Optical gain in (Zn,Cd)SeZn(S,Se) quantum wells as a function of temperature

Journal of Crystal Growth 184/185 (1998) 623-626

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Optical gain in (Zn,Cd)Se-Zn(S,Se) quantum wells as a function of temperature F.P. Loguea, P. Rees”, C. Jordan”, J.F. Donegana,*, J. Hegarty”, T. Hinob, K. Nakanob, A. Ishibashib bS~ny

F. Hieib, S. Taniguchib,

aPhysics Department, Trinity College, Dublin 2. Ireland Corporation Research Centre, Fujitsuka 174, Hodogaya Yokohama 240, Japan

Abstract

We have investigated the mechanism of stimulated emission in ZnCdSe-ZnSSe quantum wells through measurements of the optical gain spectrum between 77 and 270 K. We also calculated the optical gain using a model which included many-body effects and found excellent agreement with our measurements. Our results are inconsistent with an excitonic gain mechanism and we conclude that the stimulated emission arises from an electron-hole plasma in our samples. However, we find that the electron-hole Coulomb interaction is still significant at room temperature in II-VI heterostructures. 0 1998 Elsevier Science B.V. All rights reserved. PACS:

78.66.H

Keywords:

Gain spectra; II-VI quantum wells; Many-body

The large exciton binding energy in II-VI QWs is a manifestation of the larger electron-hole Coulomb interaction compared with narrow band-gap semiconductors. Exciton resonances have been observed at room temperature and this has led to the search for excitonic gain mechanisms [1,2]. The observation of exciton-like resonances in absorption, however, is not conclusive proof of the

*Corresponding [email protected].

author. Fax:

+ 353 1 671 1759; e-mail:

theory

existence of excitons. Rather, they indicate Coulomb enhancement of the absorption above the band gap [3,4]. Despite the large exciton binding energies in II-VI heterostructures, they become ionised at high temperatures and in the presence of high carrier densities. Recent studies have shown the interplay between excitons, bi-excitons and free carriers at low temperatures [5,6]. We have studied optical gain spectra in ZnMgSSeZnSSe-ZnCdSe QWs as a function of temperature above 77 K. Comparison is made between our measurements of the optical gain spectra and a many-body theory. The stimulated emission

0022-0248/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved PII SOO22-0248(97)00636-Z

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of Crystal Growth 1841185 (1998) 623-626

process is not excitonic in the temperature range studied, but there is still a large Coulomb enhancement to the gain spectrum even at room temperature. The sample studied was a separate confinement structure (SCH). It consisted of a GaAs buffer layer, ZnSe buffer layers, a 500 nm ZnMgSSe cladding layer, a 100 nm ZnSSe barrier layer, the 6 nm Zn 0.75Cd0.25Se quantum well, followed by a further barrier layer and a 200 nm 100 nm ZnS0,,,Se0,9j ZnMgSSe capping layer. These samples, although un-doped, have a typical laser structure [7]. Gain measurements were carried out using the variable stripe-length method [S], where the gain is determined by measuring the intensity of amplified

spontaneous emission as function of amplification path length. In our measurements the light source was the third-harmonic of a Q-switched Nd : YAG laser operating at a wavelength of 355 nm with pulses of 5 ns duration. The sample was mounted on the cold finger of a variable temperature liquidnitrogen cryostat and the temperature varied between 77 and 270 K. The edge emission intensity is given by [S] gW)L _

I(L) cc

leg&4

1)

(1)

’

where L is the length of the exciting stripe and g(zZw) is the modal gain. A gain spectrum, g(hw) is, thus, calculated from the solution of Z(L,) (eg(fiw)LI- 1) I(L,) = (es(hw)L _ 1)’

50 0

I

2.40

I

I

I

2.45

2.50

,

,

,

2.55

Energy (eV) Fig. 1. Measured gain spectra (symbols) for sample SCH. The fits using the many-body theory are also shown (solid lines). The results obtained from the fits are summarised in Table 1. Table 1 Results of fitting the experimentally

measured

gain spectra

for sample

(2)

where L, and L2 are different excitation stripe lengths. Fig. 1 shows the measured gain spectra (symbols) of the SCH sample as a function of temperature between 77 and 270 K. Table 1 summarizes the experimental parameters used to obtain these spectra. As the temperature increases, the gain spectra red shift and also broaden significantly. The shift is due to the band-gap reduction and the broadening due to increased carrier scattering at higher temperatures. This leads to a larger carrier density necessary to achieve gain and so a larger laser pump intensity is necessary. The pump intensity compares well with measurements by other workers on samples similar to ours [1,2]. The carrier density estimated from the pumping intensity is also given in Table 1. In order to interpret the experimentally measured gain spectra we have used a many-body calculation.

SCH as a function

of temperature

Pump intensity (kW cmm2)

r

(R)

Carrier density (estimated from pump intensity) (cm-‘)

Carrier density (from fits) (cm-‘)

270 170 77

10 3 1

0.042 0.040 0.034

13.0 X 1or2 3.9 X 1or2 1.3 X 1orz

3.73 X 10’1 1.21 X 1or2 6.72 x 10”

Temperature

F.P. Logue et al. /Journal

qf Crystal Growth 184/18.5 (1998) 623-626

625

This model includes band-gap renormalisation, carrier scattering which causes spectral broadening, and the Coulomb interaction of electrons and holes. Band-gap renormalisation does not vary significantly with energy [9] and so is included in the calculation before the evaluation of any optical spectra. The quasi-Fermi levels in the bands are shifted by the same amount as the bands themselves and so band-gap renormalisation does not change the distribution of carriers within the bands. The relationship between the electric field E(r) and the microscopic interband polarisation, pk(r), is derived using the Hartree-Fock approximation 2.50

ClO,lll,

2.52

2.54

Energy (eV)

= -

(.Lk -Lk)

dkE(r,t)

where E, and Eh are the renormalised conduction and valence band energies, respectively, T/, is the screened 2D Coulomb potential, P’ is the sample volume, d, is the dipole matrix element, and yk is the dephasing rate due to carrier-carrier and carrier-LO-phonon scattering. Setting I/, = 0 in Eq. (3) gives the free-carrier result, neglecting Coulomb enhancement. By writing pk(r) = X,E(r), with the optical susceptibility, X(r), given by

X(r) = + C d,X,(r), k

Eq. (4) can be solved for X(r), and the absorption (or gain) is then determined from the relation

44

=

z Im [X(W)]~

where fi is the refractive index. Inhomogeneous broadening was included in the calculation as a convolution of a Gaussian line shape [ 121 with the 2D density of states and the full-width at halfmaximum of the Gaussian was taken from the low-temperature luminescence spectrum. The solid lines in Fig. 1 show the fits to the measured gain spectra using the many-body the-

Fig. 2. Sensitivity of the fit (solid line) to variation (dashed line) of the quasi-Fermi level separation by f 3 meV corresponding to a change ofcarrier density of kO.06 x 10” cm-‘. The data is taken at T = 120 K and the fit corresponds to a carrier density of 1.26 x 10” cm-‘.

ory. These fits were obtained by calculating the optical gain spectrum for a particular separation in the quasi-Fermi level which uniquely determines the carrier density. As these are waveguide structures, the optical confinement factor r, which converts between the measured modal gain and the material gain, is also adjusted to obtain a good fit. The fits are sensitive to changes in well-width, carrier density, and carrier temperature. Fig. 2 shows the effect on the gain spectrum of changing the carrier density. The gain spectrum of sample SCH at T = 120 K is shown (circles), and the best fit obtained (solid line) giving a carrier density of 1.26 x 1012 cmP2. Also, shown is the effect on the gain spectrum (dashed lines) of changing the separation of the quasi-Fermi level by f 3 meV. Our ability to fit the experimental gain spectra with the Coulomb enhanced free-carrier gain model shows that in the range 77-270 K the gain mechanism in our samples is not excitonic. Nonetheless, as the temperature decreases, the Coulomb enhancement increases due to reduced screening at the lower carrier density necessary for gain (see Fig. 3). The enhancement is the ratio of the peak value of the gain calculated with and without the Coulomb enhancement term in Eq. (3).

F.P. Logue et al. /Journal

/

‘,

4,

,I,,

,

I

of

Crystal

7

.

Growth

1841185 (1998) 623-626

between our measured optical gain spectra and those calculated using an EHP gain model which includes many-body effects. Furthermore, the electron-hole Coulomb interaction is a significant factor in the optical gain arising from an EHP in II-VI heterostructures. This work was supported by the Forbairt basic research programme under contract number SC/96/737.

.

References 150

200

Temperature

250

(K)

Fig. 3. Coulomb enhancement to the peak of the gain spectrum as a function of temperature for SCH.

In our previous work [ 1 l] we have shown that Coulomb enhancement increases the amount of spontaneous emission leading to an increased threshold current density for laser diodes. On the other hand, Coulomb enhancement increases the amount of gain at a particular carrier density and also produces a larger amount of gain for a smaller separation in quasi-Fermi levels and so reduces carrier leakage into barrier regions. It has been noted [13] that the reduction of carrier leakage significantly decreases the threshold current of II-VI diode lasers at room temperature. Such competitive effects show that a thorough understanding of Coulomb enhancement is essential for the development and optimisation of blue-green optoelectronic devices. In conclusion, we have shown that stimulated emission arises from an electron-hole plasma (EHP) in ZnCdSe-ZnSSe QWs for temperatures above 77 K. This is shown by the excellent fits

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