Experimental and theoretical studies into longitudinal spatial hole burning as a power limit in high-power diode lasers at 975 nm

High-power diode lasers based on the AlGaAs material system are used in many applications, which require high-power conversion efficiency, η_E and optical output power, P_out to reduce operating costs.¹ However, η_E and P_out are limited by many saturation mechanisms. In long resonator devices (typically for length L > 2–3 mm), longitudinal spatial hole burning (LSHB) leads to non-uniformity in carrier density and, hence, gain profile along the resonator above the threshold current, I_th. Non-uniformity is expected to increase I_th and lead to increased carrier and photon loss at high bias and temperature resulting in lower slope S.^2–4 Moreover, lateral effects, such as current spreading and carrier accumulation at the edges, are also predicted to increase the carrier and photon losses.^5,6 Additional targeted diagnostic experimental and theoretical studies are needed to further understand and then address the interacting power saturation mechanisms. Our previous experimental study of limits to continuous-wave (CW) power demonstrated that LSHB becomes stronger as the resonator length and asymmetry between the facet reflectivities increase, and this leads to current crowding effects.^7,8 We observed that current crowding near the front facet was much stronger at high bias in experiment than in simulation, likely contributing to early power saturation. Building on these earlier studies, devices with front facet reflectivity of R_f = 0.8% and R_f = 20% (conventional, with large longitudinal optical field variation, and experimental, with small longitudinal optical field variation) are used here to investigate spatial hole burning via an experimental study of spontaneous emission (SE) from the substrate. Spatially resolved measurements of SE power and wavelength provide important information on local carrier density and temperature profiles but have been little used to date in large area high-power diode lasers.^9–11 Here, we use the measured SE intensity to study the carrier density profile and the measured SE wavelength to study local temperature. Experimental data are compared to the results of laterally one-dimensional simulation based on the “treat power as a parameter” method. Temperature-dependent S, I_th, and P_out were also measured for the same device configurations under short-pulse operation to high bias and compared to CW results to link the results of the SE analysis to device performance.

This paper is organized as follows: we first describe the device fabrication process and measurement techniques and then use the measured SE intensity profile to provide information on the local lateral and longitudinal carrier density distribution from low bias to high bias. We show that significant non-clamping occurs mainly at the stripe edges near the front facet edges and at the rear facet. We also show that non-clamping in the regions outside the stripes is a small effect. We then exploit the measured SE wavelength to give information on local temperature. We find that devices with the predicted flat optical field profile (R_f = 20%) show around half the temperature variation from front to back of conventional devices (R_f = 0.8%). We then present temperature-dependent short-pulse (600 ns) measurement results for 6 mm long devices with R_f = 0.8% and R_f = 20%, as compared to CW results. We estimate the internal differential efficiency and show it as a much weaker dependence on temperature for R_f = 20% due to the flatter optical field profile (less LSHB) and lower local temperature variation. We finally conclude and recommend further studies.

First, we discuss the design, fabrication, and measurement techniques. A proven efficient 970 nm high-power single quantum well ASLOC epitaxial design from Ref. 1 is used. The edge-emitting diode lasers were fabricated using standard techniques with W_s = 90  $μ$m stripe width, defined by implantation and with a resonator length of L = 6 mm. The devices were fabricated with a W_w = 140  $μ$m wide window introduced into the n-side contact using liftoff techniques to enable measurements of SE. After bar cleaving and passivation, devices were coated to obtain front facet reflectivities of either R_f = 0.8% or R_f = 20% and back facet reflectivity of R_b = 98%. All devices were soldered p-side down on expansion-matched CuW (90:10) carriers. The 6 mm long devices on carriers used in SE measurement were further mounted on a conduction-cooled package (CCP or CS mount)⁷ and the devices for pulsed measurement onto c-mount. The details of the SE measurement setup are explained in our previous study,⁸ and a schematic illustration is given in Fig. 1.

The power-current characteristics and the lateral beam profiles of the CCP-mounted devices with and without a window in the n-side contact were compared for CW operation up to 15 A at 25 °C heatsink temperature. No distinguishable difference between these devices was observed within the experimental error limits. Both devices have typical slope and the threshold of 0.98 W/A and 620 mA, respectively.

The devices on C-mount were tested under short-pulse operation up to currents of 35 A using 600 ns pulse width and 1 kHz repetition rate at heat-sink temperatures T_HS = 15–125 °C. The short pulse ensures that the active region temperature, T_AZ, is close to the heat-sink temperature, T_HS. A voltage pulser is used as a diode driver, and the delivered current is calculated by measuring the voltage across a 1  $Ω$ resistance connected in series with the diode. P_out was measured as a function of time using a fast photodiode located in an integrating sphere, whose responsivity was calibrated against a thermoelectric detector (itself calibrated against national standards) and whose wavelength sensitivity was accounted for.

Next, we present the measured longitudinal SE intensity distribution at different lateral positions inside the stripe for CW operation at 25 °C. To obtain a longitudinal profile, the translation stage is moved, and the CMOS camera image is recorded and used to determine the local SE intensity with edge effects from the microscope objective screened out. The lasing light scattered from the front facet is not filtered as it has an impact only at the front facet and its contribution is less than 10%, which is much lower compared to the SE intensity increase at that region. In Fig. 2, the high bias (10 A) longitudinal profiles of the SE intensity at the stripe center and at the left and right sides of the stripe [EL and ER $∼$ 35  $μ$m away from the stripe center (C), respectively] are presented. The lateral positions of EL, C, and ER are indicated in Fig. 1 for an example spontaneous emission profile obtained for the device with R_f = 0.8% at 10 A bias. The average intensity within the stripe at 10 A is shown, and the longitudinal SE intensity at the stripe center at 1 A is also included. Marked carrier non-pinning is observed at high current. The SE intensity at the center of the stripe increases at the back facet as the current increases from 1 to 10 A for both devices, strongly for R_f = 0.8% and falls at the front. At 10 A, the SE intensity at the edges of the stripes (EL, ER) at the back facet is even higher than at the center, and is high at the front facet, seen most strongly for R_f = 0.8%. The carrier accumulation at the front facet stripe edges occurs for both devices preferentially at one edge. The asymmetry in the lateral direction is observed for multiple devices. Overall, broadly twofold larger accumulation is seen for devices with R_f = 0.8% than for devices with R_f = 20%.

We now compare experiment to simulation. Laterally one-dimensional simulation based on the treat power as a parameter method (TPP, see Ref. 7) is used to calculate the longitudinal CW local gain profile at the stripe center C, taking account LSHB effects. As shown in Ref. 7, TPP simulation broadly agrees with experiment but underestimates power saturation. In the TPP model, without LSHB, gain is predicted to remain constant along the resonator, clamped at threshold values over the range studied here. In contrast, with LSHB, as the current increases above threshold, the gain (hence, carrier density) at the front facet decreases and gain (hence carrier density) at the back facet increases.^12,13 Figure 3 shows the calculated longitudinal gain profiles for 6 mm long devices with R_f = 0.8% and R_f = 20% at 1 and 10 A. For R_f = 0.8%, the gain increases from the front to back facet for both 1 and 10 A currents. The gain at the front facet at 10 A is roughly halved compared to 1 A, while the gain at the rear facet roughly doubles. The impact of LSHB is virtually eliminated for R_f = 20%, where a flat gain profile is predicted at 1 A with a very small 10% increase (decrease) of gain at the back (front) facet. Broadly consistent trends are seen at the center of the device in both simulation and experiment. The strong increase in the SE intensity at the stripe edges (EL and ER positions) at high bias was not predicted by the laterally 1D TPP simulation used here but has been predicted by other studies.^14–16 

Next, we use a more detailed analysis of the local SE intensities to extract information on the local carrier density distributions and their impact on performance. Figure 4 shows the SE intensity as a function of current at different lateral positions (EL, ER, and C) at the front and back facets for devices with R_f = 0.8% and R_f = 20%. The averaged SE intensity inside and outside the stripe is also shown. For the devices with R_f = 0.8%, the average SE intensity (carrier density) inside the stripe at the back facet increases with current with around 30% larger increase at the stripe edges (EL, ER). For R_f = 0.8%, average SE at the front facet varies little, is slightly reduced in the center (C) and strongly increased at the stripe edge (especially EL) as the current increases. In contrast, for R_f = 20%, the SE intensity at the back facet varies little with current with all values within the stripe being broadly comparable. At the front facet, the average SE intensity inside the stripe also varies little with current. However, again a strong increase in the SE intensity is seen at the stripe edge (ER), and a small reduction in the center. For both devices, the SE intensity (carrier density) outside the stripe that arises due to current spreading is observed to increase slowly, but this effect remains small, and is not expected to contribute to power saturation. The low contribution of current spreading is consistent with recent experimental studies of broad area devices with lateral current blocking.¹⁷ 

The high levels of carrier accumulation and their dependence on front facet reflectivity were proposed in the previous work⁷ as being due to different temperature profiles. To verify this claim, we next analyze the spatially integrated SE spectra that were measured using the multi-mode fiber with 450  $μ$m core diameter. Light is integrated over an area of 140  $μ$m, which is larger than the stripe width. The SE spectra obtained from the substrate window near to the front and back facets at currents of 1 and 10 A are given as insets in Fig. 5 for the devices with R_f = 0.8% and R_f = 20%, respectively. In our previous study,¹⁸ numerical simulation of the SE was performed based on an $8 × 8$ k.p band structure calculation and a free carrier theory for the optical response functions. The simulation indicated that the peaks at low and high wavelengths are due to the transitions from the first electron energy level to the first light hole and heavy hole energy levels, respectively. Other transitions are not visible due to absorption in the substrate. As the temperature increases, the peak shifts to a longer wavelength. Therefore, we use the SE wavelength to estimate changes in the local temperature. Specifically, the center wavelength of the high energy peak and the resulting temperature change were calculated using $Δ T ( I ) = [ λ ( I ) − λ ( I ≈ I thr . ) ] / ( δ λ / δ T )$⁠, assuming $δ λ / δ T ≈$ 0.34 nm/K. $Δ T ( I )$ is plotted as a function of the longitudinal position for 1 and 10 A current for the devices with R_f = 20% and R_f = 0.8% in Figs. 5(a) and 5(b), respectively. The devices with R_f = 20% have, in general, higher temperatures at 1 A compared to the devices with R_f = 0.8% due to the lower slope and, hence, power conversion efficiency. Temperature is constant along the resonator at 1 A; however, it increases from the back to front facet at 10 A for both devices. The temperature difference is double for the devices with R_f = 0.8% compared to that of the devices with R_f = 20%. The development in intensity seen in the spectral measurement is consistent with the earlier intensity data in Figs. 2 and 4.

Next, we assess the benefit of the reduced hole burning effects for R_f = 20% on power and temperature sensitivity. We present the measurement results of devices with R_f = 0.8% and R_f = 20% under short-pulse operation to separately analyze the effect of temperature and bias on device P_out, S, and I_th compared to CW data from Ref. 7. Figure 6(a) compares the pulsed P_out–I characteristics of devices with R_f = 0.8% to that of the devices with R_f = 20% at different $T HS ≈ T AZ$ temperatures of 15, 45, 75, 105, and 125 °C. P_out for the devices with R_f = 0.8% is higher at 34 A for low temperatures due to the higher S; however, it more rapidly drops compared to that of the device with R_f = 20% as the temperature increases. Indeed, the saturation power of the device with R_f = 20% becomes higher than that of the device with R_f = 0.8% above 105 °C.

To understand what causes the power drop at high temperatures, temperature-dependent S and I_th are analyzed. S and I_th for these devices are determined from a linear fit to the P_out–I characteristics between threshold and 4 A. S decreases at higher temperatures due to the lower η_i and higher optical loss α_i. Following Ref. 2, we estimate how α_i varies with temperature, based on the known values at 25 °C and the expected variation with temperature, finding that it varies in the range 0.6–0.8 cm⁻¹ over the range studied. We then combine this with the known reflectivities and estimate η_i. Both directly measured I_th and estimated η_i are plotted in Fig. 6 as a function of T_AZ. Figure 6 shows that I_th increases for both devices as the temperature increases and that temperature sensitivity of I_th is very similar for both devices at low temperatures <75 °C. In this range, the devices follow typical diode laser trends, where the reduction in gain with temperature is compensated by higher carrier density, requiring broadly similar increases in the external current. In contrast, I_th for the device with R_f = 0.8% grows more rapidly with temperature above 75 °C, which we attribute to higher levels of losses triggered by the higher carrier density at the rear facet, following Refs. 2 and 19.

In contrast, the change in η_i as a function of temperature is similar for both devices, which implies that lateral and longitudinal SHB has only a small effect on the S at low current. We further extract the slope at 20 A using a linear fit between 18 and 22 A and convert this into an estimated η_i at high bias, following the same techniques. The devices with R_f = 0.8% show much faster decrease with temperature, indicating that the losses due to high carrier density at the rear facet are now high enough to compete with stimulated emission, degrading power. Finally, we obtain the S in the CW mode in the current range between threshold and 19–21 A for the R_f = 0.8% and R_f = 20% cases by differentiating the light-current curves from Ref. 7. We convert this to an estimated η_i following the same approach and plot this again in Fig. 6, using the operating wavelength to determine the active region temperature. The CW η_i drops extremely rapidly with temperature for the R_f = 0.8% and less rapidly for the R_f = 20%. In both cases, the variation is far faster than in the pulsed mode, even at high currents. In CW operation, lateral and longitudinal local temperature differences arise, leading to carrier accumulation at the stripe edges and more rapid carrier losses. Thermally induced index changes lead to the near-field narrowing at the front facet and, hence, carrier accumulation at the stripe edges. Carriers at the stripe edges do not contribute to the lasing, instead they are lost by being used for non-radiative recombination or spontaneous emission. We propose this as being is the main reason for the large difference between CW and pulsed η_i.

In conclusion, the impact of longitudinal and lateral hole burning in GaAs-based high-power diode lasers was experimentally investigated, via studies in SE. We confirm the prediction that LSHB leads to non-uniform carrier density with much higher levels at the back facet. The non-uniformity increases as the current and the asymmetry between the facet reflectivities increase. We also experimentally confirm the prediction that higher temperature arises at the front facet compared to the back facet and that this leads to strong lateral hole burning and resulting carrier accumulation at the front facet stripe edges. We further show that the carrier accumulation effect at the front facet is halved for R_f = 20%, where the longitudinal optical profile is predicted to be flat. In addition, carrier accumulation outside of the laser stripe due to current spreading is confirmed as being a small effect. A further comparison of pulsed and CW light-current curves links the SE results to power saturation. High front facet reflectivity (flat longitudinal optical field profile) leads to slower temperature dependence of the pulsed threshold current and of the pulsed slope at high bias, as well as slower temperature dependence of the CW slope. The next step in analysis is to experimentally confirm whether the front facet lateral carrier accumulation (LCA) is truly temperature limited and study its predicted link¹⁵ to lateral beam quality. We note that reduced power saturation is likely possible in devices with low front facet reflectivity, if flatter temperature profiles can be realized with early data supporting this conclusion shown in Ref. 20.

The authors would like to thank Professor Dr. S. Sweeney for his collaboration in spontaneous emission measurement.