PHOTODIODES with high speed and sensitivity are

Transcription

1 482 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 34, NO. 3, MARCH 1998 Performance of Thin Separate Absorption, Charge, and Multiplication Avalanche Photodiodes K. A. Anselm, H. Nie, C. Hu, C. Lenox, P. Yuan, G. Kinsey, J. C. Campbell, and B. G. Streetman Abstract Previously, it has been demonstrated that resonantcavity-enhanced separate-absorption-and-multiplication (SAM) avalanche photodiodes (APD s) can achieve high bandwidths and high gain bandwidth products while maintaining good quantum efficiency. In this paper, we describe a -based resonant-cavity-enhanced SAM APD that utilizes a thin charge layer for improved control of the electric field profile. These devices have shown RC-limited bandwidths above 30 GHz at low gains and gain bandwidth products as high as 290 GHz. In order to gain insight into the performance of these APD s, homojunction APD s with thin multiplication regions were studied. It was found that the gain and noise have a dependence on the width of the multiplication region that is not predicted by conventional models. Calculations using width-dependent ionization coefficients provide good fits to the measured results. These calculations indicate that the gain bandwidth product depends strongly on the charge layer doping and on the multiplication layer thickness and, further, that even higher gain bandwidth products can be achieved with optimized structures. Index Terms Avalanche photodiodes, III V compoundes. I. INTRODUCTION PHOTODIODES with high speed and sensitivity are necessary components in long-haul, high-bit-rate optical communication systems. Avalanche photodiodes (APD s) are preferred for these systems because their internal gain results in higher sensitivity than PIN photodetectors [1], [2]. The requirements for high-performance APD s include high quantum efficiency, high speed, low dark current, a high gain bandwidth product, and low multiplication noise. Resonant-cavity separate-absorption-and-multiplication (SAM) APD s have been shown to achieve all of these properties [3], [4]. The SAM structure has separate high-field multiplication and absorption regions. Usually this results in lower dark currents [5]. Another benefit of the SAM APD structure is that only a single type of carrier is injected into the multiplication region, which is a well-known requirement for reducing the multiplication noise that arises from the stochastic nature of the multiplication process [6]. As a result of their excellent performance, SAM APD s have been widely deployed in optical communications systems [7], [8]. Manuscript received August 14, 1997; revised November 24, This work was supported by the Joint Services Electronics Program under Contract F C0045, by the DARPA-sponsored Center for Optoelectronic Science and Technology, and by the National Science Foundation. The authors are with the Microelectronics Research Center, Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX USA. Publisher Item Identifier S (98) By decoupling the optical and electrical path lengths, the resonant-cavity structure can achieve high peak external quantum efficiencies with thin absorption layers [9] [11], thus circumventing the well-known tradeoff between quantum efficiency and carrier transit time. As a result, resonant-cavity SAM APD s have achieved very high bandwidths 20 GHz in the low gain regime where the RC and transit times usually dominate [4]. At high gain, the most significant limitation on the bandwidth of APD s is the avalanche buildup time, which is a function of the gain, the thickness of the multiplication region, the electron and hole velocities, and the physics of the ionization process. It has been shown that decreasing the multiplication layer thickness can lead to high gain-bandwidth products [12]. It has also been found that the use of thin multiplication layers in SAM APD s suppresses the multiplication noise [3]. One consequence of thin multiplication layers, however, is that the electric fields required to achieve sufficient gain increase as the layer thicknesses decrease. These high fields can lead to bandto-band tunneling inside the high-field region which can, in turn, produce excessive dark current. This problem can be effectively eliminated with the separate absorption, charge, and multiplication (SACM) APD structure that is described in this paper. With a thin uniformly doped charge layer inserted between the intrinsic multiplication region and the absorption region, the high electric field inside the multiplication region becomes relatively uniform compared to the electric field profile of the SAM APD. For APD s with thin multiplication layers, the assumptions of the conventional models for gain and noise are not expected to be valid [13] [16]. In this paper, it is shown that the conventional impact ionization models do not accurately predict either the multiplication noise or the gain of thin multiplication regions. However, it is also found that a widthdependent scaling of the ionization coefficients gives fits that are consistent with measurements of both the gain and the multiplication noise. The ionization coefficients that have been determined by this empirical scaling procedure have been used to design thin, resonant-cavity-enhanced SACM APD s with improved gain bandwidth characteristics. Measurements of the dc current voltage characteristics and bandwidth of these resonant-cavity-enhanced SACM APD s are presented and compared to predictions. II. MODELS This section reviews models for the behavior of two-carrier impact ionization under the assumption that impact ionization /98$ IEEE

2 ANSELM et al.: PERFORMANCE OF THIN SEPARATE ABSORPTION, CHARGE, AND MULTIPLICATION APD S 483 is a continuous, local process. For the case that the electron and hole ionization coefficients are neither equal nor uniform across the multiplication region, a model for the gain and noise was derived by McIntyre [6]. The gain, for pure electron injection into an ionization region of width can be written as where and are the electron and hole ionization coefficients, respectively. The convention for these equations is that the electrons travel toward increasing values of. The noise spectral density can be expressed as where is the function describing the generation of carriers per unit length in the device and is the gain resulting from the generation of carrier pairs at a position and is written as The excess noise factor is a measure of the contribution of the ionization process to the noise and is defined as the noise power spectral density for a photocurrent, divided by the multiplied shot noise power density. Under the condition of uniform electric fields and pure electron injection, the excess noise factor is For the case of pure hole injection, the excess noise factor is the same except that is replaced by where is the ratio of the hole ionization coefficient to the electron ionization coefficient. From this result, it can be easily shown that lower noise is achieved if the carrier with the higher ionization coefficient is the injected carrier. If the electric field is not uniform, the excess noise is still generally written in terms of (4) using an effective value of. A conventional parameterization for the electron ionization coefficient is given by where is the electric field and and are constants. The same form is also used for the hole ionization coefficient. An early model of the frequency response of uniform APD s at high gain was developed by Emmons [17]. Under this model, which assumes uniform multiplication regions, the bandwidth of the APD is inversely related to the effective transit time. The effective transit time is proportional to the gain, the ratio of the ionization rates the actual carrier (1) (2) (3) (4) (5) transit time, and a correction factor that varies slowly with. Since the bandwidth is inversely proportional to the gain, the frequency response at high gains is usually characterized in terms of a gain bandwidth product. Emmons model also predicts that higher bandwidths result from smaller values of. Other models that allow for varying ionization rates and different carrier velocities have been developed, but they utilize complex correction factors and require that the ratio of carrier ionization rates be constant [18]. Another approach is to use the transfer-matrix method. Hollenhorst introduced the transfer-matrix model to calculate steady-state gain and the excess noise factor for arbitrary APD structures [19]. Kahraman et al. developed a more general matrix approach to analyze the frequency response of an APD with arbitrary structure [20]. In Hollenhorst s model, the device is divided into multiple layers that can each be approximated to have uniform electric fields. Except for simple structures, this approach does not yield tractable analytic solutions, but a numerical solution is straightforward. Hollenhorst derived the matrix elements for any given layer within a multilayer structure for the case that there is absorption of light with a constant absorption coefficient and for the case that there is impact ionization in the layer, but not for the more general case in which there can be both absorption and impact ionization within a single layer. Since the effect of impact ionization in the absorption layers can be significant for thin SACM APD s, we derive the response coefficients considering both impact ionization and uniform photogeneration of carriers in each layer. The uniform photogeneration of carriers within a layer is chosen not only for simplicity, but also because by using multiple layers, it is easy to simulate an arbitrary photogeneration profile. Our approach makes a single extension of Hollenhorst s model and is a special case of the treatment by Kahraman et al. As such, it is well suited to modeling resonant-cavity-enhanced photodiodes. The derivation of the transfer-matrix model starts with equations for the hole and electron current densities in the frequency domain: with the convention that the current is positive in the direction. The generation term is written as where is the photogenerated current density per unit length in the layer under consideration. Since these equations are linear, the currents on the left and right sides of the layer can be related through the use of a transfer matrix as follows: or in shorthand. The subscript refers to the current density on left side of the layer and the (6) (7) (8)

3 484 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 34, NO. 3, MARCH 1998 subscript refers to the right side. Hollenhorst also defined the contribution of a given layer to the electrode current as (9) If the linear response coefficients and are known for each layer, then the total response of the multilayer structure can be determined using combination rules described by Hollenhorst. The electrode response due to electron injection is (10) where the linear response coefficients are for the combined structure of thickness. The combined response coefficients for the first through th layers can be determined using the following recursive relations: (11) The linear response coefficients for an individual layer with a thickness can be found by solving (6) (9): where and (12) (13) (14) (15) The equations for and are identical to those Hollenhorst derived for a uniform impact-ionization layer with a slight change in notation. The terms and account for the generation of carriers and differ from Hollenhorst s results. It is assumed that the carrier velocities and are constant throughout each layer. The linear response coefficients derived here are appropriate for the cases where there is absorption, ionization, both, or neither in any given layer. Hollenhorst also Fig. 1. The electric field profile of a uniform Al 0:2Ga 0 :8As APD with a 200-nm multiplication layer and cm 03 doping in the end regions. The electric field is is calculated using the commercial simulator, Medici. derived the linear response coefficients for a carrier-trapping layer, but this effect is not considered here because carrier trapping at the graded heterointerfaces in the SACM APD s used in this study is insignificant. III. IMPACT IONIZATION IN THIN AND Al Ga As LAYERS In order to study the characteristics of thin multiplication regions in and Al Ga As, a series of PIN homojunction APD s were grown in a Varian GEN II molecular beam epitaxy reactor on n (100) substrates. The layer thicknesses were calibrated with reflection high-energy electron diffraction oscillations and were estimated to be accurate within a few percent. The doping was determined using Hall effect measurements and was estimated to be accurate within 10%. The photodiodes had n- and p-doping of cm with intrinsic layer thicknesses of 100, 200, 500, 800, and 1600 nm. The intrinsic layers were nominally undoped with a net n-type background doping concentration less than 10 cm. The Al Ga As photodiodes had n- and p-doping of 4 10 cm and 3 10 cm, respectively, with undoped intrinsic regions of 100, 200, 400, 800, and 1600 nm. Layers 1.5 m thick of or Al Ga As were grown on top of the PIN structures to act as an absorption layer and to ensure nearly pure electron injection into the high-field multiplication region. The top layer of each structure was a 300-Å-thick, p- doped (10 cm ) contact layer. The structures were grown with an arsenic overpressure of 5 10 torr at a growth temperature of 590 C. After the contacts were patterned using a lithography and liftoff process, 100- m- diameter mesas were lithographically patterned and etched using a H SO :H O :H O (1 : 8 : 30) mixture. Au Cr was used as the contact metal to the top layer and In was used as the contact on the back side of the wafer. The contacts were annealed under a nitrogen ambient at 450 C for 30 s. The structure and electric field profile of the 200-nm Al Ga As homojunction APD are illustrated in Fig. 1. The photocurrents were measured on 100- m-diameter mesas using a filtered microscope light source. Identical gain curves were achieved with a HeNe laser nm) that was carefully focused on the top of the mesa. This would seem to indicate that most of the light is absorbed in the top 1.5- m layer, which results primarily in electron injection into the multiplication region. The photocurrents at low bias were nearly constant and served as a unity-gain reference for the gain and excess noise measurements. At higher biases, each

4 ANSELM et al.: PERFORMANCE OF THIN SEPARATE ABSORPTION, CHARGE, AND MULTIPLICATION APD S 485 Fig. 2. The photocurrent and dark current of 100-m diameter homojunction APD s with multiplication layer thicknesses of nm. (a) (a) (b) Fig. 4. The excess noise factor for: (a) and (b) Al.2Ga.8As APD s of varying multiplication thicknesses. The symbols represent measured results and the dashed curves represent results calculated using (2) and the fitted ionization coefficients for each thickness. (b) Fig. 3. The measured (symbols) and fit (dashed lines) gains for (a) and (b) Al 0:2Ga 0:8As homojunction APD s. of the structures was able to achieve gain in excess of 30. The dark currents of both the and the Al Ga As APD s were low, on the order of a few to tens of nanoamps at gains near 20 for mesa diameters 100 m. The measured photocurrents and dark currents for the APD s are shown in Fig. 2. The measured currents are used to determine the gains for each of the structures, as indicated by the symbols in Fig. 3(a) and (b). No significant changes in the gains were observed upon regrowth and reprocessing of the structures. To measure the noise, the samples were mounted on a Wiltron connector that was connected through a bias tee to an HP8970 noise figure meter that was programmed to measure at 50 MHz with a bandwidth of 4 MHz. A He Ne laser ( nm) was carefully focused on top of a mesaisolated device that was operating in the unity-gain regime and the noise power density was measured as a function of photocurrent. Then the noise power density was measured as a function of gain to determine the excess noise factor. More details about the noise measurement technique can be found in [21]. The measured excess noise factors for these APD s are shown as symbols in Fig. 4(a) and (b). The excess noise factors are nearly the same for the and 800-nm APD s, but are significantly lower for thinner multiplication regions. The values of the fitted effective of the devices range from 0.48 for the 1600-nm APD s to 0.25 for the 100-nm APD s. The values of for the Al Ga As photodiodes

5 486 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 34, NO. 3, MARCH 1998 vary from 0.62 for the 1600-nm APD s to 0.26 for the 200-nm APD s. Structures containing multiple-quantum-well (MQW) multiplication regions have been proposed as a way to reduce the excess noise in APD s [22], [23], but Hu et al. [24] have shown that comparable reductions in noise can be achieved by using thin multiplication layers. If ionization coefficients for bulk and Al Ga As from [25] and [26], respectively, are used, the fit to our measured data is poor, especially for the thinnest APD s. The bulk ionization rates do not fit the measured excess noise factors and predict increasing excess noise factors with decreasing multiplication width, contrary to the observed trends. Even if the parameters, and are chosen to fit the gains for one APD, there is no single set of parameters for (5) that can be used to fit the gain for thin APD s with different multiplication region widths. One reason for these discrepancies is that the reported ionization coefficients may not be accurate in the range of electric fields required to get gain in the thin APD s. Another reason is that for very thin multiplication layers, the assumptions of the conventional impact ionization model begin to fail. Impact ionization is a discrete process which depends on the history of the carriers, but the conventional models assume that impact ionization is a continuous local process. Although these assumptions are reasonable for relatively thick multiplication layers, they are not valid for thin multiplication regions. An example of an effect that becomes prominent in thin multiplication regions is the dead space effect. After an impact ionization event, a carrier must travel a short distance (the dead space) before it can gain enough energy to have a reasonable probability of causing another impact ionization. There are several models that consider these nonlocal effects [13] [16] and they indicate that McIntyre s model overestimates the excess noise factor and gain for devices in which nonlocal effects are important. For an empirical fit of the gain and multiplication noise of the thin homojunction APD s, we have multiplied the ionization coefficients by width-dependent correction factors. Fitting the ionization coefficients using only gain data for the case of pure electron injection is not possible because the ratio of the ionization coefficients cannot be uniquely determined. However, according to McIntyre s model, the parameter is the ratio of the ionization coefficients in a uniform multiplication region. For the purpose of determining the ionization coefficients, the ratio of ionization coefficients was taken to be the value of that was derived by fitting (4) to the measured excess noise factors. Since nonlocal effects are present, the relationship between the measured effective and the ratio of the ionization coefficients is no longer clear, but it is assumed that McIntyre s model is still a reasonable approximation. This approach has the advantages that it is easy to implement and is compatible with conventional models. The gain curves that were calculated using the fitted ionization coefficients are shown as dashed lines in Fig. 3(a) and (b). The fitting was done by first determining the values of and for and that best fit the gain and excess noise for the 1600-nm APD s. The parameter was chosen to best match the curvature of the gain plots. Gains of the thinner Fig. 5. Fitted ionization coefficients of and over the range of electric fields for which they are valid. The solid lines are for electron ionization and the dashed lines for hole ionization. The heavy lines are coefficients reported in [25] for. The thinner lines are the fits for five different multiplication regions with thicknesses ranging from 100 (highest range of electric fields) to 1600 nm (lowest fields). APD s were fit by multiplying and by correction factors such that the breakdown voltages matched the measured values and the ratios of the ionization coefficients fit the values that were determined from the noise measurements. and were not changed as functions of the device thickness or electric field. The fitted values of and are listed in Tables I and II for both the and the Al Ga As APD s. From the plot of the fitted ionization rates for, shown in Fig. 5, it is seen that for the same electric field, the thinner devices have lower ionization rates for both electrons and holes. For comparison, the ionization rates of [25] are also shown. Relative to the values in the literature for bulk, it appears that the hole ionization is more strongly affected by the dead space than the electron ionization. This result depends on the assumption that the ratio of the ionization rates is given by the noise data. Although this assumption is not completely valid, preliminary Monte Carlo simulations indicate that holes are more strongly affected by the dead space than electrons in [27]. The dashed lines in Fig. 4 correspond to the excess noise factors calculated with the fitted ionization coefficients. In general, the fitted curves match well with the measured data. For the thinnest devices at gains less than 10, however, the excess noise cannot be fit to (4) for any value of effective. This effect is possibly due to the discrete nature of the multiplication process [24]. Since a proper noise model depends on the details of the impact ionization process, a description of the mechanism is better left to more sophisticated methods, such as Monte Carlo simulations. Regardless, these results show that adding a simple width dependence to the effective ionization coefficients can produce fits that are consistent with both the measured gain and multiplication noise under electron injection down to very thin multiplication regions. IV. HIGH-PERFORMANCE SACM APDS This section discusses the design and characteristics of SACM APD s using thin layers of and Al Ga As. In

6 ANSELM et al.: PERFORMANCE OF THIN SEPARATE ABSORPTION, CHARGE, AND MULTIPLICATION APD S 487 TABLE I PARAMETERS FOR IONIZATION COEFFICIENTS OF 1600 nm 800 nm 500 nm 200 nm 100 nm Bulman s coeff. A cm cm cm cm cm cm 01 E c V/cm V/cm V/cm V/cm V/cm V/cm m A cm cm cm cm cm cm 01 E c V/cm V/cm V/cm V/cm V/cm V/cm m Robbins coeff. TABLE II PARAMETERS FOR IONIZATION COEFFICIENTS OF 1600 nm 800 nm 400 nm 200 nm 100 nm A cm cm cm cm cm cm 01 E c V/cm V/cm V/cm V/cm V/cm V/cm m A cm cm cm cm cm cm 01 E c V/cm V/cm V/cm V/cm V/cm V/cm m order to have a good quantum efficiency at the designed wavelength, a resonant-cavity-enhanced structure was used. The structure and approximate electric field profile of a resonantcavity-enhanced SACM APD are shown in Fig. 6. In this structure, light at the resonant wavelength can make multiple passes through the absorption layer, resulting in a high peak external quantum efficiency even though a very thin absorption layer is used. With only 35-nm-thick In Ga As layers, resonant-cavity-enhanced SAM APD s have been shown to achieve external quantum efficiencies of nearly 80% with spectral widths of 5 nm [3]. The crystal growth was done in a molecular beam epitaxy reactor on n or semi-insulating (100) substrates. All of the layers were grown at 590 C under an arsenic overpressure of 5 10 except for the In Ga As absorption layer and the p contact layer which were grown at 540 C. The bottom mirror consists of a 20-pair n-type AlAs stack. After the mirror was finished and the growth rates were recalibrated, the optical cavity was grown. In addition to growth rate calibrations by reflection high-energy electron diffraction, a Filmetrics optical monitoring system was used to ensure that the optical thickness of the cavity was correct. The first layer in the cavity was an n (4 10 cm ) spacer layer, which acts as a bottom contact layer. This layer was followed by three Al Ga As layers: an n-doped spacer layer, an undoped multiplication layer, and a uniformly p-doped charge layer. A thin compositionally graded buffer region was then grown, followed by a 35-nm In Ga As absorption layer. The material was graded back to Al Ga As and after a thin undoped spacer layer, a p Al Ga As top layer was grown to a thickness such that the cavity was resonant at the desired wavelength. Finally, a thin 30-nm-thick p (10 cm ) layer was grown for the top contact. Two different SACM APD structures were investigated. One used a 100-nm multiplication region, Fig. 6. The structure and electric field profile under reverse bias for a resonant-cavity SACM APD. a 50-nm charge layer ( cm, cm ), and a 350-nm total intrinsic region thickness. The other structure had an 80-nm multiplication layer thickness, a 50-nm-thick charge layer cm and a 450-nm total intrinsic region. The charge layer dopings were determined by Hall effect measurements and are consistent with the observed punchthrough voltages. The high-speed APD was fabricated by first depositing two thin layers of Ni(5 nm) Pt(5 nm) followed by a conventional Ti Pt Au layer stack. This step was followed by mesa etching to the n layer. Then a Ni AuGe Au ring contact was defined around the base of the mesa by photolithographic liftoff. Both metals were annealed in forming gas at 440 C for 30 seconds to reduce the contact resistance. The device was isolated by reactive ion etching (RIE) nonselectively through the AlAs mirror layers to the semi-insulating substrate. A thick polyimide planarizing layer was then spun

7 488 IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 34, NO. 3, MARCH 1998 Fig. 7. An illustration of a resonant-cavity SACM APD processed for high-speed measurements. on the whole wafer and cured at 250 C. Planarization was a necessary step since the RIE etch leaves a 3-mm-tall mesa that makes further processing very difficult. The polyimide also served as dielectric spacer between the electrodes, which yielded lower parasitic capacitance. After depositing a thin SiO layer as an O dry etching mask on the polyimide, contact windows were etched through the polyimide to the contact metals. Finally, a coplanar waveguide metal was evaporated on top of the thin SiO layer for device characterization. ZnSe MgF layers were deposited after processing to act as a top mirror on the cavity. Typically, two pairs of dielectric mirrors, with a reflectivity near 85%, gave the best peak external quantum efficiency. A cross section of the processed devices is illustrated in Fig. 7. From the transmission-line-method (TLM) patterns, the p- type contact resistivity was determined to be cm Usually the n-type contact resistivity obtained with Ni AuGe Au contacts was well below 5 10 W cm. Based on impedance measurements, the forward-bias resistance of a 14- m-diameter mesa was determined to be 30 and the capacitance was 48 ff. Using measured capacitances of different area mesas, the parasitic capacitance was extrapolated to be about 15 ff. In order to balance the RC and transittime components of the bandwidth, the optimum intrinsic region thickness was determined to be 450 nm for a 14- m-diameter device. The estimated bandwidth was 33 GHz. Measurements of the dc current voltage characteristics showed that these SACM APD s reach avalanche breakdown near 15 V. Significant gain occurred at lower biases than typical APD structures due to the thin layers. The dark currents were also low, less than 1 na at 90% of the breakdown voltage for a 40-m-diameter mesa. The punchthrough voltages were 4 V, depending on the charge layer doping. Punchthrough is the condition at which the edge of the depletion region reaches the absorption layer and photogenerated carriers can be pulled across the barrier at the heterointerface. A near unity gain at punchthrough results in a more accurate measure of the unitygain photocurrent, which is needed for an accurate measure of the quantum efficiency, the gain, the excess noise factor, and the gain bandwidth product. If there is significant gain before punchthrough, the ionization coefficients and nonlocal effects must be well characterized if these performance parameters Fig. 8. Measured and calculated dc current voltage characteristics of a SACM APD with a 100-nm Al 0:2Ga 0:8As multiplication layer, 50-nm, p-doped Al 0:2Ga 0:8As charge layer, and 200-nm low-field region. are to be accurately determined. Measured and simulated gains for the SACM APD with 5 10 cm doping in the charge layer are shown in Fig. 8. The calculated gain using the ionization coefficients that were fitted for the homojunction APD s gives a reasonable fit to the measured data, and a much better fit than the gains predicted using the reported bulk ionization coefficients [25], [26]. The frequency response of the resonant-cavity SACM APD s was measured by analyzing the photocurrent spectrum with a microwave probe system and a 50-GHz spectrum analyzer [28]. A passively mode-locked Ti-sapphire laser with 200-fs pulsewidth and 76-MHz pulse repetition rate was used as the optical source. Care was taken to focus all the light onto the top of the device in order to avoid a diffusion tail in the photoresponse. The 3-dB bandwidths of the resonant-cavity devices were measured under a range of bias voltages. The bandwidth versus dc avalanche gain for an SACM APD with an 80-nm multiplication layer and a charge layer doping concentration of 7 10 cm is shown in Fig. 9. A bandwidth greater than 30 GHz was seen at low gains. This bandwidth is close to predictions and is the highest reported bandwidth for an APD at low gains. A gain bandwidth product of 240 GHz was observed at high gains, assuming unity gain at punchthrough. Calculations indicated that the gain at punchthrough is approximately 1.2, yielding an estimated gain bandwidth product of 290 GHz. This is the highest gain bandwidth product reported for compound semiconductor APD s. For comparison, the best reported results for a MQW APD [29] and planar SAGM APD [30] are also shown in Fig. 9. In order to model the device, the multi-layer APD approach was used with effective ionization coefficients that were interpolated from the homojunction APD s. It was assumed that half the thin charge layer was effectively part of the multiplication layer and half was part of the low-field absorption region. Since most of the anticipated impact ionization in the absorption layer is due to hot holes injected from the multiplication layer, there may be, in effect, no dead space for multiplication in the absorption layer. For that reason,

8 ANSELM et al.: PERFORMANCE OF THIN SEPARATE ABSORPTION, CHARGE, AND MULTIPLICATION APD S 489 Fig. 9. The measured bandwidth versus gain for a SACM APD with an 80-nm multiplication layer and a cm 03 p-doped 50-nm charge layer. Fig. 11. The calculated gain bandwidth products and gains at punchthrough for SACM APD s as a function of doping in the charge layer. The represented structures have multiplication regions thicknesses of 100 and 80 nm and total intrinsic region thicknesses of 350 and 450 nm. The hollow symbols indicate the measured gain bandwidth products multiplied by the calculated gain at punchthrough and the larger boxes indicate uncertainty in the doping and speed measurements. Fig. 10. The electric field in the multiplication and absorption layer as a function of doping in the charge layer. The calculations are for a SACM APD with a 100-nm multiplication and 50-nm charge layer at a gain of 100. the ionization coefficients for the thickest homojunction APD s were assumed for the absorption layer. The lack of knowledge about the ionization in the absorption layer was a significant source of uncertainty in the gain bandwidth calculations. However, based on the similarity of the measured and calculated gain for the SACM APD shown in Fig. 8, it is believed that these assumptions are reasonable. The carrier saturation velocities were assumed to be uniform throughout the intrinsic region with an electron velocity of 8 10 cm/s and a hole velocity of 6 10 cm/s. These values were used since there are few measurements of the carrier velocities at the electric fields present in these devices. However, these are thought to reasonable values since 8 10 cm/s is reported for the electron saturation velocity in Al at an electric field of 4 10 V/cm [31] and hole velocities in are near 6 10 cm/s above 10 V/cm [32]. In the design of SACM APD s the thickness of the absorption and multiplication regions and the doping of charge layers are critical parameters. Fig. 10 shows that higher doping in the charge layer results in higher peak electric fields but lower fields in the absorption layer. Fig. 11 shows the measured gain bandwidth products of three different SACM APD s. The calculated gain bandwidths are also shown as a function of doping in the charge layer. More heavily doped multiplication regions result in higher gain bandwidth products but also result in higher gains at punchthrough. Because of the lower multiplication noise and the shorter distance that carriers must travel [17], thinner multiplication regions are expected to result in higher gain bandwidth products. However, Fig. 11 shows that the SACM APD structure with the thinner multiplication layer has a lower gain bandwidth product unless a much higher charge layer doping is used. The reason is that the gain bandwidth product is very sensitive to even small amounts of unwanted multiplication outside of the multiplication layer and the performance benefits of thinner multiplication regions are obscured by impact ionization in the absorption and spacer layers. The calculations show, however, that increasing the charge layer doping reduces the problem of high fields in the absorption layer and should result in even higher gain bandwidth products. V. SUMMARY Measurements on thin and Al homojunction APD s show a significant decrease in gain and multiplication noise compared to conventional models. This effect is due to nonlocal processes that become significant in thin APD s. It was found that width-dependent effective ionization coefficients can be used to empirically fit both the excess noise under electron injection and the gain characteristics of homojunction APD s using conventional local-effect models. A resonant-cavity-enhanced SACM APD with record highspeed and record high gain bandwidth has been designed and fabricated. The 3-dB bandwidth of this APD at low gains is 33 GHz and the gain bandwidth product is approximately 290 GHz. Calculations using the width-dependent effective ionization coefficients agree reasonably well with measured results and indicate that even higher gain bandwidth products can be achieved with careful control of the electric fields in the absorption region.

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