# Prospects of 4H-SiC Double Drift Region IMPATT Device as a

Authors: Moumita Mukherjee; Nilratan Mazumder; Sitesh Kumar Roy
Journal: Active and Passive Electronic Components
 (2008)

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## Abstract

The dynamic performance of wide-bandgap 4H-SiC based double drift region (p++pnn++) IMPATT diode is simulated for the first time at terahertz frequency (0.7 Terahertz) region. The simulation experiment establishes the potential of SiC based IMPATT diode as a high power (2.5×1011 Wm−2) terahertz source. The parasitic series resistance in the device is found to reduce the RF power output by 10.7%. The effects of external radiation on the simulated diode are also studied.  It is found that (i) the negative conductance and (ii) the negative resistance of the diode decrease, while, the frequency of operation and the quality factor shift upward under photoillumination. Holes in 4H-SiC based IMPATT are found to dominate the modulation activities. The inequality in the magnitude of electron and hole ionization rates in the semiconductors may be correlated with these findings.


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## Body

## 1. Introduction

Terahertz (THz) science and
technology is rapidly developing all over the world.  There is strong interest
in the exploitation of the THz frequency range in virtually all fields of basic
natural science  (physics, chemistry, and biology) as well as medicine [1].
Terahertz applications and technologies for operation in the range between  300 GHz to 10 THz (1 millimeter to 30 micrometers) are attracting increased interest
from military and security fields. Scientists all over the world are searching
for high-power solid-state sources that can be employed as efficient
THz source. Impact avalanche transit time
(IMPATT) diodes are the most powerful solid-state sources at mm and sub-mm-wave
frequencies and are widely used in various civilian and space communication
systems as well as in high-power radars, missile seekers, and so forth. The
conventional IMPATT diodes fabricated on GaAs (gallium arsenide) and Si (silicon)
are found to be reliable, but these are limited by power and operating frequencies
due to the fundamental limitations of the material parameters. To meet the
gradual demand of high-power THz solid-state sources, extensive research is
being carried out for development of high-power (Watt level) IMPATT devices
that can be operated at high-frequency region. One approach is to employ power
combining technique to increase the output power of the IMPATT devices, but it
is practically difficult to combine large number of devices. The other option
is to develop IMPATT devices from wide bandgap (WBG) semiconductors having high-critical
electric field (EC) and high-thermal conductivity (K) [2]. High
value of EC as well as high-saturation drift velocity of charge
carriers (νsn,sp), are essential criterion for selecting suitable
base semiconductor material for IMPATT fabrication, since the RF power density (PRF) of an
IMPATT device is proportional to Ec2⋅νs2.
Moreover, to achieve good thermal stability in THz devices, the base material should
have high value of thermal conductivity (K) also. Considering all these facts, WBG
semiconductor SiC (silicon carbide) is an automatic choice for designing of
high-power IMPATT, because this material offers
at least (i) 10×Ec, (ii) 1.5×νs, and (iii) 3×K, in
comparison to those of conventional Si, GaAs, and InP (indium phosphide). That
means, SiC IMPATTs are likely to produce 400×PRF than its
counterparts. The expected excellent performances of WBG SiC-based
devices can be assessed by figures of merit (FOM). Keyes’ FOM considers the
speed of transistors and their thermal limitation, and Johnson’s FOM considers
the high-frequency and high-power capability of devices. Taking Keyes’ and
Johnson’s FOM for Si as unity, the Keyes’ and Johnson’s FOM for GaAs are 0.45
and 7.1, respectively, while those of 4H-SiC are 5.1 and 278 [2]. Following the
FOMs for high-frequency and high-temperature, operation SiC is found to be
superior to both Si and GaAs. The availability of 4H-SiC polytypes in bulk
wafer form [3, 4] has helped SiC to emerge as relatively mature wide bandgap
semiconductor technologies. So, in the
light of the maturity of the fabrication technology and the unique material
parameters, WBG semiconductors, especially, SiC appear to be the best choice,
overall, for the next decade of device development particularly at THz region. At low-frequency region, the superiority of 4H-SiC-based
IMPATT over the traditional IMPATTs is already reported [5]. But the prospects
of SiC as high-power THz source are still not explored. The authors in this
paper have reported for the first time the potential of 4H-SiC as a suitable
base material for THz IMPATT device. Presently, two SiC polytypes are
popular in SiC research: 6H-SiC and 4H-SiC. Although both the polytypes have
similar properties, 4H-SiC is preferred
over 6H-SiC because the carrier mobilities in 4H-SiC are isotropic, that is, identical along the
two planes (parallel and perpendicular to c-axis) of the hexagonal semiconductor,
whereas in 6H-SiC, carriers exhibit anisotropic mobility. Moreover, it is
already reported that the high frequency performance of 4H-SiC IMPATT is far
better than its 6H-SiC counterpart in terms of  VB as well as PRF [6]. Thus, the possibility of generating high power from an IMPATT has
been investigated by studying the DC and small-signal properties of WBG 4H-SiC-based
flat profile DDR (double drift region, p++pnn++) IMPATT diode simulated
for operation at THz regime.Parasitic
positive series resistance (RS) is a crucial parameter that limits
power dissipation and causes burn out problem in
high frequency IMPATTs.
Apart from the contribution from substrate, the p-n junction diode parameters, especially,
the width of the depletion layer, doping density, and so forth, also contribute
to RS. Moreover, the contact resistance of the device contributes
significantly to the total parasitic series resistance. The authors have
determined the value of RS of the simulated IMPATT device
considering contribution from the substrates, undepleted epitaxial layer and
ohmic contacts. The authors have evaluated the values of RS for the
designed diode through a generalized simulation technique, and its effect on
exploitable power level of the device has also been simulated.Optical control of the dynamic properties of THz IMPATT
device can have tremendous application in advanced radars and space communication
systems. Basic process involved is that, when a
photon (due to optical /other radiation) of energy hν greater than the
band gap of the semiconductor is absorbed at the edges of the reversed biased
p-n junction of an IMPATT diode,
creation of additional electron-hole pairs takes place within the active
region of the diode. These photogenerated carriers give rise to photocurrent
and thereby enhance the existing thermal leakage current in the IMPATT diode.
The enhanced leakage current alters the avalanche phase delay in the diode,
which subsequently modifies the phase and magnitude of terminal current in the
device oscillator circuit. The previous experimental [7], as well as theoretical [5, 6] studies on
optically illuminated IMPATT diodes indicated that the photogenerated carriers
reduce the efficiency and power output of the devices, but increase the tuning
range of the devices in the
mm-wave frequency band. Moreover, a
recent report on the effect of ionizing radiation on Si IMPATT diode
characteristics establishes that control of IMPATT performance by any external
radiation is an emerging technique that is currently being explored for
important application possibilities [8]. These interesting results for
photoilluminated IMPATTs have prompted the authors to investigate theoretically
the role of external radiation in modulating the dynamic properties of the
4H-SiC DDR THz IMPATT. A modified simulation scheme has been used for this
purpose.


## 2. Theory of Simulation Technique

The
simulation method consists of three parts: (i) dc analysis, (ii) small-signal
analysis, and (iii) simulation technique for studying illumination effect. The
IMPATT diode is basically a p-n junction diode that operates when it is
reverse-biased to avalanche breakdown condition. A one-dimensional model of the
p-n junction has been considered in the present analysis. The following assumptions have been
made in the simulation of dc and small-signal behavior of 4H-SiC DDR IMPATT
diodes: (i) the electron and hole velocities have been taken to be saturated
and independent of the electric field throughout the space charge layer, (ii)
the effect of carrier space-charge has been considered, and (iii) the effect of
carrier diffusion has been neglected.4H-SiC DDR diode is first designed and optimized through a generalized double iterative
simulation technique used for analysis of IMPATT action [9]. The method
involves iteration over the magnitude of field maximum (Em) and its
location in the depletion layer. The electric field and carrier current
profiles are obtained through simultaneous solution of Poisson and current
continuity equations. The experimental values of material parameters, namely,
realistic field dependence of ionization rates, saturated drift velocities, and
mobility of charge carriers in 4H-SiC [10] are incorporated in the present
analysis. The junction temperature is assumed to be 300 K. The device
dimensions, doping, and current densities of the diode (shown in Table 1) are
optimized for operation at around 700 GHz after several computer runs.Table 1
Design parameters of 4H-SiC impatt at thz frequency.
DDR
diode   typeDoping conc.   (n region)
(1024 m−3)Doping conc.   (p region)
(1023 m−3)Width of
then       region   (nm)Width of thep region   (nm)Current density  (1010 A m−2)4H-SiC3.03.080.080.01.37The small-signal analysis of the IMPATT diode is carried out through a
double iterative simulation technique [9], used to solve two second-order
differential equations involving diode resistance (ZR) and reactance
(ZX). The small-signal admittance characteristics (negative
conductance (−G) versus susceptance (B) plots), device negative resistance, and
device quality factor (Q=B/G) of the optimized SiC DDR diode is determined by
this technique after satisfying the appropriate boundary conditions [11]. The total integrated negative resistance (ZR)
and reactance (ZX) of the diodes at a particular frequency ω can be
determined from the numerical integration of the resistivity (R) and the
reactivity (X) profiles over the depletion layer (depletion layer width is w),
as follows:
(1)ZR=∫0wRdx,ZX=∫0wXdx.Diode impedance is expressed as Z(x,ω)=R(x,ω)+X(x,ω).Moreover, the total diode impedanceZtotal(ω) is
obtained by, (2)Ztotal(ω)=∫0wZ(x,ω)dx=ZR+jZX.The diode total negative
conductance (G) and susceptance (B) have been calculated from the following
expressions: (3)G=−ZR(ZR)2+(ZX)2,B=ZX(ZR)2+(ZX)2.G and B are function of
RF voltage (VRF) and frequency such that the steady-state condition
for oscillation is given by [12], (4)g(ω)=−G(ω)−{B(ω)}2RS(ω),where g is load conductance. G, B, and g are normalized to the area of
the diode. The relation provides minimum uncertainty in g at low power
oscillation threshold. The authors have evaluated RS from the
admittance characteristics using the realistic analysis of Gummel and Blue [13],
and Alderstein et al. [12] without any drastic assumption. Under the small-signal condition, VRF (amplitude of the RF swing) has been taken
as VB/2, assuming 50% modulation of the breakdown voltage VB.
For such a small value of VRF, RS has been calculated by
considering the value of g nearly equal to the diode conductance (G) at
resonance. The maximum RF power density
(PRF) from the device is obtained from the expression(5)PRF=VRF2GP2.The diode negative conductance at the
optimum frequency (−Gp) is normalized to the area of the diode. The
space step for the present simulation technique is set as ∼10−10 m.
The validity of this simulation method was reported earlier for subterahertz
and THz IMPATT diodes [11, 14].The leakage current (Js),
entering the depletion region of the reversed biased p-n junction of an IMPATT diode, is normally due to
thermally generated electrons and holes [Js⁢=Jns⁢(th)+Jps⁢(th)] and it is so small that electron and hole current
multiplication factor, (6)Mn,p=J0[Jns⁢(th)⁢orJps⁢(th)],[J0⁢=biascurrentdensity] can be considered to be infinitely
large. Thus, the enhancement of the leakage current under optical illumination
of the devices is manifested as the lowering of Mn,p. In a DDR
IMPATT structure,  the composition of photocurrent may be altered by shining a
laser beam selectively on the p++ or n++ side of the
device through fabricated optical windows of appropriate diameter, keeping the
diode mounted in a microwave cavity. Thus, the electron saturation current and
also the hole saturation current might be enhanced separately, which would
produce changes in the small-signal behavior of SiC-based device. The top mounted (TM) and flip chip
(FC) structures, shown in Figure 1  illustrate the optical
illumination schemes for generation of electron and hole dominated photocurrents, respectively. In order to assess
the role of leakage current in controlling the dynamic properties of 4H-SiC
IMPATT oscillators, simulation studies are carried out by the authors on the
effect of Mn (keeping Mp very high ∼106) and
Mp (keeping Mn very high  ∼106) on (i) the
small signal negative conductance, (ii) the RF power, and (iii) device negative
resistance (ZRP) of flat profile 4H-SiC DDR IMPATT. The details of
mathematical calculations based on modified boundary conditions due to
enhancement of leakage current are
described elsewhere [11].Figure 1
Schematic diagram of (a) Top Mounted and (b) Flip chip DDR IMPATT diode under optical-illumination.


## 3. Results and Discussions

The optimized design parameters of the unilluminated SiC DDR IMPATT
diode for whichMn and Mp are both large (= 106)
are mentioned in the last section. The DC and high-frequency properties of the
simulated diode are reported in Table 2 and will be discussed first. Table 2
shows that the THz IMPATT diode based on SiC breaks down at 55.3 V. The
simulated diode is capable of generating a maximum  PRF of 2.8×1011Wm−2 with efficiency 10.5 %.Table 2
Dc and small-signal properties of 4H-SiC IMPATT diode.
Diode parameters4H-SiC DDR IMPATTEm (108 V m−1)5.25VB (V)55.3η (%)10.5fP (THz)0.7−Gp (108 S m−2)7.40−QP1.6PRF (Rs=0.0 Ω)  (1011 Wm−2)2.8PRF (Rs,total=0.7 Ω) (1011 Wm−2)2.5Table3 shows the value of RS at 0.7 THz for the simulated
diode. The small-signal values of negative conductance (G), susceptance (B),
and expected values of load conductance (g, at low power oscillation threshold)
are also reported in Table 3. The value of RS for 4H-SiC IMPATT is found
to be 0.49×10−10 Ω m2. Ohmic contact resistance may put
a severe restriction on the high frequency (THz level) performance of the wide
bandgap IMPATT devices and thus the presence of contact resistance should be
included in the realistic consideration of parasitic positive series
resistance.  A
very recent study showed that ohmic contact to n-SiC are formed by using pure
Ni-based layer with a thin underlying Si layer. By this technique, a stable and
low n-SiC contact resistivity of ∼10−7 Ω cm2 can be
realized in practice [15]. Very low specific contact resistance for p-SiC has
not been achieved in reality. Using alloy composition such as Ni/Al to p-SiC, a
contact resistivity ∼10−6 Ω cm2 can be realized in
practice [16]. It is noteworthy to mention that, in order to get appreciable
power (Watt level) from a THz source, low specific contact resistance (∼10−7 Ω cm2) should be achieved, since at THz region intrinsic diode
negative resistance is usually very small. It may be predicted that, further
increasing the doping concentration of p-SiC semiconductor material, a desired
contact resistivity ∼10−7Ω cm2 may be achieved in
reality. Hence, more realistic values of effective parasitic series resistance
(RS,total, including the contribution of contact resistance) become
approximately 0.7×10−10 Ω m2 for 4H-SiC IMPATT.
Measurement of such a low contact resistance may be possible with transmission line
measurement (TLM) technology.  The effect of RS,total on PRF of the diode is shown in Figure 2.  It is reflected in Figure 2, that even in
the presence of aforesaid RS,total an appreciable RF power density of
2.5×1011 Wm−2 may be obtained from the
simulated THz device.Table 3
Series resistance of 4H-SiC IMPATT at 0.7 THz.
Negative conductance
(−G) (108 Sm−2)Susceptace (B)  (108 Sm−2)Load conductance
(108 Sm−2)Series
resistance (RS)
(10−10 Ωm2)Negative
resistance (−ZR)
(10−10 Ωm2)7.412.06.70.493.8Figure 2
Effect of series resistance onRF power density of 4H-Sic Terahertz IMPATT diode.Figure3 shows the small-signal impedance plot
for the THz diode. The graphs show that the device possesses negative resistance for all
frequencies above the avalanche frequency (fa), where its reactance
is capacitive. This is due to the fact that, in the oscillating frequency
range, the magnitude of ZR is found to be small compared to ZX.
This is also evident from Figure 3, that the values of |−ZR| and |−ZX|
decrease as the operating frequency increases.Figure 3
Impedance plots of 4H-SiC IMPATT diode at Terahertz region.The effects of electron and hole dominated
photocurrents on the THz performance of the WBG IMPATT is presented in Table4.
The table shows that the
values of  |−GP|  of the diode
decrease with the lowering of Mn and Mp. At the same
time, the frequency range over which the device exhibits negative conductance,
shifts towards higher frequencies with the lowering of Mn as well as
Mp. The output data for illuminated TM and FC flat DDR IMPATT diodes
(Table 4) indicate that the value of negative conductance at peak frequency  |−GP|  decreases by 6.7%
when Mn reduces from 106 to 25 for SiC-based THz device, while for the
similar lowering of Mp,|−GP|,    decreases by 23.0%. The identical trend is reflected in Figures 4(a)
and 4(b), where the admittance plots of SiC-based photoilluminated THz device are
plotted. The figures show that the effect of hole dominated photocurrent in
modulating the admittance characteristics is much prominent than the electron
dominated photocurrent. The optimum frequency of oscillation (fP)
for the illuminated SiC diode increases by 11.4% as Mn reduces from 106 to 25. However, for the similar variation of Mp, the
upward shift of fP is much higher (29.0%).Table 4
Variation of small-signal
properties of 4H-SiC DDR IMPATT under
optical-illumination.
MnMpfP     (THz)−Gp
(108 Sm−2)−ZRp (10−10 Ωm2)PRF (1011 Wm−2)−QP1061060.707.43.82.821.6100,,0.717.22.62.752.0850,,0.757.12.12.712.3925,,0.786.91.72.632.751061000.787.02.52.672.14,,500.826.41.62.452.97,,250.905.70.952.184.2(a) Effect of electron dominated photo-current on 4H-SiC DDR IMPATT diode at Terahertz region. (b) Effect of hole dominated photo-current on 4H-SiC DDR IMPATT diode at Terahertz region.
(a)(b)Figures5(a) and 5(b) show the profiles of negative resistivity at the
peak frequencies corresponding to different values of Mn (Mp=106) and Mp (Mn=106) for SiC-based
diode, respectively. Negative resistivity profiles give a physical insight into
the region of the depletion layer that contributes to RF power. In each case,
the profiles are characterized by two negative resistivity peaks in the middle of
the two drift layers of the diode interspaced by a dip in the avalanche region.
It is observed from the figures that due to the enhancement of electron and
hole photocurrents, the negative resistivity peaks in the electron, and hole
drift layers are depressed gradually. It is also found that the decrease in the
magnitude of the negative resistivity peaks are more pronounced
for variation of Mp corresponding to hole dominated photocurrent
than for the same variation of Mn corresponding to electron
dominated photocurrent.(a) Effect of electron dominated photo-current on negative resistivity profile of 4H-SiC DDR IMPATT diode. (b) Effect of hole dominated photo-current on negative resistivity profile of 4H-SiC DDR IMPATT diode.
(a)(b)Simulation study also depicts
that in case of 4H-SiC DDR IMPATT, asMn is decreased from 106 to 25, there occurs a 54.0% decrease in
the diode negative resistance (−ZRp). On the other
hand, as Mp changes from 106 to 25, −ZRp reduces by 74.3% (Table 4).The variations of power output with optimum frequency for different
values ofMn and Mp are also shown in Table 4. Again, it
is found from the study that the magnitude of device quality factor at optimum
frequency of oscillation  |−QP|   increases
appreciably for a decrease of Mp compared to the same change of Mn values (Table 4).The enhancement of leakage currents by
electron and hole dominated photocurrents thus leads to a decrease of−ZRP,
−GP and PRF along with a simultaneous upward shift of fP.
While the photo-generated leakage current dominated by holes modulates the DC
and high-frequency properties of the device appreciably, that dominated by
electrons has relatively less effect in modulating the same. For the mm-wave Si
DDR, it was reported that the electron saturation current was more dominant in
changing the PRF and the  fP [7]. In Si, the electron
ionization rate is greater than the hole ionization rate. This means that by
controlling the DDR IMPATT action through more ionizing carriers in Si, a
higher frequency shift may be achieved. By the same logic, it can also be
concluded that in 4H-SiC, holes are more ionizing carriers than electrons,
since 4H-SiC DDR IMPATT under optical illumination at THz region is more sensitive
to hole dominated photocurrent. This relative predominance of hole leakage
current in optical control of 4H-SiC DDR IMPATT performance can be attributed
to the inequality of the ionization coefficient values in 4H-SiC [10].The thermal conductivity of 4H-SiC (∼500 W m−1 K−1) is very high. This helps the SiC IMPATT to
dissipate the generated heat quickly from the junction. Moreover, if a diamond
heat sink is employed for the practical realization of 4H-SiC THz IMPATT
device, the effective thermal conductivity will increase to such a high value
that the junction temperature will not increase significantly over the ambient
(300 K), though the device yields a PRF of 2.5×1011 Wm−2.Due to lack of any experimental data on SiC THz IMPATT diode, the
simulation results could not be compared. However, the nature of variation of
THz properties of the designed diode under photoillumination has a trend
agreement with the experimental results of Si-based IMPATT diode at lower
frequency region. It may be mentioned here that a large-signal computer
simulation may provide improved quantitative information regarding the influence
of optical illumination on the frequency tuning as well asRF power output, but
the nature of response to optical illumination, as predicted by the
small-signal analysis, will remain unchanged.


## 4. Conclusion

The current simulation study establishes that 4H-SiC-based DDR IMPATT diode can generate high power even at a frequency as high as 0.7 THz. In the earlier reported paper [14], the frequency of operation was limited to 0.5 THz only. Moreover, in the present paper, the authors have realistically
simulated the value of total parasitic series resistance for THz SiC IMPATT,
which includes the contribution both from the diode as well as from ohmic
contact resistance, while, in the previous article [14], the series resistance due
to contact metals was not considered. Based on the information of total series
resistance, provided in this paper, one can get more accurate idea of exploitable
power level from the SiC DDR diode at THz region. Further, the effect of
external radiation on this device at 0.7 THz seems to be significantly prominent.
It is thus expected that the photo-irradiated 4H-SiC DDR IMPATT at still higher
frequencies will have better frequency tuning capability. A discussion on feasibility
of experimental validation was not incorporated in the previous article [14]. In
the present paper, the authors will discuss below the possibility of
experimental verification of optical illumination on the 4H-SiC DDR diode. The
realization of 4H-SiC THz IMPATT diode may be done through the following
process steps.Device fabrication following usual
process steps like photolithography, deposition of metal contacts. and mesa
formation by reactive ion etching.Characterization of THz properties
may be possible with a dielectric coplanar wave guide, the device being an
integral part of the waveguide.For terahertz (0.1–1 THz) power
transmission, a metallic slit waveguide, fabricated by sawing a 270 μm wide
slit through a 140 mm wide and 300 μm thick silicon slabs may be used (Figure6)
[18]. For higher frequency (3 THz) power transfer, a ribbon-like structure
fabricated from ceramic alumina may be utilized [17]. The schematic diagrams of
the structures are shown in Figures 7(a) and 7(b).Measurements of THz power and
frequency may be done with a THz vector
network analyzer (VNA) or, by employing photoconductive method (as shown
in right-hand diagram of Figure6).Figure 6
Waveguide goemetry:d=270 μm, w=300.0 μm, and l=140.0 mm.(a) Rectangular metal waveguide to high dielectric constant ribbon waveguide transition [17]. (b) Longitudinal cross-sectional geometry of a polymer-coated high dielectric constant ribbon. The thickness and the width of the high dielectric constant ribbon are 0.0635λ0 and 0.635λ0, respectively. The thickness of the polymer coating is approx. 0.25λ0 and the width is approx.  0.635λ0. The dielectric constant of the ribbon is 10 while that of the polymer is 2.04 [17].
(a)(b)An arrangement similar to that shown in Figures8 and 9, appropriately
modified to include the photoconductive detection of THz power and frequency,
can be used for optical illumination experiment on 4H-SiC IMPATT. The intensity
of radiation may be experimentally increased by a convex lens as indicated in Figure 8.Figure 8
Experimental setup for optical illumination experiment on 4H-SiC IMPATT diode at THz region.Figure 9
Optical experimental setup for THz IMPATT diode.It is concluded that these findings may be utilized for realizing
optically integrated THz modules for effective applications in THz
communication and in interstellar explorers.



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