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Quantum dot vertical-cavity surface-emitting lasers covering the ‘green gap’

Semiconductor vertical-cavity surface-emitting lasers (VCSELs) with wavelengths from 491.8 to 565.7 nm, covering most of the ‘green gap’, are demonstrated. For these lasers, the same quantum dot (QD) active region was used, whereas the wavelength was controlled by adjusting the cavity length, which is difficult for edge-emitting lasers. Compared with reports in the literature for green VCSELs, our lasers have set a few world records for the lowest threshold, longest wavelength and continuous-wave (CW) lasing at room temperature. The nanoscale QDs contribute dominantly to the low threshold. The emitting wavelength depends on the electron–photon interaction or the coupling between the active layer and the optical field, which is modulated by the cavity length. The green VCSELs exhibit a low-thermal resistance of 915 kW−1, which benefits the CW lasing. Such VCSELs are important for small-size, low power consumption full-color displays and projectors.


INTRODUCTION
Semiconductor lasers have attracted much attention since their invention in 1962 1,2 . Compared with solid state and gas lasers, semiconductor lasers have a small volume, low-operation current and voltage, and low cost. As determined by the band gaps of the variety of semiconductor materials, the wavelengths of semiconductor lasers can cover a wide spectral range, from violet to infrared 3 . Thus far, some of them have been well-studied and/or successfully commercialized, for example,~2-5 μm lasers for biomedical and environmental applications 4 , 1.3-1.55 μm lasers for optical fiber communications 5 , 850-1000 nm lasers for optical interconnection and pumping sources [6][7][8] , and 405-450 nm lasers for information recording, lithography, lighting, displays and projectors [9][10][11][12] . However, semiconductor lasers with wavelengths in the green region, typically 500-600 nm, are still undeveloped, which is called the 'green gap' 13 . The green light in this range is very important for a wide-gamut of applications. Presently, green lasers based on optical pumping or double-frequency technologies are usually adopted, but they are expensive and large.
A green semiconductor laser was first demonstrated by employing ZnSe-based semiconductors in the 1990s 14 . However, the lifetime of such devices was not sufficient for practical applications, and research on ZnSe is still ongoing 15 . In the last decades, much effort has been expended on GaN-based semiconductors. On the basis of these materials, a few types of optoelectronic devices such as lightemitting diodes and violet and blue lasers have been successfully demonstrated and commercialized 10,12,16,17 . Therefore, GaN-based semiconductors, including those of GaN, AlN, InN and their mixed alloys, are believed to be good candidates for green lasers. In 2009, Nichia 18 first broke the '500-nm limit' of green laser diodes, and then in the following 2 years, Osram 19 , Sumitomo 20 , Corning 21 and UCSB 22 pushed the wavelength up to 532 nm by using a c-plane and semipolar substrate. However, the expansion of the lasing wavelength is generally accompanied by an increase in the threshold current density, so the optimal filling of the 'green gap' has not been realized yet.
Two-dimensional InGaN quantum wells (QWs) are commonly used as the active region of violet, blue and green semiconductor lasers. The InGaN QW layer is sandwiched between GaN barriers. To obtain green emission lasers, a higher In content in the InGaN QW layer is necessary compared with that in the violet and blue lasers 3,13 . The existence of the 'green gap' is due mainly to the low-emission efficiency of the green InGaN QW layer. Defects and built-in electric fields in the QW are the dominant reasons accounting for the lowemission efficiency. Defects come from the lattice mismatch (or strain) between InGaN and GaN as well as between the epilayer and the substrate 23 . The built-in electric field originates from spontaneous polarization, which occurs when the QW is epitaxially grown on (0001) polar surfaces, and strain-induced piezopolarization 24 .
To overcome these problems, epitaxial growth on homogeneous polar 25 , semipolar 26 and nonpolar GaN substrates has been carried out 27 . However, these approaches cannot eliminate the strain between InGaN and GaN, and thereby the strain-induced defects and piezoelectric field in the InGaN QWs cannot be eliminated. This strain becomes pronounced when the In content is higher. In other words, InGaN QWs emitting in the green region have a lower emission efficiency than those emitting in the violet and blue regions.
To release the strain, the adoption of nanoscale quantum dots (QDs) is an effective approach. Semiconductor QDs can be formed during the epitaxial growth of a highly strained layer. The formation of QDs is driven by the strain itself, and the strain remaining in the QD can be significantly reduced compared with the case of a twodimensional QW epitaxial layer 28 . QDs are zero-dimensional structures in which electrons and holes are strictly confined in a small volume, which is particularly important to obtaining a high-emission efficiency and low-threshold current, as reported in a few review papers [29][30][31] . Using InGaN QDs as the active region, green edgeemitting semiconductor lasers have been demonstrated by a research group at the University of Michigan 32 . Lasing actions were obtained even on lattice-mismatched substrates and polar surfaces. These results indicate the potential to fabricate lasers emitting in the 'green gap' by employing InGaN QDs.
The lasers mentioned above are edge-emitting lasers (EELs), in which the laser beam propagates parallel to the layer surface/interface. The cavity length is long, commonly a few hundred micrometers 33 . In this case, the separation of longitudinal modes, inversely proportional to the cavity length, is tiny, and the lasing wavelength is determined by the emission of the active region. Therefore, to shift the lasing wavelength, one has to prepare different structures for the active regions, for example, InGaN QDs with various In contents (0.18, 0.32 and 0.4 for blue, green and red, respectively) 34 . This not only complicates the fabrication process, especially the material growth, but also makes the laser expensive. On the other hand, vertical-cavity surface-emitting lasers (VCSELs), another type of semiconductor laser, can easily control the lasing wavelength by adjusting the cavity length. The cavity length of a VCSEL is much shorter, usually~1 μm, and the mode separation is large and can be easily shifted by adjusting the cavity length. If the spontaneous emission band of the active layer is broad enough, one can obtain various lasing wavelengths by the proper design of the cavity. The laser beam of a VCSEL propagates vertical to the layer surface/interface.
There have been a few reports on GaN-based VCSELs using InGaN QW active regions [35][36][37][38][39][40] . Room temperature continuous-wave (CW) lasing has been demonstrated in the violet and blue region. However, in the green region, only pulsed lasing has been obtained, with wavelengths up to 503 nm 36 . In this paper, we report the first InGaN QD-based VCSELs. By a combination of InGaN QDs and vertical-cavity structures, we demonstrate VCSELs with different lasing wavelengths covering most of the 'green gap'. Different from InGaN QD EELs where different active structures are needed, we use the same epitaxial wafer grown on a (0001) polar surface by using a sapphire substrate. By controlling the cavity length, the lasing wavelength is shifted from 491.8 to 565.7 nm, with threshold currents of sub-mA. Moreover, room temperature CW lasing is obtained. The emission wavelength, threshold current and CW lasing are the record results for GaN-based VCSELs. The controllability of the emission wavelength is believed to be useful in full-color small-size laser displays and projectors.

MATERIALS AND METHODS
The epitaxial wafer was grown on a (0001) c-plane sapphire substrate using metal-organic chemical vapor deposition 41 . The epilayers include, in order, undoped GaN, n-type GaN, two layers of InGaN QDs and p-type GaN. The QDs with~27% indium content have diameters ranging from 20 to 60 nm, and the average height is 2.5 nm. The QD density is~1.5E10 cm − 2 . Figure 1a shows a 5 × 5 μm 2 Atomic Force Microscope (AFM) image of the uncapped QDs. The device fabrication procedure is similar to that described in our previous work 37 . We first deposited a 100-nm-thick SiO 2 current insulation layer on the surface of the epitaxial wafer, and a 10-μmdiameter current-injection aperture was opened. Then, a 30-nm-thick indium tin oxide (ITO) ohmic contact and current spreading layer was deposited, followed by the formation of a Cr/Au p-electrode and a 12.5-pair TiO 2 /SiO 2 bottom dielectric distributed Bragg reflector (DBR). The DBR was selectively deposited on the currentconfinement aperture. After that, the sample was turned upside down and bonded onto a copper plate through a metal bonding technique, and then the sapphire substrate was detached by a laser lift-off process. An inductively coupled plasma etching technique was adopted to remove the undoped GaN layer. The n-GaN layer was thinned to a desired thickness, followed by chemical mechanical polishing to make the surface flat. Then, an n-contact metal and an 11.5-pair TiO 2 /SiO 2 top dielectric DBR were deposited. A schematic structure of the green InGaN QD VCSEL is shown in Figure 1b, and a photo of the fabricated VCSEL array is given in Figure 1c. By controlling the thickness of the n-GaN layer, four samples were fabricated with different cavity lengths. Measurements of the lasing properties were performed at room temperature.

RESULTS AND DISCUSSION
We first calculated the cavity modes of the VCSEL using the matrix optics method. Figure 2a shows the calculated reflection spectrum of the GaN-based VCSEL and the measured photoluminescence (PL) spectrum of the QD wafer. The stopband of the DBR is~150 nm, and it has seven cavity modes. The spontaneous emission of the QDs starts from 450 nm and ends at 600 nm. The broad spectrum is attributed to the inhomogeneity in the QD size and the fluctuation of the In content. The wide PL spectrum of the QDs is expected to allow VCSEL lasing at different wavelengths. The light-emission properties of the QD wafer were also studied using spatially resolved spot-focus cathodoluminescence (CL) at low temperature (4 K). CL spectra were measured through the 5-μm diameter apertures of a metal mask. We can clearly see some bright spots in the aperture. Figure 2b shows the CL image and the spectra recorded at bright spot A and other regions. A narrow emission peak is observed at position A, with a linewidth of 4 meV, much narrower than the PL given in Figure 2a. Due to the resolution limitation, the CL emission linewidth is not as small as the 107 μeV that was observed by others from a single InGaN QD 42 . Nevertheless, the emission property indeed proves the QD-like structure. Figure 3a-3c shows the lasing spectra of three samples under different current levels, together with the corresponding light output-current (I-L) and current-voltage (I-V) characteristics. Figure 3d shows the polarized spectra of the fourth sample under 1 mA with different polarization angles. The polarization ratio turned out to be 91%, given by (L max − L min )/(L max +L min ), where L max and L min are the maximum and minimum relative light intensities, respectively. The lasing action under CW operation at room temperature was obtained for all the samples. This is the first report of the CW lasing of GaN-based green VCSELs at room temperature. Either double-longitudinal mode lasing (a, b, d) or single-longitudinal mode lasing (c) was observed. Apart from the lasing peaks, other small peaks related to the cavity modes were also observed. It is clearly revealed from the lasing spectra that the intensities of the lasing peaks increased dramatically above the threshold current, and no mode hopping occurred, in spite of the existence of several additional longitudinal modes.    The green VCSELs obtained in this study feature a low-threshold current density, low-thermal resistance and CW lasing. These properties are essential for practical applications. We mainly attribute the lowthreshold current to the use of QDs as the active layer, in addition to the control of the optical loss in the cavity 43 . Low-dimensional nanoscale QDs are known to enhance the emission efficiency of the active layer due to the strong quantum confinement effect or carrier localization [29][30][31] . It has been reported that the strain effect is significantly reduced in InGaN QDs 28 . In our previous work, we reported a large localization energy of 105.9 meV and a high internal quantum efficiency of 41.1% for our InGaN QDs 44 . The strong carrier localization also suppresses nonradiative recombination by impeding carriers from being captured by defects outside the QD. Moreover, compared with GaAs, the advantage of using QD is more significant in GaN because the threshold current depends on the effective masses of the carriers. The transparency carrier density of a semiconductor material and the threshold carrier density of a semiconductor laser are, respectively, given by 45 where m Ã c is the electron effective mass, m Ã v is the hole effective mass, m 0 is the free electron mass, k B is Boltzmann's constant, h is Planck's constant and T is the temperature. γ th and a are the threshold gain and differential gain, respectively. We can see that the effective masses of the carriers have a great effect on the value of n tr and thereby n th . For the well-studied semiconductor lasing material GaAs, n tr is calculated to be 1.8 × 10 18 . On the other hand, for GaN with larger effective masses (m Ã c ¼ 0:2 m 0 , m Ã v ¼ 1:1 m 0 ), n tr is 8 × 10 18 cm − 3 , much higher than that of GaAs. This suggests a higher threshold carrier density for the GaN-based laser compared with the GaAs-based laser. However, when QDs are used as the active media of semiconductor lasers, where a δ-function-like density of states is expected, the lasing property is finally independent on the effective mass of the carriers 26 . Hence, the use of QDs is more effective in GaN-based lasers and definitely contributes to the low-threshold current observed here.
In addition, the use of a small-area bottom DBR, metal bonding and a copper plate is also expected to significantly improve the thermal dissipation of VCSELs. This has an important role in the realization of CW lasing at room temperature. The efficiency of the thermal dissipation has been shown to be important in the realization of current-injection GaN-based VCSELs 37,46 . To understand the thermal behavior inside the devices, we systematically investigated the thermal characteristics of VCSELs, both theoretically and experimentally. We first calculated the heat distribution of the QD VCSELs by a finite element method (FEM) using a steady-state three-dimensional heat dissipation model [47][48][49] . The heat dissipation model is given by 47,48 À∇ðk∇TÞ ¼ Q k∇T ¼ hðT inf À TÞ þ εsðT 4 surr À T 4 Þ where Q, k, T, h, ε and σ are the heat source density, thermal conductivity, initial temperature, heat transfer coefficient, surface emissivity and Stefan-Boltzmann constant, respectively. T inf and T surr are the ambient temperature and the surrounding temperature, respectively. The heat source density Q can be obtained from the experimentally measured L-I-V data by Q ¼ UthIth V , where U th , I th and V are the threshold current, threshold voltage and volume of the active region, respectively. The heat distribution of the device is shown in Figure 4a, and the maximum increase in the temperature of the active region was 4 K at the threshold. The thermal resistance (R th ) was calculated to be 879 K W À1 by R th = ΔT/V th I th , where T,T th and V th are the temperature, threshold current and voltage at the threshold, respectively. Next, we experimentally measured the thermal resistance of the VCSELs. The thermal resistance of the VCSEL is given by R th = ΔT/ ΔP = Δλ/ΔP/Δλ/ΔT, where T, P and λ are the temperature, net consumed injection power and emission wavelength, respectively 47   We first measured the movement of the lasing wavelength as a function of the substrate temperature. The injection current was set to 0.7 mA, slightly above the threshold, to avoid any current-heating effect, and the temperature of the substrate was controlled with a thermoelectric cooler. The measured dependence of the lasing wavelength on the temperature is shown in Figure 4b. On the other hand, the powerdependence of the lasing spectra for the same VCSEL was measured under different injection electric powers, as illustrated in Figure 4c.
We can see clearly that the wavelength of the lasing peak moves linearly following both changes in the injection power and substrate temperature, with slopes of 0.169 Å mW − 1 and 0.185 Å K − 1 , respectively, which yields a thermal resistance of 915 K W − 1 . This value is close to the calculated result and is much lower than the 2600 K W − 1 reported for GaAs-based VCSELs with the same active region diameter 49 . A smaller thermal resistance indicates a higher ability of heat dissipation. The lasing wavelength of 565.7 nm was the longest ever reported for GaN-based VCSELs. It is worth noting that this wavelength is near the edge of the PL emission band, where the gain should be not so high. The lasing is due to the strong coupling between electrons and photons, that is, the large overlap between the active region and the anti-nodes of the optical field of the standing-wave pattern in the cavity. A better overlap means a larger gain enhancement factor, which can effectively decrease the threshold gain of the VCSEL. The gain enhancement factor, defined as the optical density in the active layer normalized to that in the cavity, is given by 50 are the cavity length, thickness of the active region and optical field standing-wave pattern, respectively. For VCSEL operation, the threshold gain is defined as 50 where α a and α i represent the loss coefficients of the active layer and the inner cavity excluding the active region, respectively, and L eff , R t and R b are the effective cavity length and the reflectivity of the top and bottom mirrors, respectively. From the equation, we can see clearly that Γ r has a remarkable influence on the threshold gain of VCSELs, especially when the thickness of the active region is small. The distribution of the optical field (squared electric field) of the 565.7-nm mode was calculated using the transfer matrix method and is shown in Figure 5a with the refractive index of the layers in the VCSEL. The accurate overlap between the active region and the antinode of the standing wave leads to a large gain enhancement, and Γ r is estimated to be 1.982, which can explain the occurrence of the lasing action at the edge of the PL emission spectrum. For comparison, Γ r is estimated to be 0.0235 when the active region is placed at the node of the standing wave.
Changing the cavity length shifts the optical field in the cavity and thereby modulates the coupling strength between the active layer and the optical fields of the different cavity modes. The enhancement factor and the lasing wavelength can be adjusted. The mode separations between the two adjacent cavity modes for the samples shown in Figure 3 are 15.1, 19.9, 24 and 20.41 nm, respectively, corresponding to cavity lengths of 3041, 2910, 2652 and 2807 nm, respectively. Adjusting the lasing wavelength by changing the cavity length is unique to VCSELs, as it is not possible for EELs. By using several VCSELs lasing at different wavelengths in the 'green gap' instead of the conventional RGB lasers, a larger gamut can be obtained for laser displays and projectors that can be extended to nearly 100% coverage of human vision. A CIE triangle of the HDTV gamut is given for comparison in Figure 5b. Thus, the laser lights from 490 nm (blue-green) to 560 nm (green-yellow) obtained in this study could be essential for the realization of wide-gamut compact displays and projectors.
We did not perform specialized testing on the device operation lifetime because the VCSEL was not separated and packaged. Nevertheless, the investigated devices seemed to be very stable in output performance during the measurements we carried out, which usually lasted several hours. In addition, after performing many measurements, the devices did not exhibit an observable performance deterioration; they broke down after many cycles of testing only after approximately half a year.

CONCLUSIONS
In conclusion, we have demonstrated room temperature, CW and low-threshold green lasing from InGaN QD-based VCSELs for the first time. The lasing wavelength extends from 491.8 nm (blue-green) to 565.7 nm (yellow-green), covering most of the 'green gap'. The thermal resistance of the VCSEL is as low as 915 K W − 1 . For different VCSELs, the same QD active region was used with the wavelengths controlled by adjusting the cavity length. This is Our results open up opportunities to design and fabricate semiconductor green lasers with excellent performance that may lead to wide-gamut compact displays and projectors. The VCSELs could also be bonded onto Si for integration with other optoelectronic devices/circuits.