AVALANCHE photodiodes (APD s) have been widely

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1 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 33, NO. 7, JULY Excess Noise in GaAs Avalanche Photodiodes with Thin Multiplication Regions C. Hu, K. A. Anselm, B. G. Streetman, Fellow, IEEE, and J. C. Campbell, Fellow, IEEE Abstract It is well known that the gain bandwidth product of an avalanche photodiode can be increased by utilizing a thin multiplication region. Previously, measurements of the excess noise factor of InP InGaAsP InGaAs avalanche photodiodes with separate absorption and multiplication regions indicated that this approach could also be employed to reduce the multiplication noise. This paper presents a systematic study of the noise characteristics of GaAs homojunction avalanche photodiodes with different multiplication layer thicknesses. It is demonstrated that there is a definite size effect for multiplication regions less than approximately 0.5 m. A good fit to the experimental data has been achieved using a discrete, nonlocalized model for the impact ionization process. I. INTRODUCTION AVALANCHE photodiodes (APD s) have been widely deployed in long-haul, high-bit-rate fiber optic systems because they can provide substantial improvement in receiver sensitivity compared to p-i-n photodiodes [1] [3]. The performance of APD s can be evaluated in terms of responsivity or gain, bandwidth, and the excess noise that arises from the random nature of the impact ionization process. The figure of merit (FOM) for the gain and frequency response is the gain bandwidth product. An inadequate gain bandwidth product can degrade the overall receiver performance by limiting the gain to less than its optimum value in order to have sufficient bandwidth. The gain bandwidth product and the multiplication noise are related to the electron and hole ionization rates ( and, respectively) or, more specifically, to their ratio (defined as or such that ). In the high-gain regime, Emmons has shown that the gain bandwidth product is inversely proportional to and to the multiplication width [4]. Consequently, the highest performance, i.e., high gain bandwidth product and low multiplication noise, is achieved when only one carrier is responsible for most of the avalanche gain, i.e.,. The APD structure that has been most widely used for long-haul telecommunications applications is the InP InGaAsP InGaAs separate absorption and multiplication regions (SAM) APD [5] [9]. In its most common configuration, the SAM APD consists of an InP multiplication region and an In Ga As absorbing layer separated by Manuscript received August 28, 1996; revised March 6, This work was supported by DARPA through the Center for Optoelectronic Science and Technology, the Joint Services Electronics Program, and the National Science Foundation. The authors are with the Microelectronics Research Center, Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, TX USA. Publisher Item Identifier S (97) a transition region that is frequently comprised of one or more thin, intermediate-bandgap In Ga As P layers. The value of for these APD s, a characteristic of bulk InP, ranges from [10], [11]. This, in turn, constrains the gain bandwidth product of these APD s to 100 GHz in most cases although a gain bandwidth product of 122 GHz has been achieved with an SAGCM structure [9]. As the bit rates of fiber optic systems steadily increase, it has become more and more difficult for these InP InGaAsP InGaAs SAM APD s to provide the required performance in terms of speed and sensitivity. A great deal of research has been devoted to the development of novel, low-noise, high-speed APD structures in III V compounds. Recently, substantial increases in gain bandwidth product and a simultaneous reduction in multiplication noise have been accomplished with multiple-quantum-well (MQW) APD s. This approach uses MQW s to artificially enhance the ionization rate of either the electrons or the holes, thus decreasing. factors of 0.1 and 0.14 have been reported for GaAs AlGaAs MQW APD s by Capasso et al. [12] and by Kagawa et al. [13]. Long-wavelength MQW APD s have achieved low values as well. A value lower than 0.1 has been reported [14], [15]. A gain bandwidth product as high as 150 GHz was achieved with an InGaAs InGaAlAs MQW APD [16]. Another approach to increasing the gain bandwidth product is to utilize a thin multiplication region. Campbell et al. [7], [17] achieved an increase in the gain bandwidth product of InP InGaAsP InGaAs SAM APD s from 18 to 70 GHz by reducing the multiplication-layer width from approximately 1.5 m to less than 0.5 m. In addition, these SAM APD s exhibited lower multiplication noise [18] than would have been predicted by conventional continuum noise theories [19] [21]. This continuum approach assumes that the multiplication layer is very long and, hence, that the number of ionizing collisions per primary carrier transit is large. When the multiplication width is thin, i.e., the length is a few multiples of or, this condition will not be satisfied and a different statistical treatment is required. Van Vliet et al. have developed a discrete impact ionization model that is valid for an arbitrary number of impact ionizations within a finite multiplication width [22]. Analytical expressions for multiplication and the excess noise factor have been derived from this theory [22], [23]. Campbell et al. reported that these expressions provided a good fit to measurements of the multiplication noise of InP InGaAsP InGaAs SAM APD s [18]. Nonlocal effects, such as the dead-space effect, can also become significant in APD s with thin multiplication regions /97$ IEEE

2 1090 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 33, NO. 7, JULY 1997 In the continuum models, impact ionization of a carrier is assumed to be independent of its ionization history and, consequently, the ionization rate is the same at all times. However, it is intuitively clear that after an ionizing collision, the carriers must travel a finite distance in order to acquire sufficient energy to initiate another ionization event. This means that the ionization probability is negligible for a certain distance, the dead space. The net result is that, are not only functions of the electric field but also functions of position in the multiplication region [24] [26]. Models that include the dead space effect have been developed; they predict a reduction in the excess noise factor particularly for short multiplication regions [27] [29]. This may explain the low excess noise ( ) observed in InGaAs GaAs AlGaAs resonantcavity SAM APD s that had multiplication regions as thin as 2000 Å [30]. This paper presents a systematic study of the noise characteristics of GaAs homojunction avalanche photodiodes with different multiplication layer thicknesses. It is demonstrated that there is a definite size effect for multiplication regions less than approximately 0.5 m. For a given gain, the excess noise is lower for thinner multiplication regions. A good fit to the experimental data has been achieved using a discrete, nonlocalized model for the impact ionization process. In Section II of this paper, we describe the devices structures investigated and the crystal growth. In Section III, the noise measurement technique is described and measurements of the excess noise factor as a function of the multiplication thickness are presented. A good fit to the experimental data has been achieved with a discrete, nonlocal model [22]. II. DEVICE FABRICATION AND CHARACTERIZATION For this study, a p-i-n structure was adopted for ease and accuracy of analysis. To date, InP-based APD s have been utilized for long-wavelength telecommunications applications. We have elected to use GaAs for this study because epitaxial layers with well-controlled parameters can be grown in our molecular beam epitaxy (MBE) facility. Given the similarities between the band structures of GaAs and InP, there is no reason to think that the underlying physical principles that govern impact ionization in GaAs will be significantly different for InP. Essentially all of the impact ionization occurred in the i-region, a p layer. The width of this p layer was varied to achieve a change in the width of the multiplication region; APD s with p layer thickness of 0.1, 0.2, 0.5, and 0.8 m were fabricated and tested. The 0.1-, 0.2-, 0.5- m layers were unintentionally doped and the background carrier density was approximately 2 10 cm. The 0.8- m multiplication layer was doped to 1 10 cm. For these carrier concentrations and thicknesses, the electric field intensity was essentially constant across the multiplication region. The top p -GaAs layer was 2 m thick in order to absorb all the incident light and thus to ensure pure electron injection. The devices were grown by molecular beam epitaxy on an n -GaAs substrate. First a 2000-Å n - type GaAs buffer layer was grown. The carrier densities of the n layers were 5 10 cm for the 0.2- m APD and 1 10 cm for others. Then the p -GaAs multiplication layer, the p -type GaAs absorption layer, and a 1000-Å heavily doped (1 10 cm ) GaAs contact layer were grown sequentially. The carrier densities of the p layers were in the range 1 to 3 10 cm. The growth temperature was 600 C under an As overpressure and the growth rate was 0.8 monolayer per second. The As Ga incorporation ratio as measured by reflection high energy electron diffraction was 1.8. This corresponds to a flux ratio measured by the ion gauge (beam equivalent pressure) of 10. After crystal growth, mesas having a diameter of 100 m were etched in Br HBr H O solution. The top contact was formed by photolithography and lift-off of a Cr Au layer; In was used for the back-side contact. The current voltage characteristics and the multiplicationvoltage characteristics of the APD s are shown in Fig. 1(a) and (b), respectively. It can be seen in Fig. 1(a) that the APD s have photoresponse even at zero voltage and that the photocurrent remains constant at low voltages. This provides a good unity-gain reference for determining the gain and the excess noise factor. All the devices achieved a gain over 30. Since the multiplication layers are very thin, the depletion width in the highly doped layers cannot be ignored in the calculation of the electric field. Fig. 2 illustrates the electric field profile in one of these APD s, where,, and represent the depletion widths of the n, p, and p layers, respectively, and and represent the electric field intensities at the boundaries of the multiplication layer. We have assumed one-sided abrupt junctions which is supported by our previous characterization of MBE-grown devices. By solving Poisson s equation, we obtain the following: where,, and are the charge densities in the n -type, p -type, and p -type layers, respectively, is the dielectric constant, and and are the build-in and breakdown voltages, respectively. The field intensities and for different widths and dopings of the p layers are shown in Table I. The breakdown voltage and maximum electric field versus the multiplication layer width are shown in Fig. 3. It can be seen that maximum electric field intensities at breakdown are close but not identical for the different devices. It would be expected that the electric field intensity at breakdown would decrease as the thickness of the p layer increases, however, the maximum electric field intensity for the 0.8- m device is higher than that of the 0.5- m device because its doping level is higher. III. NOISE CHARACTERISTICS For the noise measurements, light was focused onto the top GaAs absorbing layer. The technique used to measure the

3 HU et al.: EXCESS NOISE IN GaAs AVALANCHE PHOTODIODES 1091 (a) Fig. 3. Calculated breakdown voltage and maximum electric field intensity versus the multiplication region thickness. TABLE I CALCULATED FIELD PROFILES OF THIN-MULTIPLICATION-REGION APD S (b) Fig. 1. (a) Photocurrent and dark current versus bias voltage and (b) gain versus bias voltage. for the calculation of the excess noise factor. The readings of the noise figure meter were in decibels relative to the thermal noise of a 50- resistor in parallel with the photodetector. The excess noise factor was measured as a function of gain for each of the four device sets. The results are shown in Fig. 4. The symbols represent experimental data. The dashed lines are calculated excess noise factors corresponding to different effective ionization rate ratios,, using the continuum model [19], [20] which provides the following expression for the excess noise factor, : (1) Fig. 2. Electric field profile of a thin-multiplication-region APD. excess noise factor has been described in detail in [18]. For the present study, the optical source was a tunable He Ne laser with the emission wavelength set to 6328 Å. Care was taken to focus all of the incident light onto the top of the APD in order to avoid sidewall absorption which would cause mixed carrier injection and lead to an incorrect result. The excess noise factor was measured using an HP8970B noise figure meter at a frequency of 50 MHz with a bandwidth of 4 MHz. The instrument was first calibrated with a commercial noise source to eliminate the noise contribution of the post amplifier. Then the shot noise, the photodiode, was measured at unity gain as a function of the photocurrent. This yielded the noise constant The solid lines were calculated using the discrete model of Van Vliet et al. [22]. It can be seen from Fig. 4 that, for a given gain, the measured excess noise factor decreases with decreasing width of the multiplication layer. In terms of the continuum model, at high gains, decreases from 0.5 to 0.25 when the thickness of the multiplication layer decreases from 0.8 to 0.1 m. The experimental data from the 0.8- m device fit well with the continuum theory while the others do not. This would indicate that the value of for bulk GaAs is in the neighborhood of 0.5, which is consistent with the data in [31], [32]. At low gain, the experimental data does not follow a constant curve for the 0.1-, 0.2-, and 0.5- m device, but the discrete model of Van Vliet et al. [22] provides a good fit for all gains. This model utilizes recurrent generating functions to describe an arbitrary number of impact ionizations in a finite multiplication width. The ionizations are assumed to be governed by independent Bernoulli trials, with a priori ionization probabilities, and for electrons and holes, respectively. If a moment generating function for a random

4 1092 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 33, NO. 7, JULY 1997 REFERENCES Fig. 4. Excess noise factor versus gain. The dashed lines and the solid lines are calculated using a continuum model and the theory of Van Vliet et al., respectively. variable is known, then all moments of the distribution can be analytically evaluated. The excess noise factor can be expressed as where is the average of the gain or the first moment of. is the variance of the distribution of gain, given by. An expression for the excess noise factor using this technique is given as [22], [23] where. The solid lines in Fig. 4 show fits to the experimental data that were obtained using this approach. For the 0.1-, 0.2-, 0.5-, 0.8- m APD s, the values were 0.3, 0.36, 0.46, 0.53 and values were 0.5, 0.35, 0.3, 0.1, respectively. The value of as well as the value increases as the multiplication width increases. From Table I, it can be seen that the maximum electric field intensity is higher in the thinner multiplication regions. This appears to be inconsistent with the reported convergence of and at high fields [33], [34]. The values of can be calculated from and. They are 0.15, 0.13, 0.14, and as the multiplication width increases from 0.1 to 0.8 m. We conclude that both the electron and the hole ionization probabilities of thinner-multiplication-region APD s are higher relative to a bulk-multiplication-region APD but the electron ionization probability appears to be enhanced more than the hole ionization probability. We feel that this is a result of the nonlocalized nature of the thin-multiplicationregion APD s. IV. CONCLUSION Homojunction GaAs APD s with multiplication widths in the range from m have been fabricated and tested. It was found that the excess noise factor decreases as the multiplication width decreases. 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