02-01-2016, 11:32 AM
Abstract:
This paper reflects the computer-based method to calculate the parasitic series resistance Rs for Ku-band packaged IMPATT diode for 4H-SiC and Diamond© from small signal conductance-susceptance characteristics. The calculation of parasitic series resistance Rs has been done at the threshold condition when the small signal conductance of the packaged diode just becomes negative and the device susceptance becomes positive. Rsfor 4H-SiCand Diamond is calculated and compared for Ku band frequency.
The oscillation in IMPATT diode is due to its negative resistance. Crucial device parameter that limits the output power to RF circuit and efficiency of an IMPATT diode is its parasitic series resistance (Rs) [17].In this paper author has concentrated on RF output power. As the negative resistance that develops in an IMPATT diode is very small thus the positive series resistance (Rs) should not cross the value of the negative resistance, otherwise the oscillations will cease or stop. The parasitic positive series resistance of an IMPATT diode come into existence due to the substrate, the metal semiconductor contact, undepleted epitaxial layer and a small part arise from device package. Thus an appropriate technology is required to reduce the value of this positive resistance, so that the oscillation can sustain and maximum output power can result from the oscillator. A direct measurement of Rsby a network analyser is difficult due to circuit modelling difficulties and the network analyzer error [18-19].]. So a computer-basedmethod has been developed using accurate values of ionization rates and drift velocities for determination of the series resistance of Ku band DDR IMPATT diode utilizing small-signalconductance-susceptance characteristics at threshold condition (i.e. when the small-signal conductance of the packaged diode just becomes negative and the susceptance becomes just positive). Electrical series resistance is well recognized as limiting factor for power andefficiency in IMPATT diodes. In 1983 an effective method of measuring had beenproposed by Michael G. Adlerestein, Lowell H. Holway and Shiou Lung G Chu [6]. They used observation of the oscillation threshold bias current for a diode ina standard circuit. The material used was GaAs near 40 GHz. Similarly calculation of for Si [Single Drift Region (SDR) Structure] IMPATT wascarried out by M. Mitra, M. Das, S. Kar and S. K. Roy by considering unequalionization rates and drift velocities of the two types of charge carriers in Silicon in1994 [5]. Another work by T. K. Pal of Research Centre Imarat (RCI), Hyderabad, Indiadescribed a computer-based method to calculate the series resistance of an mm-waveKa-band packaged IMPATT diode from Small-Signal Conductance-Susceptancecharacteristics in 2009 [8]. So lot many researchers have been experimentally measured the parasiticseries resistance of IMPATT diodes operating at different frequencies. But theexperimental measurement of series resistance is very much time consuming and expensive method. That is why our aim is to develop a simple and generalized computer based simulation method which can predict close value of parasitic resistance of particular structure of IMPATT diode operating at particular frequency. So we have to develop the numerical model of the parasitic resistance, which should be independent of operating frequency of the device, it means the model should be sustain at any operating frequency band. In this paper a generalized simulation method for DC and Small-signal analysis of IMPATT devices is presented, the method can be applied to any diode structure. The characteristics of microwave device and the contribution of diode negative resistance from the depletion layer of the diode can be obtained through the use of this method. The method is applied to 4H-SiC and Diamond© Double Drift Region (DDR) IMPATT diodes designed to oscillate in Ku-Band. This paper mainly describes the detailed computer-based method to calculate the parasitic positive series resistance Rs of packaged DDR IMPATT diodes from high frequency small signal conductance-susceptance characteristics. This method would be suitable for determining Rsfor Ku band diodes with appropriate values of ionization rate and drift velocity at maximum electric field.
The circuit shown in the Fig. 1 [14] below represent equivalent circuit for IMPATT diode Where, G and B represent the diode conductance and susceptance respectively. We can determine the magnitudes of G and B from simulation by using values of ionization rate and drift velocities of charge carriers for 4H-Sic and Diamond taken from[20-22]. Rs is the series resistance of the device, g is the load conductance and L is the circuit inductance. Cp and Lp are the package capacitance and package inductance respectively. By using [8] Impedance of the packaged device is given,
Where = Effective susceptance caused by package parameter.
Impedance of the RF circuit is given by [8],
(3)
In a practical oscillator circuit, the steady-state condition for oscillation is given by,
(4)
Both real and imaginary parts of equation (4) must be separately equal to zero,
Real (5)
Imaginary (6)
From above eq we get(7)
As the method proposed for IMPATT oscillator by Scharfetter and Gummel [15], where the authors have shown that with increasing voltage swing, the susceptance of the diode remains almost constant. Thus the frequency of oscillation does not change much with the build-up of amplitude of oscillation. The oscillation continues to build up for several cycles until the magnitude of the device negative conductance decreases to the value of positive conductance of the load. At the threshold condition, the diode negative conductance is much larger than the positive conductance of RF circuit and so the oscillation builds up. The oscillation is started by a random noise fluctuation which grows when the total conductance of the device-circuit system is negative. For stability of oscillation it is necessary that as the oscillation amplitude grows the magnitude of the negative conductance of the active device tends to decrease. The oscillation then becomes stable. In the practical case, it is a good approximation to take g = 0 at the oscillation threshold [8].
Where, Gth is small signal conductance of the diode at the threshold condition when the total conductance of the packaged diode becomes just negative. Bthis the small signal threshold susceptance of the diode, corresponding to the threshold conductance GthConsidering the package inductance Lpand package capacitance Cp, the equivalent circuit of the IMPATT diode with package parameter is shown in Fig. 1 and the expression for series resistance.
A generalise DDR (n+ n p p+ type ) IMPATT diode has been designed for operation in Ku-band, through double iterative dc and small signal computer analysis. The following assumptions are made in dc and small signal computer analysis of IMPATT diodes [9-10]. (a) One dimensional model of the p-n junction has been considered, (b) The electron and hole velocities have been taken to be saturated and independent of the electric field throughout the space charge layer, and © Carrier diffusion has been neglected. In this method the computation starts from the field maximum near the metallurgical junction. The distribution of the electric field and carrier currents in the depletion layer are obtained by the double-iterative computer method, which involves iteration over the magnitude of field maximum and its location in the depletion layer.
with the boundary condition:
(i)The electric field at the two edges of the depletion layer becomes zero, i.e,
E(–x1) = 0 and E(+x2) = 0 and
(ii) Normalised carrier current densities at the two edges are
P (–x1) >> –1 and P (x2)>> +1
On analysing the diode impedance Z(x,ω) obtained from Gummel-Blue method[9], after separating its real part R(x, ω) and imaginary part X(x, ω), two differential equations are framed. Solving these two equations simultaneously, the small signal integrated parameters like impedance (Z), conductance (G), and susceptance (B) are obtained. The integration of R(x) and X(x) profiles over the depletion layer gives the total negative resistance ZRandZXof the diode.
The symbols used have their usual significance. Realistic field and the effect of mobile space charge has been considered. The device parameters taken for this present analysis is shown in Table 1 [20-22] and The G-B plot corresponding to each material shown in Fig. 2(a-b). For this operation the range of frequency is 12GHz–18 GHz (Ku band).
*An ,bnionization coefficient of electron and Ap,bpfor holes.
is the total current density.
*Vns,vpssaturation velocity of e-& hole. εr, is relative dielectric constant.
, are the electron and hole mobility
* αn ,αp are rapidly increasing function of electric field.
Results and Discussion:-
For calculation of the value of series resistance Rs, a typical value of package inductance and capacitance is specified by manufacturer for calculation in this paper the typical value used are given below [8].
Lp= 0.080 nH and Cp= 0.110 pF
The series resistance Rsof the diode is determined at the threshold condition of oscillation of the diode, i.e., when the circuit conductance g and the power output from the device are assumed to be minimum. Thus the series resistance Rsof the diode can be determined from the small signal analysis at the threshold condition with good accuracy using the Eqn (9). The values of series resistance Rsobtained from computer analysis have been shown in Table 2(a-b) for 4H-SiC and Diamond respectively.
The given result in a Table 2(a-b) give the change in series resistance (or positive parasitic resistance) with operating frequency in Ku band and the graph shows the variation of device conductance and susceptance with respect to Ku band frequency for different material DDR (n+ n p p+) IMPATT diode.
This paper reflects the computer-based method to calculate the parasitic series resistance Rs for Ku-band packaged IMPATT diode for 4H-SiC and Diamond© from small signal conductance-susceptance characteristics. The calculation of parasitic series resistance Rs has been done at the threshold condition when the small signal conductance of the packaged diode just becomes negative and the device susceptance becomes positive. Rsfor 4H-SiCand Diamond is calculated and compared for Ku band frequency.
Introduction
The oscillation in IMPATT diode is due to its negative resistance. Crucial device parameter that limits the output power to RF circuit and efficiency of an IMPATT diode is its parasitic series resistance (Rs) [17].In this paper author has concentrated on RF output power. As the negative resistance that develops in an IMPATT diode is very small thus the positive series resistance (Rs) should not cross the value of the negative resistance, otherwise the oscillations will cease or stop. The parasitic positive series resistance of an IMPATT diode come into existence due to the substrate, the metal semiconductor contact, undepleted epitaxial layer and a small part arise from device package. Thus an appropriate technology is required to reduce the value of this positive resistance, so that the oscillation can sustain and maximum output power can result from the oscillator. A direct measurement of Rsby a network analyser is difficult due to circuit modelling difficulties and the network analyzer error [18-19].]. So a computer-basedmethod has been developed using accurate values of ionization rates and drift velocities for determination of the series resistance of Ku band DDR IMPATT diode utilizing small-signalconductance-susceptance characteristics at threshold condition (i.e. when the small-signal conductance of the packaged diode just becomes negative and the susceptance becomes just positive). Electrical series resistance is well recognized as limiting factor for power andefficiency in IMPATT diodes. In 1983 an effective method of measuring had beenproposed by Michael G. Adlerestein, Lowell H. Holway and Shiou Lung G Chu [6]. They used observation of the oscillation threshold bias current for a diode ina standard circuit. The material used was GaAs near 40 GHz. Similarly calculation of for Si [Single Drift Region (SDR) Structure] IMPATT wascarried out by M. Mitra, M. Das, S. Kar and S. K. Roy by considering unequalionization rates and drift velocities of the two types of charge carriers in Silicon in1994 [5]. Another work by T. K. Pal of Research Centre Imarat (RCI), Hyderabad, Indiadescribed a computer-based method to calculate the series resistance of an mm-waveKa-band packaged IMPATT diode from Small-Signal Conductance-Susceptancecharacteristics in 2009 [8]. So lot many researchers have been experimentally measured the parasiticseries resistance of IMPATT diodes operating at different frequencies. But theexperimental measurement of series resistance is very much time consuming and expensive method. That is why our aim is to develop a simple and generalized computer based simulation method which can predict close value of parasitic resistance of particular structure of IMPATT diode operating at particular frequency. So we have to develop the numerical model of the parasitic resistance, which should be independent of operating frequency of the device, it means the model should be sustain at any operating frequency band. In this paper a generalized simulation method for DC and Small-signal analysis of IMPATT devices is presented, the method can be applied to any diode structure. The characteristics of microwave device and the contribution of diode negative resistance from the depletion layer of the diode can be obtained through the use of this method. The method is applied to 4H-SiC and Diamond© Double Drift Region (DDR) IMPATT diodes designed to oscillate in Ku-Band. This paper mainly describes the detailed computer-based method to calculate the parasitic positive series resistance Rs of packaged DDR IMPATT diodes from high frequency small signal conductance-susceptance characteristics. This method would be suitable for determining Rsfor Ku band diodes with appropriate values of ionization rate and drift velocity at maximum electric field.
Estimation of Series Resistance (Rs) Numerically:-
The circuit shown in the Fig. 1 [14] below represent equivalent circuit for IMPATT diode Where, G and B represent the diode conductance and susceptance respectively. We can determine the magnitudes of G and B from simulation by using values of ionization rate and drift velocities of charge carriers for 4H-Sic and Diamond taken from[20-22]. Rs is the series resistance of the device, g is the load conductance and L is the circuit inductance. Cp and Lp are the package capacitance and package inductance respectively. By using [8] Impedance of the packaged device is given,
Where = Effective susceptance caused by package parameter.
Impedance of the RF circuit is given by [8],
(3)
In a practical oscillator circuit, the steady-state condition for oscillation is given by,
(4)
Both real and imaginary parts of equation (4) must be separately equal to zero,
Real (5)
Imaginary (6)
From above eq we get(7)
As the method proposed for IMPATT oscillator by Scharfetter and Gummel [15], where the authors have shown that with increasing voltage swing, the susceptance of the diode remains almost constant. Thus the frequency of oscillation does not change much with the build-up of amplitude of oscillation. The oscillation continues to build up for several cycles until the magnitude of the device negative conductance decreases to the value of positive conductance of the load. At the threshold condition, the diode negative conductance is much larger than the positive conductance of RF circuit and so the oscillation builds up. The oscillation is started by a random noise fluctuation which grows when the total conductance of the device-circuit system is negative. For stability of oscillation it is necessary that as the oscillation amplitude grows the magnitude of the negative conductance of the active device tends to decrease. The oscillation then becomes stable. In the practical case, it is a good approximation to take g = 0 at the oscillation threshold [8].
Where, Gth is small signal conductance of the diode at the threshold condition when the total conductance of the packaged diode becomes just negative. Bthis the small signal threshold susceptance of the diode, corresponding to the threshold conductance GthConsidering the package inductance Lpand package capacitance Cp, the equivalent circuit of the IMPATT diode with package parameter is shown in Fig. 1 and the expression for series resistance.
Computer Based DC and Small Signal Analysis:-
A generalise DDR (n+ n p p+ type ) IMPATT diode has been designed for operation in Ku-band, through double iterative dc and small signal computer analysis. The following assumptions are made in dc and small signal computer analysis of IMPATT diodes [9-10]. (a) One dimensional model of the p-n junction has been considered, (b) The electron and hole velocities have been taken to be saturated and independent of the electric field throughout the space charge layer, and © Carrier diffusion has been neglected. In this method the computation starts from the field maximum near the metallurgical junction. The distribution of the electric field and carrier currents in the depletion layer are obtained by the double-iterative computer method, which involves iteration over the magnitude of field maximum and its location in the depletion layer.
with the boundary condition:
(i)The electric field at the two edges of the depletion layer becomes zero, i.e,
E(–x1) = 0 and E(+x2) = 0 and
(ii) Normalised carrier current densities at the two edges are
P (–x1) >> –1 and P (x2)>> +1
On analysing the diode impedance Z(x,ω) obtained from Gummel-Blue method[9], after separating its real part R(x, ω) and imaginary part X(x, ω), two differential equations are framed. Solving these two equations simultaneously, the small signal integrated parameters like impedance (Z), conductance (G), and susceptance (B) are obtained. The integration of R(x) and X(x) profiles over the depletion layer gives the total negative resistance ZRandZXof the diode.
The symbols used have their usual significance. Realistic field and the effect of mobile space charge has been considered. The device parameters taken for this present analysis is shown in Table 1 [20-22] and The G-B plot corresponding to each material shown in Fig. 2(a-b). For this operation the range of frequency is 12GHz–18 GHz (Ku band).
*An ,bnionization coefficient of electron and Ap,bpfor holes.
is the total current density.
*Vns,vpssaturation velocity of e-& hole. εr, is relative dielectric constant.
, are the electron and hole mobility
* αn ,αp are rapidly increasing function of electric field.
Results and Discussion:-
For calculation of the value of series resistance Rs, a typical value of package inductance and capacitance is specified by manufacturer for calculation in this paper the typical value used are given below [8].
Lp= 0.080 nH and Cp= 0.110 pF
The series resistance Rsof the diode is determined at the threshold condition of oscillation of the diode, i.e., when the circuit conductance g and the power output from the device are assumed to be minimum. Thus the series resistance Rsof the diode can be determined from the small signal analysis at the threshold condition with good accuracy using the Eqn (9). The values of series resistance Rsobtained from computer analysis have been shown in Table 2(a-b) for 4H-SiC and Diamond respectively.
The given result in a Table 2(a-b) give the change in series resistance (or positive parasitic resistance) with operating frequency in Ku band and the graph shows the variation of device conductance and susceptance with respect to Ku band frequency for different material DDR (n+ n p p+) IMPATT diode.
Conclusion :-
After observing the above result we can conclude that the series resistance for 4H-SiC is less as compared to the Diamond IMPATT diode, as Rs is the factor which will limits the output power from IMPATT diode to the RF circuit. So for maximum output power the value of Rs should be as small as possible. Therefore 4H-SiC IMPATT diode deliver move power to the output RF circuit as compare to Diamond IMPATT diode.