Sources, Modulators, and Detectors For Fiber-Optic Communication Systems Part 10

Electrorefraction in Semiconductors

Near the band edge in semiconductors, the change in refractive index with applied field can be particularly large, especially in quantum wells, and is termed electrorefraction, or the electrore-fractive effect. Electrorefraction is calculated from the spectrum of electroabsorption using the Kramers-Kronig relations. Enhanced electroabsorption means enhanced electrorefraction at wavelengths below the band edge. Electrorefraction allows significant reductions in length and drive voltages required for phase modulation in waveguides. The voltage-length product depends on how close to the absorption resonance the modulator is operated. It also depends on device design. As with electroabsorption modulators, the field is usually applied across a pin junction. Some reported n voltage-length products are 2.3 V mm in GaAs/AlGaAs QW (at 25-V bias), 1.8 V mm in InGaAs/InAlAs QW and 1.8 V mm in GaAs/AlGaAs double heterostructures.61 These voltage-length products depend on wavelength detuning from the exciton resonance and therefore on insertion and electroabsorption losses. The larger the voltage-length product, the greater the loss.

Typical Performance. Electrorefraction is polarization dependent, because the quantum-confined Stark effect is polarization dependent. In addition, the TE polarization experiences the electro-optic effect, which may add to or subtract from the electrorefractive effect, depending on the crystal orientation. Typically, An for TE polarization (in an orientation that sums these effects) will be 8 x 10-4 at 82 kV/cm (7 V across a waveguide with an i layer 0.85 |im thick). Of this, the contribution from the electro-optic effect is 2 x 10-4. Thus, electrorefraction is about 4 times larger than the electro-optic effect. The voltage-length product will thus be enhanced by a factor of four, reducing to 5 Vmm. Of course, this ratio depends on the field, since the electro-optic effect is linear in field and electrorefraction is quadratic in the field.

Advanced QW Concepts. Compressive strain increases electrorefraction, as it does QCSE. Measurements at the same 82 kV/cm show an increase from 2.5 x 10-4 to 7.5 x 10-4 by increasing compressive strain.63 Strained QWs also make it possible to achieve polarization-independent electrorefractive modulators (although when integrated with a semiconductor laser, which typically has a well-defined polarization, this should not be a necessity).

Advanced QW designs have the potential to increase the refractive index change below the exciton resonance. One example analyzes asymmetric coupled QWs and finds more than 10 times enhancement in An below the band edge, at least at small biases. However, when fabricated and incorporated into Mach-Zehnder modulators, the complex three-well structure lowered Vn by only a factor of 3, attributed to the growth challenges of these structures.64

Nipi Modulators. One way to obtain a particularly low voltage-length product is to use MQWs in a hetero-npi waveguide. These structures incorporate multiple pin junctions (alternating n-i-p-i-n-i-p) and include QWs in each i layer. Selective contacts to each electrode are required, which limits how fast the modulator can be switched. A voltage-length product of 0.8 Vmm was observed at a wavelength 115 meV below the exciton resonance. The lowest voltage InGaAs modulator had Vn = 0.5 V, at speeds up to 110 MHz. Faster speeds require shorter devices and higher voltages.61

Band-Filling Modulators. When one operates sufficiently far from the band edge that the absorption is not large, then the electrorefractive effect is only 2 to 3 times larger than the bulk electro-optic effect. This is because oscillations in the change in absorption with wavelength tend to cancel out their contributions to the change in refractive index at long wavelengths. By contrast, the long-wavelength refractive index change during band filling is large because band filling decreases the absorption at all wavelengths. However, because band filling relies on real carriers, it lasts as long as the carriers do, and it is important to find ways to remove these carriers to achieve high-speed operation.

Voltage-controlled transfer of electrons into and out of QWs (BRAQWET modulator) can yield large electrorefraction by band filling (Sec. 4.11 discusses electroabsorption in this structure under "Electron Transfer Modulators"). The refractive index change at 1.55 |im can be as large as An = 0.02 for 6 V. One structure consists of 12 repeating elements,65 with the single QW replaced by three closely spaced strongly coupled QWs, demonstrating VnL = 3.2 Vmm with negligible loss.

Semiconductor Interferometric Modulators

The issues for Mach-Zehnder modulators fabricated in semiconductors are similar to those for modulators in lithium niobate, but the design and fabrication processes in semiconductors are by no means as finalized. Fabrication tolerances, polarization dependence, interaction with lasers, and operation at high optical input powers are just some of the issues that need to be addressed. The interferometer can be composed of Y branches, fabricated by etching to form ridge waveguides. Alternatively, 3-dB couplers are often formed by a multimode interferometer (MMI), composed of two parallel waveguides placed very close together with a bridging region that introduces coupling between them. Proper choice of this coupling region yields a 3-dB coupler.

One example reports a Mach-Zehnder interferometer at 1.55 |im in InGaAlAs QWs with InAlAs barriers.66 A polarization-independent extinction ratio of 30 dB was reported, over a 20-nm wavelength range without degradation at input powers of 18 dBm (63 mW). The interferometer phase-shifting region was 1000 |im long, and each MMI was 200 |im long. The insertion loss of 13 dB was due to the mismatch between the mode of the single-mode optical fiber and of the semiconductor waveguide, which was 2 |im wide and 3.5 |im high. Various semiconductor structures to convert spot size should bring this coupling loss down.

PIN DIODES

The detectors used for fiber-optic communication systems are usually pin photodiodes. In high-sensitivity applications, such as long-distance systems operating at 1.55-^m wavelength, avalanche photodiodes are sometimes used because they have internal gain. Occasionally, metal-semiconductor-metal (MSM) photoconductive detectors with interdigitated electrode geometry are used because of ease of fabrication and integration. For the highest speed applications, Schottky photodiodes may be chosen. This section reviews properties of pin photodi-odes. The next section outlines the other photodetectors.

The material of choice for these photodiodes depends on the wavelength at which they will be operated. The short-wavelength pin silicon photodiode is perfectly suited for GaAs wavelengths (850 nm); these inexpensive photodetectors are paired with GaAs/AlGaAs LEDs for low-cost data communications applications. They are also used in the shorter-wavelength plastic fiber applications at 650 nm. The longer-wavelength telecommunication systems at 1.3 and 1.55 |im require longer-wavelength detectors. These are typically pin diodes composed of lattice-matched ternary In0.47Ga0.53As grown on InP. Silicon is an indirect bandgap semiconductor while InGaAs is a direct band material; this affects each material’s absorption and therefore its photodiode design. In particular, silicon photodiodes tend to be slower than those made of GaAs or InGaAs, because silicon intrinsic regions must be thicker. Speeds are also determined by carrier mobilities, which are higher in the III-V materials.

The pin junction consists of a thin, heavily doped n region, a near-intrinsic n region (the i region), and a heavily doped p region. When an incident photon has energy greater than or equal to the bandgap of the semiconductor, electron-hole pairs are generated. In a well-designed photodiode, this generation takes place in the space-charge region of the pn junction. As a result of the electric field in this region, the electrons and holes separate and drift in opposite directions, causing current to flow in the external circuit. This current is monitored as a change in voltage across a load resistor. The pin photo-diode is the workhorse of fiber communication systems.

Typical Geometry

Typically, the electric field is applied across the pn junction and photocarriers are collected across the diode. A typical geometry for a silicon photodiode is shown in Fig. 30a. A pn junction is formed by a thin p+ diffusion into a lightly doped n~ layer (also called the i layer since it is almost intrinsic) through a window in a protective SiO2 film.

FIGURE 30 Geometry for pin photodiodes: (a) cutaway of silicon, illuminated from the top, showing the ring electrode and static electric field lines in the space-charge region; (b) cross-section of InGaAs/InP, illuminated from the bottom. The p+ region is formed by diffusion. The low-doped n- layer is the i or nearly intrinsic layer.

The n~ region between the p+ and n+ regions supports a space-charge region, which, in the dark, is depleted of free carriers and supports the voltage drop that results from the pn junction. When light is absorbed in this space-charge region, the absorption process creates electron-hole pairs that separate in the electric field (field lines are shown in Fig. 30a), the electrons falling down the potential hill to the n region and the holes moving to the p region. This separation of charge produces a current in the external circuit, which is read out as a measure of the light level. Free carriers generated within a diffusion length of the junction may diffuse into the junction, adding to the measured current.

Long-wavelength detectors utilize n- or i layers that are grown with a composition that will absorb efficiently in the wavelength region of interest. The ternary In0.47Ga0.53As can be grown lattice-matched to InP and has a spectral response that is suitable for both the 1.3- and 1.55-^m wavelength regions. Thus, this ternary is usually the material of choice, rather than the more difficult to grow quaternary InGaAsP, although the latter provides more opportunity to tune the wavelength response. Figure 30b shows a typical geometry. Epitaxial growth is used to provide lightly doped n- layers on a heavily doped n+ substrate. The InP buffer layers are grown to keep the dopants from diffusing into the lightly doped absorbing InGaAs layer. The required thin p region is formed by diffusion through a silicon nitride insulating window. Because InP is transparent to 1.3 and 1.55 |im, the photodiode can be back-illuminated, which makes electrical contacting convenient. In some embodiments, a well is etched in the substrate and the fiber is glued in place just below the photosensitive region.

Carriers generated outside the depletion region may enter into the junction by diffusion, and can introduce considerable time delay. In silicon, the diffusion length is as long as 1 cm, so any photocarriers generated anywhere within the silicon photodiode can contribute to the photo-current. Because the diffusion velocity is much slower than the transit time across the space-charge region, diffusion currents slow down silicon photodiodes. This is particularly true in pn diodes. Thus, high-speed applications typically use pin diodes with absorption only in the i layer.

To minimize diffusion from the p+ entrance region, the junction should be formed very close to the surface. The space-charge region should be sufficiently thick that most of the light will be absorbed (thickness = 1/a). With sufficient reverse bias, carriers will drift at their scattering-limited velocity. The space-charge layer must not be too thick, however, or transit-time effects will limit the frequency response. Neither should it be too thin, or excessive capacitance will result in a large RC time constant. The optimum compromise occurs when the modulation period is on the order of twice the transit time. For example, for a modulation frequency of 10 GHz, the optimum space-charge layer thickness in silicon is about 5 |im. However, this is not enough thickness to absorb more than ~50 percent of the light at 850 nm. Thus, there is a trade-off between sensitivity and speed. If the wavelength drops to 980 nm, only 10 percent of the light is absorbed in a 10-^m thickness of silicon space-charge layer.

The doping must be sufficiently small that the low n- doped region can support the voltage drop of the built-in voltage Vbi plus the applied voltage. When the doping density of the p+ region is much higher than the doping density of the n- layer, the thickness of the space-charge layer is:

To achieve Ws = 10 |im in a silicon photodiode with 10 V applied requires ND ~ 1014 cm-3. If the doping is not this low, the voltage drops more rapidly, and the field will not extend fully across the low-doped region.

In InGaAs photodiodes (also GaAs/AlGaAs photodiodes), the n+ and p+ layers are transparent, and no photocarriers are generated in them. Thus, no photocarriers will enter from the n+ and p+ regions, even though the diffusion length is ~100 |im. The thickness of the i layer is chosen thin enough to achieve the desired speed (trading off transit time and capacitance), with a possible sacrifice of sensitivity.

Typically, light makes a single pass through the active layer. In silicon photodiodes, the light usually enters through the p contact at the surface of the diode (Fig. 30a); the top metal contact must have a window for light to enter (or be a transparent contact). The InGaAs pho-todiodes may receive light from the p side or the n side, because neither is absorbing. In addition, some back-illuminated devices use a double pass, reflecting off a mirrored top surface, to double the absorbing length. Some more advanced detectors, resonant photodiodes, use integrally grown Fabry-Perot cavities (using DBR mirrors, as in VCSELs) that resonantly reflect the light back and forth across the active region, enhancing the quantum efficiency. These are typically used only at the highest bandwidths (>20 GHz) or for wavelength division multiplexing (WDM) applications, where wavelength-selective photodetection is required. In addition, photodiodes designed for integration with other components are illuminated through a waveguide in the plane of the pn junction. The reader is directed to Vol. I, Chap. 17 to obtain more information on these advanced geometries.

Sensitivity (Responsivity)

To operate a pin photodiode, it is sufficient to place a load resistor between ground and the n side and apply reverse voltage to the p side (V< 0). The photocurrent is monitored as a voltage drop across this load resistor. The photodiode current in the presence of an optical signal of power Ps is negative, with a magnitude given by:

where ID is the magnitude of the (negative) current measured in the dark. The detector quantum efficiency nD (electron-hole pairs detected per photon) is determined by how much light is lost before reaching the space-charge region, how much light is absorbed (which depends on the absorption coefficient), and how much light is reflected from the surface of the photo-diode (a loss which can be reduced by adding antireflective coatings). Finally, depending on design, there may be some loss from metal electrodes. These factors are contained in the following expression for the quantum efficiency:

where R is the surface reflectivity, T is the transmission of any lossy electrode layers, W is the thickness of the absorbing layer, and a is its absorption coefficient.

The sensitivity (or responsivity X) of a detector is the ratio of milliamps of current out per milliwatt of light in. Thus, the responsivity is:

For detection of a given wavelength, the photodiode material must be chosen with a bandgap sufficient to provide suitable sensitivity. The absorption spectra of candidate detector materials are shown in Fig. 31. Silicon photodiodes provide low-cost detectors for most data communications applications, with acceptable sensitivity at 850 nm (absorption coefficient -500 cm-1). These detectors work well with the GaAs lasers and LEDs that are used in the inexpensive datacom systems and for short-distance or low-bandwidth local area network (LAN) applications. GaAs detectors are faster, both because their absorption can be larger and because their electron mobility is higher, but they are more expensive. Systems that require longer-wavelength InGaAsP/InP lasers typically use InGaAs photodiodes. Germanium has a larger dark current, so it is not usually employed for optical communications applications. Essentially all commercial photodetectors use bulk material, not quantum wells, as these are simpler, are less wavelength sensitive, and have comparable performance.

The spectral response of typical photodetectors is shown in Fig. 32. The detailed response depends on the detector design and on applied voltage, so these are only representative examples. Important communication wavelengths are marked.

Table 1 gives the sensitivity of typical detectors of interest in fiber communications, measured in units of amps per watt, along with speed and relative dark current.

Speed

Contributions to the speed of a pin diode come from the transit time across the space-charge region and from the RC time constant of the diode circuit in the presence of a load resistor RL. Finally, in silicon there may be a contribution from the diffusion of carriers generated in un-depleted regions.

In a properly designed pin photodiode, light should be absorbed in the space-charge region that extends from the p+ junction across the low n-doped layer (the i layer). Equation (92) gives the thickness of the space charge region Ws, as long as it is less than the thickness of the i layer Wi.

FIGURE 31 Absorption coefficient as a function of wavelength for several semiconductors used in pin diode detectors.

Define Vi as that voltage at which Ws = Wi. Then

For any voltage larger than this, the space-charge width is essentially Wi, since the space charge extends a negligible distance into highly doped regions.

If the electric field across the space-charge region is high enough for the carriers to reach their saturation velocity vs and high enough to fully deplete the i region, then the carrier transit time will be t, = WJvs. For vs = 107 cm/s and W, = 4 |im, the transit time = 40 ps. It can be shown that a finite transit time t, reduces the response at modulation frequency m67:

Defining the 3-dB bandwidth as that modulation frequency at which the electrical power decreases by 50 percent, it can be shown that the transit-limited 3-dB bandwidth is (Electrical power is proportional to I2 and K2, so the half-power point is achieved when the current is reduced by 1/V2.) There is a trade-off between diode sensitivity and diode transit time, since, for thin layers, from Eq. (94),Thus, the quantum efficiency-bandwidth product is:

FIGURE 32 Spectral response of typical photodetectors.

The speed of a pin photodiode is also limited by its capacitance, through the RC of the load resistor. Sandwiching a space-charge layer, which is depleted of carriers, between conductive n and p layers causes a diode capacitance proportional to the detector area A:

For a given load resistance, the smaller the area, the smaller the RC time constant, and the higher the speed. We will see also that the dark current Is decreases as the detector area decreases. The detector should be as small as possible, as long as all the light from the fiber can be collected onto the detector. Multimode fibers easily butt-couple to detectors whose area matches the fiber core size. High-speed detectors compatible with single-mode fibers can be extremely small, but this increases the alignment difficulty; high-speed photodetectors can be obtained already pigtailed to single-mode fiber. A low load resistance may be needed to keep the RC time constant small, but this may result in a small signal that needs amplification. Speeds in excess of 1 GHz are straightforward to achieve, and speeds of 50 GHz are not uncommon.

Thicker space-charge regions provide smaller capacitance, but too thick a space charge region causes the speed to be limited by the carrier transit time. The bandwidth with a load resistor RL is:

 

TABLE 1 Characteristics of Typical Photodiodes

	Wavelength, |im	Sensitivity K, As/W	Speed t, ns	Dark current, normalized units
Sil	0.85	0.55	3	1
	0.65	0.4	3
GalnAs	1.3-1.6	0.95	0.2	3
Ge (pn)	1.55	0.9	3	66

This shows that there is an optimum thickness Wi for high-speed operation. Anyadditional series resistance Rs or parasitic capacitance CP must be added by using C + CP. The external connections to the photodetector can also limit speed. The gold bonding wire may provide additional series inductance. It is important to realize that the photodiode is a high impedance load, with very high electrical reflection, so that an appropriate load resistor must be used. As pointed out in Vol. I, Chap. 17, it is possible to integrate a matching load resistor inside the photodiode device, with a reduction in sensitivity of a factor of two (since half the photocurrent goes through the load resistor), but double the speed (since the RC time constant is halved). A second challenge is to build external bias circuits without high-frequency electrical resonances. Innovative design of the photodetector may integrate the necessary bias capacitor and load resistor, ensuring smooth electrical response.

Silicon photodetectors are inherently not as fast. Because their highly doped p and n regions are also absorbing, and because they are indirect bandgap materials and do not have as high an absorption coefficient, there will be a substantial contribution from carriers generated in undepleted regions. These carriers have to diffuse into the space charge region before they can be collected. Therefore, the photoresponse of the diode has a component of a slower response time governed by the carrier diffusion time:

where WD is the width of the absorbing undepleted region, and D is the diffusion constant for whichever carrieris dominant (usually holes in the n region). For silicon, D = 12 cm2/s, so that when