Non-uniform carrier accumulation in optical conﬁnement layer as ultimate power limitation in ultra-high-power broad-waveguide pulsed InGaAs=GaAs=AlGaAs laser diodes B. Ryvkin and E. Avrutin The effect of spatially non-uniform accumulation of carriers in the optical conﬁnement layer of broad-waveguide InGaAs=GaAs= AlGaAs-based ultra-high power lasers operating at 1.06 mm under very high pulsed pumping has been analysed and shown to be an important limitation for the output power. A calculation using a semi- analytical theory is in good agreement with the recently published experimental data. A narrow asymmetric waveguide laser construction is predicted to alleviate the problem. Introduction: High-power semiconductor laser constructions tend to use large optical cavity, or separate conﬁnement, structures, in which the optical conﬁnement layer (OCL) of the optical waveguide, typically of a thickness, h, of fractions of a micrometre, incorporates a thin active region consisting of one or several quantum wells at a certain position l a , usually l a ¼ h=2. Among the advantages of such structures is the possibility of reducing optical losses (due to the decreased waveguide mode overlap with the highly doped contact layers, especially the p-contact), whilst at the same time maintaining a broad transverse mode distribution (usually characterised quantita- tively by the equivalent spot size d=G, where d and G are the active layer thickness and conﬁnement factor, respectively [1]). In recent years, progress in increasing output power has relied largely on very broad waveguide constructions, with the thickness exceeding the previously applied limit—the cutoff of the second order transverse mode [2–4])—which allowed record values of output power, with good beam directionality, to be realised. However, at very high current densities, a marked saturation of the light–current characteristic has been observed in broadened waveguide CW- and quasi-CW-operated lasers, and it has been established that the effect is not necessarily thermal [5]. In a series of recent papers [6–8], we attributed it, to a signiﬁcant extent, to the detrimental effect of (nonuniform) carrier accumulation in the broad OCL due to the ﬁnite speed of ambipolar diffusion, ﬁrst considered in [9] in the context of electron leakage into the p-claddings in structures where the corresponding barrier is relatively low. We have shown that, even if the leakage is not signiﬁcant, these carriers reduce the output efﬁciency of the laser (via intervalence band absorption) and the injection efﬁciency (via recombination in the OCL). An analytical theory has been developed to quantify these effects. A narrow asymmetric waveguide structure has been proposed as a construction potentially free from these limitations. We have shown that these structures can offer superior performance to broadened symmetric waveguide lasers in terms of slope efﬁciency [6], injection efﬁciency [7], and far ﬁeld [8]. So far, we have concentrated on the effects of carriers in the OCL in lasers fabricated from InGaAsP materials for operation in the 1.55 mm window, where these effects are very pronounced owing to the relatively low hole diffusion coefﬁ- cients. Moreover, the advantages of an asymmetric structure are particularly clear in InGaAsP lasers owing to the strong absorption in p-doped materials compared to n-doped materials with the same impurity density. Here, we show that, at very high pulsed current density, effects of carrier accumulation in the OCL can become important even in lasers that use GaAs OCLs, with relatively large hole diffusion coefﬁcients, and operate at shorter wavelengths. In particular, in a series of recent experiments, record, ultra-high powers have been achieved from a laser operating at 1.06 mm, both under CWoperation (16 W, [4]) and particularly under pulsed operation to avoid lattice heating (145 W, [10]), in both cases from a single 100 mm stripe with a cavity 3 mm long. The latter experiment required current densities as high as 70 kA=cm 2 , meaning that signiﬁcant carrier densities could be accumulated in the OCL. Analysis: To analyse this situation, we can use the previously devel- oped theoretical model of a laser with an OCL without intentional doping and a single-quantum-well active layer, as in the experiment. It has been shown [6] that the carrier proﬁle in the ‘p-side’ of the OCL (l a < x < h) has a characteristic, almost linear shape: N e ðxÞ’ N h ðxÞ’ N ðxÞ¼ N x ðx  l a Þþ N b ; l a < x  h ð1Þ Here, the ﬁrst term is the nonuniform carrier build-up, with the parameter N x given by [7]: N x ¼ j 2eD h Z R ; Z R ðjÞ¼ 1 K 3 ð ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 þ 2K 3 p  1Þ; K ¼ Bjðh  l a Þ 3 6eD 2 h  1=3 ð2Þ where j ¼ i=(Lw) is the current density (with i denoting the total current, L, the cavity length, and w, the stripe width), D h is the hole diffusion coefﬁcient, and B is the bimolecular recombination coefﬁcient. The expression (2) has been shown [7] to hold very accurately when K <1 and the linear recombination is negligible. The term N b in (1) is the background carrier density, which is caused by carrier leakage from the active layer and can therefore be minimised, given fast enough carrier capture into the QW from its nearest vicinity, by increasing the OCL bandgap and=or by using 2–3 quantum wells instead of using a single well. In 1060 nm InGaAs=GaAs=AlGaAs lasers with low output losses (and thus low threshold carrier densities) such as those of [4, 10], N b can be expected to be small. The carrier density in the ‘n-side’ of the OCL (0 < x < l a ) is also negligible, owing to the high electron mobility; however, the spatially nonuniform part of N(x) on the ‘p-side’ is a fundamental effect associated with current passing through the structure and cannot be eliminated. From (1) and (2), explicit if somewhat lengthy expressions for the free-carrier loss in the OCL are readily derived as a convolution between the modal power proﬁle and the carrier density proﬁle (the latter determining the absorption proﬁle) similar to the way described in [6], except that, for better accuracy, the result has to be mulﬁplied by Z R ( j). These expressions, in turn, can be used to evaluate the slope efﬁciency Z s using the standard expression Z s ¼ a out =(a out þ a in ), where a out is the outcoupling loss, and the internal loss a in is dominated by the loss a QW in the active layer at low to moderate current, and by the loss a OCL in the OCL in a broad waveguide at very high current densities of interest here. The output power is then evaluated straightforwardly as P ¼ (h o=e)Z (i  i th ), with the threshold current i th estimated from the laser parameters (the accurate value is not important here as we are mainly interested in operation at i  i th ), and the external differential quantum efﬁciency is estimated as Z ’ Z R Z s . No nonlinear effects apart from those discussed here have been considered. The broadened (1.7 mm) symmetric cavity structure was taken as identical to that used in [10]; the refractive indices used in calculations were as in [8]. A laser cavity 3 mm long, a stripe 100 mm wide and reﬂectance coefﬁcients of 0.05=0.95 are assumed, as in the experiments. 0 50 100 150 200 250 drive current, A output power, W drive current density, kA/cm 2 broadened symmetric – ideal case broadened symmetric – theory narrow asymmetric – theory broadened symmetric – experiment 0 10 20 30 40 50 60 70 80 0 50 100 150 200 Fig. 1 Theoretical L–I curves in 1.06 mm lasers, compared to measured data from [10] Results: Fig. 1 shows calculated current–power characteristics. Shown alongside the realistic curve calculated taking into account ELECTRONICS LETTERS 26th October 2006 Vol. 42 No. 22