Deep Level Transient Spectroscopy in Quantum Dot Characterization
© to the authors 2008
Received: 11 March 2008
Accepted: 5 May 2008
Published: 28 May 2008
Deep level transient spectroscopy (DLTS) for investigating electronic properties of self-assembled InAs/GaAs quantum dots (QDs) is described in an approach, where experimental and theoretical DLTS data are compared in a temperature-voltage representation. From such comparative studies, the main mechanisms of electron escape from QD-related levels in tunneling and more complex thermal processes are discovered. Measurement conditions for proper characterization of the levels by identifying thermal and tunneling processes are discussed in terms of the complexity resulting from the features of self-assembled QDs and multiple paths for electron escape.
Deep level transient spectroscopy (DLTS) is a technique for filtering signal transients from the emission of charge carriers at localized band gap energy levels to the conduction or valence band of semiconductors. Performing measurements for varying temperature, the method was developed to transfer data from the time domain into temperature spectra with characteristic features that can be used to identify properties of deep energy levels in semiconductors . When using DLTS to investigate emission properties of charge carriers in quantum dots (QDs), additional problems occur due to the specific properties connected with this kind of structures. Therefore, interpreting DLTS data from self-assembled QDs in the traditional way may give rise to considerable misinterpretations. One reason for this is the varying sizes of QDs, which gives rise to varying properties of most quantities associated with the different elements of the QD ensemble. Another influence on measured results is the possibility of QDs to capture a larger number of electrons, which means that multiparticle statistics must be used to analyse data.
In a series of recent papers, we have demonstrated how such properties can be taken into account and how data can be presented so that the properties of carrier emission from QD structures can be understood [2–6]. This was done by using systems where the QDs are embedded in the depletion region of a Schottky barrier and by measuring the DLTS data as a function of temperature and reverse voltage . Creating graphs as surfaces in a temperature—voltage—DLTS signal space (TVD-space) and comparing such data with theory [2–4] gives an opportunity to recognize various paths of charge carrier escape. In the present paper, we demonstrate how the statistics for electron emission from InAs/GaAs QDs is treated in order to understand experimental DLTS-data.
Electron Escape from Quantum Dots and DLTS
An example of DLTS spectra from the QD-samples specified below and investigated in the present work is shown in Fig. 1b. One notices that the curves are considerably influenced by the applied reverse voltage. This originates from a number of properties specific for QDs, which commonly are not found in DLTS measurements on deep level semiconductor impurities. Besides the energy distribution of electron states due to QD size fluctuations, a considerable tunneling contribution exists in combination with multiparticle emission, which gives rise to the metamorphosis among the DLTS curves in Fig. 1b when the voltage is varied. This motivates a more detailed emission statistics for interpreting this kind of data.
The self-assembled InAs/GaAs QDs investigated in this work have a dome-like shape with height/base dimensions in the range of 6/18 nm. This geometry has been found to give rise to two observable electron shells, one with s-character at energy distances in the range of 0.11–0.14 eV from the GaAs conduction band edge and a second shell of p-character with a corresponding energy interval of 0.08–0.11 eV .
Emission statistics for pure thermal processes, and for a combination of thermal and tunneling processes, has been developed from a starting point where the QDs were assumed to be elements of a grand canonical ensemble [3, 4]. Such a statistics must include the particular properties of the s- levels to capture two electrons with an energy level difference smaller than about 4 meV as found by theory in a Hartree-Fock and configuration interaction approximation and from experiment . For the p-electrons, only one of four possible states was considered. Here the level splitting is expected to be larger, which limits the p- emissions observable by commonly used DLTS set-ups to the state with the deepest energy position.
In Eqs. 1-3 above, c x,r is the electron capture rates, where x = s p denotes the s and p transitions and r = 1, 2 denotes the number of electrons captured. Further, Θ r is a “sticking probability” as expressed by Eq. 2 with t r labelling the time for an electron to relax from the p-level to an empty s-state. The X x,r factors are the “entropy factors” representing the change in entropy when an electron is emitted. For the present system it has been found that these factors are determined mainly by the electronic degeneracies of the QD system . The quantities e st,r and e pt are the tunneling emission rates from s- and p- states, respectively, while ΔE s and ΔE p are the energy distances from the GaAs conduction band edge to the s- and p-states, respectively. Finally, k is Boltzmann’s constant and T is absolute temperature.
Average binding energy,s- electrons
Average binding energy,p-electrons
Capture cross sections,s- electrons
Capture cross sections,p-electrons with one electron ins- shell
Capture cross section,p-electron with no electron ins-shell
5 × 10−10 cm2
Time forp tos electron relaxation (t r )
GaAs doping level in depletion region
1.4 × 1016 cm−3
The values along the vertical coordinate in Fig. 3b represent the product between a normalized energy distribution and the emission rate. The two surfaces in the three-dimensional plot, therefore, correspond to the probabilities for emitting an electron from the two energy shells, respectively, at a certain point on the bottom plane. The graphs illustrate the additional complexity involved in the emission process as a result of the varying electron energy eigenvalues, which in turn is a result of varying dot size.
In traditional DLTS experiments, the activation energies for particle emission is obtained by measuring multiple temperature spectra for different tuning conditions of the DLTS filter. This requires that the DLTS surface inTVD-space has the properties shown in Fig. 4a and b without any gradient contribution in V direction. For the surface shown in Fig. 4d, this occurs only at the “Cape”.
The samples subjected to the study contained a single InAs QD plane, which was located 0.4 μm from the Schottky contact and surrounded by barriers made of GaAs. The structures were grown by solid source MBE on (100) oriented highly doped GaAs substrates. GaAs buffer and cap layers were grown at a substrate temperature of 580 °C and were doped with Si to approximately 1.4 × 1016 cm−3. An InAs layer with a nominal thickness of 3 monolayers (MLs) was grown at 510 °C under a repeated sequence, where 0.1 ML depositions included a 2 s growth interruption under an excess of As2. For DLTS measurements, a DLS-83D system (Semilab, Hungary) equipped with a closed cycle helium cryostat was used. Schottky contacts were fabricated for DLTS investigation by evaporating gold dots of 1 mm diameter through a mechanical mask. AuGeNi ohmic contacts were evaporated on the opposite side of the samples and formed by annealing at 400 °C for 1 min. The leakage current of the prepared Schottky diodes was lower than 10−7 A for reverse bias voltages up to 6 V in the temperature range 20–80 K, which was the temperature range used in the experiment. A complementary study was carried out by means of Atomic Force Microscopy (AFM). AFM image and statistical analysis revealed that the uncapped InAs/GaAs QDs with height/base dimensions of about 6/18 nm and density of 3.5 × 1010 cm−2 exhibited remarkably low size dispersion on a level of 10% .
A number of features recognized from Fig. 5b and discussed in relation to Fig. 4 can be observed. The tunneling ridges originated froms- andp-electrons are noticed at the lower temperatures, separated by the “Tunneling Lake”, which is the minimum signal originating from tunnel emissions between the two distributions of s- and p- levels. For the higher temperatures, the two-step thermal emission can be identified as the “Thermal Slope” at the lower voltages, turning into the “Thermal-Tunneling Slope” at about V = 2 V on the farther side of the “Cape”. The theoretical correspondence, calculated by including the parameter values of Table 1, shows all the features pointed out in Fig. 5a, even if certain differences are observed in some details. However, the theoretical graph in Fig. 5b in combination with the theoretical activation plots in Fig. 3 serve the purpose of identifying the features of the experimental data.
Due to the overlap of the s and p energy distribution, pure separation of influences from the two electron shells can be done only at the lowest temperatures and the highest and the lowest voltages. This is important to be taken into consideration in tunneling transient spectroscopy, which has been proposed and used at a low temperature to probe the pure tunneling from the self-assembled InAs/GaAs QDs [10, 11]. The most serious problem results from the QD size fluctuation effect and the related width of the energy level distributions. In spite of using Gaussian fitting procedure, it makes basic difficulties in positioning signals in DLTS spectra and also in differing between the p- and s-states. As noticed in Fig. 3b, a deeper energy part of the p-state distribution and a lower energy part of the s-state distribution both contributes to the DLTS signal at the same rate window. As shown in Ref. , this causes an illusory anomaly in the dependence of p- DLTS tunneling signals on the electric field. In order to separate p- and s- influence along the temperature direction, one may either follow the “Cape”  and thus lock the measurement to the kink point in Fig. 3a or use special voltage pulse schemes .
We have demonstrated that the main electronic properties of QDs can be revealed and understood by plotting experimental DLTS spectra in a TVD-space and comparing with theory obtained from a statistical analysis. The resulting 3D/contour graphs compile tunneling and thermal processes involved in the two-level system presented. For a rigorous characterization of QD-related electron states by DLTS, measurement conditions need to be chosen such that data are collected in directions on the TV-plane where contour DLTS lines are either horizontal or vertical. However, due to overlapping energy distributions and mixed emission mechanisms, standard DLTS methodology  becomes less straightforward for finding parameters of confined QD energy states. Therefore, in order to extract QD data as presented in Table 1, fitting theory to experimental TVD surfaces gives the most reliable results.
This work was supported by the Chalmers MC2SOI project, by the Polish Min. of Science and Higher Education (project no. 3T11B00729 and 1.12.053) and by the European Seventh Framework Program through the Network of Excellence NANOSIL.
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