Optimization of optical waveguide modulators based on Wannier-Stark localization: an experimental...

214 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 28, NO. 1, JANUARY 1992

Optimization of Optical Waveguide Modulators Based on Wannier-Stark Localization:

An Experimental Study E. Bigan, M. Allovon, M. Carre, C. Braud, A.Carenco, and P. Voisin

Abstract-We present optical waveguide modulation results obtained using Wannier-Stark localization in InGaAs-InAlAs superlattices grown by molecular beam epitaxy on InP substrates. We show that our results are in good agreement with a previously reported wavefunction model. We experimentally investigate the modulation behavior as a function of the electroabsorptive superlattice thickness. For this purpose we introduce the extinction ratio per unit waveguide length and per unit electric field as a relevant figure of merit that is broadly applicable to any electroabsorptive waveguide modulator. We show that inhomogeneous broadening imposes an optimum thickne5s for the electroabsorptive superlattice. Using a 20 period 65 A InGaAs-20 A InAlAs superlattice located in the core of an optical waveguide, we obtain a 14 dB extinction ratio by applying a drive voltage as low as 0.6 V to a 320 pm long waveguide device operating at 1.57 pm incident light wavelength under TE-polarization mode.

I. INTRODUCTION IRECTLY modulated semiconductor lasers exhibit a D dynamic wavelength shift called wavelength chirping

[ l ] that is detrimental to long distance and high bit rate data transmission [2] because of the optical fiber chro- matic dispersion. This chirp can be reduced using external modulation [3], [4]. Light intensity modulators using electroabsorption in semiconductors under waveguide configuration are receiving much attention because such components are suitable for monolithic integration with a DFB laser source: first demonstrations operating in the 1.5 pm wavelength range were realized using the Franz- Keldysh effect in bulk semiconductors [5], [6] and they have led to the recent demonstration of low chirp and high bit rate transmission experiments using monolithically integrated DFB lasers and electroabsorptive modulators [7], [8]. Electroabsorption effects in multiple quantum well structures (quantum-confined Stark effect) were subse- quently introduced [9], [ 101 and optimized [ 1 11-[ 151 be-

Manuscript received January 4, 1991; revised May 7, 1991 This work was supported in part by “Ministkre de la Recherche et de la Technolo- gie.” CNET-Bagneux and LPMC-ENS are Unit& Associkes au Centre Na- tional de la Recherche Scientifique (CNRS).

E. Bigan, M. Allovon, M. C a d , C. Braud, and A. Carenco are with the Centre National d’Etudes des TCltcommunications, Laboratoire de Bagneux, 92220 Bagneux, France.

P. Voisin is with the Laboratoire de Physique de la Matihe CondensCe de I’Ecole Normale SupCrieure (LPMC-ENS), 75005 Pans, France.

IEEE Log Number 9103676.

cause larger absorption variations can be obtained with similar applied electric fields [16], [17]. However drive voltages are most often higher than a few volts which implies a large energy dissipation under high speed modulation. More recently [18], [19] we have shown that electroabsorption effects in strongly coupled superlattices named as Wannier-Stark localization [20]-[22] could be used to achieve very low drive voltage optical waveguide modulation in the 1.5 pm wavelength range. Here we present improved device performance resulting from an experimental study of modulation characteristics dependence on the electroabsorptive superlattice thickness. In order to compare our different structures we introduce a figure-of-merit that is broadly applicable to any electroabsorptive waveguide modulator.

11. PHYSICAL BACKGROUND

When quantum wells are separated by very thin barriers in a periodic structure the discrete energy levels broaden into minibands because of the resonant tunneling effect. Carriers are delocalized and the superlattice (SL) structure exhibits to some extent a three-dimensional (3-D) behavior. The application of a low electric field to such a structure breaks the resonance because the energy levels of adjacent quantum wells are misaligned by eFd where:

e is the elementary electron charge F is the applied electric field d is the SL period.

Carriers tend to localize and the structure recovers a two- dimensional (2-D) behavior [20]-[22]. This is very unlike the quantum-confined Stark effect that is a quadratic phe- nomenon [23] and where no significant change is expected under low applied electric fields. More precisely, Bleuse et al. [20] have shown that the SL absorption spectrum could be viewed as the sum of absorption steps corresponding to transitions connecting holes and electrons localized in wells separated by p periods and occurring at energies E,, + peFd( p = 0, st 1, +_2, * * ) where E,, is the fundamental transition energy associated to the isolated quantum well, The corresponding oscillator strengths are related to the overlap between hole and electron wavefunctions and are given by J: (A/2eFd) where

0018-9197/92$03.00 0 1992 IEEE

BIGAN et al.: OPTIMIZATION OF OPTICAL WAVEGUIDE MODULATORS 215

Jp is the pth order Bessel function A is the SL total miniband width.

Then the SL electroabsorption spectrum per unit period can be expressed as

- (EQW + peFd)) (1)

where

hvo is the incident light photon energy a. is the absorption step height of the discrete quan-

H is the heaviside function defined by: H(x) = 0 if

It can be shown [20] that in the zero-field limit this expression asymptotically tends towards the superlattice arcosine absorption spectrum corresponding to the superlattice miniband dispersion as first introduced by Esaki et al. [24]. On the other hand, when eFd approaches A, the Bessel function argument gets sufficiently small so that only the ( p = 0) and ( p = f 1) transitions have significant oscillator strengths [20]. The corresponding absorption spectra of a superlattice at zero-field and in this so- called high-field limit eFd/A = l are given in Fig. l . It should be noted that neither excitonic contributions nor broadening effects have been taken into account. Both play a major role in determining the actual absorption spectrum shape. Excitonic effects have been observed by many authors primarily in the localization regime because of the two-dimensional-like behavior [ 191, [25]-[30], but also under flatband conditions [27]-[30]. Excitonic contributions as well as coulombic enhancement of the continuums associated with oblique and direct transitions have been considered recently [31]-[34] and remain a subject under investigation. How the noninclusion of these effects will limit the significancy of this model will be discussed when we will compare experimental results to calculated data. Two interesting electroabsorption configurations can be distinguished on this schematic:

i) incident photon energy is higher than the zero-field SL bandgap and lower than the single quantum well bandgap (i.e., : E,, - A/2 < hvo 5 EQw): there is a negative absorption variation named as ‘blue-shift” [25] which has been successfully used to realize a self electrooptical bi- stable device [26] electroabsorptive modulator arrays [27], as well as a normally-off asymmetric Fabry-Perot reflection modulator [35], [36], all in the GaAs-GaAlAs material system. We have already pointed out [18], [19] that this configuration is not suitable for any application requiring both high contrast and low attenuation because excitonic effects as well as broadening mechanisms contribute to increase significantly the on-state absorption originating from the ( p = - 1) oblique transition.

ii) incident photon energy is lower than the zero-field SL bandgap (i.e.,: hvo < E,, - A/2): there is a positive

tum well

x < 0 and H(x) = 1 otherwise.

WAVELENGTH (a.u.1

Fig. 1 . Absorption spectra (schematic) of an ideal superlattice without applied electric field (solid line) and in the “high-field’’ limit (dashed line).

absorption variation originating from the ( p = -1) oblique transition which is similar to conventional “red- shift” electroabsorption effects except it can be obtained with much smaller electric fields. In our previous work [IS], [I91 we have proposed the use of this ( p = - 1) oblique transition to achieve efficient very low drive voltage optical waveguide modulation and we have demon- strated it using a InGaAs-InAl As superlattice featuring both high extinction ratio and low on-state attenuation. All of the following will concentrate on this ii) electroabsorptive configuration.

111. EXPERIMENTAL Our structures (sample I, 11, and 111) are InGaAlAs p-

i-n double heterostructures grown by MBE onto n + -1nP substrates (Sn doping level: 1.5 X 10l8 ~ m - ~ ) . The nominally undoped region consists of a 10 (!ample I), 20 (!ample 11), or 30 (sample 111) period 65 A InGaAs-20 A InAlAs electroabsorptive SL (absorption edge: 1.5 pm) surrounded on toth sides by 15. (sample I) or 8 (sample 11) period 25 A InGaAs-30 A InAlAs confining SL. Sample I11 has no confining SL. The nominally undoped region width is thus kept constant (0.26 pm). The nominally undoped region was surrounded by a 0.1 pm thick n-InAIAs buffer layer (doping level: 5 x 10” cmP3) and a 1.8 pm thick p-InAlAs confining layer (doping level: 5 X loL7 A 0.1 pm thick pf-InGaAs contact layer (doping level: 2 x l O I 9 cmP3) was grown on top of the structures. The refractive index of the confining SL is in- termediate between the refractive index of the electroabsorptive SL and the refractive index of the InAlAs confining layers. The purpose of its inclusion is to increase the optical confinement factor over the electroabsorptive SL. Magnitudes for the optical confinement factor of the three samples will be specified when we will compare the per- formances of the different modulator structures. Fig. 2 gives a schematic of the structures. 50 pm wide TiAu electrodes were evaporated on top of 100 pm wide mesas etched down to the InP substrate. After thinning and Au electrode deposition on the backside of the samples broad- area modulators of various lengths ranging from 100 to 500 pm were cleaved. They were characterized using a tunable NaC1-OH F-center laser. We only investigated the

216 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 28, NO. I , JANUARY 1992

f P + - I n G a A s

I P - I n A l A s I I - I n G a A s / I n A I A s confining SL

I - I n G a A s / I n A I A s e l e c t r o a b s o r o t i v e SL

N+ - InP s u b s t r a t e

Fig. 2. Cross-sectional view of the modulator structures (schematic).

TE-guided modes in this work. Relative transmission was measured as a function of reverse bias at different incident light wavelengths of the electroabsorptive SL transparent region. Photocurrent versus reverse bias was simultaneously measured and the combination of both measurements allowed a determination of the on-state attenuation 1371. These characterizations were carried out for different waveguide lengths and for each length on different modulators. Averaged results allowed us to obtain a meaningful comparison of the three different structures. In order to analyse the electroabsorption effects involved in our structure we have carried out photocurrent (PC) spectroscopy under waveguide configuration. PC spectra are representative of electroabsorption spectra if only a small fraction of the incident light is absorbed. This condition is most often satisfied when light propagates per- pendicularly to the epitaxial layers but this is not the case under waveguide configuration with usual waveguide lengths. In order to obtain PC spectra that are representative of electroabsorption spectra we fabricated devices having one cleaved facet and one etched facet by applying conventional photolithography and wet chemical etching techniques to individual devices. The waveguide length could thus be reduced to 5 pm.

IV. RESULTS AND DISCUSSION A . Isolated Devices

PC spectra are given in Fig. 3. They were measured on short waveguides for different reverse bias voltages. A very similar behavior is observed for the three different samples: at +0.35 V (forward bias) the electroabsorptive SL is only partially depleted and the corresponding PC spectra are given by the dashed lines. When the bias voltage goes from +0.20 V (forward bias) to -0.40 V (reverse bias) the electric field is increased and three features that are characteristic from Wannier-Stark localization can be clearly observed:

i) a strong increase of the excitonic oscillator strength which results from the going from a 3-D behavior to a 2- D behavior. This occurs around 1.48 pm incident light wavelength.

1.45 1.50 1.55 1. WAVELENGTH lpml

0

Sample !l

1.50 1.55 1.60 WAVELENGTH ipml

I I 1 Sample m L=5pm

Fig. 3 . Photocurrent spectra of the three samples for different bias. Wave- guide length is 5 pm. The 0.35 V forward bias spectra are given by the dashed lines.

ii) an expected blue-shift of the absorption edge around 1.52 pm incident light wavelength.

iii) the (- 1) oblique transition occurring in the electroabsorptive SL transparent region (around 1.58 pm incident light wavelength).

The electron-to-heavy hole excitonic absorption peak position gives us direct information on the actual well width. The 1.485 pm ayerage position is in reasonable agreement with the 65 A nominal well width. Further- more, the dispersion in this peak position is only 5 nm (2.8 meV) over the three samples which indicates excellent growth control.

Fig. 4 shows typical relative transmission curves versus reverse bias at different wavelengths. Apart from the mag- nitude of the extinction ratio that is sample dependent and that will be discussed in the next subsection, the three samples exhibit a similar general behavior in the same


100

901 - 80- E 70- - 60-

5 5 0 - m

a + 4 0 - > ‘4 30-

1

0- - 0 5 0 0.5 1 1 5 2

REVERSE BIAS IV)

Sample 1 L I 3 2 0 p m

1.57pm 70 1.58pm

1.59pm 1.60pm

VI ,b I 10

0 -0.5 0 0.5 1 1.5 2

REVERSE BIAS [ V I

100

9 0 1

1.59pm 1.60pm

Sample Q l L=400pm TE i

scribed in our previous work [ 191. Furthermore we notice that:

i) the optimum voltage for minimum relative transmission shifts linearly with increasing incident light wavelength

ii) once this optimum has been reached and relative transmission is increasing again the relative transmission curves for the different wavelengths superimpose to each other. Points i) and ii) will be clarifed in the following discussion. From (1) we determine the absorption variation A a as a function of the electric field F for a given photon energy hvo lower than the SL bandgap E,, - A / 2 (zero-field absorption is zero):

At low electric field F, only high order (-p) oblique transitions contribute to the absorption. The corresponding oscillator strengths are low because the Bessel function orders are high. When F varies from zero to infinity, absorption undergoes jumps for electric field values of E,, - hvo/med, m being an integer. These jumps correspond to the apparition of the (-m) oblique transitions in our operating wavelength region. Between these jumps the absorption decreases [38]. This F-’ oscillatory behavior has already been observed in a GaAs-GaAlAs superlattice at low temperature using electroreflectance [22]. Maxi- mum absorption variation is obtained under the (-1) oblique transition [38]. It can be expressed as [38]

- 0 5 0 0 5 1 1.5 2 REVERSE BIAS ( V I

Fig. 4. Relative transmission of the TE-guided mode versus reverse bias voltage for three individual devices taken out from samples I, 11, and 111. Measurements were carried out for four different wavelengths.

wavelength range. This last point, combined with the low dispersion gf the well width, indicates that the dispersion of the 20 A nominal barrier width is low over the three structures. This precise control of the MBE growth was confirmed by X-ray diffqction measurements. Measured periods are 83 and 53 A for the electroabsorptive SL (samples I , 11, and 111) and the confining SL (samples I and 11). Maximum relative transmission is obtained under forward bias because the p-i-n built-in electric field is sufficiently large to partially induce Wannier-Stark localization. We did not investigate behavior above 0.35 V forward bias in order to avoid any perturbation due to forward current flowing through the diode. When forward bias (reverse bias, respectively) is decreased (increased, respectively) relative transmission drops very rapidly, reaches a minimum value, then increases again. Such behavior has already been observed and qualitatively de-

(3)

(4)

with the condition

eFd 2 E,, - hvo.

Because we operate below the SL bandgap the Ressel function argument is smaller than unity and Aahuo is a decreasing function of F. Therefore maximum absorption variation is obtained when

eFd = E,, - hvo. (5) Now we are going to verify that our results are in good

agreement with (5). Neglecting the exciton binding energy (a few meV), as well as any displacement of the exciton due to the quantum-confined Stark effect (using Bas- tard variational approach [23] the calculated Stark shift for an isolated quantum well at 0.4 V reverse bias is 0.75 meV) we estimate the quantum well band-gap energy E,, from the excitonic absorption peak position at 0.4 V reverse bias: E,, = 835 * 3 meV (* stands for dispersion over the three samples). First let us consider device operation at X = 1.57 pm that is to say hvo = 790 meV. The mean electric field over the intrinsic region of optimum modulation Fopt is estimated by


- 1.57pm _-_ 1.58pm

where

Vopt is the reverse bias for optimum modulation Vbi is the built-in potential tl is the intrinsic layer thickness.

Using$tructure parameters tl = 0.26 pm, Vbi = 0.8 V, d = 85 A and measuring Vopt on the relative transmission curves: VOpt = 0.5 f 0.1 V (i- stands for dispersion over the three samples) we get: eFoptd = 43 &- 3 meV (i- stands for dispersion over the three samples). We see that ( 5 ) is verified within a few meV. Equation ( 5 ) also implies that optimum electric field dependence on incident light energy is linear [point i)] and is only related to the superlattice period. From ( 5 ) we derive this dependence

1 ed WO,, = - - 6(hvo) . (7)

Using the structure parameters and the expression of the electric field (6) we calculate the optimum voltage dependence on the incident light wavelength: 6Vop,/6X = 0.15 V/O.O1 pm which compares favorably to the experimental value determined from the relative transmission curves: 6Vopt/6X = 0.13 V/O.O1 pm. This clarifies point i). Equation (3) implies that, provided we operate under the ( - 1) oblique transition, the absorption variation is a decreasing function of the electric field F that only depends on the superlattice parameters A and d , but does not depend on the incident light wavelength. This [point ii)] can be verified on our relative transmission curves except at short wavelength and for large reverse bias where relative transmission starts decreasing again. We find a good agreement between the experimental results and the calculated data and this raises up a few comments: ( 5 ) means that the shift between the direct and (- 1) oblique transition is equal to the energy level misalignment between two adjacent wells, which is the basis of a Stark ladder formation. In determining these transition positions we have neglected the related excitonic binding energies. It should be noted that these energies (a few meV) are much smaller than the misalignment values we are dealing with (45 meV) and that such a further correc- tion would fall within the precision we are interested in (a few meV). Excitonic contributions as well as Coulom- bic enhancement of the continuums associated to direct and oblique transitions will affect the measured absorption variations but not the general behavior. This is why we did not attempt to compare measured extinction ratios with calculated absorption variations. The same remarks can be made about broadening effects that will smooth out Wannier-Stark localization features, but that should not change considerably their positions.

B. Averaged Results

Fig. 5 shows the averaged extinction ratio per unit waveguide length simultaneously with the averaged on-

state attenuation per unit waveguide length versus the number of periods of the electroabsorptive superlattice. They are given for four different incident light wavelengths. For a given sample (number of periods is fixed) the larger extinction ratios are obtained close to the superlattice bandgap which has been explained in the previous analysis. For a given wavelength the on-state attenuation increases with increasing the number of periods. This is expected because of the increase in the optical confinement factor. To estimate the optical confinement factor for the three samples, we carried out multilayer calculations [39]. We used bulk InGaAs and InAlAs refractive index values determined from single effective oscillator modes [40] for the well and barrier refractive index values. Oscillator and dispersion energies were taken out from the data reported by Nojima et al . [41] for InGaAs and InAlAs and by Broberg et al . [42] for the InP substrate. Calculations were performed at the mean wavelength 1.585 pm and the corresponding values of the con- stitutive materials are: nInGaAs = 3.61, nInAIAs = 3.21, and nInP = 3.17. One must be aware that such an approxi- mation neglects the enhanced dispersion near the band- edge of quantum structures [43], [44]. A more precise determination of the modal properties of the SL waveguide could be achieved using grating coupling techniques [45], [46]. Estimated values of the optical confinement factor are 0.13, 0.27, and 0.40 for samples I , 11, and 111, respectively. At long wavelengths (1.59 pm, 1.60 pm) the extinction ratio increases with increasing the number of periods. At shorter wavelength (1.58 pm) this extinction ratio saturates and eventually slightly decreases when going from 20 to 30 periods at 1.57 pm incident light wavelength. This behavior seems contradictory with a mere increase of the optical confinement factor. The results are replotted in Fig. 6 in a different way: the averaged extinction ratio per unit waveguide length is divided by the averaged on-state attenuation per unit waveguide length.

Using the notations developed in the appendix, this figure is equal to Aa/ao. It has already been used for opti-


O 0-0 NUMBER OF PERIODS

Fig. 6. Average extinction ratio divided by average on-state attenuation (modulation depth parameter: A a / a o ) versus number of periods of the electroabsorptive SL. Measurements were carried out for four different wavelengths.

mizing quantum-confined Stark effect-based modulators [12] and it can be referred to as the modulation depth parameter. We can see on this plot that

i) A a / a o decreases with increasing the number of periods for each investigated wavelength

ii) A a / a o increases with increasing the operating wavelength. We believe that this behavior can be explained by broadening. The overall effect of broadening is to increase a. and to decrease A a which makes A a / a o a parameter that is very sensitive to broadening. We attribute the A a / a o increase with operating wavelength to homogeneous broadening: although the largest values of A a are obtained close to the absorption edge cyo values are also very large in this range because of homogeneous broadening. These large values of a. then decrease faster than A a when increasing the operating wavelength. The A a /ao decrease with increasing the number of periods is a characteristic feature of inhomogeneous broadening. The major source of such broadening can be electric field inhomogeneity arising from finite residual doping in the nominally undoped layer. Background carrier concentration within the nominally undoped region was estimated to be 1.2 X loL6 cmT3 from C-V measurements as well as from photocurrent level at short wavelength. The ori- gin of such a high carrier concentration is not clear at present but it has already been observed by Wakita et al. [15] in MQW modulators realized in the same material system using the same growth technique.

It is clear from Fig. 5 and Fig. 6 that A a / a o is not a relevant figure of merit for modulator optimization: a value of A a / a o as large as 25 is obtained at 1.60 pm operating wavelength using the 10 period electroabsorptive superlattice (sample I). However this corresponds to a very poor modulator since the averaged extinction ratio per unit waveguide length is lower than 1 dB/ 100 pm.

On the other hand the averaged extinction ratio per unit waveguide length divided by the applied electric field is a relevant figure-of-merit as fully explained in the appendix. It takes into account the compromises arising be-

tween extinction ratio, diode capacitance, and drive voltage through waveguide length and intrinsic layer thickness. This figure-of-merit is labelled as r * A a / A F where

r is the optical confinement factor A a is the absorption variation A F is the applied electric field difference between on-

It is shown in Fig. 7, versus the number of periods. For this figure-of-merit determination we took A F = AV/ t , . The on-state was taken as the 0.2 V forward bias state in order to satisfy the depletion condition that is necessary to ensure full comparison capability of this figure-of-merit (see Appendix).

This value of 0.2 V forward bias for intrinsic layer depletion was determined from photocurrent measurements at short wavelength (1.45 pm) on sample I11 in which the whole intrinsic layer contributes to photocurrent. It was confirmed by capacitance-voltage measurements that were carried out on the three samples. The off-state was taken as the bias value that gave the largest extinction ratio. We should notice that on-state and off-state could have been chosen using the bias values that maximize I' * A a / A F . Slightly higher values of this figure-of-merit can thus be obtained corresponding to lower drive voltage configurations. For simplicity purposes, this further refinement of modulation optimization was not investigated in this work. For long wavelengths (1.59-1.60 pm) r * A a / A F increases with increasing the number of periods. At shorter wavelength (1.58 pm) it decreases slightly between 20 and 30 periods and eventually exhibits a sharp maximum for 20 periods at 1.57 pm incident light wavelength. Far away from the absorption edge, optimum operation is achieved using a large number of periods. Closer to the absorption edge where broadening effects play a major role, optimum operation is achieved with a smaller number of periods. Operation is optimum as close as possible to the absorption edge as expected from the analysis developed in the individual device section: larger absorption variation is obtained with smaller electric field when operating wavelength is closer to the absorption edge. As mentioned in the appendix, one should however check that on-state attenuation is not prohibitive. For the 20 period sample (sample 11) we obtained a A a / a o parameter value of 3 and a r - Acy/AF parameter of 1.7 dB/100 pm/V/pm at 1.57 pm operating wavelength. Both parameters were determined from the averaged measurements with the on-state defined as the 0.2 V forward bias state to guarantee intrinsic layer depletion. This is the rea- son why the A a / a o value is lower than shown in Fig. 5 where the on-state was defined as the 0.35 V forward bias state.

Our best individual device was a 320 pm long waveguide device. On-state attenuation was 4.6 dB, extinction ratio was 14 dB, and the drive voltage was 0.6 V (from 0.2 V forward bias to 0.4 V reverse bias) at 1.57 pm operating wavelength. These data correspond to a A a / a o parameter value of 3.05 and a r A a / A F parameter value

state and off-state.

220 IEEE

0 L

-2 - 0.

\ 0.5 - U-

0 - -

JOURNAL OF QUANTUM ELECTRONICS, VOL. 28, NO. 1, JANUARY 1992

,’,,,/’, ’ ’,, / -

’ / / 1 LO

Fig. 7 . Average extinction ratio per unit waveguide length divided by applied electric field (figure-of-merit: r . A a / A F ) versus number of periods of the electroabsorptive SL. Measurements were camed out for four different wavelengths.

of 1.9 dB/ 100 pm/V/pm. Both values are very close to the averaged values. Such low dispersions of the modulator characteristics were obtained for the three samples. This demonstrates excellent growth uniformity.

V. CONCLUSION We have reported Wannier-Stark localization obser-

vation in InGaAs-InAlAs superlattice waveguides. We have achieved efficient waveguide intensity modulation using the (- 1) oblique transition connecting a hole localized in a well with an electron localized in the adjacent well. We show that our results are in fairly good agreement with the superlattice wavefunction model developed by Bleuse et al . [20]. We have carried out an experimental study of the dependence of modulation characteristics on the electroabsorptive superlattice thickness. In order to compare our different structures we propose the use of the extinction ratio per unit waveguide length and per unit applied electric field as a relevant figure of merit for electroabsorptive waveguide modulator optimization. Using both this figure of merit and the modulation depth parameter we show that inhomogeneous broadening effects impose an optimum electroabsorption superlattice thickness for optimum modulation. Using a 20 period electroabsorptive superlattice we have realized a modulator having a 14 dB extinction ratio and a 4.6 dB on-state attenuation with a drive voltage as low as 0.6 V. The device is a 320 pm long waveguide operating at 1.57 pm under TE polarization mode.

APPENDIX In this section we introduce a figure of merit that is

applicable to any electroabsorptive waveguide modulator. We consider a device consisting of a p-i-n waveguide diode. The geometrical parameters of the device are listed below

L is the waveguide length W is the p-i-n diode width tI is the intrinsic layer thickness.

The intrinsic layer contains the electroabsorptive material and the electric field is applied by reverse biasing the diode. Let us precise the electrical parameters of the p-i-n diode. First we assume that the residual doping in the intrinsic layer is sufficiently low to ensure that the mean electric field value F over the intrinsic layer thickness tI is meaningful. Electric field inhomogeneity resulting from finite residual doping can be further introduced as an additional inhomogeneous broadening factor in the electroabsorption analysis. In order to avoid dramatic increase of the p-i-n diode capacitance the intrinsic layer should be kept depleted all the time. This is our second assumption: intrinsic layer remains depleted even in the lowest mean electric field state (which is the on-state for conventional positive absorption variation configurations, off-state for “blue-shift” configurations). Third we assume that the p and n doping levels are sufficiently high so that the extension of the depletion region in the p and n doped region is negligible. Under these assumptions we can write

where

V is the applied bias F is the mean electric field value

index on or 08 stands for on-state or off-state.

This can be rewritten as

A V ~ = AF

tl where

A V is the drive voltage A F is the electric field difference between on-state and

Now we introduce the electroabsorption properties. Let a. be the on-state absorption and Act the absorption variation occurring under variation of the mean electric field F. If we define the optical confinement factor r as the fraction of guided energy contained in the electroabsorptive material then we can express the extinction ratio on /off and the on-state attenuation att. (notwithstanding coupling losses) as [ 171 :

off-state.

on/off = er’Aa.L (A31 art. = er.ao.L (A41

Another important parameter of the electroabsorptive modulator is the electric 3 dB bandwidth. Here we assume that it is RC limited. This has been discussed in great de- tail by Wood [17]. It means we neglect the photogenerated carriers transit time over the intrinsic layer thickness. Experimental data on quantum confined Stark effect-based modulators show that this is a valid assumption up to speeds in excess of 20 GHz [15]. This can be qualitatively explained first by the fact that such modulators operate at

BIGAN et al.: OPTIMIZATION OF OPTICAL WAVEGUIDE MODULATORS 22 1

large electric fields and the transit time is known to decrease with increasing electric fields [47], and second because the intrinsic layer of such guided wave modulators is thin (around 0.5 vm) which shortens the transit time of photogenerated camers. Although up to now no experimental data is available about Wannier-Stark localization-based modulators, we can notice that i) although the operating electric field is low, transit is expected to be fast because of the very small bamer width ii) second the total intrinsic layer is even thinner in the structures that have been considered up to now [19], [this work]. Then the 3 dB bandwidth V3dB can be expressed as

1 (A51

1 tl =-. T * R CPi-,, T * R E/ * (W * L ) v3dB =

where

R is a load resistor connected in parallel with Cp-l-,, (the assembly being driven by a matched voltage generator with impedance R)

Cp+" is the p-i-n capacitance cl is the intrinsic layer dielectric constant.

Here we have neglected the extension of the depleted region in the p and n regions which is valid provided p and n doping levels are sufficiently high. The four characteristics of an electroabsorptive optical waveguide modulator are given by (A2-A5). System applications require a large extinction ratio simultaneously with a low on-state attenuation. Therefore the A a / a o parameter must be sufficiently large. However this single parameter cannot be considered as a relevant figure of merit because it does not take into account neither the 3 dB bandwidth nor the drive voltage. From the four characteristics expressions given above, it can be seen that extinction ratio, drive voltage, and 3 dB bandwidth are related to each other. One wishes to get simultaneously a large extinction ratio, a low drive voltage, and a high 3 dB bandwidth. To determine a figure-of-merit taking into account the relation- ship between these characteristics we should consider two different electroabsorption configurations determined by the following parameters

Ll,2

(t l) 1,2

AF1.2. Indexes 1 and 2 refer to configurations 1 and 2. cl is

assumed to display no significant change from one configuration to another which is valid for 111-V materials. We wish to compare the potentialities of different electroabsorption configurations to achieve efficient optical waveguide modulation but we do not plan to determine an optimum device geometry or technology. This is why we do not discuss neither the influence of the W parameter (intrinsic layer width) that depends on technological choices for achieving transverse single-mode operation, nor the

contribution of the bonding pad capacitance to the total device capacitance. These are independent of the electroabsorption configurations to a large extent.

If we let the extinction ratios as well as the drive voltages be equal, i.e.:

then

which means the higher the extinction ratio per unit waveguide length and per unit applied electric field the higher the bandwidth.

Similarly, if we let the extinction ratios as well as the bandwidths be equal, i.e.:

then:

which means the higher the extinction ratio per unit length and per unit applied electric field the lower the drive voltage.

Eventually, if we let the drive voltages as well as the bandwidths be equal, i.e.,

then

(r * Aa)l * LI (I' - Aa)l (t1)l AFI (r * & (r Aa)2 (t1)2 (r - Aa),

AF2

(A1 1) . - - - - -

which means the higher the extinction ratio per unit length and per unit applied electric field the higher the extinction ratio.

We have shown that if any two of the three characteristics: extinction ratio, drive voltage, and bandwidth are equal, the third one compares to the extinction ratio per unit length and per unit applied electric field expressed by


r A~ A F

This demonstrates why this parameter is a relevant figure-of-merit that takes into account the compromises between extinction ratio and bandwidth through the waveguide length and between drive voltage and bandwidth through the intrinsic layer thickness. But it does not suf- fice by itself since it does not take into account the on- state attenuation. Both A a / a o and r - A a / A F parameters should be considered. However these two figures of merit do not play a symmetric role. We have demon- strated that a linear increase of the figure-of-merit r - A a / A F results in a linear improvement of either the extinction ratio, the drive voltage or the 3 dB bandwidth. Let us have a closer look to the effect of A a / a o : this parameter is equal to the extinction ratio divided by the on-state attenuation (both being expressed in dB). If we impose a given extinction ratio ../of the output power drop through the modulator in the on-state (on-state attenuation) is given (in dB) by: o n / o $ l ( A a / a o ) where on/o$is expressed in dB and A a / a o is the dimensionless modulation depth parameter. This means that once A a /ao is sufficiently large for the on-state attenuation to be small an important increase in A a / a o does not bring any significant improvement. Therefore A a / a o must be given a minimum value that is determined from system consid- erations while the actual optimization should be made on the A a / A F figure-of-merit.

ACKNOWLEDGMENT We wish to thank J . Landreau for processing assistance

and J . Primot for X-ray measurements.

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P. Voisin, photograph and biography not available at the time of publica- tion.

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