Chapter 2 LITERATURE SURVEY. 2.1 A General Review of PDs

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1 Chapter 2 LITERATURE SURVEY A considerable amount of efforts have been spent in modeling and characterizing optically controlled MESFET as PD over the past few decades. The major works reported in this area are reviewed extensively and presented in this chapter. The following sections present a summary of the major works reported on modeling and characterizing of optically controlled devices under the following headings: 1. A general review of PDs 2. MESFET 3. MESFET as PD 4. Optical illumination 5. Static I V characterization of GaAs OPFET 6. Frequency dependent characterization of GaAs OPFET 7. Intrinsic parameters of MESFETs 8. 2D modeling of MESFET 9. Noise in optical detectors 10. Stability 2.1 A General Review of PDs The PD is an essential component of the optical fiber communication system and optoelectronic based system. Therefore, it is considered as one of the crucial elements which dictate the overall system performance. When considering signal attenuation along the link, the system performance is determined at the detector. Improvement of detector characteristics and performance thus allows the installation of lesser repeater stations and lowers both the capital investment and maintenance cost [2]. The role played by detector demands that it must satisfy very stringent requirements of performance and compatibility. Some of the following important criteria define the performance and compatibility requirements which should be kept in mind while designing detectors. 13

2 The first and the most important requirement for the PD is that it should be highly sensitive at the operating wavelength. The sensitivity of the device depends on the semiconductor material used. This is because the amount of absorption of photons in the PD to produce carrier pairs and thus photo current is dependent on the absorption coefficient α 0 of the light. The absorption coefficients of semiconductor materials are strongly dependent on wavelength of operation [2, 27]. Along with sensitivity, another factor required for designing of PDs at any particular wavelength is responsivity. Responsivity gives the ability of the device to convert the received optical signal into electrical current. The variation of the responsivity of PDs with the wavelength of the incident radiation for different semiconductor materials is presented by Senior [1]. It is seen that the responsivity increases steadily until a particular wavelength called cutoff wavelength corresponding to the energy band gap of the semiconductor and decreases sharply afterwards. For wavelengths beyond cutoff the photons do not have sufficient energy to break the electronic bond between electron hole pairs and hence responsivity decreases sharply after cutoff wavelength [2, 27]. While designing PDs, the next important parameter is speed of operation. This is because the present systems have to handle input data rate from hundreds of MHz to GHz range and above. This simply means that there is a need of PDs with higher saturation velocity. Higher saturation velocity gives the carriers a higher mobility and hence they can be used for high speed detector applications. The variation of electron drift velocity with electric field for different semiconductor materials is given in [2, 27]. Finally, to receive the data at the receiver end with minimum errors, the requirement is that minimum noise should be introduced by the detector, i.e. dark currents, leakage currents and shunt conductance, must be low. The variation of dark noise with normalized bias voltage for different semiconductor materials show that although Germanium has high absorption and high cutoff wavelength, it in not preferred as PD material because it has high dark current which decreases SNR of the device and hence deteriorates its performance [27]. The study shows that the alloys of III V elements are the materials of choice for detector because they satisfy all the critical requirements of PDs. Now once the detector material is decided there is a need to understand the devices which can be used as detector. The next section presents the overview of MESFET based PD also called OPFET (Optical Field Effect Transistor) and also present the review of the historical stages of the development in the area of FET and MESFET. 14

3 2.2 MESFET The concept of Schottky barrier FET was introduced by Schottky in 1938 [28]. The authors gave an idea about the formation of a potential barrier due to the difference of work function between the metal and the semiconductor contact. Since its inception considerable amount of efforts have been spent in modeling and characterizing FETs. In 1966 Carver Mead [29] invented MESFET which is a type of FET while author was trying to find alternatives to the large, power hungry, high maintenance, slow devices for radar applications. The author recognized that Schottky barriers provide useful high quality rectifying junctions to wide band gap semiconductors. In 1970, Middlehoek realized the silicon based MESFETs with 1μm gate length. They had maximum oscillation frequency up to 12GHz for microwave applications. In 1971, Turner took a step ahead when 1μm gate length FETs were made on GaAs with maximum oscillation frequency up to 50GHz. Such a high performance is attributed to GaAs which offers superior electrical properties compared to the silicon [28]. Beside high frequency of oscillation GaAs MESFETs also provide high output power with low noise figure. All this was possible because of the following advantages of the GaAs MESFET compared to its counter parts: 1. High electron velocity inside the channel, 2. Smaller transit time leading to faster response and 3. Reduced parasitic capacitances due to the fabrication of active layer on semi insulating GaAs substrates [18]. 2.3 MESFET as PD In 1977 Back et al were the first who reported that GaAs MESFET can be used as a low power high speed PD. The photo sensitivity of the MESFET has opened up the possibility of their use for a variety of optoelectronic applications because the flow of charge carriers in the channel is controlled by a Schottky barrier gate [22]. Table 2.1: Schottky barrier heights for several metals [6] Schottky metal Schottky barrier heights with n GaAs (V) Gold, Au 0.9 Silver, Ag 0.88 Platinum, Pt 0.86 A Schottky barrier is a metal semiconductor contact that possesses properties similar to p n diode except that it has much faster response [6]. When the metal is brought in contact with a semiconductor, charge transfer occurs until the fermi levels align at 15

4 equilibrium. When the charge transfer takes place from metal into semiconductor it is called rectifying contact and non rectifying for the reverse condition. Table 2.1 depicts that the barrier height is seen to have weak dependence upon the metal used. Fig. 2.1 highlights the energy band diagram of GaAs MESFET Schottky barrier. Depletion region Channel E c Schottky Junction Metal n-gaas Semi-insulating GaAs E f E V a Figure 2.1: Energy band diagram of GaAs MESFET Table 2.2: Summary of reported work by different researchers Author Year Title Dimension Mizuno et al [30] 1983 Alvaro Augusto et al [19] Michael Shur et al [31] Chakrabarti et al [32] Shan Ping Chin and Ching Yuan Wu et al [33] Shan Ping Chin and Ching Yuan Wu et al [34] Microwave characteristics of an optically controlled MESFET 0.5μm 1983 Optical control of GaAs MESFET 0.5μm 1985 Capacitance model for GaAs MESFET B.K.Mishra [5] 1995 Shubha et al [35] 1998 An improved model of ion implanted GaAs OPFET A new two dimensional model for the potential distribution of short gate length MESFET s and its applications A new I V model for short gate length MESFET s Computer aided modeling of solid state photo detectors (Thesis) Optically controlled ion implanted GaAs MESFET characteristic with opaque gate 1.3μm, 1.7μm 1μm 0.5μm 0.3μm, 1μm 1μm 4μm 16

5 Chakrabarti et al [36] Chakrabarti et al [37] Nandita Saha et al [38] Madheswaran et al [39] B.L.Ooi et al [40] 2003 Chakrabarti et al [41] 2004 Jit et al [42] 2005 Menon [28] 2008 Numerical simulation of an ion implanted GaAs OPFET A proposed OEIC receiver using MESFET photo detector Frequency dependent characteristics of an ion implanted GaAs MESFET with opaque gate under illumination Quasi two dimensional simulation of an ion implanted GaAs MESFET photo detector An improved but reliable model for MESFET parasitic capacitance extraction Noise behavior of an optically controlled GaAs MESFET An analytical model for the S parameter for optically controlled MESFET Modeling techniques of submicron GaAs MESFETs and HEMTs (Thesis) 1.2μm 1.5μm 3μm 1.2μm 2μm 1μm 0.5μm 0.28μm Other important developments reported on MESFETs were that, they were used in microwave integrated circuits by Ladbrooke, Golio, Bose and Khalaf. GaAs MESFETs also demonstrated excellent noise and gain performance at microwave frequency and they were used quite often in pre amplifiers of communication devices. In today s world, high frequency communication is possible because of the superior electrical properties offered by GaAs MESFETs both in analog as well as in digital applications. A properly designed GaAs MESFET can operate comfortably at a frequency higher than 100GHz. The excellent microwave performance of the GaAs MESFET is certainly related to its channel properties [28]. Table 2.2 presents a summary of all the reported work with different device dimensions under research. These reported results have opened up the gates for MESFET in microwave devices and circuits with direct optical control terminal. The study also shows that there is a need of good models for channel length shorter than 0.3µm. From next section onwards the behavior of GaAs MESFETs under dark and illuminated conditions as reported by various researchers is studied in detail for their application as PD in optoelectronic communication systems. 17

6 2.4 Optical Illumination For the first time in 1977 Back et al [22] carried out an experiment to detect a light pulse with a GaAs MESFET and a commercially available APD. The reported results show that GaAs MESFET is very sensitive PD for optical fiber communication since the switching speed of GaAs MESFET under illumination is high, almost double than that of an APD. Application of GaAs MESFET as an optically switched amplifier and also as optical/microwave transformer was experimentally found by Mizuno [30]. Later on, an optically controlled MESFET was named as OPFET by Gammel et al [43]. The mechanism that controls the behavior of GaAs MESFET under illumination was explained on the basis of photoconductive and photovoltaic effects. It showed that the optical illumination absorbed in the channel generates the additional carriers in the active channel. The excess photo generated carriers have been accounted for the alteration of the built in voltage of Schottky barrier. These excess carriers, in turn, increase the conductivity of the active channel. Hence the conductivity of the active channel gets modulated in the presence of illumination. An integral analytical model of an optically controlled microwave/millimeter wave device structure was reported by Simon et al [26]. Authors have analytically investigated the effect of light on several III V compound semiconductor devices, such as GaAs MESFET, InP MESFET, Al 0.3 Ga 0.7 As/GaAs HEMT, and GaAs HBT. The results show that with the increase in optical power density, the light induced voltage increases. De Salles [19] carried out work to investigate the performance of GaAs MESFET under illumination. For the first time both the photovoltaic and photoconductive effects in the active channel and the substrate were considered for the analysis of GaAs MESFET. It was concluded that when the incident optical radiation has energy greater than the band gap energy of the semiconductor, there will be considerable change in the DC characteristics. Due to this effect, the intrinsic parameters of the device change. On the basis of this observation many possible applications of the device like optically controlled amplification and oscillation, injection phase locking, optical detection etc were predicted. Later on, Seeds and De Salles reviewed the use of optical signal to control the operation of microwave amplifiers, oscillators, switches and mixers. Nandita Saha et al [38] are among other researchers who worked to investigate the performance of GaAs MESFET under illumination. On the basis of the work done by Baack et al, Nandita Saha et al have evaluated the photo voltage due to optical radiation in an opaque gated GaAs MESFET. The incident light enters the device through the gate source and the gate drain spacing. The photo voltages developed across Schottky junction due to generation of carriers in the side walls of the depletion layer below the 18

7 gate and the other channel substrate depletion region. The changes in channel potential which results in the variation of the drain current have been studied by Nandita Saha et al. The GaAs MESFET with semi transparent Schottky gate was evaluated by Chakrabarti et al [36]. The investigations evaluated the light generated voltage due to optical illumination falling on GaAs MESFET with semi transparent Schottky gate. It is shown that without the surface recombination taken into account at the surface, the photo voltage at the Schottky barrier and at the channel substrate barrier increases with an increase in the incident optical power density (P opt ), and finally saturate at higher values of optical power density due to the reduction in the lifetime of the carriers in the presence of illumination. The numerical model presented by Chakrabarti et al for an ion implanted GaAs optical field effect transistor (OPFET) is a physics based one, and overcomes the major limitations of the existing models. It considers the photoconductive effect in the channel and photovoltaic effect at the gate Schottky barrier as well as the channel substrate barrier. The exact potential profile in the channel and variation of gate depletion width and substrate depletion width in the channel as a function of position between source and drain is computed for the first time for a non uniformly doped channel. The variation of gate depletion width and substrate depletion width with distance along the channel under dark and illuminated conditions (with surface recombination) is evaluated in the paper. It is seen that the width of the gate depletion region at any point in the channel decreases in the presence of illumination. It shows that in the presence of illumination the channel voltage increases, the width of the gate depletion region decreases for a given applied gate voltage. This may be accounted for the fact that the photovoltaic effect in the illuminated condition reduces the applied gate reverse bias and causes the net reduction in the width of the gate depletion region in the illuminated condition. Surface recombination has been found to have little effect on this variation [36]. Similar considerations were taken into account by Pal [44] for developing the analytical model of an ion implanted GaAs OPFET. As reported by Chakrabarti et al absorption of incident optical radiation in the GaAs MESFET induces the photovoltaic and photoconductive effects which are found to increase with the increase in illumination. The amount of absorption of incident optical radiation in the GaAs MESFET was explained by R.B.Darling et al [45]. The paper by Darling et al revealed the important fact that the thickness of metal gate determines the amount of absorption of incident optical radiation in the GaAs MESFET. R.B.Darling et al have shown in their work that the optical transmission through the gate ohmic contacts depends upon the thickness of the metallization, T s. The transmission coefficient for the gate metal was plotted as a function of the metal thickness. It shows 19

8 that no significant transmission occurs for metallization that are thicker than about 500Å. The gate metallization of typical GaAs MESFETs are rarely thinner than about 3000Å, so the optical response is generally caused by transmission through the inter electrode spaces. Even though optical transmission through the gate metal is usually negligible, the center sub channel is most sensitive to the generation of carriers. For generality, optical gating into channel region and the extended depletion region on the drain and the source side is considered. Increased transmission through the gate offers one method of increasing the responsivity. However, drastic thinning of the gate metal to achieve this must be balanced against the increased series resistance of the gate which will lower the gain bandwidth product and increase the noise figure of the device [45]. Therefore, a lot of research work is reported on MESFET s with opaque (thick film metallization) gate to explore its usability as a PD [5, 19, 29 30, 38]. This is basically because the thick film technology (vapor deposition) is cost effective and shows long term stability and reliability and thick film circuits have an application in high frequency operations up to about 1GHz [46 47]. MESFET with semi transparent metal gate finds its use in applications above 1GHz. The major drawback of devices with thin film metal gates is that they are not suitable for very high volume fabrication and low cost applications as the thin films are fabricated using sputtering technique, which is a slower, complicated and costly process as compared to vapor deposition used for thick film deposition [46 47]. The study presented reveals that the device performance is enhanced by illumination due to the change in depletion width with illumination. This change is more prominent for semi transparent gate because the amount of flux absorbed is proportional to thickness of metal at the gate. The change in the depletion width with the amount of optical power absorbed causes the different parameters like device current, intrinsic device parameters, noise and stability to vary. The models developed by various researchers for determining the I V characteristics of ion implanted GaAs MESFET with opaque and semi transparent gate under illuminated conditions are considered and reviewed in the following section. 2.5 Static I V Characterization of GaAs OPFET The effect of illumination on the DC characteristics of the MESFET with opaque and semi transparent gate was subsequently studied by a number of individuals [5, 18, 29 30, 35, 36, 38]. Shubda et al [35] have developed an analytical model for an ion implanted GaAs MESFET having an opaque Schottky gate to incident radiation. The model developed showed significant increase in device current, channel conductance and trans 20

9 conductance compared to previous models. The model considers the radiation entering into device through the spacing between source, gate and drain for MESFET with opaque gate. The model solves continuity equations for the excess carriers generated in the neutral active region, the extended gate depletion region and the depletion region of active (n) and substrate (p) junction. The photo voltage across the channel and the p layer junction and that across the Schottky junction are the two important controlling parameters. At a given point in the channel, the width of the substrate depletion region decreases in presence of illumination. The photovoltaic effect is more prominent at substrate channel junction. Chakrabarti et al [36] carried out an extensive theoretical work to investigate the performance of GaAs MESFET with semi transparent gate. The model is physics based and considers both the photovoltaic at the Schottky gate and photoconductive effect in the channel. The exact potential profiles in the channel, variation of gate depletion width and substrate depletion width in the channel as a function of position between source and drain have been computed. The variations obtained show that the current increases with increasing V ds and optical power density for fixed V gs. Chakrabarti et al also report about the effect of illumination on device parameters like trans conductance and gate to source capacitance (C gs ). The results show that the trans conductance of the device decreases with increase in V gs for a given V ds and trans conductance increases in the illuminated condition for a fixed V gs. Similarly, the variation of the C gs of the device with gate to source voltage (with and without recombination) reveals that C gs decreases with an increase in V gs. However, for a particular value of V gs, C gs increases in the presence of illumination due to the photovoltaic effect at the Schottky barrier [36]. This section shows that device parameters viz. device current, channel conductance, trans conductance and intrinsic device parameters viz. C gs, C gd vary with illumination. All these models solved the one dimensional continuity equation to determine the charge in the channel under illuminated condition. The study in this section does not include the effect of frequency on the device parameters under illumination. The variation of the drain current, photo voltage etc. with frequency which have been studied and reported by number of individuals is presented below. 2.6 Frequency Dependent Characterization of GaAs OPFET The first AC model of a Si OPFET was developed by Singh et al [48]. The effect of operating frequency on the I V characteristics and the threshold voltage was calculated. Mishra et al [49] developed AC model based on the work conducted by Singh et al [48]. Authors considered the effects of radiation and surface recombination on device 21

10 parameters. In their study they considered the life time of the minority carriers to be a constant. A more accurate model was developed by Youssef Zebda et al [20] using perturbation technique that gives the time varying characteristics of the optically illuminated ion implanted MESFET. The model considers the carrier life time as a function of the carrier concentration in the channel. The carrier concentration in the active channel increases due to the absorption of the incident light. Hence the carrier life time decreases with the increase in illumination. The influence of this effect on the device parameters and characteristics are studied and analyzed to evaluate the threshold voltage of the OPFET for different incident light power intensities. Youssef Zebda et al [20] illustrates that the threshold voltage of the device is reduced as the operating frequency is increased. When the operating frequency is high the channel charge reduces as recombination increases and hence results in the decrease in the minority carrier lifetime of the carriers. Results also show that, the device threshold voltage decrease less for higher operating frequencies. The photo voltage of the GaAs OPFET with opaque gate under AC condition was numerically calculated by Nandita et al [38]. The results show that photo voltage remains more or less constant and independent of signal frequency up to 1MHz and decrease above 1MHz. This behavior is due to the AC lifetime for minority carriers. The photo voltage developed at the substrate channel junction is larger than the photo voltage developed at the Schottky junction for a particular flux density. The reverse saturation current density in the active layer substrate junction is less compared to that for the Schottky junction. Further, the number of holes generated in the side walls of the Schottky depletion region is much less than that generated in the n p junction depletion region. The internal and external photo voltages developed are dependent on frequency also, so there is significant effect of the frequency on the device characteristics. The current dependence on frequency as reported by Nandita et al [38] shows that with the increase in frequency the drain source current gradually decreases, the change being 0.44mA/decade and for a fixed frequency the current increases with the increase in illumination. This opaque gate model is more frequency sensitive compared to the previous results where the change in current was 0.03mA/decade at the same frequency of operation [38]. In the model [50] presented by Nandita Saha et al, the authors have considered a cavity in the substrate of an ion implanted GaAs MESFET where the fiber is inserted and the optical radiation is allowed to fall on the device from the substrate side. Two cases are of interest: one in which the fiber is inserted partially into the substrate and the radiation enters the device through the substrate and the other in which fiber is inserted up to the 22

11 active layer substrate junction so that strong absorption occurs in the active layer of the OPFET. At a frequency of 0.1GHz and flux density of /m 2 s, the present model shows higher current compared to [49] and [20] because in both the models, the channel width modulation due to photo voltage has not been considered. Further, the models considered illumination incident on the semi transparent gate of the device. Under illumination the photo voltage developed at the gate forward bias the gate and hence the depletion width at the Schottky junction changes. The effective channel width changes with the change in illumination. This phenomenon is called channel width modulation. The effective channel width controls the device resistance, conductance, admittance, capacitance and device current. Thus back illumination OPFET provides improved absorption and thus is more sensitive optical system. In other approaches for improved absorption M.K.Verma et al [51] have developed a model which presents the analysis of buried gate GaAs MESFET under dark and illuminated conditions. It was noted that the absorption increases and hence there is increase in channel current. The dependence of current in MESFETs on frequency and illumination as observed by the different researchers showed that the current changes with the frequency and illumination because of the change in the charge concentration in the channel with frequency and illumination. Lifetime of photo generated carrier s decreases when optical flux density and operating frequency increases [5, 38]. Therefore, the photo generated current and voltage remains constant up to a certain frequency and then decreases with the increase in the frequency. The changes in channel charges with frequency and illumination will result in the dependence of different device parameters like intrinsic capacitors, Y parameters, S parameters etc. on frequency and illumination. The next section presents some of the studies carried out by different researchers on intrinsic device parameters of MESFETs and the effect of illumination on these parameters. 2.7 Intrinsic Parameters of MESFETs The parameter extraction of MESFET involves extraction of extrinsic and intrinsic model element values. The extrinsic set consists of bias independent elements associated with the leads and contacts of the device and the intrinsic set consists of bias dependent parameters associated with internal device structure. These parameters are affected by biasing and external illumination falling on the device which affects the data detection rate. In III V compound materials (such as GaAs and InP), a negative resistance region is produced when the electric field in the material reaches a threshold level because the 23

12 mobility of electrons decreases as the electric field increases above threshold. Due to this there is a limitation on the carrier velocity. The limitation of carrier velocity results in charge accumulation effects at the drain side of the gradual channel portion giving rise to a large field increase in this region. This is known as Gunn effect, which causes an enhancement of the field and can be interpreted as the formation of a Gunn domain. The intrinsic parameter modeling of MESFET and other devices is very complicated because of Gunn domain formation at the drain side at pinch off [31, 52]. In 1985 the first capacitance model for GaAs MESFET which considered the Gunn domain formation was given by Michael Shur. The paper suggested capacitance model of MESFET as shown in fig It takes into consideration the Gunn domain formation which exists at microwave frequency and was not considered by earlier researchers [31, 52]. C gdp I gd Gate R g R D Drain I gs C gs C gd I ch C dom R dom C ds C gsp R sh R S Source Figure 2.2: Capacitance model for MESFET [Ref.31 & Ref.52] Chen and Shur [31, 52] carried out various simulations to compute gate source capacitance (C gs ) and gate drain capacitance (C gd ) with the variation of V gs and V gd for MESFETs. The results show that with the increase in V ds the capacitance C gd and C gs decrease because as the V ds increases the depletion width at the drain side increases. It also shows that both the capacitances increase as V gs becomes more and more positive. De Salles [19, 53] carried out an extensive theoretical and experimental work to investigate the performance of GaAs MESFET under illumination. It was reported that under illumination there is a considerable change in the DC characteristics. Due to this effect, the intrinsic parameters of the device change. Hence, its Y parameters and S parameters which are functions of the intrinsic parameters will also change. 24

13 Microwave characteristics of an optically controlled GaAs MESFET were studied by Mizuno [30]. The paper presented the results of an experimental investigation on the microwave characteristics of a GaAs MESFET under direct optically controlled condition. The parameters like gain, drain current and S parameters were measured under various optical conditions in the frequency range from 3.0 to 8.0GHz, and it was found that they can be controlled by varying the light intensity. Using the study carried out by above researchers Murty and Jit [42] presented an analytical S parameter model of optically controlled GaAs MESFET. Their study showed the variation of S parameters under illuminated condition. It illustrates the effect of illumination on S 11 parameter in saturation region near pinch off voltage. From the study it was observed that the input capacitance increased with the increase in the incident illumination level. These changes were prominent when the device is operated near pinch off. The study also illustrates the effect of illumination on S 21 near pinch off and shows that as input optical power is increased, the forward gain is also increased. However, the phase of S 21 is insensitive to illumination. Further, it was observed that there is very little change in the remaining parameters i.e. S 12, S 22 with illumination as compared to the others. Due to the variation of intrinsic parameters of GaAs MESFET with illumination, GaAs MESFET is widely used in OMMICs. The performance of these OMMIC s can be significantly enhanced by scaling down the device geometry of GaAs MESFET [39]. With the improvement in the process technology, a short gate length MESFET device with sub quarter micrometer size can be fabricated. However, the present long channel model cannot be used for short channel devices because for short gate length devices the short channel effects predominates the device characteristics. Therefore, for modeling of such MESFET two dimensional (2D) modeling is required. Section 2.8 includes the review of some of the major works related to 2D modeling of the MESFET and the major considerations in short channel device modeling viz. low field mobility, field distribution and channel voltage profile D Modeling of GaAs MESFET It has been long known that as the device dimensions reduce, the device modeling becomes more complicated due to the short channel effects. Streetman [46] explains the various short channel effects in FETs like drain induced barrier lowering and punch through, velocity saturation etc. This explains clearly that the long channel model may not be applicable when the channel length reduces below 2µm. 25

14 Madheswaran et al [39] have already reported that as far as high speed detection is concerned, the devices are to be considered as short channel. For short channel devices, the drain current saturation occurs because of the velocity saturation of the carriers in the channel rather than at pinch off. In order to consider the effect of velocity saturation, it is necessary to consider the field dependent mobility of carriers in the channel for current calculations. The model considered the gradual channel approximation and velocity saturation approximation for a short channel photo MESFET. In this model the doping profile in the channel has been assumed to be Gaussian in nature. About the electric field in short channel devices, a model was suggested by Ching Hsu [54]. The paper describes the influence of electric field and mobility profile on GaAs MESFET characteristics while considering the 2D model. The model includes the calculation of electric field along the channel using 2D numerical simulations. Using this information a new I V model was proposed by Shang Pin Chin et al [33 34] for short gate length MESFETs operating in the turn on region. In this 2D potential distribution contributed by the depletion layer charges under the gate and in the non gate region are separately obtained by conventional 1D approximation and Green s function solution technique. The reported results show that the channel potential increases with the decrease in channel length for fixed V ds. It is observed that for fixed gate length as the V ds increases the channel potential also increases. The variation of electric field with normalized distance as reported by [54] shows that the field increases with the increase in V ds and is maximum near the drain. It has also been shown that the two region mobility model is another factor that influences the performance of the device. The accuracy of describing the low field trans conductance is also strongly dependent on the mobility profile. A better mobility model was suggested by Madheswaran for the 2D modeling of the device. The paper described the field dependent mobility [39]. Mobility is an important parameter for carrier transport because it describes that the drift velocity of an electron is influenced by an applied electric field. At low electric field, the field dependence of the drift velocity is linear, corresponding to a constant mobility. As the drift velocity approaches the thermal velocity, its field dependence on the electric field starts deviating from its earlier linear relationship. As the electric field is further increased, the drift velocity increases less rapidly. After certain field called the critical field, the drift velocity approaches a saturation velocity. The experimental results can be approximated by the empirical expression as suggested in [18, 55]. The drift velocity reaches a maximum, and then decreases as the field further increases. This region which describes the region of negative differential mobility is also the region 26

15 of operation. Microwaves devices such as oscillators at microwave frequency are designed in the negative resistance region. R.W.H.Engelmann et al [56] proposed a semi empirical model to describe the Gunn domain formation in the saturated current region of GaAs MESFETs. 2D numerical analysis based on the drain current, current saturation range, intrinsic low frequency trans conductance and gate to source capacitance (C gs ) has revealed that Gunn domain formation causes an enhancement of the field at drain. M.A.R.Al Mudares et al [57] describes the computer simulation which confirms that GaAs MESFETs made from a single suitably doped layer, can sometimes exhibit negative resistance properties in the static I V characteristics. Akira Yoshii et al [58] also developed a 2D full Monte Carlo particle simulation to characterize the Si and GaAs MESFET, including non stationary carrier transport effect such as overshoot phenomena in sub micrometer gate. The results indicate that the non stationary carrier transport is very important for the accurate modeling in sub micrometer gate GaAs MESFETs. A new 2D device simulator for GaAs MESFET was reported by Mayumi Hirose et al [54] which proved to be useful for the design of FET structure. Implementation features a novel mobility model, in which mobility value is determined as a function of the electric field component. It was demonstrated that the mobility based model gives agreement in I V characteristics with experimental results for the device with submicron gate length. A high breakdown voltage is desired for high power or high resolution circuits such as an analog to digital circuit. However, the breakdown phenomenon related to the impact ionization mechanism was often observed at or before the designated applied voltage. To understand and remedy this, an understanding of the field distribution in the channel is required. 2D or 3D modeling is very attractive for this purpose due to the fact that the field distribution near the drain is very complicated. The mobility profile is modified by the electric field along the channel and also influences the shape of drain I V characteristics. The authors have carried out the 2D numerical simulation to investigate the mobility profile. It was reported that the linear region in drain current voltage characteristic is dominated by low field mobility profile while the saturation region is limited by the saturation velocity [59]. A 2D numerical model of GaAs MESFET with non uniform doping is developed and various characteristics are estimated under different illumination conditions by Madheswaran [60]. The Poisson s equations in the gate depletion region and the space charge region of the channel substrate junctions are solved numerically under dark and illumination conditions to calculate channel potential profile. 27

16 It has been shown that the potential at the source and drain ends remain constant whereas in the channel, the channel potential increases under the illuminated condition compared to the dark condition [60]. The study provides the details about the model for the short channel MESFET considering all the short channel effects for analytical and numerical approach. But for device dimensions lesser that 0.3µm there is a need of better model that can give optimized results. Jacoboni and Lugli [61] provide a numerical technique (Monte Carlo finite difference method) for solving 2D Poisson s equation accurately for devices with smaller dimensions. The models presented in this section do not consider noise in the device under illumination. So for accurate model noise under illumination at high frequency of operation should be considered. This is because optical absorption creates noise in active region of the device and deteriorates its SNR. Many authors have reported the GaAs noise modeling under dark and illuminated conditions. Section 2.9 provides the literature survey on the noise in GaAs MESFETs. 2.9 Noise in Optical Detectors The overall sensitivity of a photodiode results from the random current and voltage fluctuations which occur at the device output terminals in the presence and absence of an incident optical signal. Jong Hee Han [62] gave a physical thermal noise model for MESFET under dark which was compatible not only with small signal equivalent circuit and large signal I V but also with C V models. This paper takes static feedback effect into account while modeling noise characteristics. Marcel presented a comparative study of the microwave drain noise characteristics without illumination for MESFET and MODFET. It shows that though MODFET has lower noise figure than MESFET, its measured drain noise currents are greater. These noise models of MESFET described the noise behavior of the device under dark condition [63]. The noise behavior of an OPFET was modeled and analyzed for the first time by Chakrabarti [41]. It shows that the noise characteristics of an OPFET depend on a number of device parameters and these parameters in turn depend on the value of incident optical power. This paper investigated the noise behavior of an optically controlled MESFET. It also talks about different noise components in an OPFET. The paper shows that the intrinsic 28

17 parameters like internal capacitances of MESFET are strongly influenced by the incident optical signal and hence results in the change in the transfer function with illumination. Senior [2] suggested that the photo generated carriers also play a significant role in deciding the overall noise performance of an OPFET. It describes the major noise components of an OPFET in illuminated condition as: 1. Gate and drain diffusion noise, 2. Gate and drain shot noise and 3. Thermal noise arising from various resistances. The variation of these parameters with frequency was given by Chakrabarti et al [41]. The study also reveals that the operating frequency can be adjusted suitably to make the noise behavior of the OPFET independent of the value of the incident optical power. The shot noise and diffusion noise are strongly influenced by the incident radiation. The study by Chakrabarti et al shows that the noise power increases when optical power increases. This is because photo generated carriers enhance the gate to source leakage current and degrade the noise performance of MESFETs under optically controlled condition [41]. R g G Y 1 C gsop C 1 C 2 g mop V gs C dcop C dsop r dsop R D Ri D R gs Source Figure 2.3: Norton equivalent circuit with miller effect [Ref.41] As both the signal strength and noise change with illumination, the paper shows that a large improvement in the SNR can be achieved by increasing the incident optical power density. However, it talks about the relative intensity noise (RIN) of the optical control signal which may become significantly high at very high value of incident optical power density and the overall SNR would no longer be limited by the intrinsic noise 29

18 characteristics of the OPFET. Therefore, according to Chakrabarti et al, an OPFET may not be suitable for use as an optical detector in optical communication [41]. To calculate these noise components and transfer function of the device the Norton equivalent circuit of the MESFET was given by [41] and [37]. The model suggested by [41] is reproduced here in fig. 2.3 for reference. Thus the study shows that under illumination at high frequency the device performance deteriorate due to the change in the minority carrier lifetime with illumination and frequency of operation. For device under illumination its noise behavior and the effect of noise on device stability are important. Next section presents a detailed literature survey on the stability performance of the device under illuminated condition Stability Stability analysis helps to find whether the system is stable or unstable. The studies show that the stability of the system can be analyzed using: 1. Stability circles and 2. Pole plot of system s closed loop transfer function in s plane Stability Circles Pozar [64] and Ludwig [65] talk about the stability of system at microwave frequency using stability circles. Stability circles help to understand the region of operation in which amplifier will show stable operation. Hence the effect of the noise on the device with the change in illumination can be explained with the help of stability circle. We can check whether the system is unconditionally stable or conditionally stable by checking following conditions: 1. The system is unconditionally stable if input reflection coefficient Г in <1 and output reflection coefficient Г out <1 for all passive source and load impedances (i.e. Г S <1 and Г L <1). 2. The system is conditionally stable if Г in <1 and Г out <1 only for a certain range of passive source and load impedances. Masahiko Shimizu et al [66] had discussed the performance of microwave GaAs MESFET gate mixer to clarify the existence of conditionally stable RF frequency range as well as an unconditionally stable frequency range in which maximum available conversion gain can be defined using stability circle. It shows that optimum IF load impedance and the RF source impedance for the unconditionally stable RF frequency 30

19 region can be determined using stability circles. It also shows stability circles and equal gain loci for conditionally stable RF frequency region. It is observed from the results that the instability can be avoided by increasing the RF source impedance. The approach of plotting stability circles is a little complicated and requires skills. So to find the relative change in stability under illuminated condition another approach as suggested by Gopal [67] is explained in the next section Pole Position of System s Closed Loop Transfer Function in s plane Gopal [67] has shown that for a stable system the poles of the transfer function should lie in the left hand side (LHS) of the s plane and shows that the system performance is dependent on the position of the dominant poles i.e. the poles nearer to the imaginary axis. It also talks about the relative stability of a system under different conditions can be compared by comparing their poles position in the s plane. According to Gopal the condition under which the dominant poles of the system are more into the LHS of the s plane is a relatively more stable condition. Thus the study shows that stability of the device can be easily determined under illuminated condition by finding the change in position of the poles of transfer function in the s plane Conclusion The study shows that there are different device models present for MESFET under illumination. Models for device dimensions lesser that 0.3µm which considers all the short channel 2D effects have not been reported. In addition, the reported models present AC characteristics, DC characteristics, microwave characteristics and noise parameter dependence on illumination but stability model is not reported by any researcher. These shortcomings of the existing models are the source of motivation to develop a new model. The problem and scope of work have been defined in section 1.5. Since fabrication facilities are not there, only simulation is done and the results are compared with the reported results. 31