AlGaN heterostructures

MATERIALS SCIENCE & EHCINEERINC

B

Materials Science and Engineering B46 (1997) 79-83

Optical and electrical properties of 2-dimensional GaN/AlGaN heterostructures

electron gas in

H. Alause a,*, W. Knap a, S. Contreras Azema a, J.M. Bluet a, M.L. Sadowski b, S. Huant b, J. Young c,mM. Asif Khan c, Q. Chen c, M. Shur d ’ Groupe

a”Etmles des Ser,licor?n’ltctenrs, University Montpellier 2, C.N.R.S. UMR357 Place E. Bataillon, 34095 Montpellier, France b Grenoble High Magnetic Field Laboratory, MPI-FKF cud CNRS, BP 166, 38042 Grenoble, France ’ APA Optics Inc., 2950 N.E. 84th Lane, Blake, MN 55434, USA * Deparment of Electricnl Engineering, Unicersity of ??rgilzia, McCormick Road, Thornton Hall, Chtrrlottesdle, VA 22903-2442, USA

Abstract

Cyclotron resonancestudiesof two-dimensionalelectronsconfined at the GaN/AlGaN interface are presented.The value of the ZD-electron

cyclotron

mass is determined

and discussed in view of non-parabolicity

effects. The influence of non-parabolicity

is

enhancedby the spatial confinementof electronsand is calculated in the triangular well approximation. After subtraction of non-parabolicity corrections, the samemass0.226~ with 2% precisionis obtained for 2D and bulk electronsin GaN. 0 1997 Publishedby Elsevier ScienceS.A. Keyu,ords:

Semiconductors; Heterojunctions; Cyclotron resonance; Electronic band structure

1. Introduction In spite of the fundamental technological interest in

GaN based devices [l], little is still known about the basic properties of the material, including a precise determination of the electron effective mass. Most of the results reported up to now come from combined optical and transport measurements [2,3] and, only recently cyclotron resonance (CR) experiments on conduction band electrons in GaN films [4] and GaN/AlGaN heterojunctions have been reported [5,6]. In this work, we present cyclotron resonance and magnetotransport experiments on a two-dimensional electron gas confined at the GaN/AlGaN interface. High sample quality allowed the observation of well resolved cyclotron resonance (CR) absorption and quantum Hall effect (QHE) plateaus. Calculations of the complete magneto optical response of the multilayer sample structure show that all observed spectra can be well reproduced by the superposition of a single CR line and an interference pattern due to the sapphire substrate. We calculate the energy levels in the het-

erojunction and estimate the effective mass enhancement due to the non-parabolicity. We show that even in a wide band-gap semiconductor like GaN the effect of non-parabolicity can be important-especially for 2D electron gas.

2. Experimental details

We have used sample deposition

and processing tech-

niques as described in [7]. The sample structure is

shown in the insert of Fig. 1. On similar HFET structures previous investigations [7] demonstrated the existence of a two-dimensional (2D) electron gas of surface density 10” to lOI crnw2 and mobility around 10’ cm2 V- ’ s - l at the GaN/AlGaN interface. Our CR measurements have been performed at 2 K in a magnetic field ranging up to 13 T. The intensity of the unpolarized infrared radiation transmitted through the sample was measured using a Fourier transform spectrometer connected, via a waveguide system, to a superconducting coil cryostat. Most of the spectra were taken in the frequency range 30-250 cm-’

* Corresponding author.Tel.: + 3367144608; fax: f 3367143760; e-mail: [email protected]

tion l-3 cm-l. Spectra taken with high resolution showed interference pattern coming from sapphire sub-

0921-5107/97/$17.00 0 1997 Published by Elsevier Science S.A. All rights reserved. P//SO92J-5107(96)01936-S

at resolu-

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strate. For lower resolution 3 cm -I, the spectrometer light had shorter coherence length and the interference pattern was smeared out. Most of the measurements were performed at constant magnetic field applied perpendicularly to the sample surface. In order to eliminate all spectral features which were not related to the magnetic field B, the transmitted intensity T(B) was systematically normalised to the reference value T(0) collected at zero magnetic field.

3. Results and discussion

2.0

Results for two samples grown in slightly different conditions are shown in Fig. 1. For convenience we display the normalised difference [I - T(B)/T(O)]. In a tist approximation we take low resolution spectra for which we can neglect the interference pattern due to the sapphire substrate. In this case, the CR absorption can be described in a simple model which considers a purely two-dimensional electron gas located between the vacuum and a dispersionless polar medium [8]. This gives: l _ -=W) T(O)

g’r 1+ n

(1)

where n is the refractive index of the substrate and ~~ is the real part of the reduced dynamic conductivity: 1 Ne’z 1 G(0, WC)= -= (2) 1 iT,(W - WC) w m, where o, = eB{m, is the cyclotron frequency, m, the effective mass, N, the surface carrier density and T, the scattering time. Eq. (1) holds for the transmission of an unpolarized light under the assumption that the reduced dynamic conductivity is much smaller than (1 + n). In this case, the CR absorption can be approximated by Lorentzian line for which w, determines the peak position, z, the linewidth and N, the surface under the absorption line. The values of this parameters obtained for the two investigated samples (see Fig. 1) are as follows: Sample A

40

60 Wavenumber

80 in cm-l

100

120

Fig. 1. CR absorption for two different samples with GaN/GaAIN heterojunctions. Insert: samples structure.

performed. First we measured CR absorption for magnetic field inclined by 30” with respect to the direction normal to the sample surface (growth direction). For 2D gas the CR line should be shifted to lower frequencies by a factor cos 30. The result is shown in Fig. 2. In the second experiment four indium contacts were alloyed to sample 3 and magnetotransport measurements were performed simultaneously with the CR measurements. The results are shown in the inset of Fig. 2. Well resolved quantum Hall effect plateaus were observed. Both experiments show 2-D character of electron gas. Concentration and mobility obtained from magnetotransport measurements for sample B are: Li=3900cm2V-‘s-l

and

N,=4.6

x lO’“cm-‘.

They are in rough agreement with values obtained from CR experiment. Differences between transport and CR determined concentration and mobility can be due to existence of parallel conduction by low mobility carriers. Details of the magnetotransport measurements are reported in independent work [see paper by S. Contreras et al. in this conference].

B tilted 30” p = 40.6 cm”

o, = 42.1 cm-‘, T, = 0.35 ps

and

N s = 3 ’ 1 x 10’2cm-2

and

N s =20x.

and Sample B 0,=43.1

cm-‘, 0,05

2, = 0.65 ps

10’2cm-2

This approximative value of scattering time corresponds to a mobility of ;c (sample B) = 4800 cm2 V - ’ s - I. In order to check whether our CR absorption is really due to 2D electron gas, two additional experiments were

0.00

’

40

1

1

1

J

60

80

100

120

Wavsnumbsr

in cm“

Fig. 2. Cyclotron resonance and quantum Hall effects: Comparison of results for perpendicular and tilted magnetic fields.

H. Alause

n

A

Applied

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to higher number of experimental points. In Table 1, we give a comparison of the results of this work with results of other authors: for highly doped (10’g-1020 cm - 3, bulk samples of [3], a lightly doped (1 016 cm - 3, GaN epitaxial layer of [4] and heterojunctions of [5]. The experimental results listed in the first column of Table 1 concern GaN electron systems with different

field (in T)

Fig. 3. Comparison of normalized experimental spectra with theoretical simulations taking into account the full interference pattern. For clarity, all theoretical spectra are shifted IO”% downwards along the Y axis.

To interpret performed

the CR data more precisely, we have

a complete

calculation

of the magnetooptical

response of our multilayered system (see inset Fig. 1) by using the standard transfer matrix method [lo]. For an N layer system, the final infrared transmission spectrum can be modelled by using the product of N elementary matrices which characterise the optical response of the N successive layers. In our case the general approach can be very much simplified because, in the range 30-200 cm- ‘, all resonant phonon contributions can be neglected. This is true for GaN, GaAlN, and sapphire (see for instance [2,11]). In this case all the complex values of the refractive index reduce to the same static dielectric constant E= 9.5. This is true for all layers except the 2D gas, whose magneto-optical properties are described by the dynamic conductiviry (Eqs. (1) and (2)). Theoretical and experimental spectra are compared in Fig. 3. The calculations reproduce well both the interference and CR absorption features. Generally the fitting parameters are w. 2, and N,. However, we find that z, and N, do not depend on the magnetic field. Thus, in fact o, was the only free parameter when fitting the spectra for different magnetic fields. For fields higher than 10 T, w, was determined with a precision equal to or better than 1 cm - l. We have not observed any indication of the line broadening or level crossing as reported in [S]. The cyclotron frequencies have been plotted as a function of the magnetic field in Fig. 4. The solid line assumes a linear dependence and was obtained from a least mean square fit method. It corresponds to an average experimental effective mass: m, = 0.236n1,. We estimated the error of this average effective mass to be not higher than 1%. This error is mainly due to approximation of CR absorption by a lorentzian line which is not strictly valid for data at low magnetic fields. The precision of determination of ~1, is increased with respect to our earlier results reported in [q owing

40

60

80

100

120

Ii0

160

100

60

260

WC

100i B=12T.y

i0

Ii0

80

100

ii0

140

160

LI B=8TAA

180 200

e

80 1 40

60

80

100

120

140

160

180

200

Wavenumber (cm1 ) Fig. 4. The cyclotron frequency as a function of the magnetic field. The results obtained with both samples are given. The full line is a least mean square fit.

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Table 1 Comparison of values for m, and m,

Ref. Ref, Ref. This

[3] [4] [5] work

0.22 0.220 0.230 0.236

0.21 0.220 0.219 0.226

= 90/o % 2% 252%

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spect to the bottom of the conduction band is relatively high and makes the non-parabolicity correction necessary. In the simple two-band approximation, increase of the effective mass due to non-parabolicity can be written as \

carrier density and spatial confinement. In order to compare them one has to subtract the corrections of the effective mass for non-parabolicity effects.

4. Non-parabolicity corrections

The experimental effective mass of 2D electrons is a few percent higher than that found for bulk electrons in a lightly doped epitaxial layer (0.22n7,) [4]. Below we will show that part of this difference can be explained by non-parabolicity effects. Once the sheet carrier density is known, we can use a triangular well approximation [lo] to find the potential distribution profile shown in Fig. S(a). Non-parabolicity effect for both samples was evaluated with N, = carrier concentration of sample A, 3.1 x lOI cm-’ because the diffeEence of non-parabolicity corrections between the two samples is inside the error of the triangular approximation. First electric level E, is located 125 meV above the bottom of the conduction band and the Fermi energy is about 30 meV higher. As a consequence the mean energy of electrons with re-

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%I

(3)

where Eg is the energy gap, ??J,~ is the mass at the bottom of the conduction band and HZ,(E) is the mass of carriers with energy E with respect to the bottom of the conduction band. To get a value of E for the two-dimensional gas, one has to add to the Fermi energy the kinetic energy due to confinement. For a triangular well the mean energy of electrons at the first eIectric subband can be estimated as E,/3 where E, is the energy of the first electric subband [9]. The factor 3 takes into account the fact that electrons are not located at the interface but their distribution has a maximum at distance, zO, from the interface (see Fig. 5(a)). Calculating & in triangular well approximation for GaN with carrier surface density ranging from 10” to 10” cm-‘, we estimated the non-parabolicity correction to the effective mass according to Eq. (3) (E, = 3.5 eV). The results are presented in Fig. 5(b). One can see that, for surface carrier concentrations higher than IO” cm B-2 the non-parabolicity corrections are of the order of a few percent. For both our samples we estimate E = 75 meV and deduce a non-parabolicity correction of about (5 2 I)%. The carrier concentration in the heterojunction of samples of [5] are estimated to be very similar to that of our sample. This is because the scattering time (T, = 0.2 ps) and the amplitude of the CR absorption (1 - T(B)/ T(0) = 0.1) are close to the ones found in our experiments (see Eq. (1) and Eq. (2)). Therefore, the same non-parabolicity correction of 5% was used. For the highly doped bulk samples of [I] one can take E equal to the Fermi ener,T (SO meV). Non-parabolicity correction can be neglected for the GaN epitaxial layer of [4] because for small electron concentration (10’k cmT3) E is negligible with respect to Eg The values of the effective masses after subtraction of non-parabolicity are collected in column 2 of Table 1. All effective masses are the same within the experimental error. We estimate that non-parabolicity corrections increase the error of determination of effective mass 1~~ by about 1%.

5. Conclusion Fig. 5. (a) Potential profile obtained using a triangular well approximation (see text). (b) Non-parabolicity correction to the 2D effective mass as calculated for a triangular well according to Eq. (3).

In conclusion, cyclotron resonance and magnetoresistance experiments on 2D electrons confined in GaN/AlGaN heterostructure have been performed. They

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confirmed the 2-D character of the electron gas confined at GaN/AlGaN interface. Determination of the carrier density and the effective mass allowed the calculations of the potential distribution and energy levels in the heterostructure. The differences between the values of effective masses found by different authors were explained by non-parabolicity effects due to different carrier densities and spatial confinement. A comparison of all existing results shows that after subtracting non-parabolicity corrections, within experimental error, the effective mass for both 2D and bulk electrons in GaN is the same.

Acknowledgements We would like to thank the authors of [5] for sending us a preprint of their paper prior to publication. We thank also M. Dyakonov for illuminating discussions and J. Florentin for technical assistance in experiments.

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