(10)

(11)

, ,

*n*

1

*p*

*M xt*

*n*

given by the quiescent zero bias solution, i.e. solution when

file over the total depletion layer width, i.e.

current (i.e. the external current) is given by,

*M xt*

2

( )

1

High-Power Hexagonal SiC Device: A Large-Signal High-Frequency Analysis

(8)

341

http://dx.doi.org/10.5772/52982

(9)

( )

2

0

*J xt*

The initial values of electron and hole densities are either furnished by a previous run or are

*p*

, ,

0

*J t*

*J xt J t*

$$J\_{\boldsymbol{n}}\left(\mathbf{x},t\right) = qn\left(\mathbf{x},t\right)\nu\_{\boldsymbol{n}}\left(\mathbf{x},t\right) + qD\_{\boldsymbol{n}}\left(\frac{\partial n\left(\mathbf{x},t\right)}{\partial \mathbf{x}}\right) \tag{5}$$

Where the symbols \_ *<sup>n</sup>*, \_ *<sup>p</sup>*, *v <sup>n</sup>*, *v <sup>p</sup>*, *µ <sup>n</sup>*, *µ <sup>p</sup>*, etc. have their usual significance.

In the above mentioned simulation method, the computation starts from the field maximum \*!.z 0\$!z)!0((1.#%(z&1\*0%+\*^z\$!z+1\* .5z+\* %0%+\*/z "+.z 0\$!z!(!0.%z "%!( z0z 0\$!z !,(!¥ tion layer edges are given by,

$$\begin{aligned} \xi \left( -\mathbf{x}\_1, t \right) &= 0 \\ \xi \left( +\mathbf{x}\_2, t \right) &= 0 \end{aligned} \tag{6}$$

Similarly the boundary conditions for normalized current density *P(x,t) = (J <sup>p</sup> (x,t) – J <sup>n</sup> (x,t)) / J <sup>0</sup> (t)* (where, *J <sup>0</sup> (t) = J <sup>p</sup> (x,t) + J <sup>n</sup> (x,t)*) at the depletion layer edges ie, at *x = -x <sup>1</sup>* and *x = x <sup>2</sup>* are given by,

$$\begin{aligned} P\left(-\mathbf{x}\_1, t\right) &= \left(\frac{2}{M\_p\left(-\mathbf{x}\_1, t\right)} - 1\right) \\ P\left(\mathbf{x}\_2, t\right) &= \left(1 - \frac{2}{M\_u\left(\mathbf{x}\_2, t\right)}\right) \end{aligned} \tag{7}$$

*Mn(x2,t)* and *M <sup>p</sup> (-x <sup>1</sup> ,t)* are the electron and hole multiplication factors at the depletion layer edges are given by.

#### High-Power Hexagonal SiC Device: A Large-Signal High-Frequency Analysis http://dx.doi.org/10.5772/52982 341

$$\begin{aligned} \mathcal{M}\_{\rho} \left( -\mathbf{x}\_{1}, t \right) &= \frac{J\_{\rho} \left( t \right)}{J\_{\rho} \left( -\mathbf{x}\_{1}, t \right)} \\ \mathcal{M}\_{n} \left( \mathbf{x}\_{2}, t \right) &= \frac{J\_{\rho} \left( t \right)}{J\_{n} \left( \mathbf{x}\_{2}, t \right)} \end{aligned} \tag{8}$$

The initial values of electron and hole densities are either furnished by a previous run or are given by the quiescent zero bias solution, i.e. solution when

( ) ( ) ( ( ) ( ) ( ) ( ) ( ) ( )) , , , ,, , ,, *<sup>p</sup>*

( ) ( ) ( ( ) ( ) ( ) ( ) ( ) ( )) , , , ,, , ,, *<sup>n</sup>*

( ) ( ) ( ) ( , ) , ,, *p pP p xt J x t qp x t v x t qD*

( ) ( ) ( ) ( , ) , ,, *n nn*

In the above mentioned simulation method, the computation starts from the field maximum

\*!.z 0\$!z)!0((1.#%(z&1\*0%+\*^z\$!z+1\* .5z+\* %0%+\*/z "+.z 0\$!z!(!0.%z "%!( z0z 0\$!z !,(!¥

, 0 , 0

Similarly the boundary conditions for normalized current density *P(x,t) = (J <sup>p</sup> (x,t) – J <sup>n</sup> (x,t)) /*

*J <sup>0</sup> (t)* (where, *J <sup>0</sup> (t) = J <sup>p</sup> (x,t) + J <sup>n</sup> (x,t)*) at the depletion layer edges ie, at *x = -x <sup>1</sup>* and *x = x <sup>2</sup>* are

1

2

( ) ( ) 1 2

( ) ( )

<sup>2</sup> , 1 ,

*M xt*

 \$ % &

*n*

*Mn(x2,t)* and *M <sup>p</sup> (-x <sup>1</sup> ,t)* are the electron and hole multiplication factors at the depletion layer

*M xt*

*p*

\$ % &

1

*P xt*

2

*Pxt*

( ) ( )

<sup>2</sup> , 1 ,

*x t x t*

 

*J x t qn x t v x t qD*

Where the symbols \_ *<sup>n</sup>*, \_ *<sup>p</sup>*, *v <sup>n</sup>*, *v <sup>p</sup>*, *µ <sup>n</sup>*, *µ <sup>p</sup>*, etc. have their usual significance.

*p xt J xt*

340 Physics and Technology of Silicon Carbide Devices

tion layer edges are given by,

given by,

edges are given by.

*t x*

*n xt J xt*

*t x*

*n n p p*

*n n p p*

 

 

*x* \$ % & (4)

*n xt*

*x* \$ % & (5)

(6)

(7)

*q n xt xt v xt p xt xt v xt*

*q n xt xt v xt p xt xt v xt*

(3)

(2)

$$\begin{aligned} J\_n\left(\mathbf{x}, t\right) &= J\_p\left(\mathbf{x}, t\right) = 0\\ \frac{\partial n\left(\mathbf{x}, t\right)}{\partial t} &= \frac{\partial p\left(\mathbf{x}, t\right)}{\partial t} = 0 \end{aligned} \tag{9}$$

\$!z.!' +3\*z2+(0#!z0z\*5z0%)!z%\*/0\*0z%/z(1(0! z5z%\*0!#.0%\*#z0\$!z/,0%(z"%!( z,.+¥ file over the total depletion layer width, i.e.

$$W\_{\alpha} \left( t \right) = \int\_{-\mathbf{x}\_{i}}^{\mathbf{x}\_{i}} \xi \left( \mathbf{x}, t \right) d\mathbf{x} \tag{10}$$

The magnitude of peak field at the junction (i *<sup>p</sup>*), the widths of avalanche and drift zones (*x <sup>A</sup>* and *x <sup>D</sup>*; where *x <sup>D</sup> = d <sup>n</sup> + d <sup>p</sup>*), breakdown voltage (*V <sup>B</sup>*) and the voltage drops across these zones (*V <sup>A</sup>*, *V <sup>D</sup>* = *V <sup>B</sup> - V <sup>A</sup>*) are obtained from double iterative DC simulation program at *t = 0*. \$!z /\*,w/\$+0/z +"z !(!0.%z "%!( z \* z 1..!\*0z !\*/%05z ,.+"%(!/z %\*z 0\$!z !,(!0%+\*z (5!.z +"z 
¥ PATT diodes can be obtained from the simultaneous numerical solution of the basic device equations (equations (1) – (5)) subject to appropriate boundary conditions (equations (6)& (7)). A software package has been developed for simultaneous numerical solution of the above said equations. Boundary conditions are imposed at the contacts (at the *n <sup>+</sup> -n*& *p <sup>+</sup> -p* contacts) by setting up the appropriate restrictions in equations (1) – (5).

\$!z!2(10%+\*z+"z1..!\*0z\* z2+(0#!z%\*z0%)!z\z/,!z +)%\*z+"z0\$!z !2%!z\* z0\$!z!-1%2¥ lent circuit has been obtained through the developed simulation program. The total terminal current (i.e. the external current) is given by,

$$I(t) = -C\_d \frac{dV(t)}{dt} + I\_c(t) \tag{11}$$

Where, *C <sup>d</sup>* is the depletion region capacitance of the diode, *V(t)* is the AC terminal voltage and *I <sup>e</sup> (t)* is the terminal current induced by the transport of carriers through the diode (Fig. 2). The optimized design parameters are obtained after several computer runs. Once the /\*,w/\$+0/z+"z!(!0.%z"%!( z\* z1..!\*0z,.+"%(!/z0z %""!.!\*0z0%)!z\z/,!z+2!.zz+),(!0!z5¥ (!z.!z+0%\*! \_z 0\$!z+,0%)%6! z2(1!/z\$2!z!!\*z1/! z "+.z/%)1(0%+\*z+"z(.#!w/%#\*(z%),!¥ dance and admittance characteristics of the device. The diode admittance (including the depletion region capacitance (*C <sup>d</sup>*) at the oscillation frequency q is given by the fundamental frequency components of current and voltage by,

$$Y\_d = j\alpha C\_d - \frac{I\_{e,1}\left(\alpha\right)}{V\_1\left(\alpha\right)}\tag{12}$$

After *I <sup>e</sup> (t)* and *V <sup>1</sup> (t)* in equations (15) and (17) are represented as phasors and substituted

*<sup>j</sup> j C AI*

0

*d RF*

<sup>2</sup> exp 2 <sup>2</sup>

% & = + \$ % & \$ % \$ & % &

racy of the simulation. Material parameters of SiC is taken from NSM archive [6].

2 2 2 2 0 0 2 0

*d*

*d a*

A generalized large-signal program has been developed to solve the equations (12), (13), (17) and (18d^z\$!z/5)+(/z\$2!z0\$!%.z1/1(z/%#\*%"%\*!^z\$!z/%)1(0%+\*z%/z..%! z+10z5z+\*/% ¥ ering a space division of *500* steps and time scale is varied from *100-150*z0+z%\*.!/!z0\$!z1¥

Figure 2. 0=JEAF9DNGDL9?=9F<;MJJ=FL>GJ9F%),00<AG<=K@GOAF?L@=K=H9J9LAGFG>L@=<=HD=LAGFJ=?AGF;9H9;As

The optimized structural parameters of Si/SiC DD hetero-structure IMPATTs for operation

\*+0!/z0\$!z2+(0#!z\* z1..!\*0z32!"+.)z"+.z%z 
z !2%!z+,!.0%\*#z1\* !.z(.#!w/%#¥

essential criteria for IMPATT oscillation. This proves the validity of the simulation software. Large-signal simulation provides the snap-shots of electric-field profiles at different phase angles as shown in figures 4(a) to 4(e). The electric field increases from t=0 and attains its

then decreases and attains the same magnitude of negative peak in the negative half-cycle at

tance *Cd* from the diode admittance *Y <sup>d</sup>*. *Y <sup>c</sup>* is the circuit admittance including the diode package.

at W-band are given in Table 1 for the bias current density of 8x108

peak value in the positive half-cycle at t =T/4 (Emax = 5x108

*<sup>j</sup> A A I I IA*

exp <sup>2</sup>

( )

http://dx.doi.org/10.5772/52982

A/m2

V/m) as shown in figure 4(b). It

phase-shift between voltage and terminal current,

^z%#1.!/zFcwdz !¥

(18)

343

2

*dc dc dc*

High-Power Hexagonal SiC Device: A Large-Signal High-Frequency Analysis

*d*

\$

into equation (12), the diode admittance is found to be,

sin

*d d*

3. Results and Discussions

nal condition. The plots depict the 1800

*Y jC*

2

 *d*

Finally the expression governing the terminal voltage *V(t)* is given as [7],

$$V(t) = \frac{A\_0 l\_d}{\varepsilon \alpha A\_r} \cos \left\{ \alpha \left( t + \frac{\tau\_d}{2} \right) \right\} - \frac{2A\_0 l\_d \sin \left( \frac{\alpha \sigma\_d}{2} \right)}{\varepsilon \alpha^2 \tau\_d A\_r} \cos \left( \alpha t \right) - \frac{\tau\_d E\_d l\_d}{2m} \frac{A\_0 \alpha \cos \left\{ \alpha \left( t + \frac{\tau\_d}{2} \right) \right\}}{I\_{dc} + A\_0 \sin \left\{ \alpha \left( t + \frac{\tau\_d}{2} \right) \right\}} \tag{13}$$

Where,

$$A\_0 = I\_{\kappa F} \frac{\left(\frac{\partial \sigma\_d}{\partial \mathbf{z}}\right)}{\sin\left(\frac{\partial \sigma\_d}{\partial \mathbf{z}}\right)}\tag{14}$$

Simultaneously,

$$I\_{\rm c} \left( t \right) = I\_{\rm dc} + I\_{\rm RF} \sin \left( \alpha t \right) \tag{15}$$

$$I\_c\left(t\right) = I\_{dc} + A\_0 \sin\left\{\alpha \left(t + \frac{\tau\_d}{2}\right)\right\} \tag{16}$$

The fundamental frequency component of *V(t)* is found by a Fourier analysis of (13) and is given as,

$$\begin{aligned} V\_1(t) &= \frac{A\_0 l\_d}{\varepsilon \omega A\_r} \cos \left[ \omega (t + \frac{\tau\_d}{2}) \right] - \frac{2A\_0 l\_d \sin(\frac{\omega \tau\_d}{2})}{\varepsilon \omega^2 \tau\_d A\_r} \cos(\omega t) \\ &- \frac{\tau\_1 E\_c l\_d \omega}{m A\_0} (I\_{dc} - \sqrt{I\_{dc}^2 - A\_0^2}) \cos \left| \omega (t + \frac{\tau\_d}{2}) \right| \end{aligned} \tag{17}$$

After *I <sup>e</sup> (t)* and *V <sup>1</sup> (t)* in equations (15) and (17) are represented as phasors and substituted into equation (12), the diode admittance is found to be,

$$Y\_d = j\rho C\_d + \frac{j\rho C\_d A\_0 I\_{RF} \exp\left(\frac{-j\rho \sigma\_d}{2}\right)}{A\_0^2 - A\_0^2 \frac{\sin\left(\frac{\rho \sigma\_d}{2}\right)}{\left(\frac{\rho \sigma\_d}{2}\right)} \exp\left(\frac{-j\rho \sigma\_d}{2}\right) - 2I\_{dc} \frac{\phi^2}{\phi\_d^2} \left(I\_{dc} - \sqrt{I\_{dc}^{'2} - A\_0^{'2}}\right)}\tag{18}$$

A generalized large-signal program has been developed to solve the equations (12), (13), (17) and (18d^z\$!z/5)+(/z\$2!z0\$!%.z1/1(z/%#\*%"%\*!^z\$!z/%)1(0%+\*z%/z..%! z+10z5z+\*/% ¥ ering a space division of *500* steps and time scale is varied from *100-150*z0+z%\*.!/!z0\$!z1¥ racy of the simulation. Material parameters of SiC is taken from NSM archive [6].

Figure 2. 0=JEAF9DNGDL9?=9F<;MJJ=FL>GJ9F%),00<AG<=K@GOAF?L@=K=H9J9LAGFG>L@=<=HD=LAGFJ=?AGF;9H9;As tance *Cd* from the diode admittance *Y <sup>d</sup>*. *Y <sup>c</sup>* is the circuit admittance including the diode package.

#### 3. Results and Discussions

(!z.!z+0%\*! \_z 0\$!z+,0%)%6! z2(1!/z\$2!z!!\*z1/! z "+.z/%)1(0%+\*z+"z(.#!w/%#\*(z%),!¥ dance and admittance characteristics of the device. The diode admittance (including the depletion region capacitance (*C <sup>d</sup>*) at the oscillation frequency q is given by the fundamental

*I*

*d d*

Finally the expression governing the terminal voltage *V(t)* is given as [7],

2

( ) ( ) <sup>0</sup> <sup>0</sup>

*d d d a cd*

> 

> > 0

*A I*

cos cos

*A l E l V t <sup>t</sup> <sup>t</sup>*

*<sup>V</sup>*1(*t*)= *<sup>A</sup>*0*<sup>l</sup>*

 m1*Ecl d*q *mA*<sup>0</sup>

*d* cq*Ar* cos{q(*t* +

(*Idc Idc*

342 Physics and Technology of Silicon Carbide Devices

*Y jC <sup>V</sup>*

( ) ( ) ,1 1 *e*

2 sin cos

 

*A l A t*

 

2 2 sin

*r d r d*

2

 \$ % & <sup>=</sup> \$

*d*

2

The fundamental frequency component of *V(t)* is found by a Fourier analysis of (13) and is

2)cos{q(*t* +

 % &

*d*

2 *d*

> qm*<sup>d</sup>* <sup>2</sup> )

cq <sup>2</sup> m*<sup>d</sup> Ar*

> m*d* <sup>2</sup> )}

\* \$ =+ +<sup>+</sup> % ! , & (16)

cos(q*t*)

sin

*It I I t e dc RF* ( ) = + sin (

( ) <sup>0</sup> sin

*c dc It I A t*

m*d* 2 ) } 2*A*0*l <sup>d</sup>* sin(

<sup>2</sup> *A*<sup>0</sup>

*RF*

*A Am IA t*

\$ \* \$ + % <sup>+</sup> % \* \$ & ! , & + % ! , & \* \$ + +<sup>+</sup> % ! , &

 (12)

2 2

*d d*

*dc*

0

) (15)

 

2

(13)

(14)

(17)

frequency components of current and voltage by,

0

 

Simultaneously,

given as,

Where,

The optimized structural parameters of Si/SiC DD hetero-structure IMPATTs for operation at W-band are given in Table 1 for the bias current density of 8x108 A/m2 ^z%#1.!/zFcwdz !¥ \*+0!/z0\$!z2+(0#!z\* z1..!\*0z32!"+.)z"+.z%z 
z !2%!z+,!.0%\*#z1\* !.z(.#!w/%#¥ nal condition. The plots depict the 1800 phase-shift between voltage and terminal current, essential criteria for IMPATT oscillation. This proves the validity of the simulation software. Large-signal simulation provides the snap-shots of electric-field profiles at different phase angles as shown in figures 4(a) to 4(e). The electric field increases from t=0 and attains its peak value in the positive half-cycle at t =T/4 (Emax = 5x108 V/m) as shown in figure 4(b). It then decreases and attains the same magnitude of negative peak in the negative half-cycle at t = 3T/4., as shown in figure 4(d). The program is also run for the second and consecutive cycles and it is observed that the above nature of variation of electric field is repeated in each and every cycle.

Figure 3. a-c) : Voltage and current waveforms of Si/SiC IMPATTs under large-signal analysis

The ettect of voltage modulation on the large-signal negative resistance, reactance, KE power, efficiency, negative conductance and Q-factor of the device has been studied and the results are presented in this paper. Large-signal admittance plots (conductance versus susceptance) for different modulation factors are shown in figure 5. It is observed that the magnitude of peak negative conductance decreases from 37.5x10° S/m² at 94 GHz to 5.0 x10° S/m² when voltage modulation increases from 10% to 50%, i.e., corresponding RF voltage increases from 20.0V to 104.0 V. In the limiting case of RF-voltage being very low, the largesignal peak negative conductance value should approach the small-signal value. When RF voltage modulation is very low, i.e., 2% and the RF voltage amplitude is 4.0V, the simulated large-signal negative conductance is 43.5x106 S/m². The authors have also carried out smallsignal simulation of the Si/SiCdevice based on Gummel-Blue approach and obtained the admittance plot with the same design structural parameters to verify whether the peak negative conductance under small-signal condition approaches that under large-signal condition with negligibly small voltage modulation of 2%. It is observed from Figure 5 that the large-signal admittance plot for lowest voltage modulation almost coincides with the simulated small-signal admittance plot which verifies the validity of the proposed large-signal modeling of the device.


Table 1. Optimised design parameters of Si/SiC DD hetero-structure IMPATTs for large-signal analysis.

Fig. 6 shows the variation of RF output power with RF voltage. It is interesting to observe that under large-signal condition RF power initially increases with the increasing voltage modulation, reaches a peak value at 50% voltage modulation and then decreases with further increase of voltage modulation. Figure 6 shows the variation of efficiency with RF voltage. It is observed that the efficiency increases with increase in RF voltage, attains a peak value corresponding to 50% voltage modulation and then starts decreasing. It is observed that, with the increasing amplitude of RF voltage from 21.0V to 104.0 V, the magnitude of negative resistance of the device decreases from 10.0 Ω to 6.0 Ω. The analysis shows the variation of negative reactance of the device for different voltage modulation. It is observed that the magnitude of negative reactance increases from 13.0 ohm to 14.5 ohm when RF voltage increases from 10% to 50%. The variation of negative reactance with RF voltage is sharper than that of the negative resistance with RF voltage. At 94 GHz window, the increase in Qfactor from 1.0 to 6.0 with change in RF voltage from 21.0V to 104V, as expected. Large-signal Q-factor for a particular RF voltage indicates the overall RF performance of the device.


Table 2. Values of series resistance (R., wal) of SiCDD hetero-structure IMPATT [bias current density = 8.0 x10° Am² and frequency =94GHz].

Figure 6. ,DGLKG>HGO=J?=F=J9LAF?=>>A;A=F;Q9F<."HGO=JOAL@9;NGDL9?=9EHDALM<=G>@=L=JGKLJM;LMJ= /A%)s

High-Power Hexagonal SiC Device: A Large-Signal High-Frequency Analysis

http://dx.doi.org/10.5772/52982

347

The author has developed a generalized technique for large- signal simulation of DDR SiC IMPATT diode. This simulator is applicable for other WBG semiconductor based IMPATTs \* z(/+z "+.z %""!.!\*0z/0.101.!/z\* z +,%\*#z,.+"%(!/z+"z 0\$!z !2%!^z\$!z2(% %05z+"z 0\$!z,.+¥ posed technique is verified from the simulated small-signal admittance plot. The results show for DC breakdown voltage of 207.0 V the large-signal (for ~ 50% voltage modulation) power output and efficiency are 25.0 W and 15.0%, respectively. To the best of author's knowledge, this is the first report on non-linear analysis of 4H-SiC IMPATTs at W-band.

+1)%0z
1'\$!.&!!z3%/\$!/z0+z'\*+3(! #!z!"!\*!z!/!.\$z\* z!2!(+,)!\*0z.#\*%6¥ tion (DRDO), Ministry of Defence, Govt. of India, and University Grants Commission cd\_z+20^z+"z \* %\_z"+.z,.+2% %\*#z\$!.z"%\*\*%(z//%/0\*!z0+z..5z+10z0\$%/z/01 5^z\$!z1¥ 0\$+.z%/z0\$\*'"1(z0+z%.!0+.z
\_z.^z^z00\_z"+.z\$%/z'!!\*z%\*0!.!/0z%\*z0\$%/z3+.'^z\$!z1¥ thor also gratefully acknowledges Prof. S. K. Roy, founder Director - CMSDS and Professor,

dia, Prof. J. P. Banerjee, former Director, CMSDS and Prof. D.N.Bose, Emeritus Professor,

!\*#(z\*%2!./%05z+"z!\$\*+(+#5\_z \*¥

PATTs for fundamental operating frequency 94 GHz (current density 8x108 Am-2)

 \_z\*%2!./%05z+"z(100\_z.+"^z^z
61) !.\_z!/0z-

4. Conclusion

Acknowledgements

Figure 4. a-b): Plots of electric field profiles (snap-shots) at various points in time (phase angle 00 and 900>GJL@=<As ode operating at a fundamental frequency 94 GHz, current density 8x108 Am-2 and efficiency = 15%. (c-d): Plots of electric field profiles (snap-shots) at various points in time (phase angle 1800 and 2700) for the diode operating at a fundamental frequency 94 GHz, current density 8x108 Am-2 and efficiency = 15%. Plots of electric field profile (snapshot) at various points in time (phase angle 3600) for the diode operating at a fundamental frequency 94 GHz, current density 8x108 Am-2 and efficiency = 15%.

Figure 5. Diode admittance plots as a function of fundamental frequency and ac-voltage amplitude.

Figure 6. ,DGLKG>HGO=J?=F=J9LAF?=>>A;A=F;Q9F<."HGO=JOAL@9;NGDL9?=9EHDALM<=G>@=L=JGKLJM;LMJ= /A%)s PATTs for fundamental operating frequency 94 GHz (current density 8x108 Am-2)

#### 4. Conclusion

Figure 4. a-b): Plots of electric field profiles (snap-shots) at various points in time (phase angle 00 and 900>GJL@=<As ode operating at a fundamental frequency 94 GHz, current density 8x108 Am-2 and efficiency = 15%. (c-d): Plots of electric field profiles (snap-shots) at various points in time (phase angle 1800 and 2700) for the diode operating at a fundamental frequency 94 GHz, current density 8x108 Am-2 and efficiency = 15%. Plots of electric field profile (snapshot) at various points in time (phase angle 3600) for the diode operating at a fundamental frequency 94 GHz, current

Figure 5. Diode admittance plots as a function of fundamental frequency and ac-voltage amplitude.

density 8x108 Am-2 and efficiency = 15%.

346 Physics and Technology of Silicon Carbide Devices

The author has developed a generalized technique for large- signal simulation of DDR SiC IMPATT diode. This simulator is applicable for other WBG semiconductor based IMPATTs \* z(/+z "+.z %""!.!\*0z/0.101.!/z\* z +,%\*#z,.+"%(!/z+"z 0\$!z !2%!^z\$!z2(% %05z+"z 0\$!z,.+¥ posed technique is verified from the simulated small-signal admittance plot. The results show for DC breakdown voltage of 207.0 V the large-signal (for ~ 50% voltage modulation) power output and efficiency are 25.0 W and 15.0%, respectively. To the best of author's knowledge, this is the first report on non-linear analysis of 4H-SiC IMPATTs at W-band.

#### Acknowledgements

+1)%0z
1'\$!.&!!z3%/\$!/z0+z'\*+3(! #!z!"!\*!z!/!.\$z\* z!2!(+,)!\*0z.#\*%6¥ tion (DRDO), Ministry of Defence, Govt. of India, and University Grants Commission cd\_z+20^z+"z \* %\_z"+.z,.+2% %\*#z\$!.z"%\*\*%(z//%/0\*!z0+z..5z+10z0\$%/z/01 5^z\$!z1¥ 0\$+.z%/z0\$\*'"1(z0+z%.!0+.z
\_z.^z^z00\_z"+.z\$%/z'!!\*z%\*0!.!/0z%\*z0\$%/z3+.'^z\$!z1¥ thor also gratefully acknowledges Prof. S. K. Roy, founder Director - CMSDS and Professor, \_z\*%2!./%05z+"z(100\_z.+"^z^z
61) !.\_z!/0z-!\*#(z\*%2!./%05z+"z!\$\*+(+#5\_z \*¥ dia, Prof. J. P. Banerjee, former Director, CMSDS and Prof. D.N.Bose, Emeritus Professor, Calcutta University, for their valuable suggestions and important comments during the development of the simulator.
