Negative charged excitons in double barrier diodes

Microelectronics Journal 36 (2005) 1038–1040 www.elsevier.com/locate/mejo

Negative charged excitons in double barrier diodes I. Campsa, A. Vercikb, Y. Galva˜o Gobatoa,*, M.J.S.P. Brasilc, G.E. Marquesa, S.S. Maklerd b

a Departmento deFisica, Universidade Federal de Santa Catanna, Floriano´polis, Brasil Faculdade Zootecnia eEngenhana de Alimentos, Departmento de Clencias Basicas, Universidade de Sa˜o Paulo, Pirassununga, 13635-900, SP, Brasil c Universidade de Campinas, Instituto de Fı´sica Gleb Wataghin CP 6165, Campinas, SP 13083-970, Brazil d Universidade Federal Fluminense, Instituto de Fı´sica, Nitero´i-RJ 24210-340, Brazil

Available online 26 May 2005

Abstract We have studied the effects of excitonic complexes formation, such as excitons and trions, on the optical and on transport properties of GaAs–GaAlAs n–i–n double barrier diodes, by measuring the current–voltage characteristics and the photoluminescence emission, as function of bias. The observation of a pre-resonance shoulder in the I(V) curves, under high laser intensities, and a negative charged excitons in the photoluminescence spectra, under the same bias conditions, were associated to the dissociation of these complexes either by thermal excitation or by scattering with ‘free’ carriers in the quantum well layer. A simple rate equation model allows us to explain the kinetics of the excitonic complexes in double barrier devices. q 2005 Elsevier Ltd. All rights reserved. Keywords: Quantum dots; Recombination energy; Interfacial layer

1. Introduction The Coulomb interaction between electrons and holes may form complexes with two, three or more particles in high quality semiconductor crystals. These excitonic complexes were predicted by Lampert [1] in 1958. Since then, many authors have studied their ground-state energies and wave functions [2,3] in the presence of electric [4] and magnetic fields [5] and also the influence of such atomic-like particles on the optical [6–9] and on the transport [10–12] properties of localized and resonant states in semiconductor devices. These systems originate from the Coulomb interaction that, in the simplest case, binds one electron to a hole and forming a neutral exciton (X0). When the free carrier density is high enough, a second electron (second hole) can become involved and form three-particle systems, the negatively (positively) charged excitons, also known as XK (XC) trions. * Corresponding author. Departmento deFisica, Universidade Federal de Santa Catanna, Floriano´polis, Brasil. Tel.: C55 16 3351 8222; fax: C55 16 3361 4835. E-mail address: [email protected] (Y. Galva˜o Gobato).

0026-2692/$ - see front matter q 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2005.04.013

In this work, we have developed a set of phenomenological coupled rate equations to explain the experimental results for photoluminescence (PL) and transport measurements on n–i–n double barrier resonant tunnelling diode (DBRTD) samples.

2. Theoretical model To describe the charge buildup in the DBRTD and the kinetics of the different particles, we are proposing a system of rate equations that describe the balance between the constituents. The mechanisms governing the population of carriers considered in this work are: (i) injection rates for electrons (holes) into and out the well, respectively; (ii) the formation of excitons due to electron–hole interaction and due to trion non-radiative decay; (iii) the formation of trions via electron–exciton interaction and free two-electron–one hole interaction; (iv) the exciton and trion radiative decays with emission of a photon (luminescence). When an electron (e) and a hole (h) interact via Coulomb forces, an exciton can be formed and this process can be represented by the chemical reaction X0 % eC h. The population balance rate between electrons, holes

I. Camps et al. / Microelectronics Journal 36 (2005) 1038–1040

1039

and excitons can be written as:

20

1.5 1.0 0.51V 0.41V

0.5 0.3V

(3)

Since the number of electrons and holes in the quantum well is always greater than the number of excitons and trions, the expressions (1)–(3) can be simplified to: T0 Z anp;

(4a)

0 TK Z bnn0 ;

(4b)

00 TK Z gn2 p

(4c)

The resulting rate equation system, considering the balance of processes described above, is written as dn 0 00 Z Gn K Rn n K T0 K TK K 2TK C RKnK; dt

(5a)

dp 00 Z Gp K Rn p K T0 K TK dt

(5b)

dn0 0 Z T0 K TK K R0 n0 ; dt

(5c)

dnK 0 00 Z TK C TK K RKnK: dt

(5d)

X

0.24V

–

X0

0.0 1.600

10

(2)

Here, b is the trion creation/annihilation rate and nK is the trion population. The other trion formation/dissociation mechanism is through the Coulomb interaction between two electrons and a hole represented by the reaction XK% eC eC h with population rate given by 00 TK Z gðn2 p K nKÞ:

T=9K

0

0.2

0.4

1.605 1.610 Energy (eV)

0.6 0.8 Voltage (V)

1.0

1.615

1.2

Fig. 1. Dark I(V) characteristics, at 9 K, (dashed line) and with laser intensity of 6.4 W/cm2 (solid line). The insert shows the PL for different bias voltage.

epitaxy, with 10 nm barriers and 5 nm well widths, respectively. The system is enclosed by 60 nm undoped GaAs layers and 300 nm Si–doped nC–GaAs (1018 cmK3) layers grown on both sides of the structure. Annular contacts on 500 mm!600 mm mesas allow optical measurements under applied voltage. The samples were mounted in a Janis close cycle cryostat. The spectra were recorded by a Spex 500 M single spectrometer. A Coherent ArC ion laser was used as excitation source and the PL signal was detected by a photocounting system connected to a thermoelectrically cooled R5108 Hamamatsu photomultiplier. The experimental I(V) curve is shown in Fig. 1. The solid (dashed) line represents the current measured with (without) (a)

The terms appearing in the set of equations are: the electron and hole injection rates Gn and Gp (taken from experimental I(V) measurements); the electrons and holes escape rate Rn (the same for the two particles) and the exciton and trion radiative decays R0 and RK taken from the photoluminescence measurements. Finally, the populations of electrons, holes, excitons and trions are obtained from the stationary regime for the solutions of the system (5a)–(5d).

3. Results and conclusions Our simulation is performed for a symmetric n–i–n GaAs–Al0.35Ga0.65As DBRTD grown by molecular beam

X –/X0 Intensity Ratio

0 TK Z bðnn0 K nKÞ:

30

Current (mA)

where a is the exciton creation/annihilation rate and n, p and n0 are the exciton, electron and hole populations. One of the formation/dissociation mechanisms for trions is the interaction between excitons and electrons, represented by the reaction XK% eC X0 , and with the population balance rate given by

PL Intensity (arb. units)

2.0

(1)

4

2

0 0

5

10

15

20

25

Current (mA) (b)

X –/X0 Intensity Ratio

T0 Z aðnp K n0 Þ;

6 4 2 0 5

10

15

20

25

Current (mA) Fig. 2. Experimental (panel a) and theoretical (panel b) trion and exciton integrated intensity ratio as function of current.

1040

I. Camps et al. / Microelectronics Journal 36 (2005) 1038–1040

Table 1 Parameters used in the present simulation Parameter R_ Rn Ro Rp a b g ns Rns Gn Gp

Value

Unit 12

1.50!10 1.25!1013 8.00!1011 6.00!109 6.00!105 1.20!108 1.00!102 1.00!104 1.09!1013 2.00!1017 1.00!1013

sK1 sK1 sK1 sK1 cmK6 sK1 cmK6 sK1 cmK8 sK1 cmK2 sK1 cmK2 sK1 cmK2 sK1

than the critical value, ns, the rates are diminished by a factor ks (equal 2 in our simulations [14]). In this work, we have studied the kinetic of charge buildup in DBRTD from tunneling of electrons via trion intermediate states from both experimental and theoretical viewpoints. Using a dynamical rate equation model, we have demonstrated that this trion-assisted tunneling mechanism is terminated when trion complexes are dissociated either by thermal excitation or by scattering with free carriers injected into the quantum well.

Acknowledgements the laser light. As can be seen, with light on there is an extra peak located before the main electron tunneling resonance. This extra peak is associated to scattering mediated trion assisted dissociation mechanism, which becomes effective when a critical density of injected electrons, ns is reached. The inset shows the measured light emissions for different bias. Each PL spectra is fitted with two Gaussians from which the radiative decay rates (from the FWMH) and the exciton and trion populations (from the peaks area) are determined. Panel a of Fig. 2 shows the measured trion to exciton population ratio versus current. In panel b, the calculation made with the results obtained solving system (5a)–(5d), using the parameters listed in Table 1. It is worth noting the great similarity between features in the simulated results and in the experimental curves. For example, with this set of parameters we can reproduce not only the sharp transition in the XK/X0 versus current curve, but also the shape of trion and exciton populations as a function of the total current in the sample. The discontinuity presented in Fig. 2 (panel b) is obtained when a change in the scattering rates (a, b and g) is introduced in the simulations, as explained next. The trion-free electron scattering was taken into account by assuming a change on the exciton and trion formation rates without (dashed line) and with (solid line) scattering. In fact, the scattering rates depend on the free electron density [13]. In our model, if the electron density is higher

The authors are grateful to the Brazilian agencies FAPESP and CNPq for financial support.

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