This tutorial focuses on reverse-biased p-n junctions that are commonly used for making optical receivers. Metal-semiconductor-metal (MSM) photodetectors are also discussed briefly.
1. p-n Photodiodes
A reverse-biased p-n junction consists of a region, known as the depletion region, that is essentially devoid of free charge carriers and where a large built-in electric field opposes flow of electrons from the n-side to the p-side (and of holes from p to n).
When such a p-n junction is illuminated with light on one side, say the p-side, electron-hole pairs are created through absorption. Because of the large built-in electric field, electrons and holes generated inside the depletion region accelerate in opposite directions and drift to the n- and p-sides, respectively. The resulting flow of current is proportional to the incident optical power. Thus a reverse-biased p-n junction acts as a photodetector and is referred to as the p-n photodiode.
Figure (a) above shows the structure of a p-n photodiode. As shown in (b), optical power decreases exponentially as the incident light is absorbed inside the depletion region. The electron-hole pairs generated inside the depletion region experience a large electric field and drift rapidly toward the p- or n-side, depending on the electric charge (figure (c)). The resulting current flow constitutes the photodiode response to the incident optical power in accordance with the equation we derived earlier. The responsivity of a photodiode is quite high (R ~ 1 A/W) because of a high quantum efficiency.
The bandwidth of a p-n photodiode is often limited by the transit time τtr. If W is the width of the depletion region and vd is the drift velocity, the transit time is given by
τtr = W/vd
Typically, W ~10 μm, vd ~ 105 m/s, and τtr ~ 100 ps. Both W and vd can be optimized to minimize τtr. The depletion-layer width depends on the acceptor and donor concentrations and can be controlled through them. The velocity vd depends on the applied voltage but attains a maximum value (called the saturation velocity) ~ 105 m/s that depends on the material used for the photodiode. The RC time constant τRC can be written as
τRC = (RL + RS)Cp
where RL is the external load resistance, RS is the internal series resistance, and Cp is the parasitic capacitance. Typically, τRC ~ 100 ps, although lower values are possible with a proper design. Indeed, modern p-n photodiodes are capable of operating at bit rates of up to 40 Gb/s.
The limiting factor for the bandwidth of p-n photodiodes is the presence of a diffusive component in the photocurrent. The physical origin of the diffusive component is related to the absorption of incident light outside the depletion region. Electrons generated in the p-region have to diffuse to the depletion-region boundary before they can drift to the n-side; similarly, holes generated in the n-region must diffuse to the depletion-region boundary. Diffusion is an inherently slow process; carriers take a nanosecond or longer to diffuse over a distance of 1 μm. The following figure shows how the presence of a diffusive component can distort the temporal response of a photodiode.
The diffusion contribution can be reduced by decreasing the widths of the p- and n-regions and increasing the depletion-region width so that most of the incident optical power is absorbed inside it. This is the approach adopted for p-i-n photodiodes, discussed next.
2. p-i-n Photodiodes
A simple way to increase the depletion-region width is to insert a layer of undoped (or lightly doped) semiconductor material between the p-n junction. Since the middle layer consists of nearly intrinsic material, such a structure is referred to as the p-i-n photodiode. Figure (a) below shows the device structure together with the electric-field distribution inside it under reverse-bias operation.
Because of its intrinsic nature, the middle i-layer offers a high resistance, and most of the voltage drop occurs across it. As a result, a large electric field exists in the i-layer. In essence, the depletion region extends throughout the i-region, and its width W can be controlled by changing the middle-layer thickness. The main difference from the p-n photodiode is that the drift component of photocurrent dominates over the diffusion component simply because most of the incident power is absorbed inside the i-region of a p-i-n photodiode.
Since the depletion width W can be tailored in p-i-n photodiodes, a natural question is how large W should be. As discussed before, the optimum value of W depends on a compromise between speed and sensitivity. The responsivity can be increased by increasing W so that the quantum efficiency η approaches 100%. However, the response time also increases, as it takes longer for carriers to drift across the depletion region. For indirect-bandgap semiconductors such as Si and Ge, typically W must be in the range 20-50 μm to ensure a reasonable quantum efficiency. The bandwidth of such photodiodes is then limited by a relatively long transit time (τtr > 200 ps). By contrast, W can be as small as 3-5 μm for photodiodes that use direct-bandgap semiconductors, such as InGaAs. The transit time for such photodiodes is τtr ~ 10 ps. Such values of τtr correspond to a detector bandwidth Δf ~ 10 GHz with τtr >> τRC.
The performance of p-i-n photodiodes can be improved considerably by using a double-heterostructure design. Similar to the case of semiconductor lasers, the middle i-type layer is sandwiched between the p-type and n-type layers of a different semiconductor whose bandgap is chosen such that light is absorbed only in the middle i-layer. A p-i-n photodiode commonly used for lightwave applications uses InGaAs for the middle layer and InP for the surrounding p-type and n-type layers. Figure (b) above shows such an InGaAs p-i-n photodiode. Since the bandgap of InP is 1.35 eV, InP is transparent for light whose wavelength exceeds 0.92 μm. By contrast, the bandgap of lattice-matched In1-xGaxAs material with x = 0.47 is about 0.75 eV, a value that corresponds to a cutoff wavelength of 1.65 μm. The middle InGaAs layer thus absorbs strongly in the wavelength region 1.3-1.6 μm. The diffusive component of the detector current is eliminated completely in such a heterostructure photodiode simply because photons are absorbed only inside the depletion region. The front facet is often coated using suitable dielectric layers to minimize reflections. The quantum efficiency η can be made almost 100% by using an InGaAs layer 4-5 μm thick. InGaAs photodiodes are quite useful for lightwave systems and are often used in practice. The table below lists the operating characteristics of three common p-i-n photodiodes.
Considerable effort was directed during the 1990s toward developing high-speed p-i-n photodiodes capable of operating at bit rates exceeding 10 Gb/s. Bandwidths of up to 70 GHz were realized as early as 1986 by using a thin absorption layer (< 1 μm) and by reducing the parasitic capacitance Cp with a small size, but only at the expense of a lower quantum efficiency and responsivity. By 1995, p-i-n photodiodes exhibited a bandwidth of 110 GHz for devices designed to reduce τRC to near 1 ps.
Several techniques have been developed to improve the efficiency of high-speed photodiodes. In one approach, a Fabry-Perot (FP) cavity is formed around the p-i-n structure to enhance the quantum efficiency, resulting in a laser-like structure. As discussed before, a FP cavity has a set of longitudinal modes at which the internal optical field is resonantly enhanced through constructive interference. As a result, when the incident wavelength is close to a longitudinal mode, such a photodiode exhibits high sensitivity. The wavelength selectivity can be used to advantage in wavelength-division multiplexing (WDM) applications. A nearly 100% quantum efficiency was realized in a photodiode in which one mirror of the FP cavity was formed by using the Bragg reflectivity of a stack of AlGaAs/AlAs layers. This appraoch was extended to InGaAs photodiodes by inserting a 90-nm-thick InGaAs absorbing layer into a microcavity composed of a GaAs/AlAs Bragg mirror and a dielectric mirror. The device exhibited 94% quantum efficiency at the cavity resonance with a bandwidth of 14 nm. By using an air-bridged metal waveguide together with an undercut mesa structure, a bandwidth of 120 GHz has been realized. The use of such a structure within a FP cavity should provide a p-i-n photodiode with a high bandwidth and high efficiency.
Another approach to realize efficient high-speed photodiodes makes use of an optical waveguide into which the optical signal is edge coupled. Such a structure resembles an unpumped semiconductor laser except that various epitaxial layers are optimized differently. In contrast with a semiconductor laser, the waveguide can be made wide to support multiple transverse modes in order to improve the coupling efficiency. Since absorption takes place along the length of the optical waveguide (~ 10 μm), the quantum efficiency can be nearly 100% even for an ultrathin absorption layer. The bandwidth of such waveguide photodiodes is limited by τRC, which can be decreased by controlling the waveguide cross-section-area. Indeed, a 50-GHz bandwidth was realized in 1992 for a waveguide photodiode.
The bandwidth of waveguide photodiodes can be increased to 100 GHz by adopting a mushroom-mesa waveguide structure. Such as device is shown schematically in the figure below.
It was measured by using a spectrum analyzer (circles) as well as taking the Fourier transform of the short-pulse response (solid curve). Clearly, waveguide p-i-n photodiodes can provide both a high responsivity and a large bandwidth. Waveguide photodiodes have been used for 40-Gb/s optical receivers and have the potential for operating at bit rates as high as 100 Gb/s.
The performance of waveguide photodiodes can be improved further by adopting an electrode structure designed to support traveling electrical waves with matching impedance to avoid reflections. Such photodiodes are called traveling-wave photodetectors. In a GaAs-based implementation of this idea, a bandwidth of 172 GHz with 45% quantum efficiency was realized in a traveling-wave photodetector designed with a 1-μm-wide waveguide. By 2000, such an InP/InGaAs photodetector exhibited a bandwidth of 310 GHz in the 1.55-μm spectral region.
3. Avalanche Photodiodes
All detectors require a certain minimum current to operate reliably. The current requirement translates into a minimum power requirement through Pin = Ip/Rd. Detectors with a large responsivity Rd are preferred since they require less optical power. The responsivity of p-i-n photodiodes is limited and takes its maximum value Rd = q/hν for η = 1. Avalanche photodiode (APD) can have much larger values of Rd, as they are designed to provide an internal current gain in a way similar to photomultiplier tubes. They are used when the amount of optical power that can be spared for the receiver is limited.
The physical phenomenon behind the internal current gain is known as the impact ionization. Under certain conditions, an accelerating electron can acquire sufficient energy to generate a new electron-hole pair. In the band picture the energetic electron gives a part of its kinetic energy to another electron in the valence band that ends up in the conduction band, leaving behind a hole. The net result of impact ionization is that a single primary electron, generated through absorption of a photon, creates many secondary electrons and holes, all of which contribute to the photodiode current. Of course, the primary hole can also generate secondary electron-hole pairs that contribute to the current. The generation rate is governed by two parameters, αe and αh, the impact-ionization coefficients of electrons and holes, respectively. Their numerical values depend on the semiconductor material and on the electric field that accelerates electrons and holes. The figure below shows αe and αh for several semiconductors. Values ~ 1 x 104 cm-1 are obtained for electric fields in the range 2-4 x 105 V/cm. Such large fields can be realized by applying a high voltage (~ 100 V) to the APD.
APDs differ in their design from that of p-i-n photodiodes mainly in one respect: an additional layer is added in which secondary electron-hole pairs are generated through impact ionization. The following figure (a) shows the APD structure together with the variation of electric field in various layers.
Under reverse bias, a high electric field exists in the p-type layer sandwiched between i-type and n+-type layers. This layer is referred to as the multiplication layers, since secondary electron-hole pairs are generated here through impact ionization. The i-layer still acts as the depletion region in which most of the incident photons are absorbed and primary electron-hole pairs are generated. Electrons generated in the i-region cross the gain region and generate secondary electron-hole pairs responsible for the current gain.
The current gain for APDs can be calculated by using the two rate equations governing current flow within the multiplication layer:
where ie is the electron current and ih is the hole current. The minus sign in the second equation is due to the opposite direction of the hole current. The total current,
I = ie(x) + ih(x)
remains constant at every point inside the multiplication region. If we replace ih by I - ie, we obtain
die/dx = (αe - αh)ie + αhI
In general, αe and αh are x dependent if the electric field across the gain region is nonuniform. The analysis is considerably simplified if we assume a uniform electric field and treat αe and αh as constants. We also assume that αe > αh. The avalanche process is initiated by electrons that enter the gain region of thickness d at x = 0. By using the condition ih(d) = 0 (only electrons cross the boundary to enter the n-region), the boundary condition then is ie(d) = I. By integrating this equation, the multiplication factor defined as M = ie(d)/ie(0) is given by
where kA = αh/αe. The APD gain is quite sensitive to the ratio of the impact-ionization coefficients. When αh = 0 so that only electrons participate in the avalanche process, M = exp(αed), and the APD gain increases exponentially with d. On the other hand, when αh = αe, so that kA = 1, M = (1 - αed)-1. The APD gain then becomes infinite for αed = 1, a condition known as the avalanche breakdown. Although higher APD gain can be realized with a smaller gain region when αh and αe are comparable, the performance is better in practice for APDs in which either αe >> αh or αh >> αe, so that the avalanche process is dominated by only one type of charge carrier. The reason behind this requirement is discussed in other tutorials where issues related to the receiver noise are considered.
Because of the current gain, the responsivity of an APD is enhanced by the multiplication factor M and is given by
RAPD = MRd = M(ηq/hν)
It should be mentioned that the avalanche process in APDs is intrinsically noisy and results in a gain factor that fluctuates around an average value. The quantity M in the equation above refers to the average APD gain. The noise characteristics of APDs are considered in another tutorial.
The intrinsic bandwidth of an APD depends on the multiplication factor M. This is easily understood by noting that the transit time τtr for an APD is no longer given by the equation for p-n and p-i-n photodiodes but increases considerably simply because generation and collection of secondary electron-hole pairs take additional time. The APD gain decreases at high frequencies because of such an increase in the transit time and limits the bandwidth. The decrease in M(ω) can be written as
M(ω) = M0[1 + (ωτeM0)2]-1/2
where M0 = M(0) is the low-frequency gain and τe is the effective transit time that depends on the ionization coefficient ratio kA = αh/αe. For the case αh < αe, τe = cAkAτtr, where cA is a constant (cA ~ 1). Assuming that τRC << τe, the APD bandwidth is given approximately by Δf = (2πτeM0)-1. This relation shows the trade-off between the APD gain M0 and the bandwidth Δf (speed versus sensitivity). It also shows the advantage of using a semiconductor material for which kA << 1.
The table below compares the operating characteristics of Si, Ge, and InGaAs APDs. As kA << 1 for Si, silicon APDs can be designed to provide high performance and are useful for lightwave systems operating near 0.8 μm at bit rates ~100 Mb/s.
A particularly useful design, shown below, is known as reach-through APD because the depletion layer reaches to the contact layer through the absorption and multiplication regions. It can provide high gain (M ≈ 100) with low noise and a relatively large bandwidth.
Design of a silicon reach-through APD
For lightwave systems operating in the wavelength range of 1.3-1.6 μm, Ge or InGaAs APDs must be used. The improvement in sensitivity for such APDs is limited to a factor below 10 because of a relatively low APD gain (M ~ 10) that must be used to reduce the noise.
The performance of InGaAs APDs can be improved through suitable design modifications to the basic APD structure. The main reason for a relatively poor performance of InGaAs APDs is related to the comparable numerical values of the impact-ionization coefficients αe and αh. As a result, the bandwidth is considerably reduced, and the noise is also relatively high. Furthermore, because of a relatively narrow bandgap, InGaAs undergoes tunneling breakdown at electric fields of about 1 x 105 V/cm, a value that is below the threshold for avalanche multiplication. This problem can be solved in heterostructure APDs by using an InP layer for the gain region because quite high electric fields (> 5 x 105 V/cm) can exist in InP without tunneling breakdown. Since the absorption region (i-type InGaAs layer) and the multiplication region (n-type InP layer) are separate in such a device, this structure is known as SAM, where SAM stands for separate absorption and multiplication regions. As αh > αe for InP, the APD is design such that the holes initiate the avalanche process in an n-type InP layer, and kA is defined as kA = αe/αh. Figure (a) below shows a mesa-type SAM APD structure.
One problem with the SAM APD is related to the large bandgap difference between InP (Eg = 1.35 eV) and InGaAs (Eg = 0.75 eV). Because of a valence-band step of about 0.4 eV, holes generated in the InGaAs layer are trapped at the heterojunction interface and are considerably slowed before they reach the multiplication region (InP layer). Such an APD has an extremely slow response and a relatively small bandwidth.
The problem can be solved by using another layer between the absorption and multiplication regions whose bandgap is intermediate to those of InP and InGaAs layers. The quaternary material InGaAsP, the same material used for semiconductor lasers, can be tailored to have a gbandgap anywhere in the range 0.75-1.35 eV and is ideal for this purpose. It is even possible to grade the composition of InGaAsP over a region of 10-100 nm thickness. Such APDs are called SAGM APDs, where SAGM indicates separate absorption, grading, and multiplication regions. Figure (b) above shows the design of an InGaAs APD with the SAGM structure. The use of an InGaAsP grading layer improves the bandwidth considerably. As early as 1987, a SAGM APD exhibited a gain-bandwidth product MΔf = 70 GHz for M > 12. This value was increased to 100 GHz in 1991 by using a charge region between the grading and multiplication regions. In such SAGCM APDs, the InP multiplication layer is undoped, while the InP charge layer is heavily n-doped. Holes accelerate in the charge layer because of a strong electric field, but the generation of secondary electron-hole pairs takes place in the undoped InP layer. SAGCM APDs improved considerably during the 1990s. A gain-bandwidth product of 140 GHz was realized in 2000 using a 0.1-μm-thick multiplication layer that required < 20 V across it. Such APDs are quite suitable for making a compact 10-Gb/s APD receiver.
A different approach to the design of high-performance APDs makes use of a superlattice structure. The major limitation of InGaAs APDs results from comparable values of αe and αh. A superlattice design offers the possibility of reducing the ratio kA = αh/αe from its standard value of nearly unity. In one scheme, the absorption and multiplication regions alternate and consist of thin layers (~ 10 nm) of semiconductor materials with different bandgaps. This approach was first demonstrated for GaAs/AlGaAs multiquantum-well (MQW) APDs and resulted in a considerable enhancement of the impact-ionization coefficient for electrons. Its use is less successful for the InGaAs/InP material system. Nonetheless, considerable progress has been made through the so-called staircase APDs, in which the InGaAsP layer is compositionally graded to form a sawtooth kind of structure in the energy-band diagram that looks like a staircase under reverse bias. Another scheme for making high-speed APDs uses alternate layers of InP and InGaAs for the grading region. However, the ratio of the widths of the InP to InGaAs layers varies from zero near the absorbing region to almost infinity near the multiplication region. Since the effective bandgap of a quantum well depends on the quantum-well width (InGaAs layer thickness), a graded pseudo-quaternary compound is formed as a result of variation in the layer thickness.
The most successful design for InGaAs APDs uses a superlatttice structure for the multiplication region of a SAM APD. A superlattice consists of a periodic structure such that each period is made using two ultrathin (~ 10-nm) layers with different bandgaps. In the case of 1.55-μm APDs, alternate layers of InAlGaAs and InAlAs are used, the latter acting as a barrier layer. An InP field-buffer layer often separates the InGaAs absorption region from the superlattice multiplication region. The thickness of this buffer layer is quite critical for the APD performance. For a 52-nm-thick field-buffer layer, the gain-bandwidth product was limited to MΔf = 120 GHz but increased to 150 GHz when the thickness was reduced to 33.4 nm. These early devices used a mesa structure. During the late 1990s, a planar structure was developed for improving the device reliability. The figure below shows such a device schematically together with its 3-dB bandwidth measured as a function of the APD gain. The gain-bandwidth product of 110 GHz is large enough for making APDs operating at 10 Gb/s. Indeed, such an APD receiver was used for a 10-Gb/s lightwave system with excellent performance.
The gain-bandwidth limitation of InGaAs APDs results primarily from using the InP material system for the generation of secondary electron-hole pairs. A hybrid approach in which a Si multiplication layer is incorporated next to an InGaAs absorption layer may be useful provided the heterointerface problems can be overcome. In a 1997 experiment, a gain-bandwidth product of more than 300 GHz was realized by using such a hybrid approach. The APD exhibited a 3-dB bandwidth of over 9 GHz for values of M as high as 35 while maintaining a 60% quantum efficiency.
Most APDs use an absorbing layer thick enough (about 1 μm) that the quantum efficiency exceeds 50%. The thickness of the absorbing layer affects the transit time τtr and the bias voltage Vb. In fact, both of them can be reduced significantly by using a thin absorbing layer (~ 0.1 μm), resulting in improved APDs provided that a high quantum efficiency can be maintained. Two approaches have been used to meet these somewhat conflicting design requirements. In one design, a FP cavity is formed to enhance the absorption within a thin layer through multiple round trips. An external quantum efficiency of ~70% and a gain-bandwidth product of 270 GHz were realized in such a 1.55-μm APD using a 60-nm-thick absorbing layer with a 200-nm-thick multiplication layer. In another approach, an optical waveguide is used into which the incident light is edge coupled. Both of these approaches reduce the bias voltage to near 10 V, maintain high efficiency, and reduce the transit time to ~1 ps. Such APDs are suitable for making 10-Gb/s optical receivers.
4. MSM Photodetectors
In a different kind of photodetector, known as a metal-semiconductor-metal (MSM) photodetector, a semiconductor absorbing layer is sandwiched between two metal electrodes. As a result, a Schottky barrier is formed at each metal-semiconductor interface that prevents the flow of electrons from the metal to the semiconductor. Similar to a p-i-n photodiode, electron-hole pairs generated through the absorption of light flow toward the metal contacts, resulting in a photocurrent that is a measure of the incident optical power. However, in contrast with a p-i-n photodiode or APD, no p-n junction is required. In this sense, an MSM photodetector employs the simplest design.
For practical reasons, it is difficult to sandwich a thin semiconductor layer between two metal electrodes. This problem can be solved by placing the two metal contacts on the same (top) side of an epitaxially grown absorbing layer using an interdigited electrode structure with a finger spacing of about 1 μm. Figure (a) below shows the basic design.
In modern devices, the concentric ring structure shown in figure (b) above is often used in place of finger-shaped electrodes. The resulting planar structure has an inherently low parasitic capacitance and thus allows high-speed operation (up to 300 GHz) of MSM photodetectors. If the light is incident from the electrode side, the responsivity of a MSM photodetector is reduced because some light is blocked by the opaque electrodes. This problem can be solved through back illumination if the substrate is transparent to the incident light.
GaAs-based MSM photodetectors were developed throughout the 1980s and exhibit excellent operating characteristics. The development of InGaAs-based MSM photodetectors, suitable for lightwave systems operating in the range 1.3-1.6 μm, started in the late 1980s, with most progress made during the 1990s. The major problem with the InGaAs is its relatively low Schottky-barrier height (about 0.2 eV). This problem was solved by introducing a thin layer of InP or InAlAs between the InGaAs layer and the metal contact. Such a layer, called the barrier-enhancement layer, improves the performance of InGaAs MSM photodetectors drastically. The use of a 20-nm-thick InAlAs barrier-enhancement layer resulted in 1992 in 1.3-μm MSM photodetectors exhibiting 92% quantum efficiency (through back illumination) with a low dark current. A packaged device had a bandwidth of 4 GHz despite a large 150 μm diameter. If top illumination is desirable for processing or packaging reasons, the responsivity can be enhanced by using a semitransparent metal contacts. In one experiment, the responsivity at 1.55 μm increased from 0.4 to 0.7 A/W when the thickness of gold contact was reduced from 100 to 10 nm. In another approach, the structure is separated from the host substrate and bonded to a silicon substrate with the interdigited contact on bottom. Such an "inverted" MSM photodetector then exhibits high responsivity when illuminated from the top.
The temporal response of MSM photodetectors is generally different under back and top illuminations. In particular, the bandwidth Δf is larger by about a factor of 2 for top illumination, although the responsivity is reduced because of metal shadowing. The performance of a MSM photodetector can be further improved by using a graded superlattice structure. Such devices exhibit a low dark-current density, a responsivity of about 0.6 A/W at 1.3 μm, and a rise time of about 16 ps. In 1998, a 1.55-μm MSM photodetector exhibited a bandwidth of 78 GHz. By 2002, the use of a traveling-wave configuration resulted in a GaAs-based device operating near 1.3 μm with a bandwidth > 230 GHz. The planar structure of MSM photodetectors is also suitable for monolithic integration.