Plasmon Coupling—The Root Cause of Raman Anomaly and Laser Cooling in Nanocrystal Ge

Laser cooling of matter through anti‐Stokes photoluminescence, where the emitted frequency of light exceeds that of the impinging laser light by virtue of absorption of thermal vibrational energy, has been successfully realized in condensed media, and in particular with rare‐earth‐doped systems achieving sub‐100 K solid‐state optical refrigeration. Studies suggest that laser cooling in semiconductors has the potential of achieving temperatures down to ≈10 K and that its direct integration can usher in unique high‐performance nanostructured semiconductor devices. While laser cooling of nanostructured II–VI semiconductors has been reported recently, laser cooling of indirect bandgap semiconductors such as group IV silicon and germanium remains a major challenge. Herein, the anomalous observation of dominant anti‐Stokes photoluminescence in germanium nanocrystals principally associated with plasmon coupling is reported. Specifically, this Raman anomaly to the confluence of ultrahigh‐purity nanocrystal germanium, generation of high density of electron–hole plasma, the inherent degeneracy of longitudinal and transverse optical phonons in nonpolar indirect bandgap semiconductors, and simultaneous spatial confinement effects are attributed. At high laser intensities, plasmon‐assisted laser cooling with lattice temperature as low as ≈50 K is inferred.

DOI: 10.1002/adpr.202200251 Laser cooling of matter through anti-Stokes photoluminescence, where the emitted frequency of light exceeds that of the impinging laser light by virtue of absorption of thermal vibrational energy, has been successfully realized in condensed media, and in particular with rare-earth-doped systems achieving sub-100 K solid-state optical refrigeration. Studies suggest that laser cooling in semiconductors has the potential of achieving temperatures down to %10 K and that its direct integration can usher in unique high-performance nanostructured semiconductor devices. While laser cooling of nanostructured II-VI semiconductors has been reported recently, laser cooling of indirect bandgap semiconductors such as group IV silicon and germanium remains a major challenge. Herein, the anomalous observation of dominant anti-Stokes photoluminescence in germanium nanocrystals principally associated with plasmon coupling is reported. Specifically, this Raman anomaly to the confluence of ultrahigh-purity nanocrystal germanium, generation of high density of electron-hole plasma, the inherent degeneracy of longitudinal and transverse optical phonons in nonpolar indirect bandgap semiconductors, and simultaneous spatial confinement effects are attributed. At high laser intensities, plasmon-assisted laser cooling with lattice temperature as low as %50 K is inferred.
systems, solid-state optical refrigeration is now in the sub-100 K range.
Laser cooling of semiconductors in comparison has been an even more arduous trek. [10][11][12][13][14][15][16][17][18] Semiconductors are particularly attractive given the potential of achieving even lower temperatures of %10 K, and thus, the opportunity to enhance the performance of various optoelectronic devices through direct integration. In contrast to rare-earth-doped systems, where Boltzmann statistics leads to a significant reduction in the population of the ground state manifold as temperatures drop below 100 K, semiconductors follow Fermi-Dirac statistics where the valence band remains populated all the way down to absolute zero temperatures, and hence, cooling transitions remain accessible. Early work on cooling of direct bandgap III-V GaAs was hampered by surface recombination losses and low external quantum efficiency due to its large optical index; in time these were substantially overcome through surface passivation and optical impedance-matching techniques albeit large parasitic band tail absorption has prevented the attainment of net cooling. Laser cooling effects in spatially confined II-VI direct bandgap semiconductors have been reported recently, where some of the key contributing factors are nanolength scale effects and low nonradiative surface recombination and Auger losses. This report has since sparked significant interest in the optical cooling of a variety of direct bandgap semiconductor nanocrystal and nanostructure systems. However, laser cooling of indirect bandgap semiconductors such as germanium and silicon remains elusive.
Raman spectroscopy is a common technique used in the study of photon-phonon interactions, where optical excitation energy and material polarization effects lead to Stokes and anti-Stokes scattering. Accordingly, Raman spectroscopy is a conventional method to investigate local lattice temperature. At thermal equilibrium and for relatively nonabsorbing samples, the Boltzmann-Einstein distribution relates the relative intensity of Stokes and anti-Stokes to the lattice temperature via where I A and I S are the intensities of anti-Stokes and Stokes bands with vibrational frequencies of þω k and Àω k , respectively, ω i is the excitation frequency, T is the lattice temperature, and k B and ℏ are the Boltzmann and Planck constants, respectively. [19,20] In thisrelationship, the Stokes (S) to anti-Stokes (AS) intensity ratio does not depend on material bandgap since the Stokes and anti-Stokes Raman scattering events are transitions coupled with the virtual/pseudo energy levels (e.g., vibrational and rotational modes) of the system. Indeed, transitions with excitation energy exceeding the bandgap energy do transpire, where S and AS Raman transitions follow the selection rule with respect to the k B T energy levels of the system. Correspondingly, Raman signals are inherently linked to lattice phonons and their interactions with any prevailing alterations of the lattice. Now, typically in bulk material and under "normal" conditions the Stokes intensity always exceeds that of the anti-Stokes. However, there are a few reported instances where the anti-Stokes intensity is greater than the Stokes intensity-occurring for the most part in confined 2D [21] or 3D materials. Occurrences of this rare Raman anomaly-also referred to as Raman cooling-is due to phonon absorption. The probability of photon scattering is characterized by scattered photon frequency (ω), the photonic density of states at the scattered photon frequency (DðωÞ), and the matrix element of the scattering interaction (M) as follows where ¼ ω i AE ω k , the (þ) and (À) symbols represent the anti-Stokes and Stokes transitions, respectively, ω i the incident photon frequency, ω k the phonon frequency, and N i the number of incident photons. The concept of laser cooling is shown in Figure 1a, where E EX and K B T are the excitation and the phonon energies, respectively, E SPP is the plasmon energy, and E PL is the photoluminescent energy. Laser [10][11][12][13][14][15][16][17][18] and Raman [22,23] cooling of doped and undoped direct bandgap semiconductors have been practically confirmed. Theoretically, it has been shown that laser cooling in all semiconductors-direct and indirect bandgap materials-ought to be possible through engineering of the photonic density of states. [24] That is, the net radiative transition rate can be tailored considering that the interband transition rate in semiconductors follows Fermi's golden rule, W i!f ¼ 2π ℏ jMðE PL Þj 2 gðE PL Þ, where jMðE PL Þj and gðE PL Þ are the matrix element for radiative transition and joint density of state function, respectively, and noting that the latter term is a function of the density of electronic states and the density of photonic states. In this regard, it has been shown [17] that while in semiconductors at T > 150 K and low carrier concentrations Auger process remains the limiting factor for laser cooling, at high carrier concentrations there exists an optimal cooling range of 50-120 K where Auger recombination is low enough and radiative recombination is bimolecular but short of the saturation carrier concentration above which the radiative process becomes linear (i.e., dependent only on the hole concentration N rather than both electron and hole concentrations N 2 ).

Results and Discussion
Herein, we find that net laser cooling is possible in ultrahigh purity nanocrystal germanium via resonant photon-phonon coupling upon generation of high-density electron-hole plasma. We present experimental Raman spectra showing that the intensity of Stokes and anti-Stokes from germanium nanocrystals (ncGe) with diameters ranging from %16 to 30 nm can be inverted with increasing laser power density using 785 nm (1.58 eV) wavelength light.
Detailed synthesis process of the ncGe and characterization results are provided in the first part of our report, [25] and in this article our aim is to provide a hypothesis for the observed anomaly. Normal dispersion is the term given to the phenomenon of rising permittivity and refractive index with frequency, whereas anomalous dispersion is the decrease in permittivity and index of refraction that takes place around the resonance frequency, which could be the natural resonance frequency of the substance or a pseudoresonance and energy bandgaps in plasmonic crystals. [26] Hence, anomalous dispersion is the property of the material absorption region where reflection drops and characterization like UV-Vis provide the first evidence of reflection changes as it is projected in Figure S18, Supporting Information.
The ncGe nanoparticles were fabricated using an organic-free process entailing thermal disproportionation of GeO prepared from thermally induced dehydration of Ge(OH) 2 . [25] We posit that the high purity of ncGe and associated amorphous phase and any residual oxygen and hydrogen play an important passivation role that contributes to this first evidence of laser cooling in indirect gap semiconductor nanocrystal.
Two types of experiments were carried out to investigate laser cooling of ncGe nanoparticles; first, where ncGe nanoparticles are dispersed in isopropyl alcohol (IPA) solution in a Teflon capillary tube, and second, where few droplets of ncGe in hexanol solution are dispensed on a quartz microscope slide resulting in dried ncGe powder. Considering that the Stokes and anti-Stokes measurements were not simultaneous, a series of Stokes and anti-Stokes measurements were carried out in alternating sequence on fresh nGe in IPA samples thus ensuring the absence of any systematic effects. Further, a series of background measurements were also carried out on IPA samples only sans ncGe. Similarly, a series of Stokes and anti-Stokes measurements were carried out on ncGe powder such that each measurement was carried out on a fresh region of the sample. We note that all ncGe samples were stored in IPA and hexanol to mitigate any oxidation effects. Experimental details are illustrated in Figure 1b-d, and further information is provided in the Supplementary.
Typical anti-Stokes and Stokes photoluminescence spectra, due to 785 nm laser excitation at room temperature, for nanocrystal germanium, both 25 nm ncGe dispersed in IPA solution and 25 nm ncGe powder in hexanol dispersed on a quartz substrate, are shown in Figure 2a,b, respectively. Considering that the hexanol evaporates rapidly the resulting sample is denoted powder ncGe. Both ncGe sample sets exhibit anti-Stokes intensity exceeding the Stokes intensity at ω k % 292 cm À1 , which is the first-order Raman active optical phonon mode of nanocrystalline germanium with %37 meV energy. It is also observed that while the Raman Stokes and anti-Stokes signal intensities associated with ncGe in IPA ( Figure 2a) are anomalous at %292 cm À1 , the Raman peaks for IPA at 200 cm À1 remain normal.
A series of Stokes and anti-Stokes spectra were obtained for ncGe in IPA and ncGe powder as a function of laser power ranging from 0.1% (0.015 mW) to 100% (15 mW) at 785 nm wavelength. These spectra were then analyzed for the anti-Stokes (I A ) to Stokes (I S ) signal strength ratio as a function of the laser power, as shown in Figure 3a, where the dashed trend lines are a guide to the eye. Under low laser intensity ≲10% (1.5 mW) illumination, the anti-Stokes to Stokes signal strength ratios are typical of less than unity, whereas at higher laser intensities we observe anomalous anti-Stokes to Stokes ratios exceeding unity. We further note that the general trends for ncGe in IPA and ncGe powder are similar, suggesting that the simpler dispensation of ncGe powder on quartz is a viable means of studying laser cooling effects in ncGe samples. Three sets of ncGe powder samples with the following diameters, 16 nm AE 4 nm, 25 nm AE 5 nm, and 30 nm AE 7 nm size (where AE s indicates the estimated standard deviation of the distribution in nanoparticle size) were studied. We note that while there is scatter in the data, which is not surprising considering that the Stokes and anti-Stokes measurements were each carried out sequentially over a fresh region of the sample, the similarity in the trends of I A /I S with laser power is striking.
The inferred lattice temperatures are presented as a function of the laser power in Figure 4. It is observed that the lattice www.advancedsciencenews.com www.adpr-journal.com temperature increases with increasing power up to a laser intensity of %10%; in fact, the inferred lattice temperatures are remarkably high at 10% power level and in particular increase with decreasing ncGe nanoparticle diameter. At laser intensities above 10% laser power, the lattice temperature drops below %100 K for the most part, whereas minimum lattice temperatures of % 50 K are observed at 25% (%4 mW) power. It is interesting to observe that at laser powers exceeding 25% (%4 mW), the inferred lattice temperatures increase with increasing power, which may indicate that the system is entering the saturation carrier density regime where the radiative transition rate assumes a linear dependence on N.
We now examine the physical processes at play in the nanocrystal germanium system that under elevated carrier and phonon densities give rise to the observed Raman anomaly. In most materials, the total thermal conductivity, k with the parameters σ, C p , υ q , Λ ph defined as electrical conductivity, heat capacity, average phonon velocity, and phonon mean free path, respectively. In semiconductors at low carrier densities, heat is dominantly carried by the lattice, i.e., principally the acoustic phonons, whereas at high carrier densities both lattice and electronic contributions play a role. It is interesting to note that the slope in Figure 3 is indicative of the thermal conductivity of the sample and as such the principal slopes at low and high laser power intensities are reflective of dominant processes at play which results in sample heating and cooling, respectively. Specifically, the thermal conductivity of the sample is k ¼ Lq ΔT , where L represents the sample thickness and q ¼ Q=A is the heat flux, with Q being the conducted heat and A the cross-sectional area corresponding to the laser spot size, and ΔT is the change in the local temperature due to the heat flux in the specimen. Recognizing that the local temperature is proportional to the ratio of the anti-Stokes to Stokes intensities, and that L/A is essentially a constant, thus, the slope in Figure 3 is inversely proportional to the thermal conductivity of the specimen. [27] At low laser intensity, we observe high lattice temperatures implying significant heat accumulation which is consistent with a relatively low thermal conductivity of the sample. This is further understood by noting that at temperatures above the Debye temperature (T ≫ Θ) heat capacity is constant (C p ¼ 3NK B where N is Avogadro's number) and independent of temperature whereas the phonon mean-free path Λ ph diminishes, and hence, leads to a low thermal conductivity k ↔ % k ↔ L . The mean-free path depends on phonon-phonon interaction and accordingly is a function of the phonon density n(q) which is given by the Bose-Einstein expression. The phonon density, nðqÞ ¼ ðe ℏωðqÞ=k B T À 1Þ À1 , at high temperature reduces to nðqÞ % K B T=ℏωðqÞ. Higher phonon density at higher temperatures promotes phonon-phonon scattering processes which lower the mean-free path, and hence, the thermal conductivity. In addition, higher temperatures give rise to higher q values which lead to Umklapp processes that limit thermal conductivity in crystalline materials. In addition, phonon-boundary scattering has a bearing on the www.advancedsciencenews.com www.adpr-journal.com phonon mean free path as the nanocrystal size becomes comparable to Λ ph . However, as the laser intensity increases the excited carrier density also increases to the point where the plasmon condition is satisfied. This now introduces an electronic contribution to thermal conductivity where the latter only depends on lattice (phonon) contribution. This is appreciated by noting that while at low temperatures lattice thermal conductivity has a T 3 dependence, given C p ∝ T 3 , the electronic thermal conductivity under high laser intensity becomes the dominant contributor given its dependence on carrier density. This in turn promotes electron-phonon scattering, where the system transitions (knee near %10% power in Figure 3) to elevated carrier and phonon densities, and hence, the process of phonon absorption begins to dominate over the phonon emission process. Expectedly, the maximum inferred lattice temperature is a function of the nanocrystal size, where the smaller nanocrystals exhibit higher peak temperatures considering constrained heat dissipation owing to the smaller surface area. This is further appreciated upon examining Figure 4 where we observe an increase in the inferred lattice temperature up to the knee point of %10% power prior to the cooling effect beginning to dominate. It is crucial to note that Raman measurements were not carried out consecutively across the laser power range examined here, rather each result obtained with respect to a given power level was an isolated individual Raman measurement on a fresh sample-done so as to avoid the influence and complexity of prior tests on the result. The trend line for the Raman Stokes to anti-Stokes intensity ratio shown in Figure 3 suggests that the thermal conductivity slope changes at %10% power where Stokes to Anti-Stokes ratio exceeds unity. At this point and above, where the Anti-Stokes is greater than the Stokes, and hence, conventional inferred lattice temperature no longer holds; to comply with Raman and Krishnan theory, the modified Boltzmann distribution equation is used to infer the lattice temperature shown in Figure 4. Thereafter, as the laser intensity increases and as does the density of excited carriers, in this 3D confined structure electron-electron interaction and Coulomb force both intensify which in turn gives rise to a new thermalization slope. The implications of this observation are twofold, first, it indicates that the electronic contribution slows down the increase in lattice temperature increase owing to the plasmon condition. Second, electronphonon coupling results in phonon absorption which leads to localized lattice laser cooling.
Examining this further, we note that conservation of energy and momentum require that E f ¼ E i AE ℏω q and k f ¼ k i AE q, where AE denotes absorption/emission of a phonon of energy ℏω q in the scattering of an electron by a phonon of wavevector q; E i , E f , k i , and k f represent the initial and final electron energy and initial and final electron wavevector, respectively, and ω q is the phonon frequency. Now, the electron transition probability from an initial state i to a final state f is a function of the availability of the final electronic states and the probability of phonon emission or absorption. Considering that all the electronic states in the conduction band are essentially accessible, the availability of the final states is simply the density of the final electron states times the probability that the final state is unoccupied (viz., unity); that is The probability of phonon absorption and emission is proportional to the electron-phonon coupling strength G(q), the phonon density for absorption n(q), and the phonon density for emission [1 þ n(q)], where nðqÞ ¼ ðe ℏω q =k B T À 1Þ À1 . Combining the absorption and emission terms and summing over all the final states yields the scattering probability (1=τ c ) www.advancedsciencenews.com www.adpr-journal.com where the first and second terms in the square bracket correspond to phonon absorption and emission, respectively. The electron-phonon coupling coefficient G(q) in nonpolar crystals is dominated by the deformation-potential coupling mechanism, and accordingly both phonon absorption and emission factors (G(q)n(q) and G(q)(1 þ n(q)) are independent of q for the LA branch. For the acoustic phonon, the primary scattering comes from the long wavelength acoustic phonons, [28,29] so ω % q and GðqÞ % q. This further simplifies the scattering probability where it is only a function of temperature and the density of final electron states for either phonon absorption or emission, that is, independent of the phonon. Further, as determined by the Lyddane-Sachs-Teller relationship for negligibly damped purely covalent crystals of the group IV elements, the LO and TO phonon modes are degenerate in Ge-having the same frequency at the Brillouin zone center. Thus, the LO modes can couple to the plasmon waves, [30] thus, enhancing electron-phonon interaction leading to phonon absorption, plasmon emission, and light scattering by plasmon, [31] and hence laser cooling. [32] Nanostructures such as Ge nanowires have been reported to exhibit optical phonon peak shifts, which are dependent on the laser excitation power but independent of wavelength. [27,33,34] Silicon and germanium, nonpolar crystals with indirect bandgaps, have been generally deemed to be inaccessible to laser www.advancedsciencenews.com www.adpr-journal.com cooling. [24] However, in nanostructures the distinction between direct and indirect bandgap fades as the electron and hole wave functions spread in momentum space, breaking the usual crystal momentum selection rules. [35] Overlapping of electron and hole wave functions accompanying reduction in size increases the coupling between their transition matrix elements, and thus, allows zero-phonon transitions, where the amplitude of this transition is strongly size dependent. As in other reports, [36] we also observe ( Figure 5) downshifting and broadening of the Stokes and anti-Stokes peaks for nanostructures smaller than 300 Å. In addition, we note that ordinarily unpassivated surface atoms in ncGe would tend to weaken the oscillation strength, and hence, surface modes would appear at low frequencies; in fact, these have been reported [37] to be below 50 cm À1 with one exception at 260 cm À1 . Moreover, Lamb modes, also known as breathing modes for spherical systems which tend to be inversely proportional to the nanoparticle diameter (1=d), have Raman peaks at low frequencies of < 100 cm À1 . In contrast, in our high purity and well-passivated ncGe the Raman peaks are observed at %292 cm À1 (%36 meV)-the principal transverse optical mode of ncGe. We further note that extensive Coulombic interactions within the spatially confined structures contribute to various charge scattering processes. Carrier multiplication (CM) is a charge scattering process that reduces the amount of energy lost to local heating by generating additional free carriers. These free carriers can then participate in band-to-band transitions and thus energy is radiatively removed from the system through the emission of lower energy photons. Indeed, the CM process has been observed in ncGe, [38] where interestingly charge multiplication has been detected below the onset of twice the Ge bandgap. In the present experiment, Raman cooling was observed with a laser wavelength of 785 nm or %1.58 eV, photon energy well above the Ge bandgap. In this regard, it is worth mentioning that although photoluminescence relies on excited electronic states corresponding to eigenstates of a physical system, Raman scattering can transpire via pseudo or virtual states of a system. The presence of pseudo resonant states in plasmonic crystals has been reported [26] and the experimental results presented herein are potentially suggestive of this phenomenon. Finally, with regard to the influence of nanocrystal confinement, Figure 6 exhibits ncGe blue shift as function of ncGe particle size. This result was obtained at 1% laser power to avoid any blue shift that would result due to the laser power influence as shown in Figure 5.

Conclusion
In summary, we report the first experimental evidence of Raman laser cooling in an indirect bandgap semiconductor. The highpurity nanocrystal germanium system exhibits optical cooling under high-intensity laser illumination. Raman cooling measurements are reported for both liquid and dry samples. The analysis suggests that the induced plasmon under elevated laser intensity is the root cause of the observed Raman anomaly-whereby the increased material's thermal conductivity via the electronic contribution promotes electron-phonon coupling favoring phonon absorption, and hence, laser cooling. Experimental measurements confirm the spatial confinement effect via comparison of the blue shift of the Raman peak in 5, 16, and 30 nm nanocrystals. We identify a range of key potential phenomena that contribute to the observed anomalous dominant anti-Stokes emission.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author. www.advancedsciencenews.com www.adpr-journal.com