**Multiscale Computer Aided Design of Microwave-Band P-I-N Photodetectors**

### Mikhail E. Belkin

*Moscow State Technical University of Radio-Engineering, Electronics and Automation, Faculty of Electronics, Joint Research Laboratory "Microwave and Optoelectronic Devices", Moscow Russian Federation* 

### **1. Introduction**

230 Photodetectors

[13] Gershenfeld, Neil A. (1999).The Nature of Mathematical Modeling. Cambridge, UK:

[14] A.V Akindinov, et al., (1997). New results on MRS APD, Nuclear Instruments and

[15] Z. Sadygov et al., (2010). Microchannel avalanche photodiode with wide linearity range,

Methods in Physics Research Section A, Vol. 387, pp.231-234

Cambridge University Press.

arXiv.org>physics>ArXiv:1001.3050

Long wavelength InP-based p-i-n photodetectors (PD) are ubiquitous in modern optoelectronic circuits due to their inherent combination of ultra-high speed, high sensitivity in the most popular for modern telecom systems spectral range of 1.3-1.6 µm, and low bias voltages features that are impossible in principle for Si, GaAs or Ge counterparts. Typical material systems for the telecom spectral range are GaInAsP and GaInAs on InP substrate (Capasso et al., 1985). Now in the number of classical and present-day works (see, e.g. Bowers & Burrus, 1987; Beling & Campbell, 2009) is well-proved that compound semiconductor p-i-n photodetectors have the valid merits such as: high responsivity (up to 1 A/W), lowest dark current (below 10 fA), ultra-high bandwidth (up to 100 GHz and above), possibility of monolithic optoelectronic receiver module creation on common InP substrate.

Through a wide time period this type of PD found the most intensive application inside a receiver of the long-haul digital fiber-optic systems. But recently the p-i-n PDs for the wavelength of 1.3 and 1.55 µm are advancing in various RF and microwave photonic apparatus, particularly, in microwave-band optoelectronic oscillators (X.S.Yao, 2002), frequency converters (J. Yao, 2009), as well in so called photonic antennas for the base stations of radio over fiber (RoF) systems (Sauer et al., 2007). While designing a receiving module for the above devices and systems the stage of circuit schematic development referred to active and passive, electronic and photonic components' modeling would be most complicated and labour-intensive. Based on microwave IC design practice in this case the modeling is realized as a description of electrical and optical features of the integrated functional elements by means of mathematical equations, equivalent circuits or tables.

At present time computer-aided design (CAD) exploitation for innovative high-tech production R&D acceleration is a common way (Minixhofer, 2006). This is especially important for microwave semiconductor component base with measurement equipment and experimental work's cost being considerably more expensive compare to that in lower frequency bands. Using modern CAD software the next two approaches may be relevant for this case: by means of so-called physical models and by means of equivalent circuit models. A physical modeling is generally the most accurate but at the same time the most complicated. It is executed through a computer simulation of dedicated physical processes

Multiscale Computer Aided Design of Microwave-Band P-I-N Photodetectors 233

solitary MW-ECAD simulations for designing a long wavelength microwave-band p-i-n

Generically, a photodiode as any electronic diode is a nonlinear device with a saturation effect and when it works in large-signal mode the fundamental signal is usually accompanied by a remarkable level of nonlinear distortions (Yu & Wu, 2002). The main distortion sources of the PD's conversion characteristic include absorption saturation, transit-time effects, and electric field screening arising from the space charge in the depletion layer (Williams et al., 1996). The latter effect also arises due to series resistance

Nevertheless, in digital optical fiber systems handling with typical receiving power levels lower than 1 mW a photodiode is able to represent as linear device. On the other hand, in order to secure the needed spurious free dynamic range (SFDR) in the above microwave photonics devices and RoF systems the power levels may be up to 100 mW. For example a simple analysis of an opto-electronic oscillator model using quasi-linear interpretation

> *ph <sup>V</sup> I R*

where *Iph* is the PD photocurrent; *R* is the PD load impedance; *Vπ* is so called half-wave voltage of Mach-Zehnder modulator. Relationship between the photocurrent *Iph* and the PD

where *S0* is the PD current responsivity. From (1) and (2) one can clearly conclude that selfoscillating condition could be simplified through increasing optical power at PD input. Namely, for typical values of *R*=50 Ω, *Vπ*=5 V, *S0*=0.5 A/W it would be more than 64 mW. Naturally, it is unpractical to represent photodiode in such a regime as a linear element.

Large-signal operation of PD in the above-mentioned devices and system called out an additional issue that a pre-amplifier following the PD must concurrently have low noise figure and enough high linearity. A good chance to circumvent this issue is in utilizing a special type high-linear PD and a scheme without pre-amplifier (Joshi & Datta, 2009). Note that operating the photodiodes at larger photocurrent has added benefit of reducing overall noise figure of the device or link. But an employment of special type PDs that are structurally more complicate than standard ones might degrade the economical features of optical receivers. Thus, a direct linearity comparison of the widespread top-illuminated PD

As known from RF and microwave amplifier design experience (Kenington, 2000), device linearity in large-signal mode is regularly characterized by so-called harmonic and intermodulation distortions (IMD). Among them a two-tone third-order IMD (IMD3) is the most severe issue in design practice. The reason is in their closer positioning to carrier signals to allow rejecting by filters. Also for super wideband microwave photonic devices and systems when the bandwidth is more than an octave the two-tone second-order IMD (IMD2) is in

and middle-power microwave transistor amplifier is a subject of practical interest.

, (1)

*ph* 0 0 *I PS* , (2)

results in the next expression for self-oscillating regime (X.S.Yao, 2002):

optical power *P0* is addressed to the well-known formula:

photodetector as a basic component of a multichannel analog system are presented.

**2. General review** 

outside a junction region of a PD.

running in the semiconductor chip's epitaxial layers. On the other hand, equivalent circuit model is simpler and includes current and voltage sources as well as passive elements that subject to frequency band are built on a linear circuitry with lumped (for RF band) or distributed (for microwave band) parameters. Correct simulation of the real device features is ensured by the account of nonlinearity and lag effects in the sources and passive elements. Their parameters and characteristics are specified by the DC or low-frequency measurements also by the small- or large-signal mode measurements in operating band and adjusted due to parametric optimization process. The main advantage of the approach is in clarity of device operation scripts and in versatility for the same class components when the parameter spread could be simply taken in account by proper changing the numerical value of the separate element. Therefore, a simulation issue optimal decision based on criteria of accuracy and computation time would rely on multiscale combination of the physical and equivalent circuit models. For computations the means of one or a number of CAD tools could be applied. Such approach might be called as multiscale or end-to-end design.

Generally a transparent way for microwave photonic devices' computer design lies in simulating with a help of so called optoelectronic CAD (OE-CAD) tool (Lowery, 1997). Nevertheless, our review of modern commercial OE-CAD software has shown up their lack of development to simulate a microwave circuitry. An alternative approach is to model by two classes of CAD tools: so-called technology CAD or TCAD software (Blakey, 2008) and microwave-band electronic CAD or MW-ECAD software (Kielmeyer, 2008). By means of the first one a designer could realize the analysis procedures for a number of semiconductor chip physical, electrical and optical features and its DC characteristics; also simulate semiconductor laser, photodiode, transistor, or diode structure's small-signal frequency response. But for designing a number of relevant microwave photonics devices, e. g. optically controlled microwave amplifiers and switches, optoelectronic oscillators, transmitter and receiver optoelectronic modules, and so on one needs to know quite a number of the active semiconductor device parameters specifying its functioning in the operating bandwidth and in large-signal mode: output intercept point, harmonic and intermodulation distortions, largesignal output reflection coefficient. It is impossible to simulate the above features by the means of a TCAD tool. One more significant drawback of the tool is that the account of device package and assembling parasitic elements impacts is also impractical. This matter results in the solution error up to 30% even at the lower part of the microwave band that is growing along with a modulation frequency is being increased (Belkin & Dzichkovski, 2009).

The both issues are overcome by the application of ECAD tool optimizing for microwave band operation. The MW-ECAD tool special preference is in powerful electromagnetic (3D) analysis and optimization resources of microwave electronic circuitry and layouts design, for instance low-noise and power amplifiers, highly complex receiver optoelectronic modules. So introducing a convenient interface between these CAD tools one could realize multiscale end-to-end design of the device or module with microwave bandwidth. Usually for this goal well-known HSPICE interface is feasible. In this case, input data are multilayer semiconductor heterostructure with the certain cross section, and output data are a whole number of the outer parameters that totally and correctly characterize its features in microwave band. Also it might be a layout drawing of the module in development.

Thus, there exists a need for a reliable circuit-level photodetector model suitable for a designer of receiving modules of modern optical fiber-based systems and microwave photonics devices. In this chapter our recent results of the combined TCAD&ECAD and solitary MW-ECAD simulations for designing a long wavelength microwave-band p-i-n photodetector as a basic component of a multichannel analog system are presented.

### **2. General review**

232 Photodetectors

running in the semiconductor chip's epitaxial layers. On the other hand, equivalent circuit model is simpler and includes current and voltage sources as well as passive elements that subject to frequency band are built on a linear circuitry with lumped (for RF band) or distributed (for microwave band) parameters. Correct simulation of the real device features is ensured by the account of nonlinearity and lag effects in the sources and passive elements. Their parameters and characteristics are specified by the DC or low-frequency measurements also by the small- or large-signal mode measurements in operating band and adjusted due to parametric optimization process. The main advantage of the approach is in clarity of device operation scripts and in versatility for the same class components when the parameter spread could be simply taken in account by proper changing the numerical value of the separate element. Therefore, a simulation issue optimal decision based on criteria of accuracy and computation time would rely on multiscale combination of the physical and equivalent circuit models. For computations the means of one or a number of CAD tools

could be applied. Such approach might be called as multiscale or end-to-end design.

along with a modulation frequency is being increased (Belkin & Dzichkovski, 2009).

microwave band. Also it might be a layout drawing of the module in development.

Thus, there exists a need for a reliable circuit-level photodetector model suitable for a designer of receiving modules of modern optical fiber-based systems and microwave photonics devices. In this chapter our recent results of the combined TCAD&ECAD and

The both issues are overcome by the application of ECAD tool optimizing for microwave band operation. The MW-ECAD tool special preference is in powerful electromagnetic (3D) analysis and optimization resources of microwave electronic circuitry and layouts design, for instance low-noise and power amplifiers, highly complex receiver optoelectronic modules. So introducing a convenient interface between these CAD tools one could realize multiscale end-to-end design of the device or module with microwave bandwidth. Usually for this goal well-known HSPICE interface is feasible. In this case, input data are multilayer semiconductor heterostructure with the certain cross section, and output data are a whole number of the outer parameters that totally and correctly characterize its features in

Generally a transparent way for microwave photonic devices' computer design lies in simulating with a help of so called optoelectronic CAD (OE-CAD) tool (Lowery, 1997). Nevertheless, our review of modern commercial OE-CAD software has shown up their lack of development to simulate a microwave circuitry. An alternative approach is to model by two classes of CAD tools: so-called technology CAD or TCAD software (Blakey, 2008) and microwave-band electronic CAD or MW-ECAD software (Kielmeyer, 2008). By means of the first one a designer could realize the analysis procedures for a number of semiconductor chip physical, electrical and optical features and its DC characteristics; also simulate semiconductor laser, photodiode, transistor, or diode structure's small-signal frequency response. But for designing a number of relevant microwave photonics devices, e. g. optically controlled microwave amplifiers and switches, optoelectronic oscillators, transmitter and receiver optoelectronic modules, and so on one needs to know quite a number of the active semiconductor device parameters specifying its functioning in the operating bandwidth and in large-signal mode: output intercept point, harmonic and intermodulation distortions, largesignal output reflection coefficient. It is impossible to simulate the above features by the means of a TCAD tool. One more significant drawback of the tool is that the account of device package and assembling parasitic elements impacts is also impractical. This matter results in the solution error up to 30% even at the lower part of the microwave band that is growing Generically, a photodiode as any electronic diode is a nonlinear device with a saturation effect and when it works in large-signal mode the fundamental signal is usually accompanied by a remarkable level of nonlinear distortions (Yu & Wu, 2002). The main distortion sources of the PD's conversion characteristic include absorption saturation, transit-time effects, and electric field screening arising from the space charge in the depletion layer (Williams et al., 1996). The latter effect also arises due to series resistance outside a junction region of a PD.

Nevertheless, in digital optical fiber systems handling with typical receiving power levels lower than 1 mW a photodiode is able to represent as linear device. On the other hand, in order to secure the needed spurious free dynamic range (SFDR) in the above microwave photonics devices and RoF systems the power levels may be up to 100 mW. For example a simple analysis of an opto-electronic oscillator model using quasi-linear interpretation results in the next expression for self-oscillating regime (X.S.Yao, 2002):

$$I\_{\rm plt}R \geq \frac{V\_{\pi}}{\pi} \, \prime \tag{1}$$

where *Iph* is the PD photocurrent; *R* is the PD load impedance; *Vπ* is so called half-wave voltage of Mach-Zehnder modulator. Relationship between the photocurrent *Iph* and the PD optical power *P0* is addressed to the well-known formula:

$$I\_{ph} = P\_0 S\_0 \quad \text{ } \tag{2}$$

where *S0* is the PD current responsivity. From (1) and (2) one can clearly conclude that selfoscillating condition could be simplified through increasing optical power at PD input. Namely, for typical values of *R*=50 Ω, *Vπ*=5 V, *S0*=0.5 A/W it would be more than 64 mW. Naturally, it is unpractical to represent photodiode in such a regime as a linear element.

Large-signal operation of PD in the above-mentioned devices and system called out an additional issue that a pre-amplifier following the PD must concurrently have low noise figure and enough high linearity. A good chance to circumvent this issue is in utilizing a special type high-linear PD and a scheme without pre-amplifier (Joshi & Datta, 2009). Note that operating the photodiodes at larger photocurrent has added benefit of reducing overall noise figure of the device or link. But an employment of special type PDs that are structurally more complicate than standard ones might degrade the economical features of optical receivers. Thus, a direct linearity comparison of the widespread top-illuminated PD and middle-power microwave transistor amplifier is a subject of practical interest.

As known from RF and microwave amplifier design experience (Kenington, 2000), device linearity in large-signal mode is regularly characterized by so-called harmonic and intermodulation distortions (IMD). Among them a two-tone third-order IMD (IMD3) is the most severe issue in design practice. The reason is in their closer positioning to carrier signals to allow rejecting by filters. Also for super wideband microwave photonic devices and systems when the bandwidth is more than an octave the two-tone second-order IMD (IMD2) is in

Multiscale Computer Aided Design of Microwave-Band P-I-N Photodetectors 235

20 GHz OIP3 (-9 V, 1 GHz)=15.3 dBm

20 GHz OIP3 (-5 V, 1 GHz)=24 dBm

10 GHz OIP3 (-3 V, 10 GHz)=32 dBm

6.5 GHz OIP3 (-5 V, 0.83 GHz)=43 dBm

photodiode 20 GHz OIP3 (-4 V, 1.1 GHz)=32.6 dBm Draa et al.,

planar p-i-n photodiode 3.2 GHz OIP3 (-16 V, 0.83 GHz)=49 dBm Joshi &

4.5 GHz OIP3 (-5 V, 1 GHz)=20 dBm

24 GHz OIP3 (-5 V, 0.32 GHz)=45 dBm

OIP3 (-9 V, 18 GHz)=2.4 dBm

OIP3 (-5 V, 18 GHz)=8 dBm

OIP3 (-5 V, 10 GHz)=40 dBm

OIP3 (-9 V, 0.83 GHz)=49 dBm

23 GHz OIP3 (-7 V, 0.31 GHz)=52 dBm Beling et al.,

OIP3 (-1 V, 1 GHz)=30 dBm OIP3 (-3 V, 1 GHz)=38 dBm OIP3 (-5 V, 1 GHz)=43 dBm

OIP3 (-2 V, 1 GHz)=17 dBm OIP3 (-8 V, 1 GHz)=30 dBm OIP2 (-2 V, 1 GHz)=33 dBm OIP2 (-8 V, 1 GHz)=46 dBm

OIP2 (-5 V, 1 GHz)=40 dBm

8 GHz OIP3 (-2 V, 5 GHz)=32.5 dBm Itakura et al.,

OIP3 (-9 V, 0.32 GHz)=50 dBm Li et al., 2010

Output Intercept Point Reference

Jiang et al., 2000

Liao et al., 2003

Gustavsson et al., 2005

Joshi et al., 2008

2008

2008

Tulchinsky et al., 2008

Godinez et al., 2008

Datta, 2009

Ramaswamy et al., 2009

2010

Smallsignal bandwidth

10 GHz

Table 1. Results of photodetector's output intercept point measurements

No Description of the PD under test

> Large optical cavity p-i-n waveguide InGaAs photodiode

Uni-traveling carrier waveguide integrated InGaAs photodiode

Backside illuminated unitraveling carrier InGaAs photodiode

GRIN lens-coupled topilluminated InGaAs photodiode

<sup>5</sup>P-i-n waveguide InGaAs

Charge compensated modified uni-traveling carrier InGaAs photodiode

Partially-depleted absorber backilluminated mesa structured photodiode

<sup>8</sup>Top-illuminated InGaAs

<sup>9</sup>Top-illuminated InGaAs

Ge n-i-p on silicon-oninsulator substrate photodiode

Backside illuminated InGaAs p-i-n photodiode array

Modified uni-traveling carrier InGaAs photodiode with cliff layer

p-i-n photodiode 8 GHz

1

2

3

4

6

7

10

11

12

great importance too. Generally, two-tone IMD is a product of passing two unmodulated carriers at the frequencies of *f1* and *f2* through a nonlinear device. When viewed in the frequency domain, output spectrum of the circuit includes besides *f1* and *f2* a lot of overtones. In the general case of distortions created by any order nonlinear circuit new frequencies will be generated in the form:

$$f\_i = mf\_1 \pm nf\_2 \tag{3}$$

where *m* and *n* are positive integers (including zero), *m+n* is equal to the order of the distortion. Then in the case of second-order nonlinearity each of the two tones will have a second harmonic and additional sum and difference beatings will occur at frequencies of *f1 ± f2*. Also in the case of third-order nonlinearity each of the two tones will have a third harmonic and additional sum and difference beatings will occur at frequencies of 2*f1 ± f2* and 2*f2 ± f1*. These overtones are known as second-order and third-order intermodulation products correspondingly. One can calculate the above distortions through carrier transport equations (Williams et al., 1996) but the most simple and accurate way lies in measuring them in microwave band.

An obvious methodological drawback of IMD is referred to the dependence from powers of input signals that make impossible to compare devices at different input powers. To cope with it another well-known figure of merit for microwave amplifier linearity so called output intercept point (OIP) (Kenington, 2000) is widespread for microwave-band optoelectronic devices acting in large-signal mode. Following RF and microwave amplifiers, a rough estimate of the photodiode's 2-order OIP (OIP2) and the 3-order OIP (OIP3) can be produced by the following simple equations.

$$\text{COMP2} = P\_{\text{out}} - \text{IMD2} \,, \tag{4}$$

3 3/2 *OIP P IMD out* , (5)

where *Pout* is output AC power of the fundamental tone in the photodiode load. Each parameter is usually expressed as a power in dBm. However, a common practice to define

Fig. 1. A typical example of OIP3 determination for a photodiode

great importance too. Generally, two-tone IMD is a product of passing two unmodulated carriers at the frequencies of *f1* and *f2* through a nonlinear device. When viewed in the frequency domain, output spectrum of the circuit includes besides *f1* and *f2* a lot of overtones. In the general case of distortions created by any order nonlinear circuit new

where *m* and *n* are positive integers (including zero), *m+n* is equal to the order of the distortion. Then in the case of second-order nonlinearity each of the two tones will have a second harmonic and additional sum and difference beatings will occur at frequencies of *f1 ± f2*. Also in the case of third-order nonlinearity each of the two tones will have a third harmonic and additional sum and difference beatings will occur at frequencies of 2*f1 ± f2* and 2*f2 ± f1*. These overtones are known as second-order and third-order intermodulation products correspondingly. One can calculate the above distortions through carrier transport equations (Williams et al., 1996) but the most simple and accurate way lies in measuring

An obvious methodological drawback of IMD is referred to the dependence from powers of input signals that make impossible to compare devices at different input powers. To cope with it another well-known figure of merit for microwave amplifier linearity so called output intercept point (OIP) (Kenington, 2000) is widespread for microwave-band optoelectronic devices acting in large-signal mode. Following RF and microwave amplifiers, a rough estimate of the photodiode's 2-order OIP (OIP2) and the 3-order OIP (OIP3) can be

where *Pout* is output AC power of the fundamental tone in the photodiode load. Each parameter is usually expressed as a power in dBm. However, a common practice to define

OIP3= 15.3 dBm

0 10 20 30 40 50 60

Input RF Power (dBm)

*<sup>i</sup>* 1 2 *f mf nf* (3)

2 2 *OIP P IMD out* , (4)

3 3/2 *OIP P IMD out* , (5)

frequencies will be generated in the form:

produced by the following simple equations.


Fig. 1. A typical example of OIP3 determination for a photodiode




PD Output Power (dBm)

0

40

them in microwave band.


Table 1. Results of photodetector's output intercept point measurements

Multiscale Computer Aided Design of Microwave-Band P-I-N Photodetectors 237


Such double-heterojunction p-i-n photodiode structure as will be shown below is lightly slower than more popular single-heterojunction one (Bowers & Burrus, 1987) but has a number of physics and technological advantages with minor deterioration of operating

decrease of growth defects (growth pits, packing defects, absorption layer surface

 the possibility of desired form photodiode mesa-structure creation, using indium phosphide and solid solution etching selectivity, and small-area photodiodes forming

the possibility of compensating in part space-charge effect due to different thickness of

All the advantages above allow minimizing photodiode dark current ensuring maximum

 volatile components (such as As and P, and Zn doping agent) evaporation exclusion; the possibility of using InP "wide-gap window" effect that permits to collect photons on absorption layer without their surface recombination in the air-absorption layer

dimensions are 200x200 μm2, the mesa's top diameter is 50 μm.

Fig. 2. The cross section of the photodetector in research

the possibility of the buffer and absorption layers precise doping;

speed (Belkin et al., 2008):

erosion);

interface;

selectivity;

current responsivity.

the layers 2 and 4.

OIP relies on a graphical representation of measured amplitude curves for fundamental and second- or third-order IMD tones. Following it Figure 1 illustrates a typical example of OIP3 determination for a photodiode (Jiang et al., 2000) extrapolated from the measured data of fundamental (squares) and IMD3 (circles) plots. In the Figure's logarithmic scale on the both axes the graphs represent straight lines where the fundamental tone has a slope of 1:1 and IMD3 tone has a slope of 1:3.

Up-to-date there is a series of papers referred to OIP measurements. Table 1 lists the results of some of them.

At a glance the values of photodiode OIP were eventually increased and for today the highest OIP of more than 50 dBm possesses charge-compensated modified uni-traveling carrier InGaAs photodiode (Beling et al., 2008). Standard vertical-illuminated p-i-n PDs have some lower OIP values up to 46-49 dBm. The general tendencies for all types of PDs consist in decreasing OIP as the test frequency and the negative voltage bias are increased.

Another known property of nonlinear circuits is that vector addition of the output fundamental and harmonic components also determines a phase variation of the resultant output signal when the input level varies. This effect is a requisite of dynamic systems and as the figure of merit for microwave amplifier linearity is called amplitude-to-phase (AM-to-PM) conversion for single-tone mode that is usually expressed as a certain phase deviation, in degrees or radians at predetermined input power (Pedro & Carvalho, 2003). In the case of photodetectors the similar parameter in terms of power-to-phase conversion (PPC) is being investigate by a joint research team (Tailor et al., 2011) for emerging microwave photonicsbased timing applications in the fields where it is important to precisely know the arrival time of light pulse such as RoF, phased-array radars, optical fiber coherent communications and so on. Our results of MW-ECAD's photodiode nonlinear modeling will be highlighted in section 4.

### **3. Combined TCAD&ECAD simulation**

To illustrate effectiveness of multiscale approach, the end-to-end design of the photodiode modules with bandwidth near thirty gigahertz was fulfilled. At the first step following the modern CAD tools capabilities (see the Introduction), the simulation of the super highspeed pin-photodiode was carried out with the aid of Synopsys Sentaurus TCAD software tool1. Sentaurus package allows for correct modeling of the wide spectrum of semiconductor devices due to transport equations and various physical models combining. There is fundamental capacity of photodetector simulation too but up to date the examples of it are not frequently (see e. g. Zakhleniuk, 2007).

### **3.1 P-i-n photodiode heterostructure TCAD simulation**

For the simulation a widespread mesa-construction with semi-insulator-buried and vertically-illuminated p-i-n photodiode heterostructure similar to partially-depleted absorber type (Tulchinsky et al., 2008) was selected (Figure 2). In the Figure: region 1 is p+ type contact layer, region 2 – p-type buffer layer, region 3 – i-type absorption layer, region 4

<sup>1</sup> http://synopsys.com/home

OIP relies on a graphical representation of measured amplitude curves for fundamental and second- or third-order IMD tones. Following it Figure 1 illustrates a typical example of OIP3 determination for a photodiode (Jiang et al., 2000) extrapolated from the measured data of fundamental (squares) and IMD3 (circles) plots. In the Figure's logarithmic scale on the both axes the graphs represent straight lines where the fundamental tone has a slope of 1:1 and

Up-to-date there is a series of papers referred to OIP measurements. Table 1 lists the results

At a glance the values of photodiode OIP were eventually increased and for today the highest OIP of more than 50 dBm possesses charge-compensated modified uni-traveling carrier InGaAs photodiode (Beling et al., 2008). Standard vertical-illuminated p-i-n PDs have some lower OIP values up to 46-49 dBm. The general tendencies for all types of PDs consist

Another known property of nonlinear circuits is that vector addition of the output fundamental and harmonic components also determines a phase variation of the resultant output signal when the input level varies. This effect is a requisite of dynamic systems and as the figure of merit for microwave amplifier linearity is called amplitude-to-phase (AM-to-PM) conversion for single-tone mode that is usually expressed as a certain phase deviation, in degrees or radians at predetermined input power (Pedro & Carvalho, 2003). In the case of photodetectors the similar parameter in terms of power-to-phase conversion (PPC) is being investigate by a joint research team (Tailor et al., 2011) for emerging microwave photonicsbased timing applications in the fields where it is important to precisely know the arrival time of light pulse such as RoF, phased-array radars, optical fiber coherent communications and so on. Our results of MW-ECAD's photodiode nonlinear modeling will be highlighted

To illustrate effectiveness of multiscale approach, the end-to-end design of the photodiode modules with bandwidth near thirty gigahertz was fulfilled. At the first step following the modern CAD tools capabilities (see the Introduction), the simulation of the super highspeed pin-photodiode was carried out with the aid of Synopsys Sentaurus TCAD software tool1. Sentaurus package allows for correct modeling of the wide spectrum of semiconductor devices due to transport equations and various physical models combining. There is fundamental capacity of photodetector simulation too but up to date the examples of it are

For the simulation a widespread mesa-construction with semi-insulator-buried and vertically-illuminated p-i-n photodiode heterostructure similar to partially-depleted absorber type (Tulchinsky et al., 2008) was selected (Figure 2). In the Figure: region 1 is p+ type contact layer, region 2 – p-type buffer layer, region 3 – i-type absorption layer, region 4

in decreasing OIP as the test frequency and the negative voltage bias are increased.

IMD3 tone has a slope of 1:3.

of some of them.

in section 4.

**3. Combined TCAD&ECAD simulation** 

not frequently (see e. g. Zakhleniuk, 2007).

<sup>1</sup> http://synopsys.com/home

**3.1 P-i-n photodiode heterostructure TCAD simulation** 


Fig. 2. The cross section of the photodetector in research

Such double-heterojunction p-i-n photodiode structure as will be shown below is lightly slower than more popular single-heterojunction one (Bowers & Burrus, 1987) but has a number of physics and technological advantages with minor deterioration of operating speed (Belkin et al., 2008):


All the advantages above allow minimizing photodiode dark current ensuring maximum current responsivity.

Multiscale Computer Aided Design of Microwave-Band P-I-N Photodetectors 239

Agethen, et al., 2002), but to increase the thickness for bandwidth enhancement because of the need to consider not only time of carrier drift through depletion region, but diode's selfcapacitance charge/discharge time too; 2) optimal thickness of absorption region for photodiode modeled is near s=1 μm as for the larger ones the bandwidth became almost invariable. That's why the above value was determined as optimal for the project goal

> Frequency (GHz) 0,1 1 10 100

Fig. 4. The bandwidth vs. absorption region doping density simulation (1: ND=8·1015 cm-3; 2:

Fig. 5. The bandwidth vs. absorption region thickness simulation (1: s=0.3 μm; 2: s=0.55 μm;

ND=1·1016 cm-3; 3: ND=2·1016 cm-3; 4: ND=3·1016 cm-3; 5: ND=4·1016 cm-3)

achievement.

1

0,5

0

3: s=0.8 μm; 4: s=1 μm; 5: s=1.3 μm)

The SYNOPSYS Sentaurus TCAD platform was used to model the Fig. 2's photodiode structure. The simulating procedure based on the following methodology. As the first step optical field distribution profile was inspected (Figure 3). In the result we determined that optical field is absorbed completely in the depletion layer 3 of Fig. 2 (dark horizontal stripe in Fig. 3). Then, by optical power-dependence reverse current-voltage characteristics computation we found that optimal photodiode operating voltage was -10 V (Belkin et al., 2008). The final step was AC small-signal current responsivity-frequency characteristics analysis and optimization in dependence of the absorption layer doping density, ND, thickness, s and the photosensitive window width, w (in 2D-model).

Fig. 3. Optical field distribution profile (The PD structure is upside-down to that of Fig. 2)

As known (Bowers & Burrus, 1987), the general limitations on the speed of p-i-n photodetectors are: 1) carrier drift time across depletion layer, 2) diode inherent capacitance charge/discharge time, 3) charge trapping at heterojunctions, 4) diffusing time out of undepleted regions, 5) package parasitic effects. Among them, in photodetector heterostructure with target bandwidth of 30 GHz the major effect is due to the first two factors because the hole trapping time even for abrupt p-InP/i-GaInAs heterojunction was estimated to be about 5 ps (Wey et al., 1995).

In the course of simulations by means of the program developed, some data for technology research and photodiode structure design, that are optimized for all the three above parameters, are received. First, optimal absorption layer doping density with s=1 μm and w=25 μm was investigated (Figure 4). Absorption region doping level analysis showed: 1) photodiode bandwidth was increased with the level diminishing, 2) there was no sense to provide lower than ND= 1016 cm-3 as the bandwidth became almost invariable (The latter is important from the technology point), 3) to meet the above project goal of 30 GHz the simply realized by well-known liquid-phase epitaxy ND=110-16 cm-3 is quite enough. That's why the above value was used in the future simulations.

Furthermore, optimal absorption layer thickness with ND=110-16 cm-3 and w=25 μm was investigated (Figure 5). Absorption layer thickness analysis showed: 1) as for super highspeed p-i-n photodiode it is necessary not to diminish, according to known results (see e.g.

The SYNOPSYS Sentaurus TCAD platform was used to model the Fig. 2's photodiode structure. The simulating procedure based on the following methodology. As the first step optical field distribution profile was inspected (Figure 3). In the result we determined that optical field is absorbed completely in the depletion layer 3 of Fig. 2 (dark horizontal stripe in Fig. 3). Then, by optical power-dependence reverse current-voltage characteristics computation we found that optimal photodiode operating voltage was -10 V (Belkin et al., 2008). The final step was AC small-signal current responsivity-frequency characteristics analysis and optimization in dependence of the absorption layer doping density, ND,

Fig. 3. Optical field distribution profile (The PD structure is upside-down to that of Fig. 2)

As known (Bowers & Burrus, 1987), the general limitations on the speed of p-i-n photodetectors are: 1) carrier drift time across depletion layer, 2) diode inherent capacitance charge/discharge time, 3) charge trapping at heterojunctions, 4) diffusing time out of undepleted regions, 5) package parasitic effects. Among them, in photodetector heterostructure with target bandwidth of 30 GHz the major effect is due to the first two factors because the hole trapping time even for abrupt p-InP/i-GaInAs heterojunction was

In the course of simulations by means of the program developed, some data for technology research and photodiode structure design, that are optimized for all the three above parameters, are received. First, optimal absorption layer doping density with s=1 μm and w=25 μm was investigated (Figure 4). Absorption region doping level analysis showed: 1) photodiode bandwidth was increased with the level diminishing, 2) there was no sense to provide lower than ND= 1016 cm-3 as the bandwidth became almost invariable (The latter is important from the technology point), 3) to meet the above project goal of 30 GHz the simply realized by well-known liquid-phase epitaxy ND=110-16 cm-3 is quite enough. That's

Furthermore, optimal absorption layer thickness with ND=110-16 cm-3 and w=25 μm was investigated (Figure 5). Absorption layer thickness analysis showed: 1) as for super highspeed p-i-n photodiode it is necessary not to diminish, according to known results (see e.g.

thickness, s and the photosensitive window width, w (in 2D-model).

estimated to be about 5 ps (Wey et al., 1995).

why the above value was used in the future simulations.

Agethen, et al., 2002), but to increase the thickness for bandwidth enhancement because of the need to consider not only time of carrier drift through depletion region, but diode's selfcapacitance charge/discharge time too; 2) optimal thickness of absorption region for photodiode modeled is near s=1 μm as for the larger ones the bandwidth became almost invariable. That's why the above value was determined as optimal for the project goal achievement.

Fig. 4. The bandwidth vs. absorption region doping density simulation (1: ND=8·1015 cm-3; 2: ND=1·1016 cm-3; 3: ND=2·1016 cm-3; 4: ND=3·1016 cm-3; 5: ND=4·1016 cm-3)

Fig. 5. The bandwidth vs. absorption region thickness simulation (1: s=0.3 μm; 2: s=0.55 μm; 3: s=0.8 μm; 4: s=1 μm; 5: s=1.3 μm)

Multiscale Computer Aided Design of Microwave-Band P-I-N Photodetectors 241

Our last TCAD modeling was referred to the photodetector bandwidth estimation due to additional epitaxial layer introduction (Fig. 2, region 2). For this purpose the same photodiode structure response with closed region 2 was simulated (Figure 7). From the Figure one may conclude that the photosensitive window width needed for the project goal of near 30 GHz was increased slightly (up to 24 μm). So its effect has not to simplify

As mention above for end-to-end design of a microwave-bandwidth photodiode an appropriate ECAD tool is required. The most convenient way for this microwave network research is the approximation by a physical equivalent circuit (Figure 8). In the Figure, *Iph* is the complex photocurrent source (frequency *F* dependent), *Rd*, *Cd*, *Rs* are the p-i-n photodiode heterostructure differential resistance, intrinsic capacitance and serial resistance respectively. Furthermore, *Lw* and *Cc* are the connecting wire inductance and case

Based on the usual RF circuit simulation technique the photodiode transducer gain *kpd* can

*<sup>j</sup> <sup>С</sup> z j <sup>k</sup>*

1 2 1 (1 ) (1 ) 1 (1 ) *c L*

 

> 

(7)

*w d d s L dL*

*L С j С Rz j С z*

The values of *Iph(F)*, *τ, Rd*=3.5 MΩ, *Cd*=80 fF, *Rs*=21 Ω were found analytically from the Sentaurus program. Also the values of *Lw* and *Cc*=0.11 pF were determined experimentally by the microwave vector network analyzer. Figure 9 illustrates some results of the AWRDE 2 ECAD environment simulation. It follows from the graphs that the designer can realized twofold expansion of the photodiode 3 dB bandwidth (20 to 40 GHz) owing to the

*pd L ph k II* (6)

substantively the mesa etching process.

capacitance approximation.

**3.2 P-i-n photodiode MW-ECAD simulation** 

Fig. 8. The p-i-n photodiode electrical equivalent circuit

where *IL* is complex load current. Then from the Figure 8:

*ph*

where *ω*=*2πF*, *zL* is load impedance, *τ* is transit time.

appropriate fitting of the connecting wire inductance *Lw*.

be determined from this scheme as:

2 http://web.awrcorp.com

Finally, the optimal photosensitive window width with ND=110-16 cm-3 and s=1 μm was investigated (Figure 6). Photosensitive window width analysis showed: 1) the photodiode bandwidth was increased with the width diminishing; 2) the project goal value of 30 GHz is arrived when w≤22 μm that relatively similar with the other results (Bowers & Burrus, 1987; Agethen, et al., 2002).

Fig. 6. The bandwidth vs. photosensitive window width simulation (1: w=18 μm; 2: w=20 μm; 3: w=22 μm; 4: w=24 μm; 5: w=26 μm; 6: w=28 μm; 7: w=30 μm)

Fig. 7. The bandwidth vs. photosensitive window width simulation for a usual topilluminated p-i-n photodiode structure with single heterojunction (1: w=18 μm; 2: w=20 μm; 3: w=22 μm; 4: w=24 μm; 5: w=26 μm; 6: w=28 μm; 7: w=30 μm)

Our last TCAD modeling was referred to the photodetector bandwidth estimation due to additional epitaxial layer introduction (Fig. 2, region 2). For this purpose the same photodiode structure response with closed region 2 was simulated (Figure 7). From the Figure one may conclude that the photosensitive window width needed for the project goal of near 30 GHz was increased slightly (up to 24 μm). So its effect has not to simplify substantively the mesa etching process.

#### **3.2 P-i-n photodiode MW-ECAD simulation**

240 Photodetectors

Finally, the optimal photosensitive window width with ND=110-16 cm-3 and s=1 μm was investigated (Figure 6). Photosensitive window width analysis showed: 1) the photodiode bandwidth was increased with the width diminishing; 2) the project goal value of 30 GHz is arrived when w≤22 μm that relatively similar with the other results (Bowers & Burrus, 1987;

Fig. 6. The bandwidth vs. photosensitive window width simulation (1: w=18 μm; 2: w=20

Fig. 7. The bandwidth vs. photosensitive window width simulation for a usual top-

3: w=22 μm; 4: w=24 μm; 5: w=26 μm; 6: w=28 μm; 7: w=30 μm)

illuminated p-i-n photodiode structure with single heterojunction (1: w=18 μm; 2: w=20 μm;

μm; 3: w=22 μm; 4: w=24 μm; 5: w=26 μm; 6: w=28 μm; 7: w=30 μm)

Agethen, et al., 2002).

As mention above for end-to-end design of a microwave-bandwidth photodiode an appropriate ECAD tool is required. The most convenient way for this microwave network research is the approximation by a physical equivalent circuit (Figure 8). In the Figure, *Iph* is the complex photocurrent source (frequency *F* dependent), *Rd*, *Cd*, *Rs* are the p-i-n photodiode heterostructure differential resistance, intrinsic capacitance and serial resistance respectively. Furthermore, *Lw* and *Cc* are the connecting wire inductance and case capacitance approximation.

Fig. 8. The p-i-n photodiode electrical equivalent circuit

Based on the usual RF circuit simulation technique the photodiode transducer gain *kpd* can be determined from this scheme as:

$$k\_{pd} = I\_L \int I\_{plr} \tag{6}$$

where *IL* is complex load current. Then from the Figure 8:

$$\dot{k}\_{ph} = \frac{\left(1 + jo\mathcal{C}\_c z\_L\right)^{-1} \left(1 + jo\tau\right)}{1 - o^2 L\_w \mathcal{C}\_d + jo\mathcal{C}\_d R\_s + z\_L \left(1 + jo\mathcal{C}\_d z\_L\right)^{-1}}\tag{7}$$

where *ω*=*2πF*, *zL* is load impedance, *τ* is transit time.

The values of *Iph(F)*, *τ, Rd*=3.5 MΩ, *Cd*=80 fF, *Rs*=21 Ω were found analytically from the Sentaurus program. Also the values of *Lw* and *Cc*=0.11 pF were determined experimentally by the microwave vector network analyzer. Figure 9 illustrates some results of the AWRDE 2 ECAD environment simulation. It follows from the graphs that the designer can realized twofold expansion of the photodiode 3 dB bandwidth (20 to 40 GHz) owing to the appropriate fitting of the connecting wire inductance *Lw*.

<sup>2</sup> http://web.awrcorp.com

Multiscale Computer Aided Design of Microwave-Band P-I-N Photodetectors 243

bandwidth: LC package parasitics, matching networks, front-end amplifier and so on. To confirm the actuality and accuracy of the proposed methodology the specific p-i-n photodiode with bandwidth of near 30 GHz was simulated. The simulation results were

The main concept of this approach can be formulated as follows: a designer of analog receiving modules usually does not know a lot about the PD heterostructure's specific parameters, usually has not an access to a specific cost-expensive TCAD tool but he has facilities suitable for measuring transmittance and reflectance (or S-parameters) of the photodiode chip under test in the optical system's modulation band. Then equipped with experimental results, and equivalent circuit interpretation as well as AWRDE or another MW-ECAD tool facilities he builds up a non-linear "optoelectronic" equivalent circuit and if

Figure 11 represents cascaded equivalent circuit of PD that does it quite effective for simulation by means of a highly-developed MW-ECAD tool. There are two sub-circuits inside it: linear (right) and nonlinear (left). The linear sub-circuit simulating the frequency distortions due to parasitic elements impact agrees with small-signal PD model of Fig. 8. The nonlinear sub-circuit includes a diode D1 and a capacitance of p-n junction that is changed in according with applied reverse voltage (element PNCAP). To supply the nonlinear elements a DC source V2 is introduced. Inductance L1 is assigned for DC/AC isolation; resistance R2 models PD's DC termination. Non-ideality, phase shift, and delay of the optical-to-electrical conversion

> CAP ID=C1 C=1e9 fF

RES ID=R2 R=50 Ohm

PORT P=1 Z=1e3 Ohm

CAP ID=C5 C=60 fF

> DCVS ID=V2 V=t V

IND ID=L1 L=100 nH

SWPVAR ID=SWP1 VarName="t" Values=stepped(-6,0,1) UnitType=None

CAP ID=C6 C=20 fF

IND ID=L2 L=0.5 nH

R=30 Ohm Xo . . . Xn

experimentally verified with fine accuracy.

necessary some linear or nonlinear electronic circuits behind it.

process are modeled by voltage-controlled current source U1.

ID=D1 Nu=1.2 T=21.85 DegC Io=1e-5 mA

+

v=0.001 t=-6

PNCAP ID=PC1 CJ0=100 fF

Fig. 11. MW-ECAD nonlinear p-i-n photodiode model based on electrical equivalent circuit

For the simulation an equivalent electrical AC source V1 is placed at the circuit input. A frequency of this source is tuned through the microwave-band modulation bandwidth, and its amplitude is in exact numerical agreement with a power of intensity-modulated optical signal. As it follows from Figure 11 for the given model experiment the next values are assumed: an equivalent power of optical carrier is 100 mW (DC voltage 0.1 V), equivalent

RES ID=R1

**4. Solitary MW-ECAD simulation** 

**4.1 P-i-n photodiode nonlinear model** 

R1 R2

R=50 Ohm DIODE1

VCCS ID=U1 M=-0.8 S A=180 Deg R1=50 Ohm R2=1e6 Ohm F=0 GHz T=0.1 ns

> 3 4

1 2

Xo . . . Xn

SWPVAR ID=SWP2 VarName="v" Values={0.001,0.025,0.08} UnitType=Voltage

> RES ID=R4

ACVS ID=V1 Mag=v V Ang=0 Deg Offset=0 V DCVal=0.1 V

Fig. 9. The photodiode packaging effect simulation

### **3.3 Experimental verification**

Based on the above simulation results some p-i-n photodiode samples were produced and mounted into the microwave microstrip test fixture. The typical time response of the photodetector sample measured by the two-section mode-locked laser and high-speed sampling oscilloscope is shown in the Figure 10. The pulse duration from the Figure is near 10 ps, so the accuracy of the above simulation results is verified.

Fig. 10. Experimental photodiode impulse response (horizontal scale 25 ps/div.)

Thus, the methodology of the end-to-end computer-aided design for a p-i-n photodiode with microwave bandwidth is addressed. First, using the technology CAD tool a designer can define and optimize the dependence of the major photodiode structure parameters (absorption layer doping density and thickness, photosensitive window diameter, so on) on small-signal bandwidth and get the data for the following calculations. Then the electronic MW-CAD simulation based on the photodiode electrical equivalent circuits is performed that allow to take into account various effects in real receiver module with microwave bandwidth: LC package parasitics, matching networks, front-end amplifier and so on. To confirm the actuality and accuracy of the proposed methodology the specific p-i-n photodiode with bandwidth of near 30 GHz was simulated. The simulation results were experimentally verified with fine accuracy.

### **4. Solitary MW-ECAD simulation**

242 Photodetectors

Lw=0.16 nH Lw=0.36 nH

1 10 50 Frequency (GHz)

Based on the above simulation results some p-i-n photodiode samples were produced and mounted into the microwave microstrip test fixture. The typical time response of the photodetector sample measured by the two-section mode-locked laser and high-speed sampling oscilloscope is shown in the Figure 10. The pulse duration from the Figure is near


**3.3 Experimental verification** 

Fig. 9. The photodiode packaging effect simulation

10 ps, so the accuracy of the above simulation results is verified.

Fig. 10. Experimental photodiode impulse response (horizontal scale 25 ps/div.)

Thus, the methodology of the end-to-end computer-aided design for a p-i-n photodiode with microwave bandwidth is addressed. First, using the technology CAD tool a designer can define and optimize the dependence of the major photodiode structure parameters (absorption layer doping density and thickness, photosensitive window diameter, so on) on small-signal bandwidth and get the data for the following calculations. Then the electronic MW-CAD simulation based on the photodiode electrical equivalent circuits is performed that allow to take into account various effects in real receiver module with microwave

Transmission Gain (dB)

The main concept of this approach can be formulated as follows: a designer of analog receiving modules usually does not know a lot about the PD heterostructure's specific parameters, usually has not an access to a specific cost-expensive TCAD tool but he has facilities suitable for measuring transmittance and reflectance (or S-parameters) of the photodiode chip under test in the optical system's modulation band. Then equipped with experimental results, and equivalent circuit interpretation as well as AWRDE or another MW-ECAD tool facilities he builds up a non-linear "optoelectronic" equivalent circuit and if necessary some linear or nonlinear electronic circuits behind it.

### **4.1 P-i-n photodiode nonlinear model**

Figure 11 represents cascaded equivalent circuit of PD that does it quite effective for simulation by means of a highly-developed MW-ECAD tool. There are two sub-circuits inside it: linear (right) and nonlinear (left). The linear sub-circuit simulating the frequency distortions due to parasitic elements impact agrees with small-signal PD model of Fig. 8. The nonlinear sub-circuit includes a diode D1 and a capacitance of p-n junction that is changed in according with applied reverse voltage (element PNCAP). To supply the nonlinear elements a DC source V2 is introduced. Inductance L1 is assigned for DC/AC isolation; resistance R2 models PD's DC termination. Non-ideality, phase shift, and delay of the optical-to-electrical conversion process are modeled by voltage-controlled current source U1.

Fig. 11. MW-ECAD nonlinear p-i-n photodiode model based on electrical equivalent circuit

For the simulation an equivalent electrical AC source V1 is placed at the circuit input. A frequency of this source is tuned through the microwave-band modulation bandwidth, and its amplitude is in exact numerical agreement with a power of intensity-modulated optical signal. As it follows from Figure 11 for the given model experiment the next values are assumed: an equivalent power of optical carrier is 100 mW (DC voltage 0.1 V), equivalent

Multiscale Computer Aided Design of Microwave-Band P-I-N Photodetectors 245

the PPC linearity threshold is twofold as the PD bias is decreased from -1 to -4 V. Also from Figure 13 one can see that second-order output intercept points are almost constant vs. optical power and their numerical deviations vs. bias are near 26 dB (from 47 dBm at -8 V to 21 dBm at -1 V). In spite of this, shown in Figure 14 third-order output intercept points begin to degrade with optical power at the bias more than -4 V, and their numerical deviations vs. bias are near 17 dB (from 44 dBm at -8 V to 27 dBm at -1 V). Note that the results of power-to-phase conversion simulation are comparable in principle with recent experimental data (Tailor et al., 2011), also the results of OIP2 and OIP3 simulation are

closed to recent experimental data of Table 1.

Fig. 13. Output second-order intercept point characteristics

Fig. 14. Output third-order intercept point characteristics

Generally, based on our model experiments we are able to state that simple in design and producing cost-effective top-illuminated photodetector has been inspected holds somewhat (3-5 dB) lower linearity as compared to a special high-linear charge-compensated modified uni-traveling carrier photodiode (see Table 1). But the latter has at the same time

modulated optical power is changed in the range of 10-100 mW (0.01-0.1 V) that meets the optical modulation rate between 10 and 100 percentage. A reasonableness of the optoelectronic circuit's simulation by ECAD tool is founded on the proposed method of equivalent voltage which uses identical linear dependences of a current vs. voltage in an electrical circuit and a photocurrent vs. optical power in an optoelectronic circuit of a photoreceiver.

Thus, the next linear or nonlinear effects are taken into account in the given model: (i) nonlinearity of depletion layer capacity; (ii) frequency distortions due to parasitic elements of the PD package and receiver circuitry; (iii) reflections from photosensitive window; (iv) dark current and its dependence of temperature and bias voltage; (v) DC photocurrent generation due to optical carrier impact; (vi) deviation of the optical signal modulation rate; (vii) electric field screening due to series resistance.

### **4.2 Simulation results and discussion**

At the first step, to calibrate the model the device-under-test small-signal frequency characteristics are simulated. As the result, 3-dB bandwidth is limited in the range of 20-30 GHz depending on reverse bias voltage and agreed well with the Figure 9 at the bias of 10 V. Then, the above-described three nonlinear distortion parameters depending on equivalent input optical power and reverse bias (Ub) are simulated through one-button operations. Figure 12 shows an example of equivalent AM-to-PM distortion characteristics at the fundamental frequency 15 GHz.

Fig. 12. Photodiode power to phase conversion characteristics

Also Figure 13 depicts an example of OIP2 characteristics for the input tones of 5 GHz and 6 GHz, and distortion tone of 11 GHz. At last Figure 14 shows an example of OIP3 characteristics for the input tones of 5 GHz and 5.1 GHz, and distortion tone of 4.9 GHz.

A combined outcome from Figures 12-14 follows that large-signal conversion features of a pi-n photodetector are notably degraded as far as negative reverse DC bias is increased that is quite coincided with the experimental data of Table 1. In particular, Figure 12 depicts that

modulated optical power is changed in the range of 10-100 mW (0.01-0.1 V) that meets the optical modulation rate between 10 and 100 percentage. A reasonableness of the optoelectronic circuit's simulation by ECAD tool is founded on the proposed method of equivalent voltage which uses identical linear dependences of a current vs. voltage in an electrical circuit and a photocurrent vs. optical power in an optoelectronic circuit of a

Thus, the next linear or nonlinear effects are taken into account in the given model: (i) nonlinearity of depletion layer capacity; (ii) frequency distortions due to parasitic elements of the PD package and receiver circuitry; (iii) reflections from photosensitive window; (iv) dark current and its dependence of temperature and bias voltage; (v) DC photocurrent generation due to optical carrier impact; (vi) deviation of the optical signal modulation rate;

At the first step, to calibrate the model the device-under-test small-signal frequency characteristics are simulated. As the result, 3-dB bandwidth is limited in the range of 20-30 GHz depending on reverse bias voltage and agreed well with the Figure 9 at the bias of 10 V. Then, the above-described three nonlinear distortion parameters depending on equivalent input optical power and reverse bias (Ub) are simulated through one-button operations. Figure 12 shows an example of equivalent AM-to-PM distortion characteristics

Also Figure 13 depicts an example of OIP2 characteristics for the input tones of 5 GHz and 6 GHz, and distortion tone of 11 GHz. At last Figure 14 shows an example of OIP3 characteristics for the input tones of 5 GHz and 5.1 GHz, and distortion tone of 4.9 GHz.

A combined outcome from Figures 12-14 follows that large-signal conversion features of a pi-n photodetector are notably degraded as far as negative reverse DC bias is increased that is quite coincided with the experimental data of Table 1. In particular, Figure 12 depicts that

photoreceiver.

(vii) electric field screening due to series resistance.

Fig. 12. Photodiode power to phase conversion characteristics

**4.2 Simulation results and discussion** 

at the fundamental frequency 15 GHz.

the PPC linearity threshold is twofold as the PD bias is decreased from -1 to -4 V. Also from Figure 13 one can see that second-order output intercept points are almost constant vs. optical power and their numerical deviations vs. bias are near 26 dB (from 47 dBm at -8 V to 21 dBm at -1 V). In spite of this, shown in Figure 14 third-order output intercept points begin to degrade with optical power at the bias more than -4 V, and their numerical deviations vs. bias are near 17 dB (from 44 dBm at -8 V to 27 dBm at -1 V). Note that the results of power-to-phase conversion simulation are comparable in principle with recent experimental data (Tailor et al., 2011), also the results of OIP2 and OIP3 simulation are closed to recent experimental data of Table 1.

Fig. 13. Output second-order intercept point characteristics

Fig. 14. Output third-order intercept point characteristics

Generally, based on our model experiments we are able to state that simple in design and producing cost-effective top-illuminated photodetector has been inspected holds somewhat (3-5 dB) lower linearity as compared to a special high-linear charge-compensated modified uni-traveling carrier photodiode (see Table 1). But the latter has at the same time

Multiscale Computer Aided Design of Microwave-Band P-I-N Photodetectors 247

As shown from Figure, simulated by VPI (solid curve) spectral density of average output noise power represents frequency and noise source power independent horizontal line that is unrealistic. On the other hand, simulated by AWRDE results follow the real frequency characteristic of the photodiode under test and differ subject to small-signal (triangles) or large-signal (circles) power regime of the noise source. The numerical value

This chapter presented a multiscale approach to the combined TCAD&ECAD and solitary MW-ECAD simulations for designing a microwave-band p-i-n photodetector as a basic component of the receiving modules for radio-over-fiber systems and microwave photonics devices. Within the limits of the first approach, primarily, using a TCAD tool a designer can define and optimize the dependence of the major photodiode structure parameters on smallsignal bandwidth. Then an electronic MW-CAD simulation based on the photodiode electrical equivalent circuits is performed that allow to take into account various effects in real receiver module with microwave bandwidth. To confirm the actuality and accuracy of the proposed methodology the specific p-i-n photodiode with bandwidth of near 30 GHz was simulated. The main concept of the second approach can be formulated as follows: a designer of analog receiving modules usually does not know a lot about the PD heterostructure's specific parameters, usually has not an access to a specific cost-expensive TCAD tool but he has facilities suitable for measuring transmittance and reflectance of the photodiode chip under test in the optical system's modulation band. Then equipped with experimental results, and equivalent circuit interpretation as well as AWRDE or another MW-ECAD tool facilities he builds up a non-linear "optoelectronic" equivalent circuit and if necessary some linear or nonlinear electronic circuits behind it. Following the simulation results we have concluded: (i) even a standard p-i-n photodetector is more linear circuit element than pre-amplifier and can be used without it in the most photoreceiving schemes of microwave photonics devices and RoF system's photonic antennas; (ii) to secure a comparable p-i-n photodetector linearity the reverse bias voltage must be less than -4 V at

The modeling results are validated by the experimental data for TCAD&ECAD similation and by close agreement with the known measured data for MW-ECAD large-signal

This work was supported by the Russian Ministry of Education and Science program "Progress of scientific potential of the higher school (2009-2011)". Author wishes to thank Dr. E. Portnoi from Ioffe Physico-Technical Institute RAS for the mode-locked laser's

Agethen, M., et.al. (2002). InGaAs pin Detectors for Frequencies above 100 GHz, *IEEE Indium Phosphide and Relative Materials Conference, IPRM'2002*, A8-2, pp. 673-676

of error is up to 10 dB.

optical power up to 100 mW.

**7. Acknowledgment** 

photodiode measurement.

**8. References** 

simulation.

**6. Conclusion** 

significantly higher bandwidth running up to THz band (Nagatsuma et al., 2007). Nevertheless the researched type of photodetector thanks to inherent cost-effectiveness also has a potential for RoF systems and microwave photonics applications with moderate frequency and power requirements.

For example, the typical values of the allowable AM-to-PM distortion and OIP3 for middlepower reasonable-noise microwave amplifiers are not more than 10º as well near 30-35 dBm correspondently. Following it we are able to conclude: (i) even a standard p-i-n photodetector is more linear circuit element than pre-amplifier and can be used without it in the most photoreceiving schemes of microwave photonics devices and RoF system's photonic antennas; (ii) to secure a comparable p-i-n photodetector linearity the reverse bias voltage must be less than -4 V at optical power up to 100 mW.

### **5. Comparison of OE-CAD and MW-ECAD photodiode simulations**

As we communicated in Introduction, the available optoelectronic CAD tools are unpractical for designing nonlinear device operating in microwave band. That's why it is in essential importance to state the numerical value of error while simulating for instance noise features of a photodetector in microwave band using MW-ECAD and OE-CAD software. Our direct comparison was fulfilled by AWRDE and advanced OE-CAD tool VPItransmission MakerTM version 8.6.

In the case of VPI software a library p-i-n photodiode model considering thermal and shot noise sources and dark current of 0.15 nA was selected. On the other hand, for photodiode MW-ECAD simulation the equivalent circuit model of Fig. 11 was used. For the both simulating experiments a broadband Gaussian-distributed white noise generator model with identical power levels was employed as a source. Varying its levels output noise power was measured in the band from 1 GHz to 50 GHz by the noise analyser model in the bandwidth of 1 Hz. Figure 15 depicts the simulation results.

Fig. 15. OE-CAD tool vs. MW-ECAD tool simulation

As shown from Figure, simulated by VPI (solid curve) spectral density of average output noise power represents frequency and noise source power independent horizontal line that is unrealistic. On the other hand, simulated by AWRDE results follow the real frequency characteristic of the photodiode under test and differ subject to small-signal (triangles) or large-signal (circles) power regime of the noise source. The numerical value of error is up to 10 dB.

### **6. Conclusion**

246 Photodetectors

significantly higher bandwidth running up to THz band (Nagatsuma et al., 2007). Nevertheless the researched type of photodetector thanks to inherent cost-effectiveness also has a potential for RoF systems and microwave photonics applications with moderate

For example, the typical values of the allowable AM-to-PM distortion and OIP3 for middlepower reasonable-noise microwave amplifiers are not more than 10º as well near 30-35 dBm correspondently. Following it we are able to conclude: (i) even a standard p-i-n photodetector is more linear circuit element than pre-amplifier and can be used without it in the most photoreceiving schemes of microwave photonics devices and RoF system's photonic antennas; (ii) to secure a comparable p-i-n photodetector linearity the reverse bias

As we communicated in Introduction, the available optoelectronic CAD tools are unpractical for designing nonlinear device operating in microwave band. That's why it is in essential importance to state the numerical value of error while simulating for instance noise features of a photodetector in microwave band using MW-ECAD and OE-CAD software. Our direct comparison was fulfilled by AWRDE and advanced OE-CAD tool

In the case of VPI software a library p-i-n photodiode model considering thermal and shot noise sources and dark current of 0.15 nA was selected. On the other hand, for photodiode MW-ECAD simulation the equivalent circuit model of Fig. 11 was used. For the both simulating experiments a broadband Gaussian-distributed white noise generator model with identical power levels was employed as a source. Varying its levels output noise power was measured in the band from 1 GHz to 50 GHz by the noise analyser model in the

frequency and power requirements.

VPItransmission MakerTM version 8.6.

voltage must be less than -4 V at optical power up to 100 mW.

bandwidth of 1 Hz. Figure 15 depicts the simulation results.

Fig. 15. OE-CAD tool vs. MW-ECAD tool simulation

**5. Comparison of OE-CAD and MW-ECAD photodiode simulations** 

This chapter presented a multiscale approach to the combined TCAD&ECAD and solitary MW-ECAD simulations for designing a microwave-band p-i-n photodetector as a basic component of the receiving modules for radio-over-fiber systems and microwave photonics devices. Within the limits of the first approach, primarily, using a TCAD tool a designer can define and optimize the dependence of the major photodiode structure parameters on smallsignal bandwidth. Then an electronic MW-CAD simulation based on the photodiode electrical equivalent circuits is performed that allow to take into account various effects in real receiver module with microwave bandwidth. To confirm the actuality and accuracy of the proposed methodology the specific p-i-n photodiode with bandwidth of near 30 GHz was simulated. The main concept of the second approach can be formulated as follows: a designer of analog receiving modules usually does not know a lot about the PD heterostructure's specific parameters, usually has not an access to a specific cost-expensive TCAD tool but he has facilities suitable for measuring transmittance and reflectance of the photodiode chip under test in the optical system's modulation band. Then equipped with experimental results, and equivalent circuit interpretation as well as AWRDE or another MW-ECAD tool facilities he builds up a non-linear "optoelectronic" equivalent circuit and if necessary some linear or nonlinear electronic circuits behind it. Following the simulation results we have concluded: (i) even a standard p-i-n photodetector is more linear circuit element than pre-amplifier and can be used without it in the most photoreceiving schemes of microwave photonics devices and RoF system's photonic antennas; (ii) to secure a comparable p-i-n photodetector linearity the reverse bias voltage must be less than -4 V at optical power up to 100 mW.

The modeling results are validated by the experimental data for TCAD&ECAD similation and by close agreement with the known measured data for MW-ECAD large-signal simulation.

### **7. Acknowledgment**

This work was supported by the Russian Ministry of Education and Science program "Progress of scientific potential of the higher school (2009-2011)". Author wishes to thank Dr. E. Portnoi from Ioffe Physico-Technical Institute RAS for the mode-locked laser's photodiode measurement.

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**12** 

*Russia* 

**Mathematical Modeling of Multi-Element** 

**Infrared Focal Plane Arrays Based** 

*A.V. Rzhanov Institute of Semiconductor Physics Siberian Branch of* 

The direct-injection readout circuit was proposed in 1973 by A. Steckl and T. Koehler (Steckl & Koehler, 1973). With such readout circuits, first hybrid multi-element InfraRed Focal Plane Arrays (IR FPAs) were implemented (Steckl, 1976; Iwasa, 1977). The direct-injection readout circuits are being used in the majority of hybrid multi-element Long-Wave InfraRed (LWIR) FPAs, which hold more-than-70% a share in the world market of thermography

A diagram of FET-based readout circuit is shown in Fig.1a, the most popular design involving a charge-coupled device, Fig.1b (Longo, 1978; Felix,1980; Takigawa, 1980; Rogalski, 2000*).* On application of a dc voltage UG to the input gate, a certain voltage, defined by the surface potential under the input gate of the photodetector channel, sets across the photodiode, and the current generated in the IR detector is integrated at the storage capacitor Сint. On applying of a transfer pulse Ft (Fig.1a), the charge accumulated in

Normally, the current through the photodiode is in the range of 10-7÷10-10A, the input FET being therefore operated in subthreshold mode. The transconductance of the input FET

Here, q is the electron charge, k is the Boltzmann constant, N\*= (CОХ+СD\*+СSS\*)/CОХ (CОХ is the specific capacitance of gate dielectric, СSS\*=qNss\* is the specific capacitance of fast surface states, CD\* is the specific capacitance of the depletion region, Т is temperature, and the asterisk \* indicates that the parameter value is taken for the conditions with surface Fermi

in in in \* <sup>G</sup> I qI <sup>g</sup> <sup>V</sup> N kT

(1)

The equivalent circuit of the direct injection readout circuit is shown in Fig. 2.

**1. Introduction** 

systems (Rogalski, 2000).

channel is:

level equal to 3/2 φFB.

the storage capacitor transfer to the column read bus.

 **on the System 'Photodiode –** 

I.I. Lee and V.G. Polovinkin

*Russian Academy of Sciences* 

**Direct-Injection Readout Circuit'** 

Zakhleniuk, N.A. (2007). Theory and Modelling of High-Field Carrier Transport in High-Speed Photodetectors. *Proceedings of NUSOD'07 Numerical Simulation of Optoelectronic Devices*, pp. 77-78, ISBN 978-1-4244-1431-4, Newark, DE, September 24-28, 2007
