 Open Access
 Total Downloads : 219
 Authors : Gananath Dash, Pranati Panda
 Paper ID : IJERTV4IS080279
 Volume & Issue : Volume 04, Issue 08 (August 2015)
 DOI : http://dx.doi.org/10.17577/IJERTV4IS080279
 Published (First Online): 14082015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Mixed Tunnelling Avalanche Transit Time Mode Analysis of Flat Doping Profile Silicon Carbide Double Drift Region Diodes for Operation in W, D, Y and Thz Bands
Pranati Panda and Gananath Dash*
Electron Devices Group at the School of Physics, Sambalpur University, Jyoti Vihar, Burla, Sambalpur 768019, Odisha, India
AbstractComputer simulation experiment is carried out to explore the prospects of SiC for application as Mixed Tunnelling Avalanche Transit Time diode in a wide ranging frequency from

THz to 1.0 THz. We have obtained a commendable power output of 2.85 W at 0.81 THz with an efficiency of 16%. The not so high noise measure of 25.6 dB at the same frequency is a clear manifestation of the 24.87% tunnelling current which ascertains the advantage of SiC in mixed mode operation.
Keywords4HSiC, IMPATT, MITATT, Tunnelling

INTRODUCTION
Silicon Carbide (SiC) has some exotic properties which make it the most suitable for modern power electronics. It is recognized as an excellent wide band gap (WBG) semiconductor for high temperature and high speed devices [1 5]. There are many different polytypes of SiC such as 3C, 2H, 4H, 6H, 9H etc. Out of them only 4HSiC and 6HSiC are commercially available. 4HSiC is the most widely explored material [68] for high power devices because its carrier mobility is better than that of 6HSiC. Many reports establish the superiority of 4HSiC over 6HSiC [911]. Yuan et al. [12, 13] and Zhao et al. [14] have reported some experimental as
diode, is noteworthy. In addition the fact that the noise measure at the same frequency is not so high (25.6 dB) may be reckoned as an additional advantage of SiC particularly for MITATT mode operation.

THEORY

General
A generalised method of analysis for DC and smallsignal characterisation of a MITATT diode has been presented by Dash and Pati [16]. Similarly Dash et al. have presented a MITATT mode noise simulation scheme [17] which can be used for any diode structure made from any semiconductor. We have extended them to incorporate parabolic barriers and briefly describe them in the following subsections. The reader can however, refer to the original publications for more detail.

DC Analysis
A schematic of the n+npp+ diode structure under consideration, along with the band picture, is shown in Fig. 1. We considered a purely field dependent tunnelling generation rate of the form
BT
well as theoretical results for the first time with a 4HSiC
gTn(x) = ATE2(x) exp
( ) , (1)
IMPATT oscillator operating at X and Ka band of frequencies. They have considered the DC and high power generation aspects of the IMPATT diode. They have reported that the diode exhibits high efficiency and high power as expected
compared to Si and GaAs IMPATT (Impact Avalanche Transit Time) diodes. Pattanaik et al. [15] have reported the
E x
where the coefficients AT and BT, for a parabolic barrier, can be expressed as
q2 2m 1
performance of 6HSiC based DDR (Double Drift Region) IMPATT diodes with reference to DC and microwave properties as well as noise characteristics. They have compared
and
AT = 4rr32 ( Eg
)2 ,
(2)
the results with those of Si and GaAs based IMPATT diodes under similar operating conditions at the D band. All these reports however do not consider the effect of tunnelling current
BT =
rr 2q
3
m E
( g )1/2. (3)
2
on the diode properties. When the diode operation is envisaged
at THz frequencies the diode active region becomes so thin that it is almost impossible to avoid tunnelling of carriers. The diode operation in such situation is referred to as MITATT (Mixed Tunnelling Avalanche Transit Time) mode. Therefore, the authors in this paper have analyzed in detail the DC, small signal and noise characteristics of 4HSiC MITATT diodes for operation in W, D, Y and THz band of frequencies. A power output of 2.85 W at 0.81 THz with an efficiency of 16%, obtained from our simulation results for the SiC MITATT
The tunnelling generation rate for holes is obtained by considering the energy band diagram of a reverse biased pn junction as shown in Fig. 1. The tunnel generation of an electron at xr is simultaneously associated with the generation of a hole at x, where (x xr) is the spatial separation between the edges of the conduction band and the valence band at the same energy level and is a function of x. Therefore, the tunnel generation rate for holes can be linked to that for electrons as gTp(x) = gTn(xr) .
The position x can be derived from the position x in the following way. The electrical potential in the depletion layer of a diode can be determined as a function of x by integrating Poissons equation twice (neglecting the presence of mobile
space charge) from which the energy of the electron as a
function of x can be determined. Taking U as a measure of energy from the lowest level of the conduction band on the n side of the diode and making use of the idea that the vertical difference between x and x is the band gap Eg, x can be easily obtained in terms of x by referring to Fig. 1 as [16]
Eg 1/2
x = x l1 U J
for 0 x
xj (4)
and
1
x = W (W x) l1 Eg J2
UB U
for xj x W
(5)
where xj is the junction point and is measured from the surface. The electrons in the valence band between x = 0 and x = x1 (Fig. 1) would have no available states in the conduction band for tunnelling. Consequently the hole generation rate due to tunnelling within this region is zero. Similarly, nonavailability of electrons to tunnel to the energy states in the conduction
Fig. 1 Schematic and Energy band diagram of a MITATT diode
band between x = x2 and x = W (Fig. 1) results in no
tunnelling of electrons in this region. These phenomena are incorporated into our simulation scheme.
Using J = Jp + Jn = constant and making a change of
generation region xg, can be determined from the conditions P(x) = 0.95. The drift zone is determined as
variable, P(x) = {J (x) J (x)} / J , the steadystate
(W xg). The voltage drops across the different zones are
p n determined by integrating the electric field over the respective
combined carrier continuity equation can be recast into the form
aP(x) = (a + a ) + (a a )P(x)
p n p n
ax
zones. The diode breakdown voltage (VB) is the sum of generation region voltage drop (Vg) and drift zone voltage drop (VD).

SmallSignal Analysis
q ( )
(6)
+ J {gT x
+ gT(x )}.
A smallsignal method of analysis including the tunnelling current to the conduction as well as displacement current is
The Poissons equation including mobile space charge at any
presented in this subsection.
An iterative and generalized
point x in the depletion layer of the diode is given by computer method is developed to study the smallsignal
aE(x) = q {N (x) N (x) + p(x) n(x)}. (7)
behaviour and this method has the advantages of its applicability to any diode structures. The DC results obtained
ax E D A
for any structure under particu ar operating conditions through the method described in the previous subsection are used as
The net mobile space charge concentration (p n) at any space point can be obtained from as
q a(p n) = J an(x) + ap(x)
input for the smallsignal analysis. We briefly describe the smallsignalsimulation method below.
The smallsignal simulation basically solves two simultaneous differential equations (9) and (10) using a
ax vp
vn
modified RungeKutta approach subject to the required
q{an(x) ap(x)}(p n)
boundary conditions. Since the initial values of R and X are
+q g
T (x)
+ gT
(x )
+
aE K
not known, iterations are performed over those until the boundary conditions are met.
vn vp ax
(8)
where K is a correction factor [16]. Equations (6), (7) and (8)
D2R + (a a )DR 2r
w DX
are now solved simultaneously to obtain the electric field and carrier current profiles subjected to the necessary boundary
n p
w2 qrp
n v
conditions. The solution starts from the
position of field
+ v2 H
v E (gT x) + gT(x )) R
maximum near the metallurgical junction. A double iterative
computer method, which performs iterations over the value and location of field maximum, is used. The edges of the
2a w
v X =
2a (9)
vE
and
n p n
D2 X + (a a ) DX + 2r w DR +
v
where Icav(xr) = A d]C is the average current generated in the interval dxr and A is the area of the diode. The mean square noise voltage is now obtained as
w2 2rp r r r
v2 H v E (gT(x) + gT(x )) X
+ 2a w R = w
(10)
< v2 > = 2q2df A Zt(xr)2 y (xr)dxr, (17) from which the Noise Measure (NM) can be defined as an
where
v v2E
indicator of noise to power trade off ratio and can be written as
< v2 >/df
r r 2a r]
NM = 4kT (Z
R ) , (18)
H = (aP an) DEm +
vE . R P
Once the iteration converges the individual space step contribution of the smallsignal resistance R(x) and reactance X(x) are obtained from the solution. The integrated values of
the device negative resistance ZR = fw R(x) dx and device
where k is Boltzman constant, T is absolute temperature, ZR is the integrated device negative resistance and RP is the parasitic series resistance.
We have considered four SiC DDR MITATT diodes in this
0
reactance ZX = fw
0
X(x) dx are then determined. The device
work. The widths of the diodes have been determined to operate in W, D, Y and THz bands, respectively around the
conductance (G), and the device susceptance (B) are
calculated using the relations
(11)
G = ZR
Z2 + Z2
centre frequencies of 94 GHz, 140 GHz, 220 GHz and 0.8 THz, in accordance with the guidelines presented in [18]. The doping concentrations are optimized for a punch through electric field profile. The current densities are set for a high
R X
B = ZX
Z2 + Z2
(12)
efficiency. The area of the diode is calculated following [19]. The optimized structural parameters of the DDR MITATT diodes operating in different frequency bands are presented in
R X Table I.
The smallsignal analysis is repeated for several frequencies and the optimum frequency (fp) corresponding to diode peak negative conductance (Gp) is determined. The diode negative resistance ZRp at fp as well as total reactance ZXp at fp can also be computed using this simulation method.

Noise Analysis
In avalanche transit time diodes noise in generated due to the random nature of impact ionisation process; therefore we assume the tunnelling to be a quiet process. Further, we assume that the avalanche process consists of a noiseless generation rate g and noise generation rate y. A noise generating source y(xr) located at xr in the depletion region is associated with an element of generated current d]C occurring in the interval dxr at xr according to the relation
d]C = qy(x)dxr. (13)
C
An element of mean square noise current < di2 >, in a frequency interval df contributed by d]C is obtained from the theory of short noise as
< di2 > = 2q df d]C A = 2q2 df y(xr) A dxr. (14)


RESULTS AND DISCUSSION
The results obtained from the simulation study are discussed in this section under two headings. The DC and small signal properties are analyzed in subsection III (A). The noise characteristics are presented in subsection III (B).

DC and SmallSignal Behaviours
Some of the important parameters to study the potentials of a MITATT diode are maximum electric field, breakdown voltage, efficiency and the percentage of tunnelling current. The values of these parameters obtained at different frequency bands of operation are listed in Table II. As the frequency band of operation is increased the width of depletion layer is thinned down. As a result the maximum electric field is pushed up. Increase in maximum electric field near the junction results in increase in the number of electrons tunnelling through the junction. So, the percentage of tunnelling current increases. To be more specific we note that as we move from W band to THz band the percentage of tunneling current increases from 10.6% to 24.87%. On the other hand the breakdown voltage decreases
C r r from 613 V to 90.8 V when we change the operating band from
Now, a noise source y(x ) located at x in the generation
W to THz. The rapid fall in breakdown voltage as we go from
region gives rise to a noise electric field e(x, x) in the entire depletion layer analogous to the vibration produced along the entire length of a bar when struck at one point. The terminal voltage vt(xr) produced by y(x) is obtained by integrating e(x, xr) over x for the whole depletion layer
w
vt(xr) = e(x, xr) dx . (15)
0
A transfer impedance can then be defined as
TABLE I. DESIGN PARAMETERS OF SIC DDR MITATT DIODES FOR OPERATION IN W, D, Y AND THZ BANDS.
I
Band
Width (Âµm)
Doping (1023 m3)
Area (1012
m2)
J (108A/
m2)
nside
pside
nside
pside
W band
1.230
1.230
1.7
1.7
452.0
3.1
D band
0.787
0.787
2.4
2.4
236.0
5.0
Y band
0.528
0.528
4.0
4.0
87.60
8.0
THz
band
0.148
0.148
19.4
19.4
03.58
27
r vt( xr)
Zt(x ) =
cav
(xr) , (16)
TABLE II. DC AND SMALL SIGNAL PROPERTIES OF SIC DDR MITATT DIODES FOR OPERATION IN W, D, Y AND THZ BANDS.
Frequency
band
Emax (108V/m)
VB (V)
T (%)
fp (GHz)
Gp(104 S)
pRF (W)
IT/I0 (%)
ZR ()
W band
3.85
613
18.8
100
13.3
62.5
10.60
15.13
D band
4.05
388
17.9
160
12.6
23.7
11.49
14.54
Y band
4.34
273
17.6
230
9.64
8.98
14.29
13.92
THz band
5.79
90.8
16.0
810
2.77
2.85
24.87
13.7
low to high frequency band is due to decrease in widths of the diodes. The efficiency of the diodes under consideration records a minor variation from W band to THz band. This fact is thus indicative of appreciable efficiency (16 %) for the SiC diode even at THz frequencies.
The performance of a power source device is assessed through the study of smallsignal properties like negative conductance, negative resistance and power output. The small signal properties of the SiC MITATT diodes for W, D, Y and THz frequency bands are presented in Table II and Fig. 2. It can be seen from Fig. 2 that the peak values of device negative conductance gradually decreases from 1.33Ã—103 S to 2.77Ã—104 S as we change the frequency band from W to THz. Moreover, the rapid fall in breakdown voltage as we move from low frequency to high frequency bands reduces the input power to the device with a consequent decrease in output power. As we move from low frequency to high frequency structure the generation region width becomes gradually narrower and the level of tunneling current increases. The device negative resistance shows degradation (Table II) as the level of tunneling current increases from low to high frequency bands. The amount of diode negative resistance is a measure of power output from the device. So, the output power decreases with increase in frequency of operation. From the above discussion we observe that there is a considerable degradation in device properties as we move from W band to THz band. But, this degradation in device properties is accompanied by an improvement in noise behaviour (with increase in frequency band of operation). The details of noise behaviour of the designed SiC MITATT diodes have been discussed in the next subsection.

Noise Behaviours
The noise properties of the 4H SiC DDR MITATT diodes considered in this paper are presented in Table III and the variations of mean square noise voltage per bandwidth with respect to frequency for different structures operating in W, D, Y and THz band of frequencies are shown in Fig. 3. As discussed above the percentage of tunnelling current gradually increases from the low frequency to high frequency diodes. Avalanching is a noisy process while tunnelling is a quiet process. So, the height of noise peak steadily decreases with
TABLE III. NOISE PROPERTIES OF SIC DDR MITATT DIODES FOR OPERATION IN W, D, Y AND THZ BANDS.
14 1
1 SiC W band 2 SiC D band 3 SiC Y band
4 SiC THz band
Negative conductance( 10 – 4 S)
12 2
10
3
8
6
4
4
2 2
4
0 1 3
0 500 1000 1500
Frequency(GHz)
Fig. 2 Device negative conductance as a function of frequency for W, D, Y and THz band SiC flat doping profile DDR MITATT diodes.
increase in percentage of tunnelling current. This behaviour is clearly noticeable from the mean square noise voltage presented in Table III and Fig. 3. It means that higher frequency diodes, which have higher level of tunnelling currents, would be less noisy.
Again, we observe from Fig. 3 that at low frequencies the mean square noise voltage remains almost constant. At medium frequencies it increases rapidly and attains a maximum near the resonant frequency. At higher frequency region it decreases very sharply. Variation of mean square noise voltage per band width versus frequency plot in Fig. 3 agrees with the reports of Hines [20], Gummel and Blue [21] and Haitz and Voltmer [22]. At frequencies above the resonant
1 2
4
3
Mean square noise voltage per band width (V 2s)
1E14
1 SiC W band 2 SiC D band 3 SiC Y band
4 SiC THz band
1 2
3
4
Frequency Band
fg
(GHz)
MSNV ( 10 14 V2s)
f1
(GHz)
NM
(dB)
MSNV
at fp
( 10 16
V2s)
NM
at
fp
(dB)
W band
50
1.5
160
26.02
3.26
33.67
D band
60
1.4
220
25.24
2.88
31.45
Y band
90
1.3
350
24.69
2.26
31.38
THz band
280
1.13
1210
21.16
1.04
25.56
1E15
10 100 1000
Frequency (GHz)
MSNVMean Square Noise Voltage
Fig. 3 Mean square noise voltage as a function of frequency for W, D, Y and THz band SiC flat doping profile DDR MITATT diodes.
50
3
Noise Measure (dB)
45
40 2 4
35 1
30
25 1 2 3
20
performance of SiC MITATT diode revealed from our simulation at around 1 THz frequency is commendable with a power output of 3 W, at an efficiency of 16%, with a tunnelling current of 25% and at a noise measure level of 22 dB.
1 SiC W band 2 SiC D band 3 SiC Y band
4 SiC THz band
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CONCLUSION

DC, smallsignal and noise properties of 4HSiC diodes in mixed tunnelling avalanche transit time mode are explored for operation at W, D, Y and THz bands. The trend of results obtained agrees well with those obtained by other authors earlier for other low band gap materials like Si and GaAs [24, 25]. The regular features of the results include decrease in efficiency and power output with increase in the frequency band of operation The tunnelling current is enhanced with frequency band. This has a twofold effect. First, because of the loss in avalanche phase delay associated with it, the diode negative conductance as well as negative resistance, responsible for useful power from the device, decreases. Second, the noise levels such as the mean square noise voltage and noise measure are suppressed. The stateoftheart
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