Spatially direct recombinations observed in multiple δ-doped GaAs layers

Superlattices and Microstructures, Vol. 23, No. 2, 1998

Spatially direct recombinations observed in multiple δ -doped GaAs layers A. Levine, E. C. F. da Silva, L. M. R. Scolfaro, D. Beliaev, A. A. Quivy, R. Enderlein, J. R. Leite Instituto de F´ısica da Universidade de S˜ao Paulo, Caixa Postal 66318, 05315-970 S˜ao Paulo, SP, Brazil

(Received 16 July 1996) Experimental and theoretical studies on n-type multiple δ-doped GaAs layers are reported. Photoluminescence is measured and compared with results of self-consistent electronicstructure calculations. A series of samples with different donor concentrations in the δ˚ were doped layer and a fixed distance between adjacent Si-doped layers (ds = 300 A) analysed. The PL spectra of the investigated samples do not show transitions involving confined electronic minibands. However, the full width at half maximum of the observed main emission band may be correlated with the calculated electronic miniband structures. c 1998 Academic Press Limited

Key words: Delta-doping, superlattices, photoluminescence.

1. Introduction Multiple δ-doped (Mδ-D) GaAs layers have been the subject of several experimental and theoretical investigations due to their technological and scientific importance [1]. A Mδ-D layer can be formed by alternating epitaxially grown material, such as GaAs, with sheets of dopant atoms. In a n-type δ-doped sample, the electrostatic interaction between the electrons released by the dopants and their positively charged core gives rise to a V-shaped potential and a degenerate electron gas. The shape of the potential well, energies and populations of the minibands will depend critically on the two-dimensional density of dopant atoms and their distribution along the growth direction, as well as on the layer-thickness between the doped planes. From the theoretical point of view, the electronic structure of Mδ-D layers has been investigated as a function of the doping period, sheet donor concentration, and spread of the impurities [2–5]. In spite of the already existent experimental data on Mδ-D GaAs structures, there is to date no detailed information about the electronic structure of such systems as derived from, for example, photoluminescence (PL) spectra [1]. Concerning PL measurements, while features attributed to confined states have been observed in the spectra of samples with widely spaced doping layers, broad structureless emission spectra have been reported for samples with closely spaced doping layers [6–9]. However, until now the correlation between the observed line width of the PL spectra and calculated miniband structure has not been clearly established. In this work we correlate the full-width at half maximum (FWHM) of the measured PL spectra with the calculated miniband electronic structure of n-type Si Mδ-D GaAs samples. Moreover, an emission band with a peak energy at approximately 1.500 eV has been observed in the PL spectra of Si Mδ-D GaAs samples with different structural parameters (doping concentration and layer spacing) and attributed, by other groups, to intrinsic Mδ-D miniband transi0749–6036/98/020301 + 04 $25.00/0

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tions [7, 8]. A similar feature is also observed in the PL spectra of our less-doped sample. Its behaviour as a function of doping concentration rules out the interpretation based on intrinsic miniband transitions.

2. Experimental The samples analyzed in this work were grown by a Gen II Mod. MBE system, in our laboratory, on EPI-Ready (100) GaAs substrates. The Mδ-D samples were grown with 50 periods and ds , the layer thickness ˚ We have investigated a series of samples with values of the Sibetween Si-doped planes was fixed at 300 A. doping concentration N D varied between 2.4 × 1011 cm−2 and 2.6 × 1012 cm−2 . Low-temperature (T = 2 K) PL measurements were carried out with the 514 nm line of an argon–ion laser as the excitation source. The emission spectra were analyzed with a 1 m grating spectrometer, detected with a S1 photomultiplier, and the electrical signal was amplified and treated by conventional lock-in techniques.

3. Theoretical calculations We have modeled the superlattice energy-band structure using self-consistent (SCF) calculations based on our sample design parameters. The theoretical model adopted by us has been currently applied to carry out SCF calculations of Mδ-D structures in Si [4] and GaAs [5]. The miniband transition energies and the theoretical cut-off energies were estimated using the following expressions [9]: E i H Hi = E gGaAs − V + εi + h i hν cut-off = E GaAs − V + E + H . T

g

F

F

(1) (2)

In these expressions E gGaAs is the fundamental GaAs band-gap energy, E i H Hi is the energy transition from the bottom of the ith conduction miniband to the top of the ith valence miniband, V is the potential depth, E F is the electronic quasi-Fermi level, εi (h i ) is the electron (hole) energy eigenvalue of the bottom (top) of the ith miniband, and HF is the quasi-Fermi level for photogenerated holes, taken to be equal to the first heavy-hole energy, h 1 . In Table 1 the values of the miniband transition energies are shown as obtained with the values of V, E F , εi and h 1 extracted from the SCF calculations.

4. Experimental results The PL spectra of the six analysed samples are shown in Fig. 1. Besides various GaAs-related emission structures which arise from the buffer and cap layer, for all samples the PL spectra also show a broad emission band (B band) which spreads above the GaAs band-gap energy. Besides the B band, in the PL spectrum of sample a (N D = 2.4 × 1011 cm−2 ) we observe another broad band (A band) convoluted with the carbon free–bound transition. It can be seen that, when donor concentration is increased, the maximum of this band shifts to higher energies, and for N D > 1.2 × 1012 cm−2 it merges with the B band. The origin of the A and B bands can be explained if we extract from each PL spectrum the values of four particular energies, edge edge edge hνA , hνAmax , hνB and hνBcut-off . The energy hνA corresponds to the intersection between the tangent to the low-energy tail of the emission band A and the background. The energy hνAmax corresponds to the position of edge the peak. The energy hνB (hνBcut-off ) is associated with the half of the maximum intensity at the onset (offset) edge of the emission band B. We assume that hνB and hνBcut-off determine the initial and final emission energies associated with the B band, and will be referred as edge emission energy and cut-off energy, respectively. edge Moreover, the difference 1E B = [hνBcut-off − hνB ] gives the FWHM of the B band. In Table 2 we present edge edge the values of hνA , hνAmax , hνB , hνBcut-off and 1E B extracted from the measured PL spectra. The criterium adopted to determine these values takes into account the intersection between adjacent band emissions. A comparison between the experimental (hνBcut-off ) and theoretical (hνTcut-off ) values of the cut-off energies

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T=2K Pexc = 10 mW cm–2

1.533 eV

f PL intensity (arbitrary units)

1.529 eV e 1.527 eV d 1.524 eV c 1.520 eV b B

A

1.515 eV

a 1.47

1.48

1.49

1.50

1.51

1.52

1.53

1.54

Energy (eV) ˚ and different nominal donor Fig. 1. Photoluminescence spectra from GaAs multiple δ-doped structures with doping period ds = 300 A concentrations N D . The letters a–f indicate the samples as in Table 1. The A and B bands are indicated.

Table 1: Theoretical values for the miniband transition energies E i H Hi in GaAs multiple δ-doped structures with different nominal donor concentrations N D . Energies are given in eV. Samples

N D (cm−2 )

E 1 H H1

E 2 H H1

E 3 H H1

hνTcut-off

a b c d e f

2.4 × 1011 7.2 × 1011 1.2 × 1012 1.7 × 1012 2.2 × 1012 2.6 × 1012

1.5172 1.5104 1.5031 1.4948 1.4865 1.4783

1.5262 1.5251 1.5239 1.5222 1.5204 1.5185

— — — 1.5343 1.5330 1.5318

1.5257 1.5304 1.5347 1.5368 1.5386 1.5405

shows a discrepancy of about 10 meV, which is due to the fact that the calculations have been done using E gGaAs (1.5192 eV) which does not take into account the band-gap renormalization effect. To compare the experimental data with the theoretical values of the miniband transition energies, we have to include the bandgap renormalization in the calculation. This can be done by subtracting the quantity 1E = [hνTcut-off −hνBcut-off ] from the transition energies shown in Table 1. The comparison between the corrected theoretical values of the miniband transition energies and the experimental data (presented in Table 2) is shown in Fig. 2. With exception of sample a (N D = 2.4 × 1011 cm−2 ), we can see in this figure that the edge emission energies of the B bands closely follow the E 2 H H1 recombination energies. Therefore, we assigned the B bands observed in the PL

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1.56

Energy (eV)

1.54 E3HH1 1.52 E2HH1 1.50

1.48 E1HH1 0

1

2

3

Donor concentration ND (×1012 cm–2) ˚ and different Fig. 2. Theoretical miniband transition energies for GaAs multiple δ-doped structures with doping period ds = 300 A edge edge nominal donor concentrations N D . The data represent the experimental values of hνBcut-off (¥), hνB (●), hνAmax (¨) and hνA (N). The lines connecting the experimental points are guides for the eyes.

spectra to emissions related with recombinations of the electrons which exist above the second miniband with photogenerated holes of the first heavy-hole miniband. It is important to observe that according to the SCF calculations, for N D < 1.25 × 1012 cm−2 the second electron miniband is localized above the δ-potential well. For N D > 1.25 × 1012 cm−2 , the second electron miniband is partially below the potential well but still has a non-negligible energy dispersion, indicating a superlattice behavior (extended electron wavefunctions). Therefore, the electronic population which gives rise to the B bands is highly delocalized in real space and can be considered as a three-dimensional electron gas (3DEG). Moreover, the radiative transition of the electrons which are above the second miniband and photocreated holes are direct in real space. It is also interesting to stress that not only the free electrons with energy above the potential well, but also those inside the δ-potential well with a superlattice behavior, participate in the emissions related with the B bands. If the B bands have the origin we are assuming, we would expect to identify the observed FWHM of the B bands with the theoretical energy differences [E F − ε2 ]. The comparison between these calculated values and the half-width of the B bands (presented in Table 2) is made in Fig. 3. A good agreement between the theoretical and experimental values is obtained, reinforcing our assumption. The widths of the B bands are larger than the theoretical values due to the fact that the electrons of the first miniband with energy above the second miniband also participate in the recombination process, contributing to the broadening of the emission band. Now we concentrate our attention on the behaviour of the observed A bands. It can be seen in Fig. 2 that, edge while the values of hνAmax are strongly dependent on the values of N D , the values of hνA stay practically constant and both of them can not be associated to any predicted theoretical miniband transition energy.

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edge edge Table 2: Values of hνA , hνAmax , hνB , hνBcut-off and 1E B extracted from the PL spectra of GaAs multiple δ-doped structures with different nominal donor concentrations N D . Energies are given in eV. 1E B is the FWHM of the B band.

hνBcut-off

1E B (meV)

1.511 1.512 1.512 1.511 1.508 1.505

1.515 1.520 1.524 1.527 1.529 1.533

4 8 12 16 21 28

1.5

2.0

Samples

N D (cm−2 )

hνA

edge

hνAmax

hνB

a b c d e f

2.4 × 1011 7.2 × 1011 1.2 × 1012 1.7 × 1012 2.2 × 1012 2.6 × 1012

1.487 1.490 1.489 — — —

1.493 1.500 1.505 1.509 — —

edge

30

25

Energy (meV)

20

15

10

5

0 0.0

0.5

1.0

2.5

3.0

Donor concentration ND (×1012 cm–2) Fig. 3. Full width at half maximum of the B band (¥) and theoretical values of (E F − ε2 ) (full curve) as a function of nominal donor concentrations N D .

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According to our SCF calculations, the first miniband has a negligible dispersion, i.e. electrons are confined in the growth direction (localized states), but occupy extended two-dimensional subbands in the dopant sheet plane. The holes in this superlattice are confined in wells, which are displaced half a superlattice period away from the confined electrons that occupy discrete states. Therefore, radiative transitions between electrons localized in the δ-planes and holes are spatially indirect and intrinsically weak. Hence we rule out the possibility that the A bands are related with recombinations involving electrons associated with the first electron miniband. Performing PL measurements as a function of increasing temperature, we observed that in the range 2 K < T < 30 K, the intensity of the A band decreases in relation to the intensity of the B band, vanishing for T > 40 K. The behavior of the A band, as a function of temperature and excitation power observed by us indicates that impurities are involved in the recombination process. Our findings indicate that the A bands are emissions related with recombinations of electrons above the second miniband with photogenerated holes bound to carbon acceptors (the main residual impurities in MBE-grown GaAs) located between adjacent (repulsive) δ-planes. The recombination transition energy from the bottom of the second miniband to the carbon level can be expressed as: E 2 A = E gGaAs −V +ε2 + H1 − E A , where E A is the ionization energy of carbon in GaAs. Therefore, the difference between the theoretical cut-off energy and the transition energy E 2 A is given by [hνTcut-off −E 2 A] = E F −ε2 +E A . According to our assumptions the theoretical values of edge [hνTcut-off − E 2 A] have the same meaning as the experimental values of [hνBcut-off −hνA ]. Using the theoretical 11 −2 values of E F and ε2 , and E A = 26 meV we obtain for N D = 7.2 × 10 cm (N D = 1.2 × 1012 cm−2 ) the value of [hνTcut-off − E 2 A] = 30.3 meV(36.8 meV). The corresponding experimental values obtained from Table 2 are 30 and 34 meV, in good agreement with these theoretical values.

5. Conclusions We have reported on the optical transitions associated with n-type Mδ-D layers in GaAs as a function of donor concentration. We did not observe radiative transitions involving confined electronic minibands. The observed radiative transitions involve only the electrons highly delocalized in real space (direct transitions), that can be considered as 3DEG. We were able to account for the spectral information with SCF calculations, and to identify the FWHM of the main emission band (B band) with the electronic quasi-Fermi level associated to minibands. Moreover, our findings indicated that the A bands are emissions associated with recombinations of electrons above the second miniband with photogenerated holes bound to carbon acceptors. We have provided evidence that these bands can not be ascribed to intrinsic miniband transitions.

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