Physica E 7 (2000) 489–493
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InAs–GaAs self-assembled quantum dot lasers: physical processes and device characteristics D.J. Mowbraya; ∗ , L. Harrisa , P.W. Frya , A.D. Ashmorea , S.R. Parnella , J.J. Finleya , M.S. Skolnicka , M. Hopkinsonb , G. Hillb , J. Clarkb b Department
a Department of Physics, University of Sheeld, Sheeld, S3 7RH, UK of Electronic and Electrical Engineering, University of Sheeld, Sheeld, S1 3JD, UK
Abstract The gain characteristics of InAs–GaAs self-assembled quantum dot lasers are studied using two complementary techniques. The modal gain is derived from a measurement of the normal incidence, inter-band photoconductivity. For a device containing a single layer of dots the maximum modal gain of the ground state transition is found to be insucient for lasing action. As a consequence lasing occurs for excited state transitions, which have a larger oscillator strength, with the precise transition being dependent upon the device cavity length. The second technique uses the Hakki–Paoli method to determine the spectral and current dependence of the gain. A quasi-periodic modulation of the below threshold gain is observed. This modulation is shown to be responsible for the form of the lasing spectra, which consist of groups of lasing modes separated by non-lasing spectral regions. Possible mechanisms for this behaviour are discussed. ? 2000 Elsevier Science B.V. All rights reserved. PACS: 42.55.Px; 78.66.−w; 42.60.Lh Keywords: Quantum dots; Semiconductor lasers; Electro-optic devices; Modal gain; III–V semiconductors
Injection lasers with self-organised quantum dot (QD) active regions are attracting considerable attention due to their potential for low threshold current density (Jth ) and temperature insensitive Jth devices [1,2]. In this paper we describe the use of two complementary techniques to study the gain characteristics of InAs–GaAs self-organised QD lasers. These techniques allow the magnitude of the ground state modal ∗ Corresponding author. Tel.: +44-114-222-4561; fax: +44-114272-8079. E-mail address: d.mowbray@sheeld.ac.uk (D.J. Mowbray)
gain and the dependence of the gain spectra on injection current to be determined. Self-organised InAs QDs were grown by molecular beam epitaxy on a (0 0 1) GaAs substrate at a tem◦ perature of 500 C [3]. The QDs have a base length of 15 nm, height 3 nm and density ∼ 5 × 1010 cm−2 . Two laser devices were studied containing either a single QD layer con ned on either side by 1375 of GaAs or 10 QD layers separated by 250 A of A GaAs layers. 16,000 A GaAs and con ned by 1000 A thick Al0:6 Ga0:4 As cladding layers were used in both devices. Devices for photocurrent measurements
1386-9477/00/$ - see front matter ? 2000 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 6 - 9 4 7 7 ( 9 9 ) 0 0 3 7 1 - 9
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Fig. 1. Photocurrent (PC) and electroluminescence (EL) spectra of a mesa device. The inset shows the ground state (GS) photocurrent transition after removal of the background. The solid points in the inset show the result of a Gaussian t to the experimental data.
consisted of 400 m diameter circular mesas with annular metal top contacts. Laser devices were of the form of SiN-coated ridges of width 20 m [4]. Photocurrent was excited using monochromated light from a tungsten-halogen projector lamp (power density ∼ 3 mWcm−2 ) and was detected using standard lockin techniques. High-resolution emission spectra were recorded using a double grating 0.85 m spectrometer and a liquid-nitrogen-cooled Ge p–i–n photodiode. All measurements were performed for a device temperature of 80 K. Fig. 1 shows a photocurrent spectrum of a reversed biased mesa device (Vbias ≈ −2:0 V) and an electroluminescence spectrum of a forward biased mesa (Vbias ≈ +1:5 V; I = 500 mA), both recorded for the single-layer QD structure. In both spectra a series of features are observed in the range 1.2–1.4 eV, which are attributed to transitions between QD-con ned hole and electron states. A broad, rising background is observed in the photocurrent spectrum, the origin of which is unclear.
For suitable temperatures and=or bias conditions all the photoexcited carriers escape from the QDs before recombining. Under these conditions the absorption strength (A) of the QDs can be determined from the magnitude of the photocurrent (I ) and the relationship I = APe=hc, where P is the total incident optical power at wavelength . To determine the ground state absorption the background photocurrent is rst removed by assuming a linear variation with energy (see inset to Fig. 1). This allows the magnitude of the photocurrent associated with the QD ground state transition to be determined which, with the incident optical power (measured with a calibrated power meter) and the above equation, gives a peak absorption of A = (2 ± 0:6) × 10−4 . 1 The value A = (2 ± 0:6) × 10−4 represents the fractional plane wave absorption for normal incidence on a single-dot plane. To determine the modal gain (g) for inplane propagation of light in a waveguide structure, the corresponding absorption coecient ( (≡ −g)) is calculated. This is related to A by = ln((1 − A)1=D )
ef ;
(1)
where D is the average dot spacing. The rst term in Eq. (1) (ln((1 − A)1=D ) ≈ A=D as A 1) represents the plane wave absorption for an in nite stack of dot layers. The second term, ef , is the geometric conversion factor from the plane wave-to-wave guide geometry, and is given by ef
I (0) = Pi=∞ ; i=−∞ I (iD)
(2)
where I (x) is the transverse optical intensity pro le, determined numerically using a three-layer model. For a measured dot density of 5 × 1010 cm−2 , a value = (7 ± 3) cm−1 is obtained for the ground state modal absorption. Because the maximum gain of a QD transition has a numerical value equal to the absorption [5], max , for the the maximum ground state modal gain, gmod 1 This is the value appropriate to the bias conditions for lasing action (Vbias = +1:5 V) and is larger than the value determined from the present photocurrent measurements which corresponds to Vbias = −2 V. The value for Vbias = +1:5 V is obtained from an extrapolation of values measured over the bias range −1 V6Vbias 68 V. This variation of the absorption with bias arises from an electric- eld-induced separation of the electron and hole wave functions which results in a reduction of the transition oscillator strength for increasing reverse bias.
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present single-layer device is (7 ± 3) cm−1 . Although the light propagation direction for the photocurrent measurements is normal to that for inplane waveguide propagation, measurements of laser devices demonstrate that the ground state emission has an inplane (TE) polarisation. Hence the polarisation direction for the two con gurations is identical. max = (7 ± 3) cm−1 determined for The value of gmod a single-dot layer is considerably smaller than that of comparable InGaAs quantum well lasers, where values of ∼ 50–100 cm−1 are typical [6]. This relamax tively small value of gmod has signi cant consequences for the properties of laser devices as it is comparable to the internal cavity loss ( i ), which typically has a value in the range ∼ 2–10 cm−1 [7,8]. As a consequence lasing on the ground state transition may not be possible and instead lasing may occur on an excited state, which generally exhibit a higher oscillator strength. The relative oscillator strengths of the lowest three transitions are shown in the upper inset of Fig. 2 where their spontaneous emission intensities are plotted as a function of current. With increasing current the transition intensities saturate as a result of state lling [9]. Higher transitions exhibit a higher saturated intensity, which may re ect a higher degeneracy of the underlying states [9], consistent with a higher maximum gain. The behaviour of the single-layer QD laser is shown in Fig. 2 where emission spectra for a 2 mm cavity device are displayed. The emission from the ground state transition saturates at low currents, indicating that the gain of this transition is insucient to overcome i plus mirror losses ((1=L) ln(R) ≈ 5:7 cm−1 ). A similar behaviour is observed for the rst excited state transition and lasing eventually occurs via the second excited state transition. A 5 mm cavity device exhibits a similar behaviour (uppermost spectra in Fig. 2) except that the reduced mirror loss ((1=L) ln(R) ≈ 2:3 cm−1 ) now permits lasing via the rst excited state. For none of the cavity lengths studied is lasing on the ground state transition possible for the single layer device [10]. The present results demonstrate that the maximum ground state gain of a quantum dot laser is relatively small and that unless care is taken with the design, ground state lasing may not be possible. Lasing on the ground state transition is desirable as carriers in the corresponding dot states are the most strongly con ned, hence minimising thermal carrier
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Fig. 2. Emission spectra of a single QD layer, 2 mm cavity laser device showing lasing occurring on the second excited state transition. The uppermost spectrum shows the lasing emission from a 5 mm cavity occurring on the rst excited state. The upper inset shows the evolution with current of the spontaneous emission from the QD transitions. The lower inset shows an emission spectrum (I = 1:3Ith ) of the 10 QD layer, 2 mm cavity device, recorded from a series of small windows formed in the top contact.
loss from the dots and resulting in the optimum temperature performance [11]. The second technique applied to study QD gain characteristics uses the Hakki–Paoli method [11]. Here the net loss coecient, , of the cavity is related to the peak-to-valley ratio, r, of the Fabry–Perot-like oscillations, observed in the below threshold spontaneous emission, by 1=2 1 r +1 1 ; (3)
= ln(R) + ln 1=2 L L r −1 where R is the mirror re ectivity and L is the cavity length. Hence by measuring r as a function of wavelength the gain spectrum (= − ) can be determined. Fig. 3 shows a series of sub-threshold emission spectra for the 10 QD layer device and a 0.5 mm cavity length (Ith = 21 mA). Close to threshold the emission intensity is modulated by the Fabry–Perot oscillations (see lower inset), the peak-to-valley ratio
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Fig. 3. Below threshold emission spectra of a 0.5 mm cavity device at 80 K. The lower inset shows the Fabry–Perot oscillations. The upper inset shows a calculated gain spectrum for I = 20 mA and a lasing spectrum (I = 40 mA).
of which increases with increasing current, consistent with decreasing loss (increasing gain). The upper inset to Fig. 3 shows a gain spectrum for a current of 20 mA. This spectrum is calculated by rst extracting the spectral dependence of the Fabry–Perot peak-to-valley ratio (r) from the corresponding spectrum of Fig. 3, and then using Eq. (3) with a calculated value for the mirror term of −23:5 cm−1 (corresponding to an R of 0.31) to determine the gain (≡ − ). Close to threshold the gain maximum occurs above the ground state energy, the corresponding gain for which saturates to a negative value. This result demonstrates that for the present, short cavity device that the ground state gain is insucient for lasing action to occur. The gain spectrum shown in the inset to Fig. 3 exhibits a quasi-periodic modulation, which is also visible in the emission spectra of Fig. 3. This modula and depth ∼ 10 cm−1 , tion, which has a period ∼ 50 A is closely linked to the form of the above threshold lasing spectra, an example of which (I = 40 mA) is shown in the upper inset of Fig. 3. The spectrum consists of three groups of longitudinal cavity modes,
separated by non-lasing spectral regions, 2 the positions of which coincide with the maxima of the below threshold gain spectrum. A similar modulation of the below threshold gain has been observed in a quantum well (QW) laser by Arzhanov et al. [12]. This behaviour was explained in terms of the penetration of the cavity optical mode through the nite thickness cladding layers and a resultant periodic modulation, which feeds back in to the cavity gain, due to interference e ects in the substrate. A similar mechanism has recently been proposed by O’ Reilly et al. [13] to explain the lasing spectra of QD lasers. In contrast to the case of a QW laser the modulation of the gain is expected to be observable in a QD laser above threshold due to strong inhomogeneous spectral broadening which results from the presence of non-interacting carriers localised in di erent dots [4]. Although the period of the gain modulation observed in the present device agrees reasonably with the predictions of Refs. [12,13], the depth of the modulation appears to be too large. Using Eq. (2) of Ref. [13] with a calculated cladding layer penetration depth of 9:3 m−1 and a cladding layer thickness of 1:6 m, a gain modulation of only ∼ 10−9 cm−1 is calculated, very much smaller than the observed modulation (∼ 10 cm−1 ). Although the model of Refs. [12,13] is therefore able to explain the periodicity of the observed gain modulation, 3 when used with parameters relevant to the present device it predicts a very small leakage of light into the substrate and hence an extremely small gain modulation. However there exists experimental evidence for signi cant light leakage through the cladding layers, as demonstrated in the upper inset of Fig. 2. This inset shows an emission spectrum, recorded from a series of small windows formed in the top contact of a 2 mm cavity device, for I = 1:3Ith . In addition to the expected broad spontaneous emission, lasing modes are observed, consistent with the leakage of some inter-cavity stimulated emission through the cladding layers. The mechanism responsible for light leakage and the resultant gain modulation in the present device hence remains unclear. Possible 2 In longer cavity devices the number of mode groups can be considerably larger e.g. ∼ 10 for a 2 mm cavity (Ref. [4]). 3 Recent measurements on devices with di erent substrate thicknesses demonstrate a good agreement between the measured lasing mode group spacing and the predictions of the theoretical model (P.M. Smowton, private communication).
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explanations include lasing on a higher-order transverse mode, which would exhibit a greater penetration through the cladding layers than the fundamental mode, or leakage enhanced by scattering from the random spatial distribution of QDs. In conclusion, two di erent techniques have been applied to study the gain characteristics of QD lasers. The maximum ground state modal gain for a single layer of dots is shown to be relatively low. A quasi-periodic modulation of the below-threshold gain is shown to determine the form of the subsequent lasing spectra. We wish to thank M. Al-Khafaji for the structural measurements and P.N. Robson, P.M. Smowton, E.P. O’Reilly, E.A. Avrutin and A.I. Onischenko for useful discussions. This work is supported by the Engineering and Physical Sciences Research Council (EPSRC) UK Grant Numbers GR=L95489 and GR=L28821. References [1] Y. Arakawa, H. Sakaki, Appl. Phys. Lett. 40 (1982) 939. [2] D. Bimberg, M. Grundmann, N.N. Ledetsov, Quantum Dot Heterostructures, Wiley, Chichester, 1998.
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