Concentration dependent electron distributions in heavily Si-doped GaAs

Solid State Communications, Vol. 99, No. 8, pp. 571-575, 1996 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0038-1098/96 S12.OO+.C4

PII SOO38-1098(96)00221-9

CONCENTRATION

DEPENDENT

ELECTRON

DISTRIBUTIONS

IN HEAVILY Si-DOPED GaAs

Nam-Young Lee,” Jae-Eun Kim,” Hae Yong Park,” Dong-Hwa Kwak,b Hee-Chul Leeb and H. Lime ’ Department of Physics, Korea Advanced Institute of Science and Technology, Taejon 305-70 1, Korea b Department of Electrical Engineering, Korea Advanced Institute of Science and Technology, Taejon 305-701, Korea ’ Department of Electronic Engineering, Ajou University, Suwon 442-749, Korea (Received 19 January 1996; accepted 3 April 1996 by M.F. Collins)

Photoluminescence spectra of heavily Si-doped GaAs grown by molecular beam epitaxy (MBE) were investigated at 20K as a function of electron concentration. We found that the two peaks in the electron populations of the conduction band and the donor band, respectively, merge as the doping concentration increases, and can not be distinguished at the electron concentration of the order of 1018cmp3. Copyright 0 1996 Elsevier Science Ltd Keywords: A. semiconductors, luminescence.

D. electronic

1. INTRODUCTION Heavily-doped GaAs and/or Al,Gat_,As epilayers are very important for device applications such as HBT [l-3] and HEMT 14, 51, and for the fabrication of the non-alloyed ohmic contacts [6]. The heavy doping, however, produces some changes in the properties of the semiconductor such as the tail formation of density-of-states [7], the increase (or decrease) in the interband transition energy [8,9] and the impurity band merging with the adjacent bands [lo]. The band tail, formed by the merging of the impurity band with the main band, is dependent on the defect concentration and temperature as well [l 1, 121. The formation of the band tail in heavily-doped GaAs can be easily observable by the existence of the strong below-gap absorption [13] and the rather broad emission peak just below the band gap energy in the photoluminescence spectra [14-161. We have also reported that the increase of the below-gap critical energy in the photoreflectance spectrum of heavily Si-doped GaAs should be related to the donor-band merging [17]. However, the detailed process of how the impurity band merges with the conduction band has not been experimentally investigated yet. The lack of the experimental observation on the band merging behavior is due to the fact that one usually observes the electron transitions

band

structure,

E.

predominantly from the defect band or from the conduction band depending on electron concentrations. In this study, we present the direct observation of how the donor band merges with the conduction band, using the photoluminescence (PL) spectra of Si-doped GaAs at low temperature.

2. EXPERIMENTAL Samples were specially prepared by molecular beam epitaxy (MBE), so that the intervals of doping level in the range of 1 x 1017 to 1 x 10’8cm-3 are small enough to examine the process of band merging. An intrinsic GaAs buffer layer of 1 pm thickness was grown on a (10 0) oriented semi-insulating GaAs substrate, then a Si-doped epilayer with thickness of 1 pm was grown on the buffer layer. The electron concentration of the samples was determined by Hall measurements using the van der Pauw technique at room temperature, and it ranges from 1.0 x lOI to 4.2 x lOI cme3. For the PL measurements, the samples were cooled in a cryogenic system (Air Products lR02-A displex) to about 20 K and excited by the 488 nm line of an Ar-ion laser with an intensity of 0.4 W cm-2. A vibrating mirror attached to a 75 cm monochromator (Spex 750M) enabled us to measure

571

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IN HEAVILY Si-DOPED GaAs 0

Vol. 99, No. 8

Pl

l

P2

-

P3

0

P4

0

00 0 oO~o 9

1.46 I 1.40

1.44

1.48 Energy

1.52

1.56

(eV)

0

l++*+o+

I

I

o *

, I I,,,,,

IO”

c lo=

Electron

Concentration

1o19 (cms3)

Fig. 1. Photoluminescence spectra of Si-doped GaAs at 20 K in the region of electron concentration where the donor band merges with the conduction band.

Fig. 3. Energy variation of photoluminescence peaks of Si-doped GaAs at 20 K. For the doublet P2 only the peak near 1.514eV is indicated.

the wavelength-modulated PL and conventional PL spectra, from which the peak energies were read.

energies. The peak positions observed in all the samples are determined from the wavelength-modulated PL spectra (see Fig. 2) and plotted in Fig. 3 as a function of electron concentration. Note that the peak centers of Pl and P3 shift to the higher-energy side as the electron concentration is increased, while those of P2 and P4 remain unchanged. After a brief discussion on P2 and P4 peaks, we will concentrate our discussions on Pl and P3 peaks. The P2 peaks at 1.5 14 eV and 1.511 eV are known to be due to the bound exciton transitions from the Si-doped epilayer at low doping [6, 141.This exciton state is difficult to produce in the samples of rather high electron concentration because of screening effects [18]. Thus, it is clear that this peak is coming from the exciton transitions in the buffer layer, since the thickness (1 pm) of the epilayer is comparable to the diffusion length of the photogenerated minority carriers [19]. The P4 peak at about 1.49 eV can be attributed either to a donor-toacceptor (DA) transition [15, 16, 181or to a PL signal which travelled to the back surface and was reflected to the front thus adding to the main peak [20]. The latter was recently described well by Szmyd and Majerfeld for heavily Se-doped [21] and C-doped [22] GaAs samples. The PI peak is due to the band-band transition, as can be easily seen from the increasing behavior of the peak energy (Burstein-Moss effect) [8,9] in Fig. 3. We should note here that we do not specify whether the transition occurs from the conduction band to the valence band or to the acceptor-like states. But the acceptor-like states may be more probable [ 15, 181. In the conventional PL spectra of Fig. 1, the energy of the P3 peak is also increasing with electron concentration

3. RESULTS AND DISCUSSION Figure 1 shows some typical PL spectra of Si-doped GaAs samples for various electron concentrations and Fig. 2 some wavelength-modulated PL spectra. Four peaks can be seen in all the spectra and we will label them Pl, P2, P3 and P4, respectively, in the order of

1.46

1.50 Energy

1.54

I .58

(eV)

Fig. 2. Wavelength-modulated photoluminescence spectra of Si-doped GaAs at 20K in the region of electron concentration where the donor band merges with the conduction band.

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DISTRIBUTIONS

and then the peak disappears by merging with the Pl peak at the doping concentration of the order of 10’8cm-3. We can thus imagine that either the Pl peak is dominant with the marginal P3 peak or the P3 peak is dominant with the marginal Pl peak after the Pl and P3 peaks merge together. The question, which of the two would really occur, can be answered by examining the behavior of the two peaks, in detail. The PL intensity of a heavily n-doped sample can be described as follows. Using the electron energy E relative to the final state, Z(E) - %%(E)IMif12,

(1)

where D(E) is the density of states in the conduction band including the donor band and f(E) the well known Fermi-Dirac distribution function of electrons given by f(E)

1 = 1 + exp[(E - Ef)/kT]

’

(2)

where Ef is the Fermi energy. Mir is the matrix element for electron transition which may be considered to be constant in energy, since we are dealing with the energy range of a few tens of meV. Then so that the electron concentration Z(E) - D(E)f(E), per unit energy becomes maximum at the peak energy of PL spectra. It is well known that the energy level of isolated Si atoms lies at about 6 meV below the conduction band minimum [23]. The carbon atoms, which are known to be the most common contaminant acceptor in MBEgrown samples [6, 15, 161, form their energy level at about 27meV above the valence band [23]. If the P3 peak is due to a DA transition, it must appear at about 33meV below the band gap energy at n = 1.0 x lOi cmp3. As can be seen in Fig. 3, however, this peak appears at about 17 meV below the Pl peak energy. Since the Fermi energy, under the assumption of parabolic band, is located at 12meV above the conduction band minimum for this dopant concentration at 20 K, the Pl transition is determined not by the conduction band minimum alone but by the combined effect of density of states and the Fermi energy. Therefore, the energy difference between the Pl and P3 peaks should be 18 meV rather than 6 meV. We thus believe that the P3 peak is due to the transition from a donor band to the valence band or to the acceptor-like states [15, 181.The merging of Pl and P3 peaks must be the direct evidence of the merging of the energy locations corresponding to the maxima of the electron populations in the conduction band and the donor band, respectively. If we look very carefully at the wavelengthmodulated spectra of the samples of n = 1.12 x

IN HEAVILY S&DOPED GaAs

573

lOi cme3 (Fig. 2), we can still find the very faint trace of the P3 peak and read the peak energies of 1.534 eV and 1.522 eV for the Pl peak and P3 peak, respectively. Using these peak energies, the conventional PL spectrum of this sample was deconvoluted and it was found that the intensity ratio of the Pl to the P3 peak is about 1 to 3. We did the same thing for all the samples of electron concentrations less than n = 3.7 x 1018cme3 where the two peaks are no longer separated. The intensity ratios of these two peaks are about 1 to 3 for the samples larger than n = 5.1 x 1017cme3. This means that the Pl peak never becomes weaker and never disappears altogether, either. The intensity ratio of the PI to the P3 peak clearly shows that one of the Pl and P3 peaks is not absorbed into the other, but two peaks merge with each other. The wavefunction of a donor will overlap with those of neighboring donor atoms if they he within the Bohr radius of each other, which is of the order of 100 A in GaAs. The weak overlapping at relatively low doping will split the isolated donor levels localized at &i below the conduction band to form the donor band. But the strong overlapping at heavy doping will cause the donor band to merge with the conduction band. The volume radius, occupied by one donor atom, is about 134 A at n = IO” cmp3 and 62 A at II = lOi cmp3. We may thus say that the donor band merges with the conduction band at the concentration of mid-1017 cme3. From a theoretical calculation, Lowney has shown that a merged band is already formed at 20 K even for an electron concentration of 1 x 1017cmp3 [l 11. Therefore, the separated Pl and P3 peaks do not indicate that the defect band is separated from the conduction band, but that the electron population has two maxima, one in the donor band and the other in the conduction band, as we have suggested above. While the donor band is merging with the conduction band, the position of the Fermi level (and thus the positions of Pl and P3 peaks) is expected to increase slowly as the electron concentration increases, due to the increasing band gap narrowing effect by the donor band formation. In Fig. 3, this phenomenon is clearly reflected by a rather slow slope in the increase of Pl peak energy until an electron concentration of about 7 x lOI cm-3. Borghs et al. have suggested that the intensity of the P3 peak increases during the band merging, while the Pl peak, as a shoulder on the high-energy side, becomes weaker and broader with increasing electron concentration [ 161. This shoulder, which is often called Mahan peak, is due to the enhanced optical transition probability near the Fermi level. However, as we have mentioned earlier, the Pl peak and P3 peak have

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Vol. 99, No. 8

increases. This fact again rules out the possibility of the Pl peak to be the Mahan peak. 4. CONCLUSION We have studied the behavior of the low temperature PL spectra of MBE-grown heavily S&doped GaAs varying the doping concentration. The energy of the P3 peak, which is related to the transition between the donor band and the valence band or the donor band and the acceptor-like states, was increasing with electron concentration. The energy value of the maximum electron population in the donor band is observed to merge with that in the conduction band at the order of lo’* cmm3 electron concentration. I

1.44

I

1.48 Energy

I

1

1.52

I

I 1.56

(eV)

Fig. 4. Temperature behavior of photoluminescence spectra of n = 7.4 x lOI cmm3. The Pl and P3 peaks are denoted by solid down-arrows and open downarrows, respectively.

Acknowledgement - This work was supported in part by the SPRC at the Jeonbuk National University.

REFERENCES 1. 2.

nearly constant ratio in their intensity. This constant ratio means that the electron-occupied states in the donor band increase with nearly the same rate of those in the conduction band. Due to the increased density of states in the donor band for a higher energy [l 11, both the Pl peak and the P3 peak must grow in intensity and get broader and finally overlap as the electron-occupied states in the donor band penetrate the conduction band. This is manifested by the overlap of the two maxima of the electron distribution at the concentration of n N lOI* cmp3. We should also note here that the modulated spectra in Fig. 2 clearly show the lesser prominence of the P3 peak compared to the Pl peak with increasing electron concentration. This may rule out the possibility that the Pl peak is related to the Mahan effect. Finally, if the Pl peak originates from the Mahan effect, then we should expect that this peak becomes weaker and broader with increasing temperature, because the Fermi level will be less well-defined at higher temperatures. Figure 4 shows the temperature dependent behavior of the PL spectra of n = 7.4 x 10” cme3. This sample is believed to show more clearly the competitive nature between the donor band and the conduction band, since the Fermi level seems to end, around this concentration, to compete with the band gap narrowing due to the donor band formation. It can be clearly seen from Fig. 4 that the Pl peak becomes larger in intensity and broader, and the P3 peak disappears, as temperature

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