International Topical Meeting on Microwave Photonics, MWP 2005, pp. 133-136.The Generation of microwave signals by heterodyning two optical signals has been demonstrated in the past. However, so far this approach is limited in bandwidth, power and efficiency. In this paper we present an analysis of optical heterodyning in the uni-traveling carrier traveling wave photo detector taking into account the effect of ballistic electrons. The analysis is validated by comparison to measurement of an existing device made at the University of California, San Diego. Based on the above analysis a new photodiode design is made, which is expected to have a bandwidth well into the sub-MM wave region. The device exploiting the ballistic electrons effect can reach a bandwidth 2-3 times larger compared to device using velocity-saturated electrons

Herczfeld, Peter R.

Madjar, Asher

Rosen, Arye

Yu, Paul

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Exploiting Ballistic Electrons in a Uni-Traveling Carrier 
Traveling Wave Photo-Detector for Efficient Generation of 
Sub-MM Waves  
Asher Madjar*, Peter  R. Herczfeld*, Arye Rosen*, Paul Yu** 
* Drexel University, ECE Department, 32nd & Chestnut sts., Philadelphia, PA 19104 
** UCSD, ECE Department, San Diego, California 
 
ABSTRACT  —  The Generation of microwave signals 
by heterodyning two optical signals has been demonstrated 
in the past.  However, so far this approach is limited in 
bandwidth, power and efficiency. In this paper we present 
an analysis of optical heterodyning in the uni-traveling 
carrier traveling wave photo detector taking into account 
the effect of ballistic electrons.  The analysis is validated by 
comparison to measurement of an existing device made at 
the University of California, San Diego.  Based on the above 
analysis a new photodiode design is made, which is 
expected to have a bandwidth well into the sub-MM wave 
region. The device exploiting the ballistic electrons effect 
can reach a bandwidth 2-3 times larger compared to device 
using velocity-saturated electrons. 
Index Terms  —  photo detector, UTC, optical heterodyne, 
sub millimeter wave. 
I. INTRODUCTION 
The generation of microwave signals by heterodyning 
two optical signals has been proposed and demonstrated 
many years ago.    A photo detector, being a square law 
device, generates the sum and difference frequencies of 
the two optical carriers.  The difference frequency is the 
desired microwave signal.  The lasers can generate 
virtually any frequency difference, however, the photo 
detector limits the useful bandwidth. Experiments using 
this approach have been reported ([1]-[11]), which 
validate this method. However, the previously reported 
results exhibit very low output power, very low 
efficiency, and a limited useful bandwidth.  In this paper 
an analytic method, which takes into account the electron 
ballistic effect in a uni-traveling carrier traveling wave 
(UTC-TW) photo detector, is presented.  The predicted 
heterodyning bandwidth of this approach is validated by 
experimental results, and performance predictions for 
sub-MM wave device are presented. 
II. THE UTC-TW PD 
A few years ago the uni-traveling carrier traveling wave 
photo detector was introduced ([12]-[14]).  The structure 
of such a PD is depicted in Fig. 1 ([14]).  This device 
maintains the basic structure of a traveling wave PIN 
diode. However, there is a separation between the optical 
waveguide section and the absorption section.  The n 
layer serves as a waveguide, which is transparent to 1.55 
µm optical signal.  The absorption occurs in the p layer.  
The structure is designed in such a manner that most of 
the optical power propagates in the n layer, and only a 
small fraction of the power is coupled to the p absorption 
layer, where it is absorbed.  This device has the 
following advantages:  1) the optical power is absorbed 
in a distributed manner over an extended volume along 
the waveguide (reduced effective absorption coefficient) 
– resulting in increased optical saturation power;  2) the 
photo generated current is composed of electrons only – 
the holes are majority carriers in a p+ region – which 
translates into a significant improvement in speed (in InP 
the holes are very slow compared to electrons). 
 
InGaAsP( n,Q1.15 )
InGaAsP
(In,Q1.24 )
InGaAs(P)
InGaAsP( n,Q1.15 )
Pd/Ti/Pd /Au
Electrode Processs
InGaAs(P)
Semi-Insulating  InP
AuGe
AuGe
Polyimide Bridge
 
 
Fig. 1 Structure of UTC-TW PD 
 
III. BANDWIDTH CONSIDERATIONS 
Due to the traveling wave nature of the electrode design 
of the device, the RC time constant, which limits the 
bandwidth of lumped photo detectors, does not limit the 
bandwidth of the device considered here.  The main 
limitation to the bandwidth of the UTC-TW PD, which 
determines the maximum frequency that can be 
generated by heterodyning, is the electron transit time 
via the p absorption and I layers. The 3-dB bandwidth 
can be approximated by: 
 
f3db = 1/(2πτt)  (1) 
 
where τt is the electron transit time. The transit time is 
usually calculated by assuming that the electric field is 
large enough so that the electrons travel in the I layer at 
their saturated velocity (107 cm/s).  This assumption was 
tested experimentally on an existing device.  The current 
device, which was fabricated at the University of 
California, San Diego, has the following parameters: 
 
• P absorption layer thickness = 0.2 µm 
efficient = 1300 cm-1
 
ssuming that the electrons travel at saturated velocity, 
Fig. 2 Results of heterodyne experiment 
IV. THE BALLISTIC ELECTRONS EFFECT 
When electrons travel across thin layers of 
F=-qE=m*a=m*d2y/dt2  (2) 
where, m* is the electron effective mass, a is the 
In the second region, adjacent to the N layer, the 
• I layer thickness = 0.45 µm 
• Mesa width = 2.5 µm 
• Effective absorption co  
A
the expected bandwidth of this device is 30 GHz.  To 
verify this result, a heterodyne experiment was 
performed. Two optical signals from two phase locked 
lasers were combined in a fiber and side illuminated the 
device, which was placed on a probe station.  The 
difference frequency between the two lasers was 
changed and the measurement repeated up to 50 GHz.  
The results are depicted in Fig. 2. Due to the difficulty of 
coupling the light from the fiber to the small area of the 
optical waveguide, the detected response is small, 
however, the 3-dB bandwidth, which depends on the 
relative response, is clearly seen to be higher than 50 
GHz (interpolation of the graph in Fig. 2 yields a 3-dB 
bandwidth around 65-70 GHz). This bandwidth, which is 
substantially larger than the expected one (30 GHz) was 
initially “puzzling” (usually the measured results are 
worse than the simulated performance). This “surprise” 
clearly suggests that an important physical phenomenon 
is occurring in the device, which needs to be taken into 
account in the simulation. This physical phenomenon is 
the ballistic nature of electron transport in thin layers of 
semiconductors. The inclusion of this effect in the 
simulations produced results, which are in good 
agreement with the measured values. 
 
 
semiconductor, their transport is not governed by the 
well known velocity vs. electric field curve that is valid 
for equilibrium travel over a relatively long distance 
(long compared to the mean distance between 
collisions).  The ballistic effect has been included in the 
UTC-TW PD model in the following manner: The I layer 
is sub-divided into two regions, as shown in Fig. 3. The 
first region, which is adjacent to the p absorption layer, 
is termed the ballistic region. Here the electrons travel 
without collisions, with a low effective mass and the 
carrier transport is governed by the classical equations of 
motion: 
acceleration, E is the electric field, q is the charge of the 
carrier and y is the displacement. The electric field is 
calculated using Gauss’s law, including the photo 
generated space charge and the applied DC voltage. The 
above equation is solved for the electron velocity and 
displacement. This type of transport is maintained until 
the electrons reach the critical energy for inter-valley 
scattering (1 eV was used in the simulations).  The 
thickness of the ballistic region and the transit time 
through it are determined from this condition. 
Fig. 3 sub-division of the I layer 
electrons are assumed to travel at their saturated velocity.  
This two-region model is a reasonable approximation to 
model the ballistic electron effect and was employed in 
simulating the device described in section III above.  The 
3-dB bandwidth of the device is plotted in Fig. 4 vs. the 
optical input power. The optical power corresponding to 
the measurements in Fig. 2 (8.5 dBm=7.1 mW) is at the 
center of the graph in Fig. 4, which reveals a simulated 
bandwidth of 72 GHz.  This value is in good agreement 
with the measured data.  For this particular simulation 
the simulated thickness of the ballistic region is 0.35 µm, 
so that the saturated velocity region is only 0.1 µm. This 
fact explains the enhanced bandwidth of this particular 
device. 
microwave output power (Bias at 10V UTC-WIP, 05/15/03)
1.3 micron, 8.5 dbm
  (Measured by Tsai Sheng Liao)
-36
-35
-34
-33
-32
-31
-30
-29
-28
-27
-26
0 10 20 30 40 50 60
Frequency (GHz)
O
ut
pu
t P
ow
er
 (d
B
m
)
P absorption layer 
I layer – ballistic region 
I laye ion r – velocity saturation reg
N waveguide Layer 
 2
 Fig. 4 simulated bandwidth of existing device including 
the ballistic electrons effect 
V. POSSIBLE SUB-MM WAVE PHOTO DETECTOR 
This new model, which now includes the electron 
ballistic transport effect, has been used to investigate the 
limits of the UTC-TW PD bandwidth.  At this stage, no 
attempt was made to optimize the device bandwidth or 
other performance parameters (output power, efficiency, 
etc.).  Instead, the model was used to simulate the 
photodetector with very thin p absorption and I layers. 
The parameters and structure of the device used in this 
calculations are identical to the one described in section 
III, except that the p absorption layer thickness is now 
0.1 µm, the I layer thickness is 0.05 µm and the mesa 
width is 1 µm. These parameters are reasonable and can 
be implemented in practice (taking care to avoid p type 
dopant from diffusing into the I layer, i.e. use of Carbon). 
The simulated performance of this device is depicted in 
Figs. 5-7. Specifically, Fig. 5 depicts the output power vs. 
input optical power, Fig. 6 shows the power efficiency 
vs. DC voltage with several values of optical power. The 
efficiency is defined as the ratio of the output power 
divided by the sum of DC and optical powers. Finally, 
Fig. 7 depicts the 3-dB bandwidth of the detector vs. DC 
voltage for several values of optical power. The plots in 
Figs. 6 & 7 start from a minimum DC voltage, which 
depends on the optical power level. The minimum DC 
voltage is determined by two requirements: 1) amplitude 
of output microwave signal; 2) sufficient DC voltage to 
maintain the photo generated space charge and ensure 
that the electric field in the I layer exceeds the required 
minimum for velocity saturation.  Figs. 5 & 6 show that 
a single device may be capable of delivering a few mW 
of power at sub-MM waves with an efficiency of a few 
percent.  It should be noted that these results match the 
requirements  for radar and communication systems in 
this frequency range. To date, no semiconductor device 
has been demonstrated with similar performance. 
The results in Fig. 7 are of interest, and require 
explanation.  For all optical power levels, the bandwidth 
initially increases as the DC voltage is increased beyond 
the minimum voltage.  This trend continues up to a 
voltage of about 1 V (practically independent on optical 
power), where it reaches a peak of around 600 GHz. 
Beyond 1 V the bandwidth is reduced with increasing 
DC voltage. This tendency continues until a saturated 
value of slightly less than 400 GHz is reached.  This type 
of behavior is explained by the dependence of the 
ballistic region of the I layer on the DC voltage.  For low 
DC voltage the electric field in the I layer is relatively 
low, and it takes a longer distance for the electrons to 
acquire the critical energy for inter valley scattering.  So, 
the ballistic region extend over most or even all of the I 
layer. The simulations show that for DC voltages up to 
almost 1 V the entire I layer is a ballistic region.  Beyond 
that, the ballistic region is reduced with increasing 
voltage, and occupies only part of the I layer.  The 
simulation shows ballistic region of 35 nm (out of total I 
layer of 50 nm) for DC voltage of 1.8 V.  Outside the 
ballistic region the electrons travel slower, so the transit 
time increases and the bandwidth is reduced. 
The bandwidth predicted in Fig. 7 for this device is very 
high.  We expect that the practical device, due to 
practical constraints will have lower bandwidth.  
However, these simulations indicate the potential of 
UTC-TW PD to operate in the sub-MM range. 
VI. CONCLUSION 
In this paper the bandwidth limitations of the UTC-TW 
photo detector have been investigated.  It was 
demonstrated that in order to correctly simulate the 
performance of this device, it is necessary to take into 
account the electron ballistic effect.  Neglecting this 
effect, results in under estimation of the bandwidth. 
Preliminary simulations indicate that this device has the 
potential of direct generation of sub-MM wave signals 
by heterodyning two optical signals. 
ACKNOWLEDGEMENT 
This work was supported by the USA Defense Advanced 
Research Projects Agency (DARPA) and ONR under 
contract number N00014-00-1-0781 mod 5. The 
photodiode was designed and fabricated by T.S. Liao at 
UCSD. 
REFERENCES 
1. Andreas Stöhr,, Andrei Malcoci, et. al., “Ultra-Wideband 
Traveling-Wave Photodetectors for Photonic Local 
Oscillators”, IEEE J. Lightwave Tech.,  pp. 3062-3070, Dec. 
2003 
2. Andreas Stohr, et al.,”THz Photomixing Employing 
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Symposium, June 2004, Fort Worth, USA. 
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3. Andrei Malcoci, el al., “Optical Submillimeter-Wave 
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13. M. Yuda, K. Kato, et al., “High-Input-Power 
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International Microwave Symposium, June 2003, 
Philadelphia, USA. 
 
 
 
 
Fig. 5 simulated high frequency UTC-TW PD output 
power 
 
 
 
Fig. 6 simulated high frequency UTC-TW PD power 
efficiency 
 
 
 
Fig. 7 simulated high frequency UTC-TW PD bandwidth 
 
 4


Exploiting ballistic electrons in a uni-traveling carrier traveling wave photo-detector for efficient generation of sub-MM waves

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Exploiting ballistic electrons in a uni-traveling carrier traveling wave photo-detector for efficient generation of sub-MM waves

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