital.
    Last edited by c1ue; 04-29-13, 06:38 PM.

    Leave a comment:


  • astonas
    replied
    Re: led paper sought

    Originally posted by Polish_Silver View Post
    Is there a google accessible paper on this idea? I would like to read about it.

    I've been out of the solid state physics business for years, but I still like to keep my feet wet.
    No, this was in a journal that isn't free to download. I'll PM it to you this weekend when I log in from my computer.

    Leave a comment:


  • Polish_Silver
    replied
    led paper sought

    Originally posted by astonas View Post
    But that too, could be addressed much better than it is in the industry today. My graduate work, for example, resulted in a surface-shaping mechanism that permitted far higher light extraction than even today's commercial LEDs achieve. The raw die increased in forward extraction by a factor of 5. (I patented the method, and it was licensed by a major player who didn't understand how to do it properly, and wound up killing it.)
    Is there a google accessible paper on this idea? I would like to read about it.

    I've been out of the solid state physics business for years, but I still like to keep my feet wet.

    Leave a comment:


  • astonas
    replied
    Re: LEDs and hot electrons

    Originally posted by Fiat Currency View Post
    I'd like to second that astonas and offer additional good wishes on your patent applications.

    It's nice to see that there's still a segment of the population trying to grind it out in the Producer economy, through the utilization of new technology and good old innovation - mixed with sweat equity.

    One of our companies is awaiting 4 international patents. Been there before, but it can sometimes feel glacial and frustrating. I did a presentation last night on the saviour and servitude elements of future technologies to a business crowd. The presentation was only 1 hour long, but I stayed for 2 and a half more hours to extinguish all the questions. I was a little shocked at the level of interest and high quality of the questions. The "kid's table" as they're known (students) in the club - peppered me to death with interest, knowledge, and even questions regarding starting-up high-tech businesses. I left feeling a little bit more optimistic about the future.

    Best wishes on your venture.
    Thanks, Fiat, for your support and advice! It is always good to know that there are some who find a path through to make it all work.

    I am intrigued by your presentation on the savior and servitude elements of future technologies. This is not a phrase I'm familiar with, and while I think I can extrapolate what you mean by it, I would be interested in learning more. Do you have a link or file that you wouldn't mind sharing, or would you perhaps be willing to summarize?

    As far as the "kid's table" goes, I'd say you're absolutely right. There's certainly some great talent around, if you know which rocks to look under. And entrepreneurship is a culture that is making its way into graduate schools everywhere in a big way. One of the things that makes it possible to do my own work on a shoestring budget is a close collaboration with a research university, and so I get to interact with the "kids" quite a bit. There's obviously a range, but the good ones give a great deal of hope.

    Leave a comment:


  • astonas
    replied
    Re: LEDs and hot electrons

    Originally posted by EJ View Post
    I learned just enough to be dangerous from the former CEO of Luminus Devices and from a good friend, MIT grad, and Managing General Partner of a VC firm here in town who has the material science and chip expertise on the team.

    One major disadvantage of a chip over a filament is that light emits 360 degrees from a filament whereas a chip emits light at a narrow angle in one direction making even dispersion problematic. The fact that light emits more broadly from the flat surface of the chip versus from a sharp point of light of a filament makes it hard to confine the light to a narrow beam to project it long distances. Cooling is inherently problematic and most of the innovations that have produced high intensity LEDs are in heat dissipation. The key advantages of LEDs is that 80% to 90% of the input energy goes into generating light output versus 80% to 90% heat output in the case of incandescent bulbs, and LEDs can last for decades versus months.

    Best of luck with your invention.
    Thank you very much! There's no doubt that small businesses need all the luck they can get these days!

    The problem of light extraction from raw GaN to air being limited (by total internal reflection) to a ~22 degree cone is indeed a big one.

    But that too, could be addressed much better than it is in the industry today. My graduate work, for example, resulted in a surface-shaping mechanism that permitted far higher light extraction than even today's commercial LEDs achieve. The raw die increased in forward extraction by a factor of 5. (I patented the method, and it was licensed by a major player who didn't understand how to do it properly, and wound up killing it.)

    So there's still LOTs of good new ideas worth pursuing in that regard, and it confuses me that the industry still insists on iterating the older ones, and killing R&D efforts on the newer ones to save costs. I can't see their project-level balance sheets and income statements, of course, but there are a still a few tricks that could be tried today that might even reduce LED unit cost, if they were only taken more seriously by the players involved. The engineering is very sound, and for certain approaches the financials should be as well.

    If my current efforts don't pan out quickly enough, I suppose that is an area of research I could return to. It wouldn't take much effort to extend my graduate work in a way that resulted in a new and separate patent (providing a sustainable advantage), since I've been mulling the problem over in the back of my mind since then. I've even got some initial experiments designed.

    As far as cooling is concerned, you are right that it is a major issue. But it is not the more fundamental issue. A better answer is to generate less heat in the first place. An ideal LED should generate light with far less heat than today's LEDs, just as they do in the GaAs, InP, and other direct bandgap semiconductor systems. The problem in the GaN system is that heating occurs mostly because of all the non-radiative recombination paths that exist in the material, due to both point and line defects (threading dislocations). To address THAT requires innovation in epitaxial growth technology, which is being pursued very heavily indeed, as well as substrate technology, which is being pursued by some startups stemming from the place I did my graduate work. There's some very real promise there, but cost remains an issue at this point.

    By the way, a company started by one of my graduate advisors, (they're taking the-reduce-dislocations-via-better-materials approach) just released its first LED product!

    Leave a comment:


  • Fiat Currency
    replied
    Re: LEDs and hot electrons

    Originally posted by EJ View Post
    Best of luck with your invention.
    I'd like to second that astonas and offer additional good wishes on your patent applications.

    It's nice to see that there's still a segment of the population trying to grind it out in the Producer economy, through the utilization of new technology and good old innovation - mixed with sweat equity.

    One of our companies is awaiting 4 international patents. Been there before, but it can sometimes feel glacial and frustrating. I did a presentation last night on the saviour and servitude elements of future technologies to a business crowd. The presentation was only 1 hour long, but I stayed for 2 and a half more hours to extinguish all the questions. I was a little shocked at the level of interest and high quality of the questions. The "kid's table" as they're known (students) in the club - peppered me to death with interest, knowledge, and even questions regarding starting-up high-tech businesses. I left feeling a little bit more optimistic about the future.

    Best wishes on your venture.

    Leave a comment:


  • astonas
    replied
    Re: My experience with Hot electrons

    Originally posted by c1ue View Post
    The article talks about hot carrier injection. This isn't the hot electron effect.

    The wiki even notes:
    Clue, you haven't seen all the conversations in the select section (and hence, some of the background and skill that Polish_Silver and others display there) so I'll just give a bit of friendly advice.

    This is the time to admit that you don't understand the science, apologize for the debate "tactic" of trying to bluff your way through by referring to your semiconductor experience, and move on.

    Please. It's nicer when the debate stays civil.

    Leave a comment:


  • Polish_Silver
    replied
    something completely different!

    Originally posted by c1ue View Post
    The article talks about hot carrier injection. This isn't the hot electron effect.

    The wiki even notes:
    Hot carrier injection! Something completely different! Or at least, somewhat different.

    Leave a comment:


  • c1ue
    replied
    Re: My experience with Hot electrons

    Originally posted by Polish Silver
    This article agrees with my experience and understanding of hot carriers in semiconductors.
    The article talks about hot carrier injection. This isn't the hot electron effect.

    The wiki even notes:

    That is, high temperatures caused by the effect are unrelated to the phrase "hot electron effect".

    Leave a comment:


  • Polish_Silver
    replied
    My experience with Hot electrons

    This article agrees with my experience and understanding of hot carriers in semiconductors.

    1) In mosfets, hot carriers cause increased body current, which is undesired.

    2) In mosfets, they are believed to gradually change the threshold voltage, by creating defects at the oxide interface. This is undesired.

    3) Hot carriers have a velocity comparable to (or greater than) the saturation velocity. Most devices are designed to work with the carriers well below the saturation velocity.

    The hot carrier current increases exponentially with the drain-source voltage, above a threshold which depends on the channel length.
    It is the greatest when the gate voltage is about 1/2 way between the drain and source voltage. It is small when Vgs~0V or when Vgd ~ 0V.
    Last edited by Polish_Silver; 04-26-13, 08:33 AM.

    Leave a comment:


  • c1ue
    replied
    Re: LEDs and hot electrons

    Originally posted by astonas
    Actually, a "hot electron" is not necessarily something that generates heat at all. And in this system they are usually behaving exactly like they're "supposed to." They don't (directly) damage the material, unless you're talking about electromigration, which depends on the number of carriers, and not their momentum, and thus still only connects to hot electrons very tangentially.

    And LEDs ARE made of semiconductors.
    You might note that I never said LEDs weren't made of semiconductors.

    What I said was that an LED was seeking to generate light by charging up an electron, and having said electron slip to a lower energy level thus generating a photon.

    This is different than standard semiconductors where electrons are primarily used as electrical current.

    Sure, LEDs do also use electrons to generate electrical current, but this is secondary to what they are intended to do: generate light.

    Originally posted by astonas
    A hot electron is just one that has high momentum (is traveling rapidly in the semiconductor).
    Completely wrong. The reason they're called 'hot' is because the recombination of holes and electrons generates heat. The heat absolutely does generate damage, and furthermore this damage tends to be inside the carrier material.

    For those not familiar - a 'hole' is a gap where an electron used to be. In semiconductors, the 'hole' can be used in a similar fashion to the missing electron. Think of a hole as a bubble going through water, while an electron might be a bowling ball rolling down the lane. When a bowling ball rolls into a bubble, the energy either/both were carrying tends to convert to heat.

    Electromigration in contrast damages material by moving ions of said material to a different location. This is a completely different mechanism - it is caused by fast moving electrons transferring momentum to the ions of the conductor, causing said ions to move and corresponds to what you note above.

    You have a lot of knowledge in certain areas, but don't assume you have greater knowledge of semiconductors. This is what I did for a long time.

    Originally posted by Polish Silver
    Is this Auger problem separate from the temperature problem? LED's lose efficiency when the junction temperature rises above 40C. I thought this was just higher temperature---> more phonons ---> more inelastic collisions between phonons and electrons.
    I doubt it. The process of charging up the electrons is a more standard semiconductor device function - and temperature affects those performance curves. In particular, the hotter a semiconductor device gets, the more leakage occurs in the devices, which in turn degrades the expected behavior.
    Last edited by c1ue; 04-25-13, 03:03 PM.

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  • Polish_Silver
    replied
    Re: LEDs and hot electrons

    Originally posted by EJ View Post
    . . .

    One major disadvantage of a chip over a filament is that light emits 360 degrees from a filament whereas a chip emits light at a narrow angle in one direction making even dispersion problematic. The fact that light emits more broadly from the flat surface of the chip versus from a sharp point of light of a filament makes it hard to confine the light to a narrow beam to project it long distances.
    .

    This is a big issue for bicycle headlights. The best of them use both a reflector and a lens to focus the beam.

    A parabolic reflector with the filament at the focus produces parallel rays---good for headlights.

    It is more difficult for LED's, but the combination of lens and reflector can make a tightly focused beam.

    http://www.ebay.com/itm/CREE-XML-XM-...item460e90c41e

    These do a good job.

    Leave a comment:

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