New Physical Understanding of the Resonant Tunneling Diode
Small-Signal Equivalent Circuit
Qingmin Liu and Alan Seabaugh
Department of Electrical Engineering, University of Notre Dame, IN 46556-5637
(574) 631-4473, Email: seabaugh.1@nd.edu
The resonant tunneling diode (RTD) stands as the highest speed, large-signal semiconductor
switching device with measured slew rates as high as 300 mV/ps [1]; the RTD continues to be
explored for use in triggers, quantizers, oscillators, and memory [e.g. 2]. Circuit designs using
tunnel diodes require an accurate small-signal equivalent circuit model and two simple equivalent
circuits are commonly used: a series-inductance model [3] and a parallel- inductance model [4].
The inductance which arises in the latter model is due to the charging of the quantum well [4-7].
These published models all assume the quantum inductance only exists when the RTD is biased
in the negative differential resistance region, and the capacitance only comes from the
geometrical capacitance. We report in this paper that the above two assumptions are incorrect.
We have de rived an analytic expression for the quantum inductance and capacitance which is bias
dependent and easily implemented into SPICE.
Our derivation parameterizes the sequential tunneling process between emitter and quantum well,
and quantum well and collector in terms of the quantum well and emitter charges and the
tunneling time constants. We show that it is possible to account for the charge build-up in the
well through the entire bias range of the device. We find that the quantum inductance is given by
L = τ / g, where τ is the electron lifetime in the quantum well, and g is the differential
conductance of the RTD. The change in the quantum well electron density also induces a change
in the image charge density in the collector that results in an additional quantum capacitance
which adds to the geometrical capacitance. The quantum capacitance is derived to be CQ = − g/v,
where v is the electron escape rate (s-1 ) from the quantum well to the collector. There is a sign
difference between our quantum capacitance model and the Broekaert model [2].
Both S-parameter measurement and DC current-voltage (I-V) measurement were made on 1.6 ×
1.6 µm2 AlAs/InGaAs/AlAs RTDs. S-parameters were measured from 45 MHz to 30 GHz using
an Agilent 8510XF vector network analyzer with a source power of –33 dBm. The inductance
and capacitance values in the equivalent circuit were extracted from fitting the measurement data.
The differential conductance values of the RTD are also extracted from S-parameter
measurements and agree closely to that of the derivatives of the DC I-V curve. The RF and DC
characterization support the model theory.
We would like to thank Prem Chahal, Frank Morris, and Gary Frazier (Raytheon) for supplying
the RTDs and Patrick Fay (Notre Dame) for valuable advice on the RF measurements. This work
was sponsored in part by a Raytheon University Research Grant and the Office of Naval
Research.
[1] E. Özbay, et al., IEEE Electron Dev. Lett. 14, 400-402 (1993).
[2] T. Broekaert, et al., IEEE J. Solid State Circ. 33, 1342-1349 (1998).
[3] J. M. Gering, et al., J. Appl. Phys. 61, 271-276 (1987).
[4] E. R. Brown, et al., Appl. Phys. Lett. 54, 934-936 (1989).
[5] P. Zhao, et al., IEEE Trans. Elect. Dev. 48, 614-626 (2001).
[6] W. Liou, et al., IEEE Trans. Elect. Dev. 41, 1098-1110 (1994).
[7] F. A. Buot, et al., Int. J. Comput. Math. Electr. Electron. Eng. 10, 241-253 (1991)
Differential Conductance (S)
Extracted from RF measurement
0.02
Extracted from DC measurement
0.015
0.01
0.005
0
-0.005
-0.01
0
0.2
0.4
0.6
0.8
Voltage (V)
Fig. 1. Resonant tunneling diode structure.
1
3q0604d
Fig. 5. Differential conductance vs. bias showing
good agreement between DC and RF
measurements.
0.005
2
Device Area: 1.6 x 1.6 µm
Current (A)
0.0025
0.008
-1
1 / L Q (pH )
0.004
-0.0025
-0.005
-1
-0.5
0
0.5
1
Voltage (V)
LQ
-0.002
-0.008
-0.2
Gd
0
0.2
0.4
0.6
0.8
Voltage (V)
1
3q0604d
Fig. 6. The reciprocal of the inductance vs. bias
showing good agreement of model with
measurement over bias.
Cp
0.01
Measurement
Simulation
0
11
-0.01
55
50
45
40
11
Im (S )
Re (S )
60
Capacitance (fF)
0.02
-0.2
Measurement
Simulation
65
Fig. 3. Parallel-inductance RTD equivalent
circuit model.
-0.24
0
-0.006
Rs
-0.22
0.002
-0.004
3q0604a
Fig. 2. RTD current-voltage characteristic.
Re (S1 1)
Measurement
Simulation
0.006
0
-0.26
-0.02
-0.28
Im (S )
-0.03
11
5
10
15
0
0.2
0.4
0.6
Voltage (V)
-0.3
0
35
-0.2
20
Frequency (GHz)
25
-0.04
30
3q0604b
Fig. 4. Measured and simulated S11 at a bias
voltage of V = 0.45 V (biased near the center of
the NDR region).
0.8
1
3q0604e
Fig. 7. Total capacitance vs. bias also showing
close agreement of model with measurement
over bias.