Differential Gain Analysis of InGaAs/InGaAsP/InP Multiquantum Well Lasers with 1.55 <FONT FACE=Symbol>m</font>m Emission Wavelength

Abstract

We present measurements of the differential gain of multiquantum well (MQW) broad area lasers emitting at 1.55<FONT FACE="Symbol">m</font>m wavelength, taking into account the nonuniform stimulated emission caused by filamentation within the optical cavity. The differential gain was determined from measurements of the threshold current density, considering the losses due to the inhomogenous carrier density distribution, as an apparent leakage current effect in the output power-current characteristics. The lasers were grown by low pressure MOCVD and incorporate an InGaAs/InGaAsP/InP separate confinement MQW active region. The results are compared with previous data reported on similar MQW heterostructures.

Differential Gain Analysis of InGaAs/InGaAsP/InP Multiquantum Well Lasers with 1.55 mm Emission Wavelength

M.T. Furtado, W. Carvalho Jr., A.M. Machado and K. Jomori

Centro de Pesquisa e Desenvolvimento,

Telecomunicações Brasileiras S/A-TELEBRÁS,

C.P.1579, 13088-061 Campinas, SP, Brazil

Received June 5, 1997

We present measurements of the differential gain of multiquantum well (MQW) broad area lasers emitting at 1.55mm wavelength, taking into account the nonuniform stimulated emission caused by filamentation within the optical cavity. The differential gain was determined from measurements of the threshold current density, considering the losses due to the inhomogenous carrier density distribution, as an apparent leakage current effect in the output power-current characteristics. The lasers were grown by low pressure MOCVD and incorporate an InGaAs/InGaAsP/InP separate confinement MQW active region. The results are compared with previous data reported on similar MQW heterostructures.

I. Introduction

The differential gain, defined as the differential of the optical material gain to the increment of the injected carrier density, is an important material parameter of the active layer of semiconductor lasers [1,2]. The higher modulation bandwidths [3] as well as the lower wavelength chirp [4,5] observed in multiquantum well (MQW) lasers for the 1.55 mm emission wavelength range, are mainly a consequence, of the two dimensional density of energy states. The latter increases the differential gain of the MQW active layer relative to the bulk material. The differential gain is most often determined from measurements of the relaxation oscillation frequency as a function of the optical emitted power under the approximation of small signal modulation [3,5,6]. However, this technique has been shown to depend on the laser structure and, in addition, the frequency response is also limited at higher optical powers due to damping caused by saturation of the optical gain [7].

The differential gain is an intrinsic property of the material in the active layer and is independent of the laser structure and measurement technique. In a recent work, we have proposed a simple method to determine the differential gain in MQW broad area lasers from measurements of the threshold current density [8]. The broad area laser has one of the most simple device structure. It is generally used for the evaluation of the intrinsic properties of the active layer material, before undertaking the fabrication of more complicated laser structures. Nevertheless, the optical field resulting from the stimulated emission can be highly nonuniform due to the lack of lateral confinement, leading to a phenomenon known as filamentation. This has been recently reported in InGaAs/InGaAsP/InP MQW lasers [9]. In such cases, the stimulated emission occurs only around local regions along the laser cavity, although the current is injected uniformly below the large stripe width. Hence, the carrier density is inhomogenously distributed in the active layer and a significant fraction of the current injected between the laser electrodes generates only spontaneous emission. These losses affect the evaluation of the threshold current density and the external quantum efficiency from the laser output power- current (P-I) characteristics. An analogous behaviour has been reported recently for MQW ridge waveguide laser structures, where the optical gain was shown to be influenced by the existence of leakage currents outside the recombination region [10].

In this work, we have determined the differential gain of MQW broad area lasers, taking into account the carrier density losses produced by filamentation. We have treated the current losses in the active layer as an apparent leakage current effect in the P-I characteristics. The laser devices were grown by metalorganic chemical vapor deposition (MOCVD), and comprised a separate confinement heterostructure (SCH) MQW active layer of lattice matched InGaAs/InGaAsP/InP emitting at 1.55 mm. In section II, we present the model employed to determine the differential gain including the carrier density losses derived from the P-I characteristics. In section III, we briefly describe the MOCVD growth of the MQW laser structure as well as the device processing and characterization. In section IV, we analyse and discuss the results obtained and compare our data with previous results reported on similar MQW lasers. Finally, in section V, we present the conclusion.

II. Basic assumptions and analysis

For a single QW layer, the optical material gain can be well approximated by a logarithmic function of the current density [11,12]

where g₀ is the gain coefficient, h_i is the current injection efficiency into the QW layer, j is the current density and j₀ is the current density at transparency. The threshold current density of a MQW laser with identical QWs is then obtained from the threshold condition where the gain equals the cavity losses, following the original derivation of Wilcox et al. [13], and it is given by the expression [8,11]:

where N_Z and G_Z are the number of QWs and the optical confinement factor of a single QW, respectively, R₁ and R₂ are the mirror reflectivities, a_i is the absorption loss and L is the cavity length. One notices that using the semi-logarithmic plot of j_th versus the inverse of L, one easily obtains g₀ from the slope, since N_Z, G_Z and R₁(R₂) are known quantities for a given laser structure. However, j₀ cannot be simply determined from the intercept at the ordinate because h_i and a_i must be found independently. In broad area lasers, h_i can be assumed approximately equal to unity in equation (2), as long as the effects of carrier escape from the QWs as well as diffusion and recombination in the barrier and waveguide layers are neglected [14]. The value of a_i is usually extracted from the linear plot of the inverse external quantum efficiency as a function of L, given by the well known expression [11,12]

Here h_id represents the internal differential quantum efficiency defined as the ratio of the increase of emitted photons to the increase of injected carriers [15,16]. Its value is very close to one, because above threshold h_id is dominated by stimulated emission, which is limited by the carrier intraband relaxation time [16,17]. Since the internal differential quantum efficiency depends on the current injection efficiency, we assume for simplicity in the following h_id» h_i, such that the current losses in the MQW active layer are considered to be limited only by the current injection efficiency. j_th and h_ext are evaluated from measurements of the threshold current and the differential efficiency, respectively, which are derived from the P-I characteristics. Nevertheless, the results can be influenced by leakage currents in the laser structure [10,18], as well as by carrier escape and recombination in the waveguide layers of SCH-MQW lasers. The latter only lowers slightly h_i at high current injection levels [19], but on lasers of very small cavity lengths, the resultant effect has been shown to be greater [20].

In contrast to previous works, we consider here the inhomogeneous lateral distribution of the stimulated emission in broad area lasers produced by filaments, despite the uniform injected current below the wide stripe. Earlier work of Thompson [21] described filamentation arising from self-focusing effects in local regions of high emission intensity due to an increase of the refractive index as well as carrier depletion. Later, more elaborate models were proposed to explain the nonlinear interaction between the optical field and the refractive index, and conditions of stability for uniform laser emission under the laser stripe were determined [22,23]. According to previous work, filamentation in InGaAs/InGaAsP/InP MQW broad area lasers arise from local differences in the distribution of defects and/or dislocations in the active layer [9]. The isolated filaments may have different threshold currents, but their emission intensities are coupled by the same current source. The P-I curve of the laser device is then the upper asymptote of the individual curves resulting from each filament [24]. The spontaneous emission generated by a significant fraction of the active layer cross section in the laser cavity, decreases the differential efficiency and increases the threshold current compared to a uniformily pumped broad area laser. Hence, as the injected current density increases in the active layer, the spontaneous emission also increases, and such behaviour is similar to that produced by a leakage current on the P-I characteristics. So, we have assumed the spontaneous emission losses resulting from filamentation in the MQW active layer, as an apparent leakage current effect on the laser characteristics. The threshold current is then given by [10,18]:

I_th = w L j_th + I_l (4)

where w is the laser stripe width and I_l is the leakage current. The latter increases with the total injected current I in the device, and consequently, affects j_th and the differential efficiency. If we assume a simple linear relationship, we may define a parameter K = dI_l/dI which should be smaller than one, such that equation (4) can be written as

If one neglects the contribution of the spontaneous emission, the P-I characteristic on each facet of the laser device is given by [18]

Here e is the elementary charge and hn is the photon energy. Hence, by differentiation of equation (6) with respect to I, one obtains h_ext as a function of the differential efficiency defined as dP/dI, including leakage current effects

One notices that the factor (1-K) appearing in equations (5) and (7) represents in fact the effective injection efficiency for stimulated emision in the active region. From the values of I_th and dP/dI measured on the P-I curve for a given L, one obtains j_th and h_ext through equations (5) and (7), respectively. The value of K is then adjusted so that the values of h_i and a_i obtained from the plots of equations (2) and (3) as a function of L can be matched. However, there is a limited range of established values for g₀, j₀, h_i and a_i in InGaAs/InGaAsP/InP MQW lasers, so K is the only unknown parameter that can be more freely adjusted for a given laser structure. Once K is determined, one notices that the values of j_th and h_ext obtained from equations (5) and (7), respectively, correspond to their values within the filaments of the MQW active layer. These values are then used for the evaluation of the differential gain, as discussed in section IV.

The differential gain dg/dn can be derived from equation (1) using an expression of j in terms of the carrier density n. The latter is obtained from the carrier density rate equation neglecting stimulated emission and carrier diffusion [18], and one obtains [11]

where L_Z is the thickness of a single QW layer. A, B and C are the nonradiative, the bimolecular (radiative) and the Auger recombination coefficients, respectively. However, we have recently demonstrated that a simpler and approximate expression may be used instead [8]

where B_eff is an effective recombination coefficient, which accounts for radiative as well as nonradiative transitions in the MQW active layer, and b is in the range 2 £ b £ 3. The parameters B_eff and b are adjusted such that equation (9) fits as close as possible equation (8) in a significant range of carrier densities. Previous investigators have attributed the values b = 2 and B_eff = 1.4×10^-10 cm³/s for bulk active layers of the InGaAsP/InP material system in the 1.55 mm emission wavelength range [25], assuming a given set of constants A, B and C. If we assume the set of constants A = 10⁸ s^-1, B = 10^-10 cm³/s and C = 10^-28 cm⁶/s, previously reported for InGaAs/InGaAsP/InP MQW layers [11,26], equation (8) can be fitted satisfactorily with b = 2.55 and B_eff» 3×10^-20 cm^4.65/s in the range of n = 1.5×10¹⁸ cm^-3 and 5×10¹⁸ cm^-3, which is of interest for laser devices [8]. Fig. 1 illustrates the good agreement obtained between equations (8) and (9) assuming the new values of B_eff and b, where the normalised current density defined as j/eN_ZL_Z is plotted versus n.

Figure 1.
Plot of the normalised current density j/ed, where d = N_ZL_Z, versus carrier density assuming h_i = 1. Equation (9) with B_eff = 3×10^-20 cm^4.65/s and b = 2.55 (solid line) and equation (8) with A = 10⁸ s^-1, B = 10^-10 cm³/s and C = 10^-28 cm⁶/s (dotted line).

Now, a simple relation for g in terms of n can be derived from equations (1) and (9), assuming j₀ = eL_ZB_effn₀b, where n₀ is the carrier density at transparency. Note that h_i does not appear in the definition of j₀, because we assume that only the injected carriers that contribute to the laser emission are included in the transparency current. Hence, we have

The differential gain is then given by the simple expression

The values of g₀ and the threshold carrier density n_th are determined from the semi- logarithmic slope of equation (2) and from equation (9) for a given value of j_th, respectively. These two equations are influenced by leakage currents in the P-I characteristics through the value of K in equation (5). However, the value determined for dg/dn in equation (11) is mainly affected by n_th, which depends on the value of j_th, as discussed in section IV.

III. Laser fabrication

The epitaxial heterostructure comprising the SCH-MQW active region was grown by low pressure MOCVD on a n⁺-InP substrate. The MQW consisted of 6 InGaAs QW layers of 74 Å thickness corresponding to a room temperature photoluminescence peak at 1.546 mm. The InGaAsP barriers and waveguide layers were 132 Å and 645 Å thick, respectively, and were grown with a bandgap composition corresponding to the emission wavelength of 1.3 mm. Both ternary and quaternary layers were grown lattice matched to InP. The lower and upper InP confining layers were Si doped with n = 10¹⁸ cm^-3 and Zn doped with p = 5×10¹⁷ cm^-3, respectively. An InGaAs contact layer Zn doped with p = 10¹⁹ cm^-3 was grown on top. The broad area lasers were processed with a metal contact stripe of 100 mm width and cleaved with various cavity lengths in the range 350 - 700 mm. The P-I characteristics were measured under pulsed conditions at a frequency of 1 kHz with pulse widths of 1 ms, to avoid heating of the MQW active layer.

IV. Results and discussion

A typical P-I plot of a SCH-MQW broad area laser is shown as the solid line in Fig. 2 for a cavity length of 700 mm. In a first analysis, we assumed I_l = 0 and determined I_th and dP/dI from the intersection and slope above threshold using equation (6), as shown with the dotted line of Fig. 2. The results obtained for 33 laser devices are shown in Figs. 3 and 4, where j_th and 1/h_ext are plotted as a function of 1/L and L, respectively. The dotted lines in these figures are least square fits of the data points, which support equations (2) and (3) with K = 0 in equations (5) and (7), respectively. Since g₀ is independent of K, we can estimate its value from equation (2) using the semilogarithmic slope of 2.246×10^-2 cm shown in Fig. 3. If we assume G_Z» 2×10^-4 L_Z(Å) [6], such that N_ZG_Z = 0.0888, and R₁(R₂) » 0.3 for cleaved facets, we find g₀» 603.66 cm^-1. This result is consistent with theoretical predictions obtained under the k.p approximation for the evaluation of the material gain [11]. If we consider the dotted line in Fig. 4 to be representative of the data and use equation (3), we obtain h_i = 0.4472 and a_i = 30.11 cm^-1. Then, assuming these values in equation (2), we find j₀ = 59.15 A/cm². The values found for a_i and j₀ agree with previous reports on similar MQW lasers and can be assumed hereafter, but h_i is extremely low and unconsistent with previous assumptions [12]. Except for L smaller than 50 mm, h_i is expected to be always close to one [20].

Figure 2.
P-I characteristic of a MQW broad area laser with L = 700 mm (solid curve). The dotted line represents equation (6).

Figure 3. Threshold current densities of MQW broad area lasers presented as a function of 1/L. The dashed and solid lines are least square fits for 33 lasers adjusted with equation (2) using K = 0 and 0.5528 in equation (5), respectively.

Figure 4. External quantum efficiencies of MQW broad area lasers presented as a function of L. The dashed and solid lines are least square fits for 33 lasers adjusted with equation (3) using K = 0 and 0.5528 in equation (7), respectively.

The j_th data points shown in Fig. 3 within the range 1.7 - 3 KA/cm² as well as the low h_ext values of Fig. 4, imply the existence of considerable current losses in the P-I characteristics of these laser devices. The constant monotonic increase observed at low powers on the P-I curve shown in Fig. 2 with a rounded shape near threshold, is consistent with a sizeable contribution of the spontaneous emission [16]. However, the presence of filamentation in the optical laser cavity cannot be simply inferred from the P-I characteristics alone. We have thus undertaken measurements of the far field pattern and the emission spectra of similar MQW broad area lasers. The former presents an asymmetric and nonuniform distribution pattern which depends on the injected current, whereas the latter usually displays more than one family of longitudinal modes. These observations support the existence of filamentation in the optical cavity [9,27], and we have then employed the apparent leakage current model presented in section II, to describe the P-I characteristics of our MQW lasers.

By assuming h_i» 1 and the values found above for g₀, a_i and j₀, we have determined the value of K in equations (5) and (7) that matches equations (2) and (3). The results are shown as solid lines in Figs. 3 and 4 with K = 0.5528. This large value of K implies a low injection efficiency for the measured P-I characteristics, according to the factor (1-K) in equations (5) and (7), but it is consistent with previous assumptions of low current injection efficiencies due to filamentation in broad area lasers [28]. The K parameter affects only the intercept at the ordinate of equation (2), in the same way as the low value found for h_i above, whereas in equation (3), K affects both the intersection at the ordinate as well as the slope.

Hence, we can estimate dg/dn using the corrected values of j_th, which generate laser emission by filamentation in the MQW active region. Assuming b = 2.55 and B_eff = 3×10^-20 cm^4.65/s in equation (9), and considering the expression shown for the solid line in Fig. 3 with L = 350 mm, we find n_th» 2.14×10¹⁸ cm^-3. From equation (11), we then obtain dg/dn » 7.19×10^-16 cm². Following the same reasoning for L = 700 mm, we find n_th» 1.89×10¹⁸ cm^-3 and dg/dn » 8.14×10^-16 cm². These results are in good agreement with our previous work [8] and with data reported by other investigators as discussed below. The increase of dg/dn obtained in terms of L results from the decrease of the mirror losses which reduce j_th. We can check the error obtained by neglecting K in the evaluation of the threshold current density. If we consider the expression shown for the dotted line in Fig. 3 and equation (9) with h_i» 1, we find after the same analysis, the values n_th» 2.94×10¹⁸ cm^-3 and dg/dn » 5.24×10^-16 cm², and n_th» 2.59×10¹⁸ cm^-3 and dg/dn » 5.94×10^-16 cm², for L = 350 mm and L = 700 mm, respectively. We note that the values obtained for n_th and dg/dn are somewhat overestimated and underestimated, respectively. Thus, the value of dg/dn is affected by K only through the value of n_th obtained with equation (9), since the value of g₀ derived from equation (2) does not change as long as h_i remains constant.

We can now compare our results with data reported on similar lattice matched InGaAs/InGaAsP/InP MQW heterostructure lasers. Zah et al. [29] and Sasaki et al. [30] measured dg/dn = 3.6×10^-16 - 6.7×10^-16 cm² and dg/dn = 8.2×10^-16 cm², respectively, with 4 QWs. Fernier et al. [31] and Cavalier et al. [32] measured dg/dn = 7.6×10^-16 cm² and dg/dn = 4.8 ×10^-16 - 6.1×10^-16 cm², respectively, with 5 QWs. Tatham et al. [33] reported dg/dn increasing from 1.9×10^-16 cm² to 7.7×10^-16 cm², as the number of QWs increased from 2 to 24. Seltzer et al. [34], reported dg/dn = 6.1×10^-16 cm² for 16 QWs. Uomi et al. [35] measured dg/dn = 5.5×10^-16 cm², 8.3×10^-16 cm² and 1×10^-15 cm², in a heterostructure with 5, 10 and 15 QWs, respectively. Most of these results were obtained with the small signal modulation technique in devices of small cavity lengths. The effect of leakage currents have not been considered, but a low frequency roll-off observed at higher optical powers can decrease somewhat the value measured for dg/dn [6]. This might explain in part our higher values compared to laser devices reported with similar number of QWs. However, different techniques have been shown to induce slightly different results with the same MQW heterostructure [32]. Other possible differences arise from unknown values of h_i as well as different values of a_i which depend on the laser strucuture. Moreover, there are uncertainties regarding the value of g₀ in InGaAs/InGaAsP/InP MQW heterostructures, since somewhat lower and higher values were also reported [11,36].

V. Conclusion

We have analysed the differential gain of MQW broad area lasers emitting at the wavelength of 1.55 mm, taking into account the carrier density losses produced by filamentation in the optical cavity. The differential gain was determined from measurements of the threshold current density including the losses due to the nonuniform laser emission as an apparent leakage current effect in the P-I characteristics. The broad area SCH-MQW lasers were grown by MOCVD and incorporated an InGaAs/InGaAsP/InP heterostructure in the active layer. For cavity lengths of 350 mm and 700 mm, we have found the values dg/dn » 7.19×10^-16 cm² and 8.14×10^-16 cm², respectively, which are consistent with previous results.

Acknowledgements

The authors would like to thank L.K.Horiuchi for technical assistance during the MOCVD growth.

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Publication Dates

• Publication in this collection
  14 June 1999
• Date of issue
  Dec 1997

History

• Received
  05 June 1997