For AlGaN/GaN high electron mobility transistors (HEMTs), the voltage and current waveforms at CW large-signal operation at 5 GHz have been reconstructed from experimental magnitude and phase information on fundamental and higher harmonics of transmitted and reflected signals. To compare with the DC behaviour, the clipped waveforms have accurately been analysed to recover the dynamic output characteristics in view of dispersion effects related to self-heating. In conjunction with small-signal S-parameter data, the large-signal experimental results have been used in an attempt to apply a HEMT large-signal model, showing satisfactory agreement of simulated and measured characteristics at least in regions where self-heating is not much pronounced

Berroth, M.

Breitschädel, O.

Chigaeva, E.

Grözing, M.

Kuhn, B.

Off, J.

Roll, H.

Scholz, F.

Schweizer, H.

Walthes, W.

Wieser, N.

English

AMS Acta

DYNAMIC LARGE-SIGNAL I-V ANALYSIS AND NON-LINEAR MODELLING OFALGAN/GAN HEMTSE. Chigaeva*, N. Wieser*, W. Walthes*, M. Grözing*, and M. Berroth*H. Roll**, O. Breitschädel**, J. Off**, B. Kuhn**, F. Scholz**, and H. Schweizer*** Institute of Electrical and Optical Communication Engineering, University of Stuttgart, Pfaffenwaldring 47,D-70569 Stuttgart, Germany, Tel.: +49 711 685 7912, Fax: +49 711 685 7900,e-mail: nikolai.wieser@int.uni-stuttgart.de**Physics Department, 4th Institute, University of Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, GermanyABSTRACTFor AlGaN/GaN high electron mobility transistors (HEMTs), the voltage and current waveforms atCW large-signal operation at 5 GHz have been reconstructed from experimental magnitude and phaseinformation on fundamental and higher harmonics of transmitted and reflected signals. To compare with theDC behaviour, the clipped waveforms have accurately been analysed to recover the dynamic outputcharacteristics in view of dispersion effects related to self-heating. In conjunction with small-signal S-parameter data, the large-signal experimental results have been used in an attempt to apply a HEMT large-signal model, showing satisfactory agreement of simulated and measured characteristics at least in regionswhere self-heating is not much pronounced.I. INTRODUCTIONIt turned out that strong internal electric fields due to spontaneous and piezoelectric polarisations areresponsible for the formation of the two-dimensional electron gas at the AlGaN/GaN interface of respectiveHEMT structures, showing a sheet carrier concentration up to 2.0⋅1013 cm-2 for Al mole fractions of 30%even without any additional doping (1). Although this and many other basic properties of nitride-basedHEMTs are well understood by now, the origin of the so-called power compression or power slump, i.e. alower RF-power than expected from DC-performance, is still an open question (2, 3). Dispersion may alsoarise from self-heating effects due to the sapphire substrate which has worse thermal conductivity but atlower cost than SiC. Comparatively less efforts have yet been done in the field of large-signal modelling inview of circuit design (4).In this paper, we present results of both large-signal experimental analysis and modelling. A microwavetransition analyser was used to measure the magnitude and phase of the fundamental and four higherharmonics of transmitted and reflected signals, yielding the RF time domain waveform information and thusthe RF large-signal transfer and output characteristics (5, 6). Due to the above mentioned discrepanciesbetween DC and RF operation, these dynamic experimental data appear to be more appropriate to be used formodelling purposes. For this, a first attempt to apply a HEMT large-signal model, which describes thecurrent source and non-linear capacitances by analytical equations (6, 7), is presented finally. The transistorunder investigation consisted of a Al(0.30)Ga(0.70)N/GaN (30nm/2µm) heterostructure with an additionalGaN cap layer on top of the barrier, grown on sapphire substrate by metal organic vapour phase epitaxy. Thegate length and width were 1 and 250 µm, respectively. Details on the metalization process may be found in(8).II. EXPERIMENTAL RESULTSFigure 1 shows the dynamic large signal transfer characteristics and respective waveforms (i.e., gatevoltage, Vgs, and drain current, Ids) measured at 5 GHz and various input power levels. The time delaybetween the input and output signals has been corrected according to ref. (9). As in the case of GaAsMODFETs (6), the transfer characteristics does not significantly depend on the input power except thevarying current swing. With increasing input power, i.e. with increasing contribution of higher harmonicsdue to compression, the time delay correction used becomes more and more inaccurate and thus  the Ids-Vgs-trajectory becomes a loop.These measurements have been performed step by step at various drain voltages, Vds, but constantVgs = -2.5 V and constant power levels, and the resulting data used to reconstruct the dynamic outputcharacteristics to compare with the DC I-V’s. Focussing on self-heating related dispersion, we restricted ourmeasurements to an input voltage swing up to Vgs = –0.5 V where the channel is not fully open and thereforepossible open channel current compression at RF operation, see e.g. (2), should not be pronounced.As shown in Figure 2, the current deduced from the power data is somewhat lower at low Vds due to self-biasing (5) at this input power level (region A in Figure 2). At increased Vds and increased Vgs the RF currentexceeds that observed at DC conditions due to reduced or even vanishing self-heating in the dynamic case(region B). The negative output conductance in the dynamic case is determined by the slope of that tracealong which the biasing has been performed (here, Vgs = -2.5 V). It should be noted that the additional RF-power is only a fractional amount of the DC-power (e.g. 15 mW vs 600 mW at Vds = 16 V and Vgs = -2.5 V).Reconstruction of the dynamic output characteristics has to be done carefully, since it depends on the powerlevel: If at low Vds  the RF input voltage amplitude is close to the cut-off boundary and biasing is performedstep by step to higher Vds along a trace with large negative output conductance, the amplitude successivelyexceeds the cut-off boundary and therefore the resulting current will successively increase due to self-biasing(increasing asymmetrical waveform clipping with increasing exceed of the cut-off boundary).Since heating leads to dispersion, large-signal modelling consequently requires rather data close to realoperating conditions, i.e. the dynamic RF power data, than DC results (5, 6) for a proper description insimulation tools.III. MODELLINGThe large-signal model includes parasitic elements and the intrinsic transistor with three nonlinear currentsources and two nonlinear capacitances. The gate current (gate-source and gate-drain current sources) ismodelled by a usual Schockley diode equation, whereas for the drain current source the expression (1),which is divided into three parts separately accounting for the transfer behaviour (f1), output conductance (f2)as well as the triode region (f3), is used:( ) ( ) ( ) ( )( ) ( ) ( )[ ]( ) ([(( ) ( )( ) ( )dsiVdsiVfcVtoVwithdsiVtoVgsiVdsiVgsiVfsVgsiVvsbCDcVgsiVcVgsiVvcCDgsiVfdsiVfdsiVgsiVfgsiVfdsiVgsiVdsI⋅=−=⋅−⋅∆++=−⋅+⋅+−⋅+−⋅+⋅=⋅⋅=αβλλδγβtanh32,211,2tanh13tanh113,21,The description of the equivalent circuit and these basic analytical equations may be found in refs. (6, 7the model parameter extraction the already presented RF output characteristics was used. Small-signparameter measurements have been performed first (i) to extract the parasitic elements as well as (determine the gate voltage dependence of the non-linear gate capacitance at Vds = 0 V and (iii) to findcharge distribution at different drain voltages for analytical fitting of the parameters. Better agreebetween simulated and measured S-parameters was achieved using the RF output characteristics insteDC data for the model parameter extraction. In the RF case the negative character of  the output conducis not so pronounced, since self-heating is a low frequency phenomenon and cannot be observed duriparameter measurements. As an example, we show in Figure 3 the resulting output characteristics, wreveal satisfactory agreement despite the fact that thermal effects have not yet been taken into account.(1))])b)iatn(4).ai ma(3)(2) Forl S-) togateentd ofnceg S-hichIV. CONCLUSIONThe combination of power measurement results obtained by the use of a microwave transitionanalyser with an analytical large-signal model was demonstrated for nitride-based HEMTs. For these devicesshowing dispersion effects, this combination appears in particular convincingly. The large-signal model usedhas to be improved by implementing thermal effects to account for the negative output conductance. Furtherwork concentrates also on simulations such as gain or output power of fundamental and higher harmonics,whereby the latter are also experimentally available by use of the microwave transition analyser.ACKNOWLEDGEMENTFinancial support by Forschungsschwerpunkt Baden-Württemberg is gratefully acknowledged.REFERENCES(1) O. Ambacher, J. Smart, J.R. Shealy, N.G. Weimann, K. Chu, M. Murphy, W.J. Schaff, L.F. Eastman, R.Dimitrov, L. Wittmer, M. Stutzmann, W. Rieger, and J. Hilsenbeck; Two-dimensional Electron GasesInduced by Spontaneous and Piezoelectric Polarisation Charges in N- and Ga-Face AlGaN/GaNHeterostructures; 1999; J. Appl. Phys. 85, 3222-3233.(2) E. Kohn, I. Daumiller, P. Schmid, N.X. Nguyen, and C.N. Nguyen; Large Signal Frequency Dispersionof AlGaN/GaN Heterostructure Field Effect Transistors; 1999; Electr. Lett. 35, 1022-1024.(3) B.M. Green, K.K. Chu, M. Chumbes, J.A. Smart, J.R. Shealy, and L. Eastman; The Effect of SurfacePassivation on the Microwave Characteristics of Undoped AlGaN/GaN HEMT’s; 2000;  IEEE Electr.Device Lett. 21, 268-270.(4) B. Green, H. Kim, V. Tilak, J.R. Shealy, J.A. Smart, L.F. Eastman; Validation of an Analytical LargeSignal Model for AlGaN/GaN HEMT’s on SiC Substrates; 2000; Seventeenth Biennal IEEE/CornellUniversity Conference on Advanced Concepts in High Performance Devices.(5) P.J. Tasker, M. Demmler, M. Schlechtweg, and M. Fernandez Barciela; Novel Approach to theExtraction of Transistor Parameters from Large Signal Measurements; 1994; 24th European MicrowaveConference, pp. 1301-1306.(6) M. Demmler, P.J. Tasker, J.G. Leckey, and M. Schlechtweg; The Determination of the TransistorDynamic I-V Characteristics from Large Signal RF Measurements; 1995; 25th European MicrowaveConference, pp. 553-557, and references therein.(7) M. Berroth, “Schaltkreissimulator für Heterostrukturfeldeffekttransistoren”, Dissertation Ruhr-Universität Bochum (1991).(8) O. Breitschädel, H. Gräbeldinger, B. Kuhn, F. Scholz, W. Walthes, M. Berroth, I. Daumiller, K.B. Schad,E. Kohn, H. Schweizer; Short-channel AlGaN/GaN HEMTs with 70 nm T-gate; 1999; Electronic Letters 35,2018-2019.(9) M. Demmler, ”Vektorkorrigiertes Großsignal-Meßsystem zur nichtlinearen Charakterisierung vonMikrowellentransistoren”, Dissertation Universität Karlsruhe (1996).0 100 200 300 400020406080I ds (mA) t (ps)0 100 200 300 400-5-4-3-2-105.5 dBm8.6 dBm11.7 dBmV gs (V) t (ps)-5 -4 -3 -2 -1 0020406080Vds =   5    VVgs =  -2.5 V5 GHz 11.7 dBm  8.6 dBm  5.5 dBmI ds (mA)Vgs (V)Figure 1: (a) Input voltage and outputcurrent  waveforms  at  various powerlevels (Vds = 5 V, Vgs = -2.5 V, 5 GHz)and (b) respective transfer characteristics.0 2 4 6 8 10 12 14 16 18020406080100-0.5 V-1 V-4.5 V-4 V-3.5 V-3 V-2.5 V-2 V-1.5 V RF DCI ds (mA)Vds (V)Region ARegion B Figure 2: Comparison of DC-outputcharacteristics  and  dynamic outputcharacteristics  deduced from powermeasurements(11.7 dBm input power @ 5 GHz).For regions A and B, see text.0 2 4 6 8 10 12 14 16 18020406080100 RF data     Simulation Vgs-0.5 V-1 V-4.5 V-4 V-3.5 V-3 V-2.5 V-2 V-1.5 VI ds (mA)Vds (V)Figure 3: Comparison ofexperimental RF-outputcharacteristics and large-signalsimulation.The simulation is based onRF data.(a) (b)

Dynamic large-signal I-V analysis and non-linear modelling of

ALGAN/GAN HEMTS

Crossref

Dynamic Large-Signal I-V Analysis and Non-Linear Modelling of Algan/Gan HEMTS

AMS Acta - Alm@DL - Università di Bologna

DYNAMIC LARGE-SIGNAL I-V ANALYSIS AND NON-LINEAR MODELLING OF
ALGAN/GAN HEMTS
E. Chigaeva*, N. Wieser*, W. Walthes*, M. Grözing*, and M. Berroth*
H. Roll**, O. Breitschädel**, J. Off**, B. Kuhn**, F. Scholz**, and H. Schweizer**
* Institute of Electrical and Optical Communication Engineering, University of Stuttgart, Pfaffenwaldring 47,
D-70569 Stuttgart, Germany, Tel.: +49 711 685 7912, Fax: +49 711 685 7900,
e-mail: nikolai.wieser@int.uni-stuttgart.de
**Physics Department, 4th Institute, University of Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany
ABSTRACT
For AlGaN/GaN high electron mobility transistors (HEMTs), the voltage and current waveforms at
CW large-signal operation at 5 GHz have been reconstructed from experimental magnitude and phase
information on fundamental and higher harmonics of transmitted and reflected signals. To compare with the
DC behaviour, the clipped waveforms have accurately been analysed to recover the dynamic output
characteristics in view of dispersion effects related to self-heating. In conjunction with small-signal S-
parameter data, the large-signal experimental results have been used in an attempt to apply a HEMT large-
signal model, showing satisfactory agreement of simulated and measured characteristics at least in regions
where self-heating is not much pronounced.
I. INTRODUCTION
It turned out that strong internal electric fields due to spontaneous and piezoelectric polarisations are
responsible for the formation of the two-dimensional electron gas at the AlGaN/GaN interface of respective
HEMT structures, showing a sheet carrier concentration up to 2.0⋅1013 cm-2 for Al mole fractions of 30%
even without any additional doping (1). Although this and many other basic properties of nitride-based
HEMTs are well understood by now, the origin of the so-called power compression or power slump, i.e. a
lower RF-power than expected from DC-performance, is still an open question (2, 3). Dispersion may also
arise from self-heating effects due to the sapphire substrate which has worse thermal conductivity but at
lower cost than SiC. Comparatively less efforts have yet been done in the field of large-signal modelling in
view of circuit design (4).
In this paper, we present results of both large-signal experimental analysis and modelling. A microwave
transition analyser was used to measure the magnitude and phase of the fundamental and four higher
harmonics of transmitted and reflected signals, yielding the RF time domain waveform information and thus
the RF large-signal transfer and output characteristics (5, 6). Due to the above mentioned discrepancies
between DC and RF operation, these dynamic experimental data appear to be more appropriate to be used for
modelling purposes. For this, a first attempt to apply a HEMT large-signal model, which describes the
current source and non-linear capacitances by analytical equations (6, 7), is presented finally. The transistor
under investigation consisted of a Al(0.30)Ga(0.70)N/GaN (30nm/2µm) heterostructure with an additional
GaN cap layer on top of the barrier, grown on sapphire substrate by metal organic vapour phase epitaxy. The
gate length and width were 1 and 250 µm, respectively. Details on the metalization process may be found in
(8).
II. EXPERIMENTAL RESULTS
Figure 1 shows the dynamic large signal transfer characteristics and respective waveforms (i.e., gate
voltage, Vgs, and drain current, Ids) measured at 5 GHz and various input power levels. The time delay
between the input and output signals has been corrected according to ref. (9). As in the case of GaAs
MODFETs (6), the transfer characteristics does not significantly depend on the input power except the
varying current swing. With increasing input power, i.e. with increasing contribution of higher harmonics
due to compression, the time delay correction used becomes more and more inaccurate and thus  the Ids-Vgs-
trajectory becomes a loop.
These measurements have been performed step by step at various drain voltages, Vds, but constant
Vgs = -2.5 V and constant power levels, and the resulting data used to reconstruct the dynamic output
characteristics to compare with the DC I-V’s. Focussing on self-heating related dispersion, we restricted our
measurements to an input voltage swing up to Vgs = –0.5 V where the channel is not fully open and therefore
possible open channel current compression at RF operation, see e.g. (2), should not be pronounced.
As shown in Figure 2, the current deduced from the power data is somewhat lower at low Vds due to self-
biasing (5) at this input power level (region A in Figure 2). At increased Vds and increased Vgs the RF current
exceeds that observed at DC conditions due to reduced or even vanishing self-heating in the dynamic case
(region B). The negative output conductance in the dynamic case is determined by the slope of that trace
along which the biasing has been performed (here, Vgs = -2.5 V). It should be noted that the additional RF-
power is only a fractional amount of the DC-power (e.g. 15 mW vs 600 mW at Vds = 16 V and Vgs = -2.5 V).
Reconstruction of the dynamic output characteristics has to be done carefully, since it depends on the power
level: If at low Vds  the RF input voltage amplitude is close to the cut-off boundary and biasing is performed
step by step to higher Vds along a trace with large negative output conductance, the amplitude successively
exceeds the cut-off boundary and therefore the resulting current will successively increase due to self-biasing
(increasing asymmetrical waveform clipping with increasing exceed of the cut-off boundary).
Since heating leads to dispersion, large-signal modelling consequently requires rather data close to real
operating conditions, i.e. the dynamic RF power data, than DC results (5, 6) for a proper description in
simulation tools.
III. MODELLING
The large-signal model includes parasitic elements and the intrinsic transistor with three nonlinear current
sources and two nonlinear capacitances. The gate current (gate-source and gate-drain current sources) is
modelled by a usual Schockley diode equation, whereas for the drain current source the expression (1),
which is divided into three parts separately accounting for the transfer behaviour (f1), output conductance (f2)
as well as the triode region (f3), is used:
( ) ( ) ( ) ( )
( ) ( ) ( )[ ]( ) ([(
( ) ( )
( ) ( )dsiVdsiVf
cVtoVwithdsiV
toVgsiV
dsiVgsiVf
sVgsiVvsbCDcVgsiVcVgsiVvcCDgsiVf
dsiVfdsiVgsiVfgsiVfdsiVgsiVdsI
⋅=
−=⋅
−⋅∆+
+=
−⋅+⋅+−⋅+−⋅+⋅=
⋅⋅=
α
βλ
λ
δγβ
tanh3
2
,21
1,2
tanh13tanh11
3,21,
The description of the equivalent circuit and these basic analytical equations may be found in refs. (6, 7
the model parameter extraction the already presented RF output characteristics was used. Small-sign
parameter measurements have been performed first (i) to extract the parasitic elements as well as (
determine the gate voltage dependence of the non-linear gate capacitance at Vds = 0 V and (iii) to find
charge distribution at different drain voltages for analytical fitting of the parameters. Better agree
between simulated and measured S-parameters was achieved using the RF output characteristics inste
DC data for the model parameter extraction. In the RF case the negative character of  the output conduc
is not so pronounced, since self-heating is a low frequency phenomenon and cannot be observed duri
parameter measurements. As an example, we show in Figure 3 the resulting output characteristics, w
reveal satisfactory agreement despite the fact that thermal effects have not yet been taken into account.(1))])b
)
i
a
t
n(4).
a
i
 
m
a(3)(2) For
l S-
) to
gate
ent
d of
nce
g S-
hich
IV. CONCLUSION
The combination of power measurement results obtained by the use of a microwave transition
analyser with an analytical large-signal model was demonstrated for nitride-based HEMTs. For these devices
showing dispersion effects, this combination appears in particular convincingly. The large-signal model used
has to be improved by implementing thermal effects to account for the negative output conductance. Further
work concentrates also on simulations such as gain or output power of fundamental and higher harmonics,
whereby the latter are also experimentally available by use of the microwave transition analyser.
ACKNOWLEDGEMENT
Financial support by Forschungsschwerpunkt Baden-Württemberg is gratefully acknowledged.
REFERENCES
(1) O. Ambacher, J. Smart, J.R. Shealy, N.G. Weimann, K. Chu, M. Murphy, W.J. Schaff, L.F. Eastman, R.
Dimitrov, L. Wittmer, M. Stutzmann, W. Rieger, and J. Hilsenbeck; Two-dimensional Electron Gases
Induced by Spontaneous and Piezoelectric Polarisation Charges in N- and Ga-Face AlGaN/GaN
Heterostructures; 1999; J. Appl. Phys. 85, 3222-3233.
(2) E. Kohn, I. Daumiller, P. Schmid, N.X. Nguyen, and C.N. Nguyen; Large Signal Frequency Dispersion
of AlGaN/GaN Heterostructure Field Effect Transistors; 1999; Electr. Lett. 35, 1022-1024.
(3) B.M. Green, K.K. Chu, M. Chumbes, J.A. Smart, J.R. Shealy, and L. Eastman; The Effect of Surface
Passivation on the Microwave Characteristics of Undoped AlGaN/GaN HEMT’s; 2000;  IEEE Electr.
Device Lett. 21, 268-270.
(4) B. Green, H. Kim, V. Tilak, J.R. Shealy, J.A. Smart, L.F. Eastman; Validation of an Analytical Large
Signal Model for AlGaN/GaN HEMT’s on SiC Substrates; 2000; Seventeenth Biennal IEEE/Cornell
University Conference on Advanced Concepts in High Performance Devices.
(5) P.J. Tasker, M. Demmler, M. Schlechtweg, and M. Fernandez Barciela; Novel Approach to the
Extraction of Transistor Parameters from Large Signal Measurements; 1994; 24th European Microwave
Conference, pp. 1301-1306.
(6) M. Demmler, P.J. Tasker, J.G. Leckey, and M. Schlechtweg; The Determination of the Transistor
Dynamic I-V Characteristics from Large Signal RF Measurements; 1995; 25th European Microwave
Conference, pp. 553-557, and references therein.
(7) M. Berroth, “Schaltkreissimulator für Heterostrukturfeldeffekttransistoren”, Dissertation Ruhr-
Universität Bochum (1991).
(8) O. Breitschädel, H. Gräbeldinger, B. Kuhn, F. Scholz, W. Walthes, M. Berroth, I. Daumiller, K.B. Schad,
E. Kohn, H. Schweizer; Short-channel AlGaN/GaN HEMTs with 70 nm T-gate; 1999; Electronic Letters 35,
2018-2019.
(9) M. Demmler, ”Vektorkorrigiertes Großsignal-Meßsystem zur nichtlinearen Charakterisierung von
Mikrowellentransistoren”, Dissertation Universität Karlsruhe (1996).
0 100 200 300 400
0
20
40
60
80
I ds
 (m
A) t (ps)
0 100 200 300 400
-5
-4
-3
-2
-1
0
5.5 dBm
8.6 dBm
11.7 dBm
V g
s (
V) t (ps)
-5 -4 -3 -2 -1 0
0
20
40
60
80
Vds =   5    V
Vgs =  -2.5 V
5 GHz
 11.7 dBm
  8.6 dBm
  5.5 dBmI ds
 (m
A)
Vgs (V)
Figure 1: (a) Input voltage and output
current  waveforms  at  various power
levels (Vds = 5 V, Vgs = -2.5 V, 5 GHz)
and (b) respective transfer characteristics.
0 2 4 6 8 10 12 14 16 18
0
20
40
60
80
100
-0.5 V
-1 V
-4.5 V
-4 V
-3.5 V
-3 V
-2.5 V
-2 V
-1.5 V
 RF
 DC
I ds
 (m
A)
Vds (V)Region A
Region B Figure 2: Comparison of DC-output
characteristics  and  dynamic output
characteristics  deduced from power
measurements
(11.7 dBm input power @ 5 GHz).
For regions A and B, see text.
0 2 4 6 8 10 12 14 16 18
0
20
40
60
80
100
 RF data     Simulation Vgs
-0.5 V
-1 V
-4.5 V
-4 V
-3.5 V
-3 V
-2.5 V
-2 V
-1.5 V
I ds
 (m
A)
Vds (V)
Figure 3: Comparison of
experimental RF-output
characteristics and large-signal
simulation.
The simulation is based on
RF data.
(a) (b)


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Dynamic large-signal I-V analysis and non-linear modelling of ALGAN/GAN HEMTS

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