Sep 20, 2007 - Ai, 42.79.Nv, 44.40.a. Linear light down-conversion (LDC) has been a conve- nient method for generating light by applying a short wave-.
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High-temperature Si linear light down converter with 220% efficiency V. K. Malyutenko and V. V. Bogatyrenko Lashkaryov Institute of Semiconductor Physics, Pr. Nauki 41, Kiev 03028, Ukraine 共Received 11 June 2007; published 20 September 2007兲 The authors report the fundamentals and technology of the linear light down-conversion process, which is based on the possibility of enhancing thermal emission of semiconductors in the spectral range of intraband electron transitions 共midinfrared and long-wave infrared兲 by the shorter wavelength interband excitation. They realized conditions 共the 1.15-m signal-in wavelength and 2- to 20-m signal-out wavelengths, T ⬃ 500 K兲 when a Si device demonstrated the 220% power conversion efficiency. They discuss the concept for incoherent broadband light down-converters made of indirect bandgap semiconductors and fueled with thermal energy 共controlling light with heat process兲. DOI: 10.1103/PhysRevB.76.113201
PACS number共s兲: 42.72.Ai, 42.79.Nv, 44.40.⫹a
Linear light down-conversion 共LDC兲 has been a convenient method for generating light by applying a short wavelength photon to a medium that responds by emitting one, two, or more longer wavelength photons. Such LDC processes like photoluminescence in semiconductors and quantum cutting in phosphors have gained significant interest due to promising practical applications. The LDC by photoluminescence is a way of creating high-temperature 3 to 5 m-light emitting devices 共LEDs兲.1 Blue LEDs coupled with a phosphor down-conversion layer offer a solid-state solution for white lighting.2 The quantum cutting in rare-earth-doped materials, finds applications in the fabrication of mercury-free fluorescent tubes, and plasma display panels.3 Proposals to convert high-energy photons toward lower energies for which the solar cell works more efficiently are also worth mentioning.4 The disadvantage, however, is that the power conversion efficiency of LDC mentioned is lower than 100% because the process comes at the cost of an incident photon. Due to activation of nonradiative decay processes 共such as the multiphonon emission or free carrier Auger recombination兲, LDC efficiency degrades when the temperature or converted wavelength increase. In this paper, we examine the application of the transparency modulation technique to the linear LDC process aimed to achieve the power conversion efficiency 共the signal-out power per signal-in power relation兲 of greater than 100%. This approach is based on the possibility of enhancing the thermal emission 共TE兲 power of semiconductors in the spectral range of intraband electron transitions 关midinfrared and long-wave infrared 共IR兲, free carrier absorption band兴 by the shorter wavelength optical signal 共visible to near-IR, fundamental absorption band兲. By demonstrating the use of silicon for this purpose, we come up with the concept for an efficient temperature-activated incoherent linear light downconverter made of indirect bandgap semiconductor 共controlling light with heat process兲. The details of our approach appear as follows. The TE spectral power P of a body with the thickness d, reflection coefficient R and absorption coefficient k, which is kept at constant temperature T P = J共T兲
共1兲
is a product of two factors. Specifically, J共T兲, that is, Planck’s spectrum of black-body radiation and the body 1098-0121/2007/76共11兲/113201共4兲
emissivity 共which equals the absorptivity兲 that can be expressed as = 共1 − R兲共1 − 兲共1 − R兲−1 , where
冉冕
d
= exp −
0
k共x兲dx
冊
共2兲
共3兲
is the optical transparency of a body and the wavelength 共兲 dependence of R and k is omitted for brevity. By definition, a black-body emissivity is unity and its TE spectrum is a wellknown Planck’s distribution 共Fig. 1, curve 3兲. Real body specificity is in the emissivity spectrum as the reflection and absorption coefficients are wavelength dependent values. Therefore, the TE spectrum fingerprints reflect the nature of energy transitions in a body both in the equilibrium and 共what is most important in our case兲 upon different excitation processes.5 In semiconductors, there are two wavelength bands with different emissivity shown in Fig. 1. In the fundamental absorption band 共1 ⬍ hc / Eg, h: Planck’s constant, c: the velocity of light, Eg: a semiconductor bandgap, band I兲, bulk materials are opaque due to high interband absorption
FIG. 1. 共Color online兲 The spectral position of bands I and II is shown schematically in respect to the Si bandgap. The k2共兲 and P2共兲 dependencies in the signal-in off 共1, 2兲 and signal-in on 共1⬘ , 2⬘兲 states, respectively. Shaded region: ⌬P value induced by a signal-in. 3: Planck’s distribution of the black-body radiation at T = 500 K.
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coefficient k1. On the contrary, beyond the fundamental absorption 共2 ⬎ hc / Eg, band II兲, undoped semiconductors are highly transparent. The absorption coefficient in this band k2 = kn + k p + k ph is connected to the lattice absorption k ph and electron 共n兲 and hole 共p兲 absorption, kn + k p = nn + p p, where n, p are free carrier absorption cross sections of IR photons. What follows from this is the possibility to enhance the TE in the band II through the photoexcitation of free carriers with higher energy photons from the band I. This light down conversion technique, also referred to as the transparency modulation technique,6 is easy to perform if the temperature of a semiconductor is higher than that of the background. Recently, we have shown that this approach makes it possible to use indirect bandgap semiconductors 共such as Ge or Si兲 as IR emitters and IR dynamic scene simulation devices7,8 and for testing recombination parameters in silicon.9 In what follows below, we will be interested in the power conversion efficiency of this down conversion optical process. When exposed to a light 共signal-in兲 with the power of P1 = I1hc / 1, an additional concentration of electrons and holes in a wafer takes the form ⌬n = ⌬p = 共1 − R1兲 I1rec / Ld, where I1 is the density of incident photons per second, rec, Ld are the effective carrier lifetime and diffusion length, respectively, and the inequality k1Ld ⬎ 1is valid. These nonequilibrium free carriers affect both k2 and P2 values 共see curves 1, 2 and 1⬘, 2⬘ in Fig. 1兲. With P02 and 02 to denote the initial values P2 and 2, the modulated TE power 共signal-out兲 bidirectionally escaping the wafer in the band II 关⌬P = P2共兲 − P02共兲兴 can be calculated by the expression5 ⌬P =
关1 − R2兴2关02共兲 − 2共兲兴 关1 − R22共兲兴关1 − R202共兲兴
关J共T兲 − J共Tb兲兴, 共4兲
where Tb is the temperature of background. According to Eq. 共4兲, R2, rec, and k2 need to be known in order to calculate the power conversion efficiency that is the integrated in the band II ⌬P value 共see shaded region on Fig. 1兲 divided by the signal-in power P1. R1 ⬇ R2 = 30% was determined from the known refractive index of Si. It was assumed that the material is intrinsic at the temperatures of test. To estimate k02共兲 and 02共兲, we neglected the lattice absorption and used intrinsic carrier concentration versus temperature dependence ni = 3.88⫻ 1016 T3/2 exp共−7000/ T兲 cm−3 共Ref. 10兲. For the temperature and wavelength dependence of the 共n + p兲 = k02 / ni, we used the equation k02 = 4.15⫻ 10−5 1.51 T2.95 exp共−7000/ T兲 cm−1 共where is in m, T is in K, and k02 is in cm−1兲 that is believed to be valid for wavelengths between 1 and 9 m and temperatures ranging from 300 to 800 ° C 共Ref. 11兲. The rec共T兲 dependence was measured by analyzing the signal-out decay curve 共beginning below 50% of the maximum decay signal兲 after excitation of free carriers with a pulsed Nd:YAG laser 共1 = 1.06 m, the pulse energy is chosen to fulfill low injection requirement兲. The hypothesis that power conversion efficiency of the LDC process could exceed 100% is confirmed by the results of calculations 共Fig. 2兲 with the following distinctive fea-
FIG. 2. 共Color online兲 Power conversion efficiency of LDC versus temperature. 1–3: theory 关rec = 4 ms. 1: Tb = 0, k02 = 0; 2: Tb = 300 K, k02 = 0; 3: Tb = 300 K, k02: data taken from Ref. 11兴. 4: Experimental results. Inset: Signal-out dependence on signal-in wavelength in respect to a He-Ne-laser line.
tures. First, this process is temperature activated. This is due to the nature of photons and phonons. The particles are bosons and their concentration increases with temperature increase. As a result, free electron/hole is easy to make an indirect transition inside the conduction/valence band by interacting with IR photon and phonon at a higher temperature. Indeed, as free carrier relaxation time 共rel兲, exponentially decreases when temperature increases, the number of IR photons generated by each free electron/hole 共that is rec / rel value兲 increases. Secondly, the power conversion efficiency of the process depends on the initial transparency of a material. This is natural consequence of the fact that only an optically thin semiconductor 共k02d Ⰶ 1兲 allows for highintensity contrast between P2共兲 and equilibrium value P02. For this reason, the thermal generation of free carriers 共that increases P0兲 makes the process less efficient at T ⬎ 500 K 共see high-temperature tail in curves 3, 4兲. Fortunately, the problem could be avoided in part by thinning a wafer. Thirdly, the background radiation that increases P02 should be minimized, while reflecting from or transmitting through a wafer, this radiation affects the intensity contrast 共see curves 1, 2兲. Finally, there is the fundamental limit for the signal-out power: P2 cannot exceed the black-body power at temperature of device. The samples for experiments were prepared as follows. We used a 5-mm-thick 170 ⍀ cm float zone n-Si wafers. Both surfaces of wafers were optically polished to prevent light scattering, and etched to minimize surface recombination velocity 共s兲. By our tests, this value was of about 100 cm/ s in the temperature range of interest while rec increased from 2 ms 共300 K兲 to 4 ms 共500 K兲. The experimental arrangement is shown in Fig. 3共a兲. The wafer was packaged into a beltlike molybdenum heater. By controlling the current in the heater circuit, wafer heating 共that was controlled by the thermocouple and IR camera兲 was achieved up to 573 K. The signal-in beam 1 was the 1.15-m line of a He-Ne laser 共3-mW power兲. This beam was modulated by a mechanical chopper at the frequency of 20 Hz and focused onto a 1.5-mm-diameter area on the back facet of a wafer. The TE escaping the front facet was registered over the 2 – 20 m band at the 4-cm distance with a
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FIG. 3. 共Color online兲 共a兲 Arrangement for measuring the LDC efficiency. 1: He-Ne-laser, 2: mechanical chopper, 3: H2O filter, 4: Si wafer, 5: heater, 6: Ge filter, 7: pyrodetector. 共b兲 Spectral distribution of P02 共1兲 and ⌬P 共2兲 at T = 500 K. 共c兲 The 2D signature of TE signal-out captured by the 3 – 5 m thermal imaging camera from the front facet.
pyroelectric detector with a 2-mm-diameter sensitive area, which fed into a lock-in amplifier. The total front-facet hemisphere output was calculated by taking into account its Lambertian angular dependence, which we confirmed with independent measurements. Special care was taken to ensure that the IR signals were, in fact, due to the TE induced by free carriers. The 1-mm-thick water filter placed between a laser and a wafer prevented the IR radiation emitted by heated laser parts from passing through a wafer. The 0.8-mm-thick Ge filter 共cut on ⬇ 2 m兲 placed in front of a detector absorbed both the laser beam, which could pass through a wafer and the interband photoluminescence signal. Positioning a monochromator between Ge filter and the detector allowed measuring spectral distribution of the TE output. The two-dimensional 共2D兲 signature of signal-out was recorded with a thermal imaging camera operating in the 3 – 5 m band. In addition, 共⌬P − I1兲 dependence had slope of unity, indicating that ⌬P varied linearly with a signal-in power, up to the highest level used 共⌬P ⬃ k2d, high-transparency mode兲. Shown in Fig. 3共c兲 is the 3 – 5 m camera image 共signalout兲 generated by a low-power laser beam at the back facet and recorded at the front facet at T = 500 K 关k1 = 17 cm−1 共Ref. 12兲兴. As the TE magnitude is proportional to the local excess carrier concentration, the radial degradation of signalout is due to free carrier recombination and diffusion processes. Therefore, decay length is directly related to the effective diffusion length Ld and is long as 1.5 mm in our test. Note, Ld = 共Drec兲0.5 = 1.7 mm by taking the measured rec = 4 ms and bipolar diffusion coefficient D = 7 cm2 / s from data in the literature13 that was received also by using the modulated thermal emission study. Figure 3共b兲 shows the signal-out spectrum recorded at T
= 500 K. Also shown is the P02共兲 dependence with fingerprints which are due to oxygen impurity and lattice multiphonon absorption.14 As can be seen, the modulated TE signal is similar to Plank’s radiation spectrum. However, emission peaks at the P02共兲 dependence transform naturally into dips in the ⌬P spectrum. Meanwhile, to a fairly good approximation, the device can be referred to as a broad-band gray emitter. Figure 2 共curve 4兲 shows the two-facet power conversion efficiency as a function of temperature for a wafer tested at Tb = 300 K. The over 100% values occur in the temperature range 425⬍ T ⬍ 575 K while the peak value is of 220%. We also observed a decrease in conversion efficiency at T ⬎ 500 K, which can be explained by gradual wafer opaqueness, induced by thermal generation of free carriers 共experimental data is somewhat lower than the theoretical curve due to the parasitic lattice absorption neglected in the theory兲. Although we have not tried removing the room-temperature background, we believe that such an experiment would result in higher efficiency than the experiment currently being discussed. Efforts to increase the device efficiency by thinning the wafer for operating at higher temperature were limited by a comparably high s value that should have affected rec in thin wafers. The estimates show that if rec were of about 10 ms in 0.1-mm-thick Si wafer that remains initially transparent at high temperature, the power conversion efficiency could have exceeded 1000% at T 艌 700 K. Note that these Si parameters are not exotic—s of 0.25– 4.0 cm/ s and rec of 35 ms and even exceeding 100 ms in FZ material are well documented in literature.15 Summarizing, we presented the concept for temperatureactivated incoherent broad-band light down converter made of indirect bandgap semiconductors and capable of light “amplification” through controlling light with a heat process. Even if the parameters of the Si wafer and signal-in wavelength were not optimized, we experimentally demonstrated power conversion efficiency of 220% at T = 500 K and ⬎100% values for a very large temperature range. Contrary to a conventional semiconductor optical amplifier based on the stimulated interband carrier radiative recombination in a narrow above bandgap amplification window 共2 ⬇ 1兲, the device is based on the intraband spontaneous emission 共carrier-IR photon-phonon interaction兲 in a wide below bandgap window 共2 Ⰷ 1兲. The challenge to practical implementation of the strategy described consists of material bandgap engineering in the electronic domain 关higher rec 共n + p兲 product, stronger k2 = f共2兲 dependence兴 and photonic engineering 共transparency coating, optimum 1 and d values兲 in the optical domain. This research was supported by a grant from the Air Force Research Laboratory 共USA兲.
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