AlAs superlattices with different miniband widths

Solid-State Electronics Vol. 37, Nos 4-6, pp. 889-892, 1994

Copyright ~ 1994ElsevierScienceLtd Printed in Great Britain.All rights reserved 0038-1101/94 $6.00+ 0.00

Pergamon

OPTICAL TRANSITIONS IN GaAs/AIAs SUPERLATTICES WITH DIFFERENT MINIBAND WIDTHS K. FUJIWARA I, K. KAWASHIMA2, T. YAMAMOTO2 and K. PLOOG 3 LKyushu Institute of Technology, Tobata, Kitakyushu 804, Japan, 2ATR Optical and Radio Communications Research Laboratories, Soraku-gun, Kyoto 619-02, Japan. 3Paul-Drude-Institut f~r Festk6rperelektronik, D-10117 Berlin, Germany Abstract--Band edge optical transitions and their external electric field effects are systematically studied in GaAs/AIAs superlattices with different miniband widths (2A) by low temperature photocurrent spectroscopy. Distinct H excitons related with saddle-type Mt critical points at the miniband top are clearly observed both for heavy-hole and light-hole excitons. Under the applied field strength F, discrete transitions due to Wannier-Stark localization are observed and it is found that their intensities of nth order Stark ladder transitions with negative indices show F - ~ and A2 dependences in agreement with the tight binding theory.

INTRODUCTION

EXPERIMENTAL

Optical transitions involved with excitons in semiconductor superlattices (SL) and quantum wells (QW) have attracted great attention[l]. One of the interesting properties of SL compared to QW is the tunabiiity of miniband widths (2A) by designing the layered structures and, as a result, controlling quantum mechanical tunnelling. From the previous studies of optical absorption in GaAs/AlxGa~_~As SL, it is known that there are various types of fine structures originating from miniband dispersions[2-5], Stark ladders[6-9], and Franz-Keldysh oscillations[10]. However, attribution of such fine structures observed by one author is not always consistent with others' data, possibly because of non-uniform sample qualities and different experimental conditions. Therefore, basic studies of optical transitions in SL and especially their relevance to miniband widths are important for understanding of the origins of the absorption spectral features. In this paper, optical absorption spectra are investigated in a series of GaAs/AIAs SL with different well and barrier parameters, thus varying the miniband width systematically, by means of low temperature photocurrent (PC) spectroscopy. Direct spectroscopic evidences are provided for the miniband dispersion effects which show excitonic effects originating from the miniband bottom (M0) and miniband top (M~) critical points. We have also studied the external field effects as a function of both field strength F and miniband width A. It is shown that the observed energies and oscillator strengths of the Stark ladder transitions are in good agreement with those predicted by the tight binding theory.

High-quality GaAs/AIAs SL samples were grown on n-type GaAs (001) substrates by molecular beam epitaxy (MBE) in a fully computer-controlled system. The nominally undoped SL layer is contained in the intrinsic layer o f p - i - n diodes[9]. Two series of seven SL samples are studied in this work. A first series consisted of AlAs barriers with a thickness of 8.6 A and GaAs wells whose width was ranged from Lz = 62.6 ,~ (No. l), 39.2 A (No. 2), 31.3 ,~ (No. 3) to 26.1 A (No. 4). Another series consisted of GaAs wells with a width L z = 31.3 A, and AlAs barriers ranged from L a = 5.7 ,~ (No. 5), 8.6 ,~, (No. 3), I 1.4 ,~ (No. 6) to 17.3~ (No. 7). The sample No. 3 is common in the two series. The SL period was measured by small-angle X-ray diffraction experiments, which were used to estimate nominal values of well and barrier parameters. The 100-period SL layers were confined between Ai04Gao.6As cladding layers in the heterostructure. PC experiments were performed around ~ 16 K in the closed-loop-helium cryostat using a combination of tungsten-halogen lamp and monochromator for excitation and a standard electrometer for d.c. detection.

889

RESULTS AND DISCUSSION

Figure 1 shows PC spectra of the SL diode samples No. I(a), No. 2(b), No. 3(c) and No. 4(d) for L, variations. Solid curves correspond to the spectra measured near the flat-band conditions (forward bias conditions), while dashed ones under a reverse bias voltage (Vb) of 10 V. In the solid PC spectra, sharp absorption thresholds are observed. The threshold

890

K. FWiWARAet al.

wavelength (energy) decreases (increases) from the spectra (a) to (d) as the GaAs well width L~ decreases. At the absorption edge a sharp peak (indicated by left upward arrows) is observed in the spectra (a)-(d) indicating excitonic effects for the optical transitions. Beside the leading absorption peak, several peaks and/or shoulders are also seen in the solid spectra of Fig. 1. A secondly sharper peak (indicated by left downward arrows) is observed next to the leading peak. Relatively broader peaks or shoulders (indicated by right arrows) are located at shorter wavelengths (higher energies). On the other hand, when the external electric field is applied along the growth z-axis, a number of new fine structures appear as shown in the dashed spectra. First we note that in the dashed curves a main steep edge appears at shorter wavelength sides of the threshold peak in the corresponding solid spectra and that the energy separation between them increases with decreasing Lz. Secondly, weaker edges are also seen in the dashed spectra of (b) to (d) at the longer wavelength. Their intensity increases with decreasing L,. The experimental results observed in Fig. 1 can rigorously be explained by the miniband dispersion

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Fig. 1. Photocurrent spectra of GaAs/AIAs SL samples at ~ 16 K; (a) No. I, (b) No. 2, (c) No. 3 and (d) No. 4. Solid spectra are corresponding to those near the flat-band conditions [forward bias of + 1.4 V except for No. I (+ 1.1 V)], while dashed ones under the reverse bias voltage of 10 V. Spectra are vertically shifted for clarity. Solid (dashed) horizontal bars are calculated wavelength ranges of valenceto-conduction subband transitions associated with heavyholes (light-holes). An inset figure shows Van Hove singularities in the joint-density of states J (E) (M0 singularity at E0i A and M~ saddle-type at E0+ A).

effects as discussed below. In the SL structure, we have a slightly different energy scheme for the optical transitions from the QW as schematically illustrated in the inset of Fig. 1. When the barrier thickness is thin enough so that the inter QW layer coupling is enhanced, we have more three dimensional characters for the subbands. That is, the miniband is formed along the growth direction whose band width 2A is basically determined by the SL structural parameters, Lz and L B. In this case we have Van Hove singularities of M0 type at the miniband bottom and of M~ type at the upper edge. In order to more quantitatively show the effects of inter-well-coupling on the transition energies, the theoretical energies of the interband transitions are calculated using the Kronig-Penney model within the effective mass approximation[5]. The expected wavelength range for the transitions are indicated in Fig. 1 by horizontal solid (dashed) bars for the heavy-hole (light-hole) related transitions. Good relationship is observed between experimental and calculated values in spite of neglecting exciton effects. The sharper two leading peaks near the threshold in the solid spectra are therefore assigned to heavy-hole (HH) and light-hole (LH) F excitons associated with the miniband bottoms. On the other hand, the high energy structures observed in the solid curves of Fig. 1 are attributed to the rl excitons which are associated with the M~ Van Hove singularity[3]. Peaked nature of the optical absorption indicates excitonic effects for their origins of the HH-related as well as LH-related transitions. We would like to stress that the peaks of high energy rI excitons and low energy F excitons show excellent correlation with the calculated miniband width. At the best of our knowledge, the peaked structures in optical absorption spectra are the first observed for the saddle point H exciton. Although not shown, we have also studied SL samples for L B variations. It is found that the transition energies and their barrier thickness dependence are in excellent agreement with those predicted by the simple theory for both I1 and F excitons[11]. The external field effect on the PC spectra is rigorously explained by Wannier-Stark localization[6-8]. We have measured PC spectra as a function of F for each SL samples and evaluated the transition energies and their intensities in details. The observed transition energies are found to evolve as E ( n ) = Eo + n e F D as expected for the Stark ladder transitions. Here E0 is the eigenenergy of an isolated QW, n is a Stark ladder index (n = 0 , + l , + 2 . . . ) , and D is Lz + La. This confirms our attribution of the observed optical transitions under the applied field to Stark ladder transitions. In the dashed spectra of Fig. 1, the threshold peaks at longer wavelengths are attributed to the - 1 s t and 0th order Stark ladder exciton transitions, as indicated by dashed vertical bars. A higher energy peak is related to the light-hole 0th order transition. From the energy difference between the localized QW (n = 0) and the SL HH

891

Optical transitions in GaAs/AIAs superlattices

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0.25 0.5 0.75 103/(eFD) 2 (meV -2) Fig. 2. Relative oscillator strength of the - 1st order Stark ladder transition normalized by the 0th order transition I I/Iovs (a) eFD and (b) 103/(eFD) 2 for SL samples No. 5 (O, A,xp= 93 meV), No. 3 (+, 68 meV), No. 6 ( . , 35 meV) and No. 7 (x, 13 meV). Solid curves in (a) indicate the theoretical ones calculated by the exact Bessel function. Dotted and dashed lines in (b) indicate least-squares fitting for the majority of closed symbols and a few points at the highest field regimes, respectively.

exciton transitions, we estimate half of the experimental miniband width, Aexpto be 15 (No. l), 35 (No. 2), 68 (No. 3) and 73 (No. 4)meV, if neglected the difference of the exciton binding energy between the two cases[5]. We note that this Aexovalue gives a lower limit for A because of the smaller binding energy for the SL exciton. In order to show field-induced variations of the oscillator strength of the Stark ladder transition, the relative intensity ( I i / I o ) of the - l s t order Stark ladder transition normalized by the 0th order transition is plotted in Fig. 2 for L a series of SL samples [La = 5.7 ,~(No. 5), 8.6 A(No. 3), 11.4 A(No. 6) and 17.3 A(No. 7)] as an example. In Fig. 2(a), a plot is given as a function of eFD. The field strength F is calculated by (IVb[+ Vo)/L where V0 is the built-in voltage and L is the width of the intrinsic layers. For SL samples with thicker L s, the intensity of the - I st order transition decreases more rapidly with F because of the weaker tunnelling probability. According to the tight-binding theory by Bleuse, Bastard and Voisin[7], the oscillator strength of the nth order transition with negative indices is approximated by I_, - J ~ [ - A/(eFD )] - {[A/(2eFD )]"/(n !)}2in the high field limit where J, is the Bessel function of integer index n and A is a sum of conduction and valence miniband half widths. Solid curves in (a) are the expected theoretical dependences assuming the A=xp values. In spite that we neglect theoretical exciton effects, good correlation is obtained between the two

dependences. It is worth to mention that the observed A dependence of the ratios I_ ~/Io is correctly accounted for by the theory. We expect, in the extreme high field limits, inverse quadratic dependence of I_ ~/Io on eFD, so that another plot is also given in (b) as a function of 103/(eFD )2. It is clearly shown in Fig. 2(b) that the oscillator strength ratios I_~/Io exhibit the expected F -2 dependence being again consistent with the theory. Furthermore, we also evaluated the rations I _ , / I o for higher n th order Stark ladder transitions and confirmed the theoretical F-2" dependence in general[12], The slope of 103/(eFD) 2 dependence in Fig. 2(b) which should be a function of A is consistent with the theory and in fact found to be steeper for larger A values. In Fig. 3, the experimental slope in the high field limit is plotted as a function of A2 to test the theoretically expected dependence for all the SL samples investigated. A solid curve indicates the theoretical quadratic dependence on A given by A:/4. This quadratic dependence is in good agreement with the observed for the narrow A samples. If we use the exact Bessel function for the slope (indicated by a dashed curve), better agreement is obtained for the absolute values when the slope is evaluated at the experimental mean fields. The results given above show that the relative oscillator strength of the Stark ladder transitions basically depends on A2 being consistent with the theory. Moreover, the F-2" dependence of the relative transition intensity is valid over the wide range of the SL miniband widths studied. In summary, miniband edge optical transitions and their variations with the external field are investigated in photocurrent spectra of GaAs/AIAs p - i - n diode superlattices with different miniband widths. Distinct

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892

K. FUJIWARAet al.

spectral features of the FI excitons due to the saddletype M, singularity are directly observed in absorption spectra. Excellent correlation with the miniband width is obtained between the experimental and theoretical transition energies both for heavy-hole and light-hole excitons. Under the applied field, Stark ladder transitions are clearly observed over a wide range of well and barrier parameters, and F - 2 " and A2 dependences of their relative oscillator strengths are observed and explained with the tight binding theory. Acknowledgement--This work was supported in part by Scientific Research Grant-in-Aid No. 05044109 from the Ministry of Education, Science and Culture of Japan.

REFERENCES

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