A new approach is proposed which takes into account both traps and thermal phenomena for the modelling of deviations between static and dynamic drain current characteristics in III-V field effect transistors. The model is based on the well-known `backgating' concept and can easily be identified on the basis of conventional static drain current characteristics and small-signal, low-frequency S parameters. Experimental results confirm the accuracy of the proposed mode

Filicori, F.

Rinaldi, P.

Santarelli, A.

Vannini, G.

AMS Acta - Alm@DL - Università di Bologna

Circuit performance The chips were measured on-wafer by using 
50Cl coplanar test probes. The measured mnmum input sensitiv- 
ity yH against input frequencyJn of the divider is plotted in Fig. 3. 
Above the minmum input voltage, reliable operation is guaran- 
teed More input power is requred at lower frequencies because 
the circuit needs a minimum turn-odoff tme for the input sine- 
wave signal That is, the input amplitude should be increased to 
maintain a required slew rate for a sinewave input signal at lower 
frequencies The resonance frequency is -48 5 GHz High sensitiv- 
ity of < 0 7V, amplitude was obtamed in the frequency range 37- 
55GHz The measured input and output waveforms, and the out- 
put spectrum of the 1 2 dynamic divlders at the input frequency of 
55GHz are shown in Fig. 4a and b, respectively. It should be 
noted that our test system has so far been defmed up to 50GHz 
The differential output voltage swing is 370mVp, at these ma=- 
mum operating frequencies The power dissipation is 300mW 
using two supply voltages of 4 and - 2 3  
27 July I998 0 IEE 1998 
Electronics Letters Online No 19981336 
Z Lao, A. Thiede, J. Hornung, M Schlechtweg, H Lienhart, 
W Bronner, A Hulsmann, T Jakobus, J Seibel, M Sedler and 
G Kaufel (Fraunhofer-Institute of Applied Solid-state Physics, 
Tullastrasse 72, 0-79108 Freiburg, Germany) 
Z Lao Now with Rockwell Semiconductor Systems, Newbury Park, 
CA 91320, USA 
Conclusion. The design and performance of a ‘digital’ dynamic fre- 
quency divider has been presented. The dynamic frequency divider 
operates reliably up to 55GHz that reaches V-band millimetre- 
wave frequencies and is close to the fT of the used transistors. The 
high-speed performance of the frequency divider is suitable for 
application in measurement equipment, mcrowave, d ime t re -  
wave, and satellite communication systems. 
Acknowledgments: The authors thank G. Weimann for encourage- 
ment. The authors also thank the HEMT processing staff for fab- 
rication of these circuits. The work was supported by the German 
Ministry for Education and Research BMBF. 
1 self-heating for del inc 
I ispersi cts in Ill-V FETs 
A. Santarelli, F. Filicori, G. Vannini and P. Rinaldi 
A new approach is proposed wluch takes into account both traps 
and thermal phenomena for the modellmg of deviations between 
s t a k  and dynamc drain current charactenstics m 111-V field 
effect transistors The model is based on the well-known 
‘backgatmg’ concept and can easily be identified on the basis of 
conventional static dram current charactenstics and small-signal, 
low-frequency S parameters Experimental results confirm the 
accuracy of the proposed model. 
Introduction: Accurate nonlinear models of 111-V field effect tran- 
sistors FETs for microwave circuit design should also account for 
low-frequency dispersion of the electrical characteristics due to 
deep level traps and surface states. These phenomena cause con- 
siderable deviations between ‘static’ and ‘dynamic’ (e.g. pulsed) 
measurements of the DC characteristics, or, in terms of differential 
parameters, frequency dependent behaviour of the trans-admit- 
tance and output impedance even at low frequencies (e.g. 
< 100kHz). 
The tme constants associated with the dynamics of self-heating, 
which become relevant in an electron device especially under large- 
signal operation, although longer, are not always very different 
from those associated with traps or surface states (typically from 
fractions to hundreds of microseconds). Consequently, dispersion 
due to ‘traps’ (with this term hereafter we refer to both surface 
state densities and deep level traps) cannot always be dealt with 
separately from the dynamics of thermal effects due to self-heat- 
ing. 
The empirical modelling approach of dispersive phenomena pre- 
sented in [l] provides very good predictive capabilities of bias- 
dependent dynamic drain current deviations due to traps and ther- 
mal effects in FETs. Moreover, its technology mdependence has 
been widely verified [ I ,  21. However, owing to the need for non- 
conventional instrumentation for pulsed measurements, model 
References 
THIEDE, A ,  TASKER, P ,  HULSMANN, A ,  KOHLER, K ,  BRONNER, W ,  
SCHLECHTWEG, M , BERROTH, M , BRAUNSTEIN, J , and NOWOTNY, U : 
‘28-51 GHz dynamic frequency divider based on 0 15pm T-Gate 
Al, ,Ga, ,As/In, zsGa, MODFETs’, Electron Lett , 1993, 29, 
(lo), pp. 933-934 
KURISU, M ,  UEMURA, G ,  OHUCHI, M ,  OGAWA, C ,  TAKEMURA, H ,  
MORIKAWA,T, and TASHIRO,T ‘A Si bipolar 28GHz dynamic 
frequency divider’ ISSCC Tech Dig, 1992, pp. 92-93 
and OBREGON, J ‘A 60-GHz HEMT-MMIC anaiog frequency 
divider by two’, IEEE J Sohd-State Czrcuits, 1995, SSC-30, (lo), 
pp. 1062-1067 
MILLER, R L ‘Fractional frequency generators utilizing regenerative 
modulation’, IRE Tech Dzg , July 1939, 27, pp 446457 
RAZAVI, B .  ‘Challenges in the design of frequency synthesizers for 
wireless applications’. IEEE CICC Tech. Dig., 1997, pp 395402 
SARKISSIAN, J -C , CAMIADE, M , SAVARY P , SUAREZ, A ,  QUERE, R , 
JAKOBUS, T ,  BRONNER, W ,  HOFMANN, P ,  HULSMANN, A ,  KAUFEL, G ,  
KOHLER, K ,  LANDSBERG, B ,  RAYNOR, B ,  SCHNEIDER, J ,  GRUN, N, 
WINDSCHEIF, J , BERROTH, M , and HORNUNG, J ‘Stability of an 
AlGaAs/GaAs/AlGaAs ED-HEMT process with double pulse 
doping’ Int Symp GaAs and Related Compounds, 1992, Inst. 
Phys. Conf. Ser. no 129, Chap. 11, pp 887-892 
identification could be cumbersome. In this Letter a simplified 
approach to modellmg the dynamic drain current is presented, 
which allows for an identification procedure based on conven- 
tional DC and small-signal low-frequency (e.g. the lowest opera- 
tion frequency of a mcrowave network analyser) s-parametet 
measurements. The model can easily be embedded both in conven- 
box models. 
tional nonlinear equivalent circuits and look-up-table b ck- 
Backgating model with se& 
on the assumption that th 
drain current due to traps 
uted electrical coupling (with very low cutoff frequency) between 
the gatddrain electrodes and the semi-insulator bulk ( ‘self-back- 
gating’) [3, 41. This can be exp introducing in the drain 
current characteristic Pc an eq ate voltage vgx: 
2 d ( t )  = FDC(vgz ( t ) ,%( t ) )  (1) 
‘ugz ( t )  = ug ( t )  + Qg (U, ( t )  - v,” 1 + ad(&? ( t )  - Vd” ) (2 
where 
V, , I/., being the average values of the applied voltages 
V l t )  and ax, a, suitable parameters to be determined. Note 
under static conditions we have v, = vg, while under dynamic 
operation, at a frequency above the cutoff of dispersive effects, a, 
and a, account for deviations due to traps by ‘feeding back’ to the 
gate (‘backgating’) dynamic voltage deviations v,(t) - 5, and vdt) 
- V, . This approach, although successfidly used by some authors 
[4, 51, can accurately predict dynamc drain current deviations 
only when self-heating effects due to power dissipation are practi- 
del accuracy can be 
al power-dependent 
ce the dynamic chan- 
nel temperature deviation 
M ( t )  = Q s ( t )  - 80 = & ( p s ( t )  - Po) ( 3 )  
which virtually represents the difference between the temperature 
e,(t) under quasi-static operation and the actual channel 
1974 ELECTRONICS LETTERS 1st October 1998 Vol. 34 No. 20 
temperature 8, (which can be assumed constant for operation 
above the thermal cutoff) due to the average dissipated power Po 
under dynamic conditions. In eqn. 3 R, is the thermal resistance, 
and p3(t) = FDC{v,(t), v,(t)} vd(t) is a virtually 'quasi-static' 
dissipated power, i.e. the power which would be dissipated if v,(t), 
v,(t) were 'slowly' time-varying voltages. 
By assuming that the current dependence on the channel tem- 
perature 8 can be approximated through a multiplying 'scaling' 
factor (i.e. temperature sensitivity is mainly due to atrrier mobility 
variations) linearly dependent on A€), we can write 
where ke is a thermal sensitivity coefficient. 
With respect to other models (see e.g. [6]), our approach can be 
applied starting from any existing model for the DC FET charac- 
teristics (based either on analytical expressions or look-up tables) 
and does not require pulsed measurements for its identification. In 
particular, the dynamic drain current is simply obtained from the 
DC expression by introducing the effects of the dynamic devia- 
tions of the voltages and dissipated power through only three 
additional parameters a,, a, and K 
on the basis of conventional small- 
ments. To this end, eqn. 4 can be 
g&c{vg,,7 vdo } = [I + K .  v d o  ' I d "  + a g ]  'gic{&o 3 vdo } (5) 
g d A C { V , , , v d o } = j l + K . v d o  . ~ d o l . g f ~ { ~ o , v d o I  
+ I:,, + a d  . S~c{vg,,, (/do} ( 6 )  
where Id, = Pc( CO, Vdo}. 
Eqns. 5 and 6 represent the low-frequency dynamic transcon- 
ductance g,"" and output conductance g f  as functions of the 
static drain current Id,,, of its partial derivatives g,"", g:" and of 
the three fiodel parameters a,, a, and K. The static transconduct- 
ance g,"" and output conductance g:" may be obtained, for 
instance, through numerical differentiation of the measured DC 
drain current or by analytical derivation of the mathematical 
expression used to model the static behaviour of the device. More- 
over, g i c  and gdAc practically coincide with the real part of the 
corresponding small-signal, 'low-frequency' Y par- meters meas- 
ured at a suitable frequency above the cutoff due to dispersive 
effects but low enough to neglect high frequency charge storage 
-l 
- 5 200 
100 
0 
0 1 2 3 4 5 
VD'V 
pzq 
Fig. 1 Static characteristics and comparison between measured and pre- 
dicted pulsed drain currents for CFX32 GaAs MESFET 
Quiescent bias condition VEo = OV, Vdo = 5V 
Prediction of model including self-heating effects is clearly better than 
prediction obtained with two-parameter model 
A static characteristics 
measured pulsed drain current 
model including self-heating effects 
~~~~ two parameter model 
phenomena. The Y parameters are easily obtainable from S- 
parameter measurements through known matrix transformation 
formulas. Thus, the three model parameters can easily be deter- 
mined by minimising, over a suitable grid of bias conditions, the 
discrepancies between measured dynamic conductartces and eqns. 
5 and 6. 
ELECTRONICS LETTERS 1st October 1398 Vol. 34 
Experimental results: The proposed model has been embedded in 
the HP-MDS programme for harmonic balance circuit analysis. In 
particular, the model equations have been mplemented by using 
SDD (symbolically defmed devices) components and two-dimen- 
sional look-up tables storing the measured values of the device DC 
characteristics E;""{ vg, vd}. 
Experimental validation was carried out on a Philips CFX32 
MESFET device which is characterised by relevant self-heating 
effects, as can be clearly seen from the negative slope at high Vp,, 
Vdo values of the DC characteristics shown in Fig. 1. In the same 
Figure the dynamic drain current characteristics predicted are 
compared With measurements obtained by applying short, simulta- 
neous voltage pulses at the gate/drain electrodes starting from the 
quiescent condition V,  = OV, Vdo = 5V. Moreover, the accuracy 
improvement, obtained) using the proposed model with respect to 
a two-parameter backgating model which does not account for 
self-heating, can be clearly seen 
Good agreement was found, for different quiescent bias condi- 
tions, not only for the dynamic drain current (see Fig. 1) but also 
for its first order derivatives. As an example, Fig. 2 shows the 
derivatives with respect to V, of the measured and predicted 
dynamic current characteristics for another quiescent bias condi- 
tion (KO = -2V, Vdo = 3V). The agreement is quite good taking 
also into account the simplicity of the proposed model, which is 
based on only three 'global' parameters. 
Acknowledgment: This work was partly supported by the Italian 
National Research Council under the MADESSII project. 
0 IEE 1998 
Electronics Letters Online No: 19981351 
A. Santarelli and G. Vannini (Research Center for Computer Science 
and Communication Systems, Italian National Research Council) 
F. Filicori (Department of Electronics, Computer Science and Systems, 
University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy) 
P. Rinaldi (Department of Electrical Engineering, University of 
Bologna, Viale Risorgimento 2, 40136 Bologna, Italy) 
G. Vannini: Also with Department of Electronics, Computer Science 
and Systems, University of Bologna, Viale Risorgimento 2, 40136 
Bologna, Italy 
I 1  August 1998 
References 
1 FILICORI, F., VANNINI, G., SANTARELLI, A., MEDIAVILLA, A., TAZON, A., 
and NEWPORT, Y.: 'Empirical modeling of Iow-frequency dispersive 
effects due to traps and thermal phenomena in III-V FETs', IEEE 
Trans., 1995, MTT-43, (12), pp. 2972-2981 
BAYENS, Y., and VAN DER ZANDEN, K.: 'Modelling of low-frequency 
dispersive effects in GaAs and InP HEMTs'. Proc. GAAS'97, 1997, 
pp. 131-134 
3 SCHEINBERG, N., BAYRUNS, R., and GOYAL, R.: 'A low frequency 
GaAs MESFET circuit model', IEEE J. Solid-state Circuits, 1988, 
23, (2), pp. 605-608 
No. 20 1975 
2 SANTARELLI, A., VANNINI, G., BORGARINO, M., MENOZZI, R., 
4 FIEGNA, C. ,  FILICORI, F., VANNINI, G., and VENTURI, F.: ‘Modeling the 
effects of traps on the IV-characteristics of GaAs MESFETs’. 
Proc. 1995 IEEE IEDM, 1995, pp. 773-776 
5 JEON, K , KWON, Y , and HONG, s.: ‘A frequency dispersion model of 
GaAs MESFET for large-signal applications’, IEEE MGWL, 1997, 
7, (3),  pp. 78-80 
6 ROH, T., KIM, Y., SUH, Y ,  PARK, W ,  and KIM, B.: ‘A Simple and 
accurate MESFET channel-current model including bias-dependent 
dispersion and thermal phenomena’, ZEEE Trans., 1997, MTT-45, 
(8). pp. 1252-1255 
Impact of subchannel design on DC and RF 
performance of 0.1 pm MODFETs with InAs- 
inserted channel 
D. Xu, J. Osaka, T. Suemitsu, Y. Umeda, Y. Yamane 
and Y. Ishii 
It isshown that a further performance improvement in MODFETs 
with Ids-inserted channel structures can be achieved by properly 
designing the subchannel layer that lies directly under the main 
channel of the InAs layer. The use of an InO3,Ga,,,As layer 
grown with tensile strain on the InP substrate contributes to 
better accommodation of the 2D electron gas in the InAs layer. 
This translates to a > 10% increase in the maximum extrinsic 
transconductance and an 8 %  increase in the current gain cutoff 
frequency of a 0.1 p device. 
Introduction: The performance of the modulation-doped field- 
effect transistor (MODFET) based on InP substrate has been sig- 
nificantly improved by using compressively strained In-rich 
InGaAs channel materials [l - 41. InAs is a desirable choice for 
channels because of its narrow bandgap of 0.35eV, which will 
form a deep quantum well and improve the confmement of the 
two dimensional electron gas (2DEG). In addition, the InAs layer 
has low alloy scattering and large T-L valley separation. The latter 
will translate to an advantage for high electric field transport, 
especially in short-gate-length MODFETs. Compared with the 
graded channel approach, intended for a larger total channel 
thickness for better 2DEG confinement [3, 51, the use of a thin 
layer of InAs in the channel is more favourable for better repro- 
ducibility of the epitaxy and subsequently fabricated devices. 
However, bulk InAs has a lattice mismatch of -3.5% with the 
InP substrate; therefore, it is very difficult to grow an InAs layer 
thick enough to form the whole channel on InP. Maeda et al. [6] 
introduced an In-rich subchannel, in addition to the InAs layer, to 
increase the average In content. However, this leads to degrada- 
tion of 2DEG confinement in the InAs layer. We will show that 
this is actually a more important consideration in designing a 
subchannel layer. With the use of a Ga-rich subchannel, theoreti- 
cal analysis clearly demonstrates a remarkable improvement in 
2DEG confinement in the InAs layer. This results in improved in 
DC and RF performance. 
1.0 ~ , , ,  , , , ,  , , ,  , , , )  , , , ,  , , , ,  
Fig. 1 Minimum conduction-band energy diagram and squares of wave 
functions of electrons in j%st subbands of quantum wells of structures A 
and B 
structure A 
structure B 
- - - -  
Theoretical analysis and device fabrication: The MBE-grown 
MODFET structures consist of a 200nm i-InAlAs buffer, a 12nm 
i-InGaAs channel, a 2nm i-InAlAs spacer, a 5nm n+-InAlAs sup- 
ply layer, a 15nm i-InAlAs barrier and cap layers for non-alloyed 
ohmic contact. All the layers except the channel are lattice- 
matched to InF’ substrates, while the the Si doping density is 
cm3 for all n+ layers. Details of device fabrication can be found in 
[7]. Two channel designs were used. Structure A consists of a 7nm 
compressively strained In, 7oGq,3,As ubchannel with a 3nm InAs 
layer and a 2nm In,,53G%,47As as the upper part of the channel [SI. 
In structure B, the 7nm compressively strained In, ,,Ga,, ,,As 
subchannel is replaced with a 7nm tensilely strained In, 3oGq,,,As 
layer. We calculated the quantum states by self-consistently solv- 
ing Schrodinger’s and Poisson’s equations. Fig. 1 shows the mini- 
mum conduction-band energy diagram and electron wave 
functions of structures A and B. Structure A has a first-subband 
energy of 0.19eV and Fermi level of 0.35eV; for structure B these 
values are slightly increased to 0.23 and 0.39eV, respectively. Use 
of In, ,,Ga, i a A ~  leads to a remarkable shift of the 2DEG towards 
the InAs layer, resulting in a 17% population increase of frst-sub- 
band electrons in the InAs layer. 
lo- 0.8 
E 
< 0 6  
c a,
E 0.4 
2 
0.2 
0 
0.8 
E 
< 0 6  
c 
e! 
0 
5 0.4 
E 
02 
‘ 0  0 5  1 0  1 5  2 0  2 5  
drain bias,V 
b w 
Fig. 2 I-V characteristics o f 0 , l p n  MODFETs based on structures A 
and B 
Gate bias for top curves = 0.6V; measurement step of gate bias = 
0.2v 
a Structure A 
b Structure B 
Device pertormanee: Fig. 2 shows the excellent I-V characteristics 
of MODFETs, which exemplify their good pinchoff characteristics 
with an identical threshold voltage of 4 . 2 V  and a low knee volt- 
age. Structure A shows a drain current I, of 0.9Mmm at gate bias 
V,  of 0.6V and drain bias V, of lV, and structure B exhibits an 
Idr > 1 ” m  under the same bias condition. The typical transfer 
characteristics for devices based on these two structures are shown 
in Fig. 3. At V, = 1, the maximum extrinsic transconductance of 
structure B is 1.7Simm with an associated I, of O.SA/mm. For 
structure A at the same bias, the peak transconductance is reduced 
to 1.5S/mm with a decreased Ids of -0 .35”m.  Therefore struc- 
ture B exhibits a 10% improvement in transconductance compared 
with structure A. The device S-parameter characteristics were 
measured using a Cascade on-wafer probe station. Fig. 4 summa- 
rises the current gain lh21/2 and Mason unilateral power gain U, 
against frequency at V, = 1 and with the F<s for peak transcon- 
ductance. The f T  and fm,, obtained by extrapolating jh2112 and U, 
with -20dB/decade are 238 and 180GHz for structure B. This f r  
value is 8% higher than that of structure A cf, = 220GHz). As 
suggested by the calculation, the performance improvement should 
1976 ELECTRONICS LETTERS 1st October 1998 Vol. 34 No. 20 


'Backgating' model including self-heating for low-frequency dispersive effects in III-V FETs

AMS Acta

Circuit performance The chips were measured on-wafer by using 50Cl coplanar test probes. The measured mnmum input sensitiv- ity yH against input frequencyJn of the divider is plotted in Fig. 3. Above the minmum input voltage, reliable operation is guaran- teed More input power is requred at lower frequencies because the circuit needs a minimum turn-odoff tme for the input sine- wave signal That is, the input amplitude should be increased to maintain a required slew rate for a sinewave input signal at lower frequencies The resonance frequency is -48 5 GHz High sensitiv- ity of < 0 7V, amplitude was obtamed in the frequency range 37- 55GHz The measured input and output waveforms, and the out- put spectrum of the 1 2 dynamic divlders at the input frequency of 55GHz are shown in Fig. 4a and b, respectively. It should be noted that our test system has so far been defmed up to 50GHz The differential output voltage swing is 370mVp, at these ma=- mum operating frequencies The power dissipation is 300mW using two supply voltages of 4 and - 2 3  27 July I998 0 IEE 1998 Electronics Letters Online No 19981336 Z Lao, A. Thiede, J. Hornung, M Schlechtweg, H Lienhart, W Bronner, A Hulsmann, T Jakobus, J Seibel, M Sedler and G Kaufel (Fraunhofer-Institute of Applied Solid-state Physics, Tullastrasse 72, 0-79108 Freiburg, Germany) Z Lao Now with Rockwell Semiconductor Systems, Newbury Park, CA 91320, USA Conclusion. The design and performance of a ‘digital’ dynamic fre- quency divider has been presented. The dynamic frequency divider operates reliably up to 55GHz that reaches V-band millimetre- wave frequencies and is close to the fT of the used transistors. The high-speed performance of the frequency divider is suitable for application in measurement equipment, mcrowave, d ime t re -  wave, and satellite communication systems. Acknowledgments: The authors thank G. Weimann for encourage- ment. The authors also thank the HEMT processing staff for fab- rication of these circuits. The work was supported by the German Ministry for Education and Research BMBF. 1 self-heating for del inc I ispersi cts in Ill-V FETs A. Santarelli, F. Filicori, G. Vannini and P. Rinaldi A new approach is proposed wluch takes into account both traps and thermal phenomena for the modellmg of deviations between s t a k  and dynamc drain current charactenstics m 111-V field effect transistors The model is based on the well-known ‘backgatmg’ concept and can easily be identified on the basis of conventional static dram current charactenstics and small-signal, low-frequency S parameters Experimental results confirm the accuracy of the proposed model. Introduction: Accurate nonlinear models of 111-V field effect tran- sistors FETs for microwave circuit design should also account for low-frequency dispersion of the electrical characteristics due to deep level traps and surface states. These phenomena cause con- siderable deviations between ‘static’ and ‘dynamic’ (e.g. pulsed) measurements of the DC characteristics, or, in terms of differential parameters, frequency dependent behaviour of the trans-admit- tance and output impedance even at low frequencies (e.g. < 100kHz). The tme constants associated with the dynamics of self-heating, which become relevant in an electron device especially under large- signal operation, although longer, are not always very different from those associated with traps or surface states (typically from fractions to hundreds of microseconds). Consequently, dispersion due to ‘traps’ (with this term hereafter we refer to both surface state densities and deep level traps) cannot always be dealt with separately from the dynamics of thermal effects due to self-heat- ing. The empirical modelling approach of dispersive phenomena pre- sented in [l] provides very good predictive capabilities of bias- dependent dynamic drain current deviations due to traps and ther- mal effects in FETs. Moreover, its technology mdependence has been widely verified [ I ,  21. However, owing to the need for non- conventional instrumentation for pulsed measurements, model References THIEDE, A ,  TASKER, P ,  HULSMANN, A ,  KOHLER, K ,  BRONNER, W ,  SCHLECHTWEG, M , BERROTH, M , BRAUNSTEIN, J , and NOWOTNY, U : ‘28-51 GHz dynamic frequency divider based on 0 15pm T-Gate Al, ,Ga, ,As/In, zsGa, MODFETs’, Electron Lett , 1993, 29, (lo), pp. 933-934 KURISU, M ,  UEMURA, G ,  OHUCHI, M ,  OGAWA, C ,  TAKEMURA, H ,  MORIKAWA,T, and TASHIRO,T ‘A Si bipolar 28GHz dynamic frequency divider’ ISSCC Tech Dig, 1992, pp. 92-93 and OBREGON, J ‘A 60-GHz HEMT-MMIC anaiog frequency divider by two’, IEEE J Sohd-State Czrcuits, 1995, SSC-30, (lo), pp. 1062-1067 MILLER, R L ‘Fractional frequency generators utilizing regenerative modulation’, IRE Tech Dzg , July 1939, 27, pp 446457 RAZAVI, B .  ‘Challenges in the design of frequency synthesizers for wireless applications’. IEEE CICC Tech. Dig., 1997, pp 395402 SARKISSIAN, J -C , CAMIADE, M , SAVARY P , SUAREZ, A ,  QUERE, R , JAKOBUS, T ,  BRONNER, W ,  HOFMANN, P ,  HULSMANN, A ,  KAUFEL, G ,  KOHLER, K ,  LANDSBERG, B ,  RAYNOR, B ,  SCHNEIDER, J ,  GRUN, N, WINDSCHEIF, J , BERROTH, M , and HORNUNG, J ‘Stability of an AlGaAs/GaAs/AlGaAs ED-HEMT process with double pulse doping’ Int Symp GaAs and Related Compounds, 1992, Inst. Phys. Conf. Ser. no 129, Chap. 11, pp 887-892 identification could be cumbersome. In this Letter a simplified approach to modellmg the dynamic drain current is presented, which allows for an identification procedure based on conven- tional DC and small-signal low-frequency (e.g. the lowest opera- tion frequency of a mcrowave network analyser) s-parametet measurements. The model can easily be embedded both in conven- box models. tional nonlinear equivalent circuits and look-up-table b ck- Backgating model with se& on the assumption that th drain current due to traps uted electrical coupling (with very low cutoff frequency) between the gatddrain electrodes and the semi-insulator bulk ( ‘self-back- gating’) [3, 41. This can be exp introducing in the drain current characteristic Pc an eq ate voltage vgx: 2 d ( t )  = FDC(vgz ( t ) ,%( t ) )  (1) ‘ugz ( t )  = ug ( t )  + Qg (U, ( t )  - v,” 1 + ad(&? ( t )  - Vd” ) (2 where V, , I/., being the average values of the applied voltages V l t )  and ax, a, suitable parameters to be determined. Note under static conditions we have v, = vg, while under dynamic operation, at a frequency above the cutoff of dispersive effects, a, and a, account for deviations due to traps by ‘feeding back’ to the gate (‘backgating’) dynamic voltage deviations v,(t) - 5, and vdt) - V, . This approach, although successfidly used by some authors [4, 51, can accurately predict dynamc drain current deviations only when self-heating effects due to power dissipation are practi- del accuracy can be al power-dependent ce the dynamic chan- nel temperature deviation M ( t )  = Q s ( t )  - 80 = & ( p s ( t )  - Po) ( 3 )  which virtually represents the difference between the temperature e,(t) under quasi-static operation and the actual channel 1974 ELECTRONICS LETTERS 1st October 1998 Vol. 34 No. 20 temperature 8, (which can be assumed constant for operation above the thermal cutoff) due to the average dissipated power Po under dynamic conditions. In eqn. 3 R, is the thermal resistance, and p3(t) = FDC{v,(t), v,(t)} vd(t) is a virtually 'quasi-static' dissipated power, i.e. the power which would be dissipated if v,(t), v,(t) were 'slowly' time-varying voltages. By assuming that the current dependence on the channel tem- perature 8 can be approximated through a multiplying 'scaling' factor (i.e. temperature sensitivity is mainly due to atrrier mobility variations) linearly dependent on A€), we can write where ke is a thermal sensitivity coefficient. With respect to other models (see e.g. [6]), our approach can be applied starting from any existing model for the DC FET charac- teristics (based either on analytical expressions or look-up tables) and does not require pulsed measurements for its identification. In particular, the dynamic drain current is simply obtained from the DC expression by introducing the effects of the dynamic devia- tions of the voltages and dissipated power through only three additional parameters a,, a, and K on the basis of conventional small- ments. To this end, eqn. 4 can be g&c{vg,,7 vdo } = [I + K .  v d o  ' I d "  + a g ]  'gic{&o 3 vdo } (5) g d A C { V , , , v d o } = j l + K . v d o  . ~ d o l . g f ~ { ~ o , v d o I  + I:,, + a d  . S~c{vg,,, (/do} ( 6 )  where Id, = Pc( CO, Vdo}. Eqns. 5 and 6 represent the low-frequency dynamic transcon- ductance g,"" and output conductance g f  as functions of the static drain current Id,,, of its partial derivatives g,"", g:" and of the three fiodel parameters a,, a, and K. The static transconduct- ance g,"" and output conductance g:" may be obtained, for instance, through numerical differentiation of the measured DC drain current or by analytical derivation of the mathematical expression used to model the static behaviour of the device. More- over, g i c  and gdAc practically coincide with the real part of the corresponding small-signal, 'low-frequency' Y par- meters meas- ured at a suitable frequency above the cutoff due to dispersive effects but low enough to neglect high frequency charge storage -l - 5 200 100 0 0 1 2 3 4 5 VD'V pzq Fig. 1 Static characteristics and comparison between measured and pre- dicted pulsed drain currents for CFX32 GaAs MESFET Quiescent bias condition VEo = OV, Vdo = 5V Prediction of model including self-heating effects is clearly better than prediction obtained with two-parameter model A static characteristics measured pulsed drain current model including self-heating effects ~~~~ two parameter model phenomena. The Y parameters are easily obtainable from S- parameter measurements through known matrix transformation formulas. Thus, the three model parameters can easily be deter- mined by minimising, over a suitable grid of bias conditions, the discrepancies between measured dynamic conductartces and eqns. 5 and 6. ELECTRONICS LETTERS 1st October 1398 Vol. 34 Experimental results: The proposed model has been embedded in the HP-MDS programme for harmonic balance circuit analysis. In particular, the model equations have been mplemented by using SDD (symbolically defmed devices) components and two-dimen- sional look-up tables storing the measured values of the device DC characteristics E;""{ vg, vd}. Experimental validation was carried out on a Philips CFX32 MESFET device which is characterised by relevant self-heating effects, as can be clearly seen from the negative slope at high Vp,, Vdo values of the DC characteristics shown in Fig. 1. In the same Figure the dynamic drain current characteristics predicted are compared With measurements obtained by applying short, simulta- neous voltage pulses at the gate/drain electrodes starting from the quiescent condition V,  = OV, Vdo = 5V. Moreover, the accuracy improvement, obtained) using the proposed model with respect to a two-parameter backgating model which does not account for self-heating, can be clearly seen Good agreement was found, for different quiescent bias condi- tions, not only for the dynamic drain current (see Fig. 1) but also for its first order derivatives. As an example, Fig. 2 shows the derivatives with respect to V, of the measured and predicted dynamic current characteristics for another quiescent bias condi- tion (KO = -2V, Vdo = 3V). The agreement is quite good taking also into account the simplicity of the proposed model, which is based on only three 'global' parameters. Acknowledgment: This work was partly supported by the Italian National Research Council under the MADESSII project. 0 IEE 1998 Electronics Letters Online No: 19981351 A. Santarelli and G. Vannini (Research Center for Computer Science and Communication Systems, Italian National Research Council) F. Filicori (Department of Electronics, Computer Science and Systems, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy) P. Rinaldi (Department of Electrical Engineering, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy) G. Vannini: Also with Department of Electronics, Computer Science and Systems, University of Bologna, Viale Risorgimento 2, 40136 Bologna, Italy I 1  August 1998 References 1 FILICORI, F., VANNINI, G., SANTARELLI, A., MEDIAVILLA, A., TAZON, A., and NEWPORT, Y.: 'Empirical modeling of Iow-frequency dispersive effects due to traps and thermal phenomena in III-V FETs', IEEE Trans., 1995, MTT-43, (12), pp. 2972-2981 BAYENS, Y., and VAN DER ZANDEN, K.: 'Modelling of low-frequency dispersive effects in GaAs and InP HEMTs'. Proc. GAAS'97, 1997, pp. 131-134 3 SCHEINBERG, N., BAYRUNS, R., and GOYAL, R.: 'A low frequency GaAs MESFET circuit model', IEEE J. Solid-state Circuits, 1988, 23, (2), pp. 605-608 No. 20 1975 2 SANTARELLI, A., VANNINI, G., BORGARINO, M., MENOZZI, R., 4 FIEGNA, C. ,  FILICORI, F., VANNINI, G., and VENTURI, F.: ‘Modeling the effects of traps on the IV-characteristics of GaAs MESFETs’. Proc. 1995 IEEE IEDM, 1995, pp. 773-776 5 JEON, K , KWON, Y , and HONG, s.: ‘A frequency dispersion model of GaAs MESFET for large-signal applications’, IEEE MGWL, 1997, 7, (3),  pp. 78-80 6 ROH, T., KIM, Y., SUH, Y ,  PARK, W ,  and KIM, B.: ‘A Simple and accurate MESFET channel-current model including bias-dependent dispersion and thermal phenomena’, ZEEE Trans., 1997, MTT-45, (8). pp. 1252-1255 Impact of subchannel design on DC and RF performance of 0.1 pm MODFETs with InAs- inserted channel D. Xu, J. Osaka, T. Suemitsu, Y. Umeda, Y. Yamane and Y. Ishii It isshown that a further performance improvement in MODFETs with Ids-inserted channel structures can be achieved by properly designing the subchannel layer that lies directly under the main channel of the InAs layer. The use of an InO3,Ga,,,As layer grown with tensile strain on the InP substrate contributes to better accommodation of the 2D electron gas in the InAs layer. This translates to a > 10% increase in the maximum extrinsic transconductance and an 8 %  increase in the current gain cutoff frequency of a 0.1 p device. Introduction: The performance of the modulation-doped field- effect transistor (MODFET) based on InP substrate has been sig- nificantly improved by using compressively strained In-rich InGaAs channel materials [l - 41. InAs is a desirable choice for channels because of its narrow bandgap of 0.35eV, which will form a deep quantum well and improve the confmement of the two dimensional electron gas (2DEG). In addition, the InAs layer has low alloy scattering and large T-L valley separation. The latter will translate to an advantage for high electric field transport, especially in short-gate-length MODFETs. Compared with the graded channel approach, intended for a larger total channel thickness for better 2DEG confinement [3, 51, the use of a thin layer of InAs in the channel is more favourable for better repro- ducibility of the epitaxy and subsequently fabricated devices. However, bulk InAs has a lattice mismatch of -3.5% with the InP substrate; therefore, it is very difficult to grow an InAs layer thick enough to form the whole channel on InP. Maeda et al. [6] introduced an In-rich subchannel, in addition to the InAs layer, to increase the average In content. However, this leads to degrada- tion of 2DEG confinement in the InAs layer. We will show that this is actually a more important consideration in designing a subchannel layer. With the use of a Ga-rich subchannel, theoreti- cal analysis clearly demonstrates a remarkable improvement in 2DEG confinement in the InAs layer. This results in improved in DC and RF performance. 1.0 ~ , , ,  , , , ,  , , ,  , , , )  , , , ,  , , , ,  Fig. 1 Minimum conduction-band energy diagram and squares of wave functions of electrons in j%st subbands of quantum wells of structures A and B structure A structure B - - - -  Theoretical analysis and device fabrication: The MBE-grown MODFET structures consist of a 200nm i-InAlAs buffer, a 12nm i-InGaAs channel, a 2nm i-InAlAs spacer, a 5nm n+-InAlAs sup- ply layer, a 15nm i-InAlAs barrier and cap layers for non-alloyed ohmic contact. All the layers except the channel are lattice- matched to InF’ substrates, while the the Si doping density is cm3 for all n+ layers. Details of device fabrication can be found in [7]. Two channel designs were used. Structure A consists of a 7nm compressively strained In, 7oGq,3,As ubchannel with a 3nm InAs layer and a 2nm In,,53G%,47As as the upper part of the channel [SI. In structure B, the 7nm compressively strained In, ,,Ga,, ,,As subchannel is replaced with a 7nm tensilely strained In, 3oGq,,,As layer. We calculated the quantum states by self-consistently solv- ing Schrodinger’s and Poisson’s equations. Fig. 1 shows the mini- mum conduction-band energy diagram and electron wave functions of structures A and B. Structure A has a first-subband energy of 0.19eV and Fermi level of 0.35eV; for structure B these values are slightly increased to 0.23 and 0.39eV, respectively. Use of In, ,,Ga, i a A ~  leads to a remarkable shift of the 2DEG towards the InAs layer, resulting in a 17% population increase of frst-sub- band electrons in the InAs layer. lo- 0.8 E < 0 6  c a,E 0.4 2 0.2 0 0.8 E < 0 6  c e! 0 5 0.4 E 02 ‘ 0  0 5  1 0  1 5  2 0  2 5  drain bias,V b w Fig. 2 I-V characteristics o f 0 , l p n  MODFETs based on structures A and B Gate bias for top curves = 0.6V; measurement step of gate bias = 0.2v a Structure A b Structure B Device pertormanee: Fig. 2 shows the excellent I-V characteristics of MODFETs, which exemplify their good pinchoff characteristics with an identical threshold voltage of 4 . 2 V  and a low knee volt- age. Structure A shows a drain current I, of 0.9Mmm at gate bias V,  of 0.6V and drain bias V, of lV, and structure B exhibits an Idr > 1 ” m  under the same bias condition. The typical transfer characteristics for devices based on these two structures are shown in Fig. 3. At V, = 1, the maximum extrinsic transconductance of structure B is 1.7Simm with an associated I, of O.SA/mm. For structure A at the same bias, the peak transconductance is reduced to 1.5S/mm with a decreased Ids of -0 .35”m.  Therefore struc- ture B exhibits a 10% improvement in transconductance compared with structure A. The device S-parameter characteristics were measured using a Cascade on-wafer probe station. Fig. 4 summa- rises the current gain lh21/2 and Mason unilateral power gain U, against frequency at V, = 1 and with the F<s for peak transcon- ductance. The f T  and fm,, obtained by extrapolating jh2112 and U, with -20dB/decade are 238 and 180GHz for structure B. This f r  value is 8% higher than that of structure A cf, = 220GHz). As suggested by the calculation, the performance improvement should 1976 ELECTRONICS LETTERS 1st October 1998 Vol. 34 No. 20 

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'Backgating' model including self-heating for low-frequency dispersive effects in III-V FETs

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