GaAs multiple quantum well p-i-n structures by photoreflectance

Microelectronic Engineering 43–44 (1998) 171–177

Direct determination of the piezoelectric field in (111) strained InGaAs / GaAs multiple quantum well p-i-n structures by photoreflectance a a, b ˜ b, ´ ´ b , E. Munoz S.A. Dickey , A. Majerfeld *, J.L. Sanchez-Rojas , A. Sacedon c c d ´ , M. Aguilar , B.W. Kim A. Sanz-Hervas a

Department of Electrical and Computer Engineering, University of Colorado, CB425, Boulder, CO 80309, USA b ´ , Ciudad Universitaria, 28040 Madrid, Spain E.T.S.I. Telecomunicacion c ´ Electronica ´ ´ Electronica ´ y Tecnologıa , 28040 Madrid, Spain Deptos. Ingenierıa d Electronics and Telecommunications Research Institute, P.O. Box 106, Yusong, Taejon, 305 -600, South Korea

Abstract The photoreflectance (PR) technique has been applied to a p-i-n structure at room temperature containing InGaAs / GaAs multiple quantum wells to directly obtain the strain induced piezoelectric field and other critical parameters of the structure which was grown by molecular beam epitaxy on a (111)B GaAs substrate. It is shown that by this technique it is possible to measure the barrier field in the intrinsic regions of the diode through the Franz–Keldysh effect as well as the optical transition energies between all the confined electron and hole states in the wells. Structural parameters such as the well and barrier widths, length of the intrinsic region and InGaAs composition were determined from high-resolution X-ray diffractometry. As the p-i-n diode has a well defined built-in potential, by using this value in conjunction with a comprehensive characterization of the sample it is then possible to determine accurately the piezoelectric field in the wells. The measured value is compared to previously reported values. 1998 Published by Elsevier Science B.V. All rights reserved. Keywords: (111)B InGaAs / GaAs multiple quantum wells (MQW); Piezoelectric field; Photoreflectance; Interband optical transitions

1. Introduction Because of the need for fast low-threshold lasers and other optoelectronic devices much interest has been generated in studying the (111)B strained In x Ga 12x As / GaAs material system. Due to the larger decoupling of the heavy and light hole valence bands by the strain and the improved confinement produced by the larger heavy hole mass in the k111l growth direction, efficient laser operation from a reduced threshold current is expected [1,2]. A fundamental property of k111l strained In x Ga 12x As / *Corresponding author. Fax: 11-303-492-2758. 0167-9317 / 98 / $19.00 1998 Published by Elsevier Science B.V. All rights reserved. PII: S0167-9317( 98 )00160-9

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GaAs structures is the presence of an internal piezoelectric field which provides an important parameter for new device applications. It has been found [3] that the evolution of the Inx Ga 12x As piezolectric constant e 14 with In fraction has significantly lower values than those expected from the linear interpolation of the binary constituents GaAs and InAs. On the other hand, this material system, particularly for the k111l crystal directions, has not been studied as extensively as others such as (001) AlGaAs / GaAs which is essentially unstrained. Consequently, there are important material parameters such as band discontinuities and effective masses in both the conduction and valence bands which are not yet well established. Only recently, advances in growth techniques have allowed the fabrication of structures with excellent interface and compositional quality in the k111l orientation [1,4,5]. Thus, it is timely to obtain accurate values of the piezoelectric constant for the InGaAs alloys at different temperatures. The room temperature photoreflectance (PR) technique for measuring modulated reflectance has been used to characterize both bulk materials and quantum confined structures [6]. Recently, Tober et al. [7] used a related technique, electroreflectance, to evaluate the polarization field within the well region of an AlGaAs / InGaAs p-i-n structure, while Shen and Dutta [8], and Berger et al. [9] used undoped GaAs / InGaAs wells on either an n or p substrate. The first method requires fabrication of devices and the second relies on the comparison of the (111) sample to a (001) reference sample, and, thus, an accurate determination of the Fermi level pinning at the surface is needed. As the k111l InGaAs / GaAs structures often show nonideal interfaces and their structural properties depend on the thickness of the InGaAs, it is desirable to have a direct measurement technique to determine the piezoelectric field in the structure, particularly at room temperature. In this work the PR technique is used for the first time to study an InGaAs / GaAs multiple quantum well (MQW) p-i-n sample. By analyzing the Franz– Keldysh oscillations (FKOs) which originate from the intrinsic GaAs regions the barrier electric field within the structure can be accurately obtained. High-resolution X-ray diffractometry (HRXRD) was employed to obtain the main structural parameters for the sample. From the analysis of the electric field contributions in the wells and barriers the piezoelectric field (Ep ) and well field (Ew ) can be determined accurately if the built-in potential Vbi is well defined (Fig. 1). These field values are used to obtain the MQW potential profile and thereby the interband optical transition energies can be

Fig. 1. Potential distribution of the conduction band for the MQW structure in the intrinsic region of the p-i-n diode showing the effect of the piezoelectric field.

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calculated. A comparison of the calculated transitions with those experimentally deduced from PR provides an important self-consistency check.

2. Experimental In this work we studied a p-i-n GaAs diode with a 10-period InGaAs / GaAs MQW centered within the intrinsic region. The sample was grown by solid-source molecular beam epitaxy (MBE) on an n 1 (Si-doped) GaAs (111)B substrate misoriented 18 towards [100]. The growth temperature was 5008C and the V/ III beam equivalent pressure ratio was 30 [5]. The HRXRD study was performed with a Bede D 3 diffractometer using Cu Ka 1 radiation after four asymmetric 022 reflections on the (011) 17.658-off surfaces of two channel-cut collimators. The sample was measured at different azimuthal orientations by recording 333 and h224j6( 1 : glancing incident; 2 : glancing exit) u /ku scans, with a detector-to-sample angular ratio k depending on the reflection and azimuthal orientation of the sample. The PR measurements were made using tungsten light passed through a double pass ˚ was used as the pump. monochromator as the probe beam, while a chopped Ar 1 laser tuned to 5145 A The reflectance signal was detected by a Si diode with a longpass sharp glass filter (Corning 3-68) placed at the collection lens to cut off the laser beam. Both optical intensities were kept low (1 mW for the laser) to prevent photovoltaic effects and maintain small-signal operation.

3. High-resolution X-ray diffraction measurements To interpret the HRXRD measurements we used a recently developed simulation model capable of computing any reflection regardless of the substrate orientation [10]. Pseudomorphic strained layers grown on misoriented substrates exhibit an asymmetric lattice distortion which must be considered to avoid misleading interpretations of the diffraction profiles. Accordingly, each diffraction scan was fitted independently using the exact Miller indices for the surface and reflecting planes. In this way, we obtained a set of structural parameters that provided the best fit to all measurements. The diffraction profiles showed distinctly the main satellites due to the MQW periodicity. The angular split ˚ From the between adjacent satellites enabled us to determine a period thickness LP 5 33162 A. position of the zeroth order satellite we obtained an average In fraction in the period kxl 5 4.47360.004%. The barrier width Lb , the well width Lw and the well In content x w were calculated in a straightforward manner by taking into account the growth times of wells and barriers during the ˚ Lw 5 86 A ˚ and x w 5 17.3%, corresponding to a MBE process. Accordingly, we deduced Lb 5 245 A, 23 strain in the growth direction ´z 5 18.3 10 . On the other hand, the oscillations coming from the total MQW thickness were not very clear. Besides, we observed a minor tilt of about 10 s of arc between reflections with opposite azimuths along the miscut direction. These two observations led us to conclude that some misfit dislocations might be present at the interface between the MQW and the intrinsic GaAs layer below it, producing a small loss of crystalline perfection and some plastic tilt of the crystallographic planes. Despite this, we did not observe a macroscopic in-plane relaxation of the strained InGaAs wells and the overall crystalline quality of the sample was good. The length Li of the whole intrinsic region of the p-i-n diode could be determined by scaling the nominal length in the

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same proportion as the variation of the MQW barrier width Lb from the nominal to the measured ˚ value. Consequently, we obtained Li 5 47006100 A.

4. Theoretical fitting and photoreflectance data reduction The electric field in the intrinsic GaAs regions can be calculated using the asymptotic representation of the Airy function [6]:

S

4 Em 2 Eg mp 5 f 1 ] ]]] 3 "u

D

3 ] 2

(1a)

where e 2 " 2 E 2b . s"ud 3 5 ]]] 2m

(1b)

In these expressions m is the number of the FKOs extrema, Em is the corresponding energy, Eg is the band gap, Eb is the electric field in the barrier and m is the reduced mass of the electron hole pair. By plotting (4 / 3p ) (Em 2Eg )3 / 2 versus m the slope of the line ( "u )3 / 2 can then be obtained and the electric field can be calculated by inserting the values of the electron and hole masses, 0.067m 0 and 0.75m 0 , respectively [4]. The quantum well transition energies E were obtained using a least squares fit to the Aspnes’ third derivative form [11]: DR ] 5 Re[Ce i w ((E 2 Ei ) 1 iG )2n ] R

(2)

where C is an amplitude, w is the phase, Ei is the interband transition or ‘‘critical point’’ energy and G is a broadening factor. In this work the exponent n was chosen as 3 as appropriate for 2-D transitions [12] which results in an excellent fit to the data. The corresponding theoretical transition energies ¨ were calculated using a finite difference solution to the Schrodinger equation for a MQW structure.

5. Results and discussion Fig. 2 shows the PR data for the sample showing clearly the FKOs which are used to extract the electric field. By plotting Eq. (1a) from the FKO data as in Fig. 3 it can be seen that the fit to the data is linear which indicates that the asymptotic approximation is valid for this sample. Using Eq. (1b) the ˚ The direction of the field is following value for the barrier field is obtained, Eb 50.598 mV/ A. obtained from the doping profile. In order to calculate the piezoelectric field, the built-in potential Vbi must be determined. Since the p-i-n is a well defined structure and we know the contact doping, the device can be simulated precisely. By taking into account the band gap narrowing of GaAs [13] due to the n 1 and p 1 contact layers a Vbi of 1.399 V at 300 K is obtained. From HRXRD we know Li and Lw very accurately, allowing the determination of the piezoelectric field Ep through the following relation:

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Fig. 2. PR spectrum of the MQW p-i-n diode showing the Franz–Keldysh oscillations and several interband transitions. Dots show the experimental results and the full line shows a theoretical fit to the data. The interband transitions derived from fitting the PR spectrum are indicated by arrows.

Li Eb 2Vbi ˚ Ep 5 ]]] 5 1.65 mV/ A, N 3 Lw ˚ and N is the number of periods. then Ew 5Ep 1Eb 51.07 mV/ A The piezoelectric constant e 14 is calculated according to:

e 9e0 e 14 5 Ep ]]] 5 0.091 C / m 2 . ] Πez 3 3 2

Fig. 3. Linear fit of the energy of the Franz–Keldysh oscillations versus the number of extrema.

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It is significant to note that the room temperature value that we obtain for e 14 is higher than the previously reported value (e 14 50.075 C / m 2 ) for the same sample from photocurrent measurements at 15 K [3]. We attribute this difference to a pyroelectric effect [7]. However, the obtained value is still much lower than the linear interpolation from GaAs–InAs at 300 K (e 14 50.14 C / m 2 ). An excellent theoretical fit to the data in the energy range 1.2–1.4 eV is obtained for the interband transitions En –HHm , indicated by the arrows in Fig. 2, using Eq. (2). From the piezoelectric field we can find the field in the well and thus the full band diagram of the device. This enables us to verify the FK analysis by calculating the energy levels in the MQW structure and by comparing those with the PR measured transitions. To compute the energy levels in the QW, we used the structural information from HRXRD along with m e 50.067m 0 , m hh 50.75m 0 , DEc 5101 meV and DEv 550 meV. The agreement between the calculated and the experimental PR transition energies is within 612 meV for all the transitions, indicating that the parameters used in the calculation such as the effective masses and band offsets are consistent at least for the In content of this sample.

6. Conclusions The combination of HRXRD and PR provides a powerful nondestructive method of characterizing InGaAs / GaAs p-i-n structures. The HRXRD technique gives very detailed structural information such as the well and barrier thicknesses, the In content of the wells and the total length of the intrinsic region. When these values are combined with the barrier field measured by PR, a direct determination of the strain-induced piezoelectric field becomes possible. It was found that the room temperature value of the piezoelectric constant (e 14 50.091 C / m 2 ) is greater than the value obtained at 15 K from photocurrent measurements on the same sample. We attribute this difference to the pyroelectric effect. The good agreement between the transition energies in the wells obtained from PR and the theoretically calculated energies suggests that the material parameters used in the calculation and the parameters derived from the field measurement are consistent.

Acknowledgements The work at the University of Colorado was supported by the Electronics and Telecommunications Research Institute, Taejon, Korea, and the NATO grant No. CRG-960094

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