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A gallium doped germanium heterodyne detector for FIR plasma diagnostics
Infrrmi Printed
P/w. Vol. 23, No. 5. pp. 247-255. in &eat Britain. All rights reserved
A GALLIUM DETECTOR
1983 Copyright
0020-0891183 $3.00 + 0.00 ~(8 1983 Pergamon Press Ltd
DOPED GERMANIUM HETERODYNE FOR FIR PLASMA DIAGNOSTICS
T. KOIZUMI and K. NAGASAKA Department of Physics. Science University of Tokyo, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162, Japan (Rrceired
I June 1983)
Abstract-First, the video response and heterodyne response of a photoconductive detector, particularly in the far-infrared (FIR) region are discussed. Subsequently, the relation between the noise equivalent power in the video mode, NEP,, and that in the heterodyne mode, NEP,, is derived. It is shown that a signal noise due to a local oscillator beam in the heterodyne detection cannot be the main noise. Our experiments using a gallium doped germanium (Ge(Ga)) heterodyne detector at 118.8 pm have achieved an NEP, as low as 2.4 x IO-” W/Hz in the case where the local oscillator power was 2.6 mW and the beat frequency was I MHz. It is also shown that by further optimizing the optical system, we might even attain an NEP, of 1.6 x IO-” J or W/Hz, which is the energy of one photon at 118.8 pm. This detector has been successfully applied to the plasma diagnostics system of the JIPP T-II tokamak to determine electron density.
1. INTRODUCTION
Gallium doped germanium (Ge(Ga)), one of the excellent materials for FIR detection at wavelengths around 100 pm due to its low noise and high sensitive performance, was investigated by Moore et al.“’ Recently, the need for fast and sensitive heterodyne detection in the FIR region has arisen in plasma diagnostics”) as well as in astronomy. Seib c3)has demonstrated practicability of FIR heterodyne detection using a Ge(Ga) detector. The noise equivalent power in heterodyne mode detection (NEP,) was 6 x lo-l6 W/Hz for the local oscillator power of 2 x IO-‘W. More recently, Dodel ef u/.‘~’ reported on the applicability of a gallium doped and antimony doped germanium (Ge (Ga, Sb)) heterodyne receiver to plasma scattering diagnostics. They achieved an NEPh of 2 x lo-” W/Hz for 100 mW of local oscillator power. Moreover, they calculated the shot noise limited NEP, of 8 x 1O-2o W/Hz for a wavelength of 67 pm.(5) Unfortunately, however, none of those authors have fully investigated the way to determine the optimum condition for the parameters covering the heterodyne detection in FIR region, such as local oscillator power, detector bias voltage, dominant noise source and optical system. No Ge(Ga) photoconductive detector has so far attained the limiting performance of heterodyne detectors whose minimum detectable signal power reaches down to 1.6 x IO-*’ W/Hz, or an energy equivalent to that of one photon at 1 IS.8 pm. The detector we shall describe in this paper was prepared to operate on the twin CH,OH laser interferometer system employed in order to determine the electron density of JIPP T-II tokamak.@) In the present paper, we report on the construction of an FIR detector and FIR interferometer, and on the observations of the heterodyne beat signals at 118.8 pm. We also develop a basic theory for the characteristics of an FIR heterodyne detector at the wavelength N 100 ,um. The conditions under which our detector was operated and the results thereby obtained on JIPP T-II tokamak are examined on the basis of this theory. 2.
EXPERIMENTAL
DETAILS
AND
RESULTS
We employed a Ge(Ga) sample with the impurity concentration of 2 x 10’4cm-3 the photoconductive responses. The size of the sample was 2 x 3 x 1 mm3. The FIR directed onto the 2 x 3 mm* face. The sample was moderately wedged in order interference of radiation reflected by two surfaces. The sample was lapped with powder, chemically polished with a 5:3:3:0.06 mixture of HNO,:HF:CH,COOH:Br with methanol. Ohmic contacts were made of pure indium metal with a supersonic 247
for obtaining radiation was to avoid the Carborundum and rinsed soldering iron.
24X
/Cold /Heat
filter anchor
Figure 1 shows a cryostat for the detector with two elements.“’ These elements were mounted on sapphire plates of thickness 0.2 mm which were adhered to the bottom of the liquid helium vessel. Sapphire is one of the rare materials that act as good electrical insulators as well as good thermal conductors at liquid helium temperature. We chose to electrically isolate the elements from the cryostat metal, though this is not compulsory, in order to allow a larger versatility in the selection and design of the preamplifier circuit. The cryostat was made of metal to minimize the length of the transmission wires from the photoconductor to the preamplifier and to avoid induction noise. The FIR radiation was introduced into the cryostat through a polyethylene window. A set 01 entrance apertures of 8 mm diameter was placed at the entrance to an integrating cavity. A black polyethylene sheet and a crystal quartz plate were employed as cold filters. The photoconductive signals were fed into a current mode preamplifier or voltage mode preamplifier which was set at the nearest position to the detector element to minimize the leak of signals through stray capacitance and to avoid induction noise due to the transmission wires. The capacitance of the wires was approximately 5 pF. The preamplifiers were made of an operational amplifier. The temperature of the elements was found to be 6.7 K even under the background radiation in the wavenumber range up to 250cm-‘. The resistivity of the element was 67&m with an optimum bias field of 1.7 V/cm under the background radiation through the filters, despite the fact that the resistivity of the sample is normally about I OhRem at 6.7 K in dark: Ix1the background radiation enhances the free carriers from the impurity states to the valence band, so that the resistivity of the sample is reduced. The photoresponse of the detector element was measured at a wavelength of 118.8 pm. The effective current responsivity, referring to the FIR power reaching the detector window rather than the FIR power absorbed by the elements. turned out to be 0.4 A/W. As shown in Fig. 2, the noise level of the detector system including the preamplifier was obtained using a fast lock-in amplifier (PAR Model 5202). The detector element was also irradiated by the FIR laser beam in order to observe the signal noise. The measurement was carried out with a time constant of 10 msec, corresponding to 50 Hz of the bandwidth. and at the reference frequency ot 1 MHz, corresponding to the modulation frequency adopted in the CH,OH laser interferometer system for plasma diagnostics. The observed output noise voltage was 2.8 /IV’. As the voltage gain
A heterodyne
detector
Beam splitter
Pyroelectric
r-l
249
diagnostics
Oscillator
*
detector
for plasma
I
I
I FIR
laser
Fig. 2. Block diagram
of a noise measurement
system
of the preamplifier is 100, the noise power is 7.8 x lOm’9 W at the input of the preamplifier. This noise is the preamplifier noise itself. On the other hand, we were unable to detect a signal noise because the maximum power of the FIR laser was only a few milliwatts. The noise of the preamplifier was larger than that of the photoconductor. The noise equivalent power in video mode (NEP,) at 118.8 pm was 1.0 x lo-” W/Hz”’ with the effective current responsivity of 0.4 A/W (effective voltage responsivity of 400 V/W) and the input noise voltage of 4 x 10e9 V/Hz”‘. The heterodyne detection system is shown in Fig. 3. We used a CH,OH laser pumped with a CO, laser beam at 9.7 pm. Laser (1) lased at 118.8 pm corresponding to an angular frequency w, and laser (2) at 118.8 - Ai. pm corresponding to a slightly shifted angular frequency w2 (= o), + Ao). By detuning both cavity lengths, the FIR laser lased at the two frequencies differing by Ao/27r Hz within the frequency range of 10 MHz. The two FIR beams were combined on the crystal quartz beam splitter and directed onto the photoconductive detector element. A beat signal with a frequency A~/271 Hz was generated in the detector element. The amplified signals were led directly to an oscilloscope. A fast storage oscilloscope (Textronics Model 466) was used to record the beat signals. Figure 4 is an oscilloscope trace of the heterodyne signal obtained at the detector output at the signal beam radiation power of 1.3 x 10m9 W. The bandwidth of the amplifier was 5 MHz. The local oscillator power was 2.6 x 10-l W. Figure 5 shows the observed heterodyne signal-to-noise ratio as a function of the signal beam radiation power P, for a given local oscillator power P,,. The beat signals and the noises were measured by using a fast lock-in amplifier with 50 Hz of the bandwidth at 1 MHz of the reference frequency. Various values of P, and P,, were obtained by inserting in the beam a calibrated attenuator made of black polyethylene sheets. As described by equation (9) in the next section, the beat signal is proportional to the square root of the product
FIR
G&a
laser(2)
detector
cop
OLm
laser
Oscilloscope
Fig. 3. FIR interferometry system. B, indicates ZnSe beam splitter; B?, crystal quartz beamsplitter; W,, KCI window: W,. polyethylene window; and M. flat mirror. Two optically pumped FIR lasers are operated at 118.8pm and 118.8 - A1 pm. Mixing the two FIR beams in the detector provides a modulated signal.
I
Fig. 4. Heterodyne
I
I
I
I
I
Time
(
1 psec
/div)
I
I I X.Xpm wth I’> of I .3 nW
signal at
I
I
I
and P, ,] 01‘ 2.6 mW.
Bandwidth
I
01. detecting
qystcrn is 5 MHI
of P, and PLO within the range where a linear relationship between photoresponse and FIR beam intensity holds. A minimum detectable power defined as the signal beam power for which the heterodyne signal-to-noise ratio is unity at P,,,. say. 2.6 mW is experimentally expected to bc 1.2 x lO--” W. In a unit bandwidth this corresponds to the noise equivalent power NEP,, of 2.4 x lo-” W/Hz. These characteristics of the detector are summarked in Table I.
10” --e
P,_=26
-
PL=600
,,,W ,,W
-A-
PL- 320
,,W
1o’O ,09
z
0 ln 0
lo*-
3
10’.
_
i-
p=110
--
PL=26
---
)lw yW
Estimated
2 -i
lo6
-
z lo5 L$
NE Ph:
24XlC?W/Hz
-,’
$
/ ,
.;
’
:
-z 0
G z I
/
/
-
/ I
10’
/
loo
c
1’
/
,’
16’6
/1
, 5”’
,‘,’ ,/
/
,/
/I
/ /
/
/
/
/ t
N /
’
’
/’ , 1 ‘1’ /
/’ /
,/
’
/
I/
I,
,I
’ /’
/ I
,/
/ ,/
/
lo*
I
,’
,/
,
103-
,
I’ 1,
,
//
I/
/
104-
I
/I,
/ /
_::
, /,
, -
, ,’
‘/ 1o-“5 10
-14 ,o-13
,o-l1
Signal
&I
power
1o-Ju ,o-’
Ps IWI
,o-”
,0-’
,0-o
1O-’
,O -4
A heterodyne Table Amplifier Voltage
detector
I. Characteristics
Impedance:
of Ge(Ga)
251
diagnostics detector
100 2.6 x 10mhV (Aff= 50Hz) IOOOR
gain: G
Output noise: V,,,,, Input
for plasma
R,,
Optical
Focusmg coefficient: K CowelatIon coellicient: < Responsivity: Y’ (A/W) NEP, (W/Hz’ ‘) NEP, (W/Hz) (P,, = 2.6 mW)
alignments
Case A’
Case Bt
0.3 0.1 0.4 1.0 x lo-”
I I 1.2 3.3 x 10-12
2.4 x IO-‘*
2.1 x lo-”
*Case A: The two FIR beams were not perfectly focused onto the detector element yet and were not completely superimposed. No effort was made to coincide the state of polarization of these beams. tCose B: The FIR beams could be focused onto the detector element with a TPX lens. so that the spot size of the beams could be smaller than the size of the element. This means that K is equal to unity: K = 1. On the other hand, when we used two beams whose polarlrations were identical but whose sizes were larger than the element, they were fully superimposed at the detector element. The correlation coefficient was realized to be umty: 5 = I. Those conditions have been achieved individually, but not simultaneously. If we could ideally satisfy both optical conditions mentioned above. this operation of our Ge(Ga) photoconductive detector should be the limiting case of a heterodyne detection at 2.6 mW of the local oscillator power.
3.
THEORETICAL
PRELIMINARIES
The relation between the power of the FIR beam reached that reached to the detector element, P’, is
in front of detector
P’ = K(I - Y)P”,
window,
PC,, and
(1)
where K is the probability of focusing the FIR beam on the detector element by using the optical equipment. while 2: is the loss due to reflection and absorption by the detector window. The FIR power absorbed by the detector element is -y’)P’=K(l
P=(l
-y)(l
-y’)Po,
(2)
where y ’ is the loss due to reflection by the detector element and transmission through it. The values of K and 7 can be determined, since POand P’ can be measured experimentally. The value of y’, on the other hand, is not so easily determined. The photoresponse current is given by I,=uP
= g;
epES
A/W,
where c( is the current responsivity, q the quantum efficiency, z, the recombination lifetime, rZo the photon energy, I the length of the sample, S the cross section of the sample, P the charge of the carrier, p the mobility and E the electric field. The drift time of the carrier from one electrode to the other is
The current
responsivity
It is always
possible
is given by
to relate r to the voltage
responsivity
B=Ri,cc where R,, is the input IN F 23.5 B
resistance
of the preamplifier
/I, since
VjW as shown
in Fig. 6.
253
A heterodyne detector for plasma diagnostics
On the other
hand,
the signal current
in the heterodyne
Ih = cc{2J(P,oP,) The signal power
at the input
signal-to-noise
of the preamplifier
power
is expressed
sin (0, - w, )t.
as (14)
is sin2(w2 - w,)t
Jsh = Ri”I2, = Ri,a2(*4PLoPs The heterodyne
mode detection
W.
(15)
ratio is given by
JSh 2%a25*PLOPs En(f)&- ’
m?
(16)
where Jsh is the time average of Jsh. Again by taking unity for the above ratio, the noise equivalent power in the heterodyne mode detection NEP,, can be defined as: 1
p,
En(f)
.p NEPh=f=2pL,(2 I&a* Using equations NEP,:
W/Hz.
(13) and (17) we get a rather simple, but highly useful relation
NEP, = &
(NEP,)”
(17) between
NEP, and
W/Hz or J.
LO
This equation can be adapted to the detector operated in the case where the signal noise is not dominant. In the next section, we shall examine the various aspects of our experiments in order to find the optimum condition.
4.
DISCUSSION
A Ge(Ga) heterodyne detector in the range 40-120 pm should be different in characteristics and operating conditions from those used at 10 pm, like Ge(Cu) or Ge(Au) for which the generation-recombination (g-r) noise can be a dominant noise source. The applied electric field, limited by the impact ionization, is of the order of 2 V/cm in the case of the Ge(Ga) element as compared to 100 V/cm for the Ge(Cu) element, the reason being that the impurity level of 10 meV in Ge(Ga) is much lower than in Ge(Cu) or Ge(Au). The current responsivity is proportional to the applied electric field E, as mentioned in the previous section. The current responsivity of the Ge(Ga) detector is considerably smaller than that of Ge(Cu) or Ge(Au) detector. Since the g-r noise is accompanied by photoresponse signals, it cannot be so large in the case of a Ge(Ga) detector as in the case of a Ge(Cu) or Ge(Au) detector. With R, = lo3 R, CI’= 0.4 A/W, ho = 1.6 x lo-*’ J (at 118.8 pm), q = 1, P, = 1O-3 W, and Af = 50 Hz, equation (A4) yields 2.6 x lo-*O W for the g-r noise power at the input of the preamplifier. This indicates that the g-r noise power is one thirtieth of the preamplifier’s noise power mentioned in the previous section. FIR laser power of more than 30 mW is required to make the g-r noise dominant in the system. Unfortunately, we have not yet obtained such a high power FIR source. In consequence of the laser power one expects the g-r noise not to be a main noise in the photoconductive detector system at the wavelength around 100 pm. The estimated NEP, of 2.4 x lo-‘” W/Hz mentioned in Section 2 is larger than the limiting value. This is believed to be mainly due to the optical system adopted in order to generate heterodyne signals. When the FIR beam is focused sufficiently well onto the detector element (K = l), the detector should have at least a factor of 3 improved current responsivity, i.e. a’ = 1.2 A/W. On the other hand, the FIR beams were mixed insufficiently well at each impurity orbit in the element due to the fact that the polarizations of the two beams did not precisely coincide, thereby prohibiting an exact superimposition. The experimental correlation coefficient r was 0.1 in our experimental system. Although we observed self beat signals generated by lasing on several modes simultaneously in one cavity, we were also fortunate enough to observe large modulation signals for which the
correlation coefficient appeared to be almost unity. With an improved focusing system. polari/atlon coincidence and superimposition of the two FIR beams (a’ = 1.2 A ‘W. -_ -= I). better values ot NEP, and NEP, should be realized. Putting E:,,= I .6 x IO “’ J. K,,, -7 IO’ Q ;111d I = I .:! A W in equation (13). we obtained 3.3 x IO-” W/Hz’ ’ for the amplifier noise limited NEP.,. Estimation of the effective detector characteristics, which refers to the FIR power reached to the detector window. can be done by substituting 2’ for r in equation ( 13). The NEP,, should then bc 2. I x IO-” W/Hz based on equation (I 8) (see also Table I ). This value of NEP,, is nearly equal to one photon energy of 1.6 x IO ” J (or W/Hz) at 11X.X/im. If we operate our Ge(Ga) detector in heterodyne mode with an optimized optical system and a suitable local oscillator power. wc should get a photon noise limited photoconductive detector with a room temperature preamplifier. This detector was in operation on the JIPP T-II tokomak from February LO March IOXO.“” providing us with the electron density. Table 2 lists conditions under which wc observed the heterodyne signals in the beat modulated CH,OH laser interferomctcr system at I1X.S /lm. The responsivity of the detector including the preamplifier was I ‘x IO’ V’W at I I X.X/lrn. The output noise was observed to be 0.7 mV at the bandwidth of 5 x IO” Hz. The outpuL signal-to-noise ratio of plasma arm was 100 for 0.69 mW of source FIR laser and 0.073 mW of reference FIR laser. and that of reference arm was 250 for 0.049 mW source FIR laser and 0.33 rnW of’ reference FIR laser. In this experimental system. the FIR laser beams were not focused perfectly onto the detectot elements. The factor K was 0.015 for reference arm and 0.019 and 0.0016 for plasma arm, respectively. The correlation coefficient was 0.97 for reference arm and 0.87 for plasma arm. respectively. It is also clear that we could achieve a better signal-to-noise ratio if we optimized the optical system, viz. the focusing and the correlation of two FIR laser beams. Whenever we think of using a detector in a multi-channel interferometer system using one laser. a question arises as to how large a signal-to-noise ratio WCcan have by using such a detector. Table 2 provides an answer to this question. It can be easily seen from Table 2 that the detector system itself has a sufficiently low NEP for the above-mentioned purposes. Nevertheless, when we arrange an interferometer system, we must properly take care of the focusing of two beams on the detector element, the correlation between two beams on the detector element. the choice of the local oscillator power and the minimization of the induction noise frotn ;I tokamak. and 7. T\uhl\hlma li>r lhcir .?~~~~z~~~~letl~rrnrnt.v --The authors wsh to thank Professors S. Narlta. H. Yoshinaga encouragement. In particular they also thank Professors K. Mlxuno. J. FuJita. M. Yamanaka and Mr A. Nishi/,tha li)r helpful discussions. They would also like to express their appreciation to Professor K. Kawabata (‘or a crItIcal rcadlng 01 the manuscript. This work was carried out under the collaborating research program at the Institute 01‘ Plaw~n Ph?w~ Nagoy;a University. Nagoya 464, Japan. This work was supported in part by the Grant-In-Aid for Scicntilic Rewtrch I’rom the Mmistry of Education, Science and Culture. Japan.
REFERENCES
I Moore W. J. and Shenker H.. Ir~fi~~rrtl Ph~.s. 5, 99 (1965). 3. Wolfe S. M., Button K. J.. Waldman J. and Cohn R. Il.. ..I/>/~/_01”
15. 265-l (1’17h)
A heterodyne
3. 4. 5 6: 1. 8. 9.
IO. II.
detector
for plasma
255
diagnostics
Seib D. H.. fEEE J. Qurrnrum Electron. ()E-10, 130 (1974). Dodel G., Heppner J. and Holtzhauer E.. 5th Int. Conf: on i.r. und mm Wmes, p. 239 (1983). Dodel G.. Heppner J., Holtzhauer E. and Gornic E., 7th Int. Co@ on ir. and mm Wazw, p. 66 (1983). Nishizawa A., Noda N.. Yamanaka M.. Takeda Y., Okajima S., Makino S.. Nagasaka K.. Koizumi T., Yabusaki Y.. Takai T.. Murakami Y.. Nagashima A.. Tsunawaki Y. and Fujita .I., 5th Inr. Cmf: on ix. and mm Wuw.s, p. 179 (1980). Kido G.. Narita N., Kawauchi K., Ogura I. and Chikazumi S., .I. Phys. E. SC;. Instrum. 9, 587 (1976). Fritzshe H. and Cuevas M.. Phys. Rev. 199, 1238 (1960). Nishizawa A.. Noda N., Fujita J.. Yamanaka M.. Okajima S.. Takeda Y., Makino S., Nagasaka K.. Koizumi T., Yabusaki H.. Takai M.. Murakamt Y., Nagashima A.. Tsunawaki Y.. Kon S.. Kondo M. and Nakata S.. to be published. Yaric A., Inrroduction to Optical Ek/ronic.r, pp. 255. Holt, Rinehart & Winston, New York (1979). Blaney T. G.. .Sptrce Sr,;. Rrr. 17. 69 I (I 975).
APPENDIX
Noises in FIR Heterodyne
Detection”‘.“’
The dominant noises in heterodyne detection are (a) amplifier noise, (b) Johnson noise and (c) generation-recombination noise. The noise power from each of these at the input of a preamplifier is given below to facilitate a comparison of their magnitudes. (u) Ampl~fiw Amplifier
noise noise power can be written
as
JnA = I& (f)~If
= Ri, I’,,&= ys
(Al)
W
where &,(f’) is the noise energy at the input resistor R,,. Af the bandwidth, k the Boltzmann constant, T,% the amplifier’s noise temperature and M( 5 1) a factor expressing an impedance mismatch between the element and the load resistor and or an impedence mismatch between the load resistor and the amplifier. (h) Johnson Johnson
noise
noise power can be written
as
JnJ = E,,(f)Af
= R,,I;, = 4kTAf
W
(A2)
where E,,,(f) is the noise energy at the input resistor of the amplifier, lnJ the noise current and T the temperature. For the cooled detector element, this would be negligibly small compared with the noises of the load resistor and amplifier at room temperature. (c) Generution
recomhinution
The total radiation
noise
power which is absorbed
by the detector
PR = P, f P, + P,,
W
element
is (A3)
where P, is the signal radiation power, P, the background radiation power and P,, the local oscillator power, which is equal to zero in the video mode detection. The free carriers are excited from the impurities to the conductive band. and finally recombined into the ionized impurities (or the neutral impurities). These processes should produce a generation-recombination noise current while they can give rise to the photoconductive current. The noises are doubled due to fluctuations in the recombination of the carriers, or 2(r,/z,). Thus the noise power is given by
Jngr= E,,,,~/‘Mf = R,, It,, = 2R,,
(A4)
where &,(f’) is the noise energy, Zner the noise current, v] the quantum efficiency, ~~ the recombination life time, TVthe drift time, ho the photon energy, e the charge of carrier and x the current responsivity.
P/w. Vol. 23, No. 5. pp. 247-255. in &eat Britain. All rights reserved
A GALLIUM DETECTOR
1983 Copyright
0020-0891183 $3.00 + 0.00 ~(8 1983 Pergamon Press Ltd
DOPED GERMANIUM HETERODYNE FOR FIR PLASMA DIAGNOSTICS
T. KOIZUMI and K. NAGASAKA Department of Physics. Science University of Tokyo, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162, Japan (Rrceired
I June 1983)
Abstract-First, the video response and heterodyne response of a photoconductive detector, particularly in the far-infrared (FIR) region are discussed. Subsequently, the relation between the noise equivalent power in the video mode, NEP,, and that in the heterodyne mode, NEP,, is derived. It is shown that a signal noise due to a local oscillator beam in the heterodyne detection cannot be the main noise. Our experiments using a gallium doped germanium (Ge(Ga)) heterodyne detector at 118.8 pm have achieved an NEP, as low as 2.4 x IO-” W/Hz in the case where the local oscillator power was 2.6 mW and the beat frequency was I MHz. It is also shown that by further optimizing the optical system, we might even attain an NEP, of 1.6 x IO-” J or W/Hz, which is the energy of one photon at 118.8 pm. This detector has been successfully applied to the plasma diagnostics system of the JIPP T-II tokamak to determine electron density.
1. INTRODUCTION
Gallium doped germanium (Ge(Ga)), one of the excellent materials for FIR detection at wavelengths around 100 pm due to its low noise and high sensitive performance, was investigated by Moore et al.“’ Recently, the need for fast and sensitive heterodyne detection in the FIR region has arisen in plasma diagnostics”) as well as in astronomy. Seib c3)has demonstrated practicability of FIR heterodyne detection using a Ge(Ga) detector. The noise equivalent power in heterodyne mode detection (NEP,) was 6 x lo-l6 W/Hz for the local oscillator power of 2 x IO-‘W. More recently, Dodel ef u/.‘~’ reported on the applicability of a gallium doped and antimony doped germanium (Ge (Ga, Sb)) heterodyne receiver to plasma scattering diagnostics. They achieved an NEPh of 2 x lo-” W/Hz for 100 mW of local oscillator power. Moreover, they calculated the shot noise limited NEP, of 8 x 1O-2o W/Hz for a wavelength of 67 pm.(5) Unfortunately, however, none of those authors have fully investigated the way to determine the optimum condition for the parameters covering the heterodyne detection in FIR region, such as local oscillator power, detector bias voltage, dominant noise source and optical system. No Ge(Ga) photoconductive detector has so far attained the limiting performance of heterodyne detectors whose minimum detectable signal power reaches down to 1.6 x IO-*’ W/Hz, or an energy equivalent to that of one photon at 1 IS.8 pm. The detector we shall describe in this paper was prepared to operate on the twin CH,OH laser interferometer system employed in order to determine the electron density of JIPP T-II tokamak.@) In the present paper, we report on the construction of an FIR detector and FIR interferometer, and on the observations of the heterodyne beat signals at 118.8 pm. We also develop a basic theory for the characteristics of an FIR heterodyne detector at the wavelength N 100 ,um. The conditions under which our detector was operated and the results thereby obtained on JIPP T-II tokamak are examined on the basis of this theory. 2.
EXPERIMENTAL
DETAILS
AND
RESULTS
We employed a Ge(Ga) sample with the impurity concentration of 2 x 10’4cm-3 the photoconductive responses. The size of the sample was 2 x 3 x 1 mm3. The FIR directed onto the 2 x 3 mm* face. The sample was moderately wedged in order interference of radiation reflected by two surfaces. The sample was lapped with powder, chemically polished with a 5:3:3:0.06 mixture of HNO,:HF:CH,COOH:Br with methanol. Ohmic contacts were made of pure indium metal with a supersonic 247
for obtaining radiation was to avoid the Carborundum and rinsed soldering iron.
24X
/Cold /Heat
filter anchor
Figure 1 shows a cryostat for the detector with two elements.“’ These elements were mounted on sapphire plates of thickness 0.2 mm which were adhered to the bottom of the liquid helium vessel. Sapphire is one of the rare materials that act as good electrical insulators as well as good thermal conductors at liquid helium temperature. We chose to electrically isolate the elements from the cryostat metal, though this is not compulsory, in order to allow a larger versatility in the selection and design of the preamplifier circuit. The cryostat was made of metal to minimize the length of the transmission wires from the photoconductor to the preamplifier and to avoid induction noise. The FIR radiation was introduced into the cryostat through a polyethylene window. A set 01 entrance apertures of 8 mm diameter was placed at the entrance to an integrating cavity. A black polyethylene sheet and a crystal quartz plate were employed as cold filters. The photoconductive signals were fed into a current mode preamplifier or voltage mode preamplifier which was set at the nearest position to the detector element to minimize the leak of signals through stray capacitance and to avoid induction noise due to the transmission wires. The capacitance of the wires was approximately 5 pF. The preamplifiers were made of an operational amplifier. The temperature of the elements was found to be 6.7 K even under the background radiation in the wavenumber range up to 250cm-‘. The resistivity of the element was 67&m with an optimum bias field of 1.7 V/cm under the background radiation through the filters, despite the fact that the resistivity of the sample is normally about I OhRem at 6.7 K in dark: Ix1the background radiation enhances the free carriers from the impurity states to the valence band, so that the resistivity of the sample is reduced. The photoresponse of the detector element was measured at a wavelength of 118.8 pm. The effective current responsivity, referring to the FIR power reaching the detector window rather than the FIR power absorbed by the elements. turned out to be 0.4 A/W. As shown in Fig. 2, the noise level of the detector system including the preamplifier was obtained using a fast lock-in amplifier (PAR Model 5202). The detector element was also irradiated by the FIR laser beam in order to observe the signal noise. The measurement was carried out with a time constant of 10 msec, corresponding to 50 Hz of the bandwidth. and at the reference frequency ot 1 MHz, corresponding to the modulation frequency adopted in the CH,OH laser interferometer system for plasma diagnostics. The observed output noise voltage was 2.8 /IV’. As the voltage gain
A heterodyne
detector
Beam splitter
Pyroelectric
r-l
249
diagnostics
Oscillator
*
detector
for plasma
I
I
I FIR
laser
Fig. 2. Block diagram
of a noise measurement
system
of the preamplifier is 100, the noise power is 7.8 x lOm’9 W at the input of the preamplifier. This noise is the preamplifier noise itself. On the other hand, we were unable to detect a signal noise because the maximum power of the FIR laser was only a few milliwatts. The noise of the preamplifier was larger than that of the photoconductor. The noise equivalent power in video mode (NEP,) at 118.8 pm was 1.0 x lo-” W/Hz”’ with the effective current responsivity of 0.4 A/W (effective voltage responsivity of 400 V/W) and the input noise voltage of 4 x 10e9 V/Hz”‘. The heterodyne detection system is shown in Fig. 3. We used a CH,OH laser pumped with a CO, laser beam at 9.7 pm. Laser (1) lased at 118.8 pm corresponding to an angular frequency w, and laser (2) at 118.8 - Ai. pm corresponding to a slightly shifted angular frequency w2 (= o), + Ao). By detuning both cavity lengths, the FIR laser lased at the two frequencies differing by Ao/27r Hz within the frequency range of 10 MHz. The two FIR beams were combined on the crystal quartz beam splitter and directed onto the photoconductive detector element. A beat signal with a frequency A~/271 Hz was generated in the detector element. The amplified signals were led directly to an oscilloscope. A fast storage oscilloscope (Textronics Model 466) was used to record the beat signals. Figure 4 is an oscilloscope trace of the heterodyne signal obtained at the detector output at the signal beam radiation power of 1.3 x 10m9 W. The bandwidth of the amplifier was 5 MHz. The local oscillator power was 2.6 x 10-l W. Figure 5 shows the observed heterodyne signal-to-noise ratio as a function of the signal beam radiation power P, for a given local oscillator power P,,. The beat signals and the noises were measured by using a fast lock-in amplifier with 50 Hz of the bandwidth at 1 MHz of the reference frequency. Various values of P, and P,, were obtained by inserting in the beam a calibrated attenuator made of black polyethylene sheets. As described by equation (9) in the next section, the beat signal is proportional to the square root of the product
FIR
G&a
laser(2)
detector
cop
OLm
laser
Oscilloscope
Fig. 3. FIR interferometry system. B, indicates ZnSe beam splitter; B?, crystal quartz beamsplitter; W,, KCI window: W,. polyethylene window; and M. flat mirror. Two optically pumped FIR lasers are operated at 118.8pm and 118.8 - A1 pm. Mixing the two FIR beams in the detector provides a modulated signal.
I
Fig. 4. Heterodyne
I
I
I
I
I
Time
(
1 psec
/div)
I
I I X.Xpm wth I’> of I .3 nW
signal at
I
I
I
and P, ,] 01‘ 2.6 mW.
Bandwidth
I
01. detecting
qystcrn is 5 MHI
of P, and PLO within the range where a linear relationship between photoresponse and FIR beam intensity holds. A minimum detectable power defined as the signal beam power for which the heterodyne signal-to-noise ratio is unity at P,,,. say. 2.6 mW is experimentally expected to bc 1.2 x lO--” W. In a unit bandwidth this corresponds to the noise equivalent power NEP,, of 2.4 x lo-” W/Hz. These characteristics of the detector are summarked in Table I.
10” --e
P,_=26
-
PL=600
,,,W ,,W
-A-
PL- 320
,,W
1o’O ,09
z
0 ln 0
lo*-
3
10’.
_
i-
p=110
--
PL=26
---
)lw yW
Estimated
2 -i
lo6
-
z lo5 L$
NE Ph:
24XlC?W/Hz
-,’
$
/ ,
.;
’
:
-z 0
G z I
/
/
-
/ I
10’
/
loo
c
1’
/
,’
16’6
/1
, 5”’
,‘,’ ,/
/
,/
/I
/ /
/
/
/
/ t
N /
’
’
/’ , 1 ‘1’ /
/’ /
,/
’
/
I/
I,
,I
’ /’
/ I
,/
/ ,/
/
lo*
I
,’
,/
,
103-
,
I’ 1,
,
//
I/
/
104-
I
/I,
/ /
_::
, /,
, -
, ,’
‘/ 1o-“5 10
-14 ,o-13
,o-l1
Signal
&I
power
1o-Ju ,o-’
Ps IWI
,o-”
,0-’
,0-o
1O-’
,O -4
A heterodyne Table Amplifier Voltage
detector
I. Characteristics
Impedance:
of Ge(Ga)
251
diagnostics detector
100 2.6 x 10mhV (Aff= 50Hz) IOOOR
gain: G
Output noise: V,,,,, Input
for plasma
R,,
Optical
Focusmg coefficient: K CowelatIon coellicient: < Responsivity: Y’ (A/W) NEP, (W/Hz’ ‘) NEP, (W/Hz) (P,, = 2.6 mW)
alignments
Case A’
Case Bt
0.3 0.1 0.4 1.0 x lo-”
I I 1.2 3.3 x 10-12
2.4 x IO-‘*
2.1 x lo-”
*Case A: The two FIR beams were not perfectly focused onto the detector element yet and were not completely superimposed. No effort was made to coincide the state of polarization of these beams. tCose B: The FIR beams could be focused onto the detector element with a TPX lens. so that the spot size of the beams could be smaller than the size of the element. This means that K is equal to unity: K = 1. On the other hand, when we used two beams whose polarlrations were identical but whose sizes were larger than the element, they were fully superimposed at the detector element. The correlation coefficient was realized to be umty: 5 = I. Those conditions have been achieved individually, but not simultaneously. If we could ideally satisfy both optical conditions mentioned above. this operation of our Ge(Ga) photoconductive detector should be the limiting case of a heterodyne detection at 2.6 mW of the local oscillator power.
3.
THEORETICAL
PRELIMINARIES
The relation between the power of the FIR beam reached that reached to the detector element, P’, is
in front of detector
P’ = K(I - Y)P”,
window,
PC,, and
(1)
where K is the probability of focusing the FIR beam on the detector element by using the optical equipment. while 2: is the loss due to reflection and absorption by the detector window. The FIR power absorbed by the detector element is -y’)P’=K(l
P=(l
-y)(l
-y’)Po,
(2)
where y ’ is the loss due to reflection by the detector element and transmission through it. The values of K and 7 can be determined, since POand P’ can be measured experimentally. The value of y’, on the other hand, is not so easily determined. The photoresponse current is given by I,=uP
= g;
epES
A/W,
where c( is the current responsivity, q the quantum efficiency, z, the recombination lifetime, rZo the photon energy, I the length of the sample, S the cross section of the sample, P the charge of the carrier, p the mobility and E the electric field. The drift time of the carrier from one electrode to the other is
The current
responsivity
It is always
possible
is given by
to relate r to the voltage
responsivity
B=Ri,cc where R,, is the input IN F 23.5 B
resistance
of the preamplifier
/I, since
VjW as shown
in Fig. 6.
253
A heterodyne detector for plasma diagnostics
On the other
hand,
the signal current
in the heterodyne
Ih = cc{2J(P,oP,) The signal power
at the input
signal-to-noise
of the preamplifier
power
is expressed
sin (0, - w, )t.
as (14)
is sin2(w2 - w,)t
Jsh = Ri”I2, = Ri,a2(*4PLoPs The heterodyne
mode detection
W.
(15)
ratio is given by
JSh 2%a25*PLOPs En(f)&- ’
m?
(16)
where Jsh is the time average of Jsh. Again by taking unity for the above ratio, the noise equivalent power in the heterodyne mode detection NEP,, can be defined as: 1
p,
En(f)
.p NEPh=f=2pL,(2 I&a* Using equations NEP,:
W/Hz.
(13) and (17) we get a rather simple, but highly useful relation
NEP, = &
(NEP,)”
(17) between
NEP, and
W/Hz or J.
LO
This equation can be adapted to the detector operated in the case where the signal noise is not dominant. In the next section, we shall examine the various aspects of our experiments in order to find the optimum condition.
4.
DISCUSSION
A Ge(Ga) heterodyne detector in the range 40-120 pm should be different in characteristics and operating conditions from those used at 10 pm, like Ge(Cu) or Ge(Au) for which the generation-recombination (g-r) noise can be a dominant noise source. The applied electric field, limited by the impact ionization, is of the order of 2 V/cm in the case of the Ge(Ga) element as compared to 100 V/cm for the Ge(Cu) element, the reason being that the impurity level of 10 meV in Ge(Ga) is much lower than in Ge(Cu) or Ge(Au). The current responsivity is proportional to the applied electric field E, as mentioned in the previous section. The current responsivity of the Ge(Ga) detector is considerably smaller than that of Ge(Cu) or Ge(Au) detector. Since the g-r noise is accompanied by photoresponse signals, it cannot be so large in the case of a Ge(Ga) detector as in the case of a Ge(Cu) or Ge(Au) detector. With R, = lo3 R, CI’= 0.4 A/W, ho = 1.6 x lo-*’ J (at 118.8 pm), q = 1, P, = 1O-3 W, and Af = 50 Hz, equation (A4) yields 2.6 x lo-*O W for the g-r noise power at the input of the preamplifier. This indicates that the g-r noise power is one thirtieth of the preamplifier’s noise power mentioned in the previous section. FIR laser power of more than 30 mW is required to make the g-r noise dominant in the system. Unfortunately, we have not yet obtained such a high power FIR source. In consequence of the laser power one expects the g-r noise not to be a main noise in the photoconductive detector system at the wavelength around 100 pm. The estimated NEP, of 2.4 x lo-‘” W/Hz mentioned in Section 2 is larger than the limiting value. This is believed to be mainly due to the optical system adopted in order to generate heterodyne signals. When the FIR beam is focused sufficiently well onto the detector element (K = l), the detector should have at least a factor of 3 improved current responsivity, i.e. a’ = 1.2 A/W. On the other hand, the FIR beams were mixed insufficiently well at each impurity orbit in the element due to the fact that the polarizations of the two beams did not precisely coincide, thereby prohibiting an exact superimposition. The experimental correlation coefficient r was 0.1 in our experimental system. Although we observed self beat signals generated by lasing on several modes simultaneously in one cavity, we were also fortunate enough to observe large modulation signals for which the
correlation coefficient appeared to be almost unity. With an improved focusing system. polari/atlon coincidence and superimposition of the two FIR beams (a’ = 1.2 A ‘W. -_ -= I). better values ot NEP, and NEP, should be realized. Putting E:,,= I .6 x IO “’ J. K,,, -7 IO’ Q ;111d I = I .:! A W in equation (13). we obtained 3.3 x IO-” W/Hz’ ’ for the amplifier noise limited NEP.,. Estimation of the effective detector characteristics, which refers to the FIR power reached to the detector window. can be done by substituting 2’ for r in equation ( 13). The NEP,, should then bc 2. I x IO-” W/Hz based on equation (I 8) (see also Table I ). This value of NEP,, is nearly equal to one photon energy of 1.6 x IO ” J (or W/Hz) at 11X.X/im. If we operate our Ge(Ga) detector in heterodyne mode with an optimized optical system and a suitable local oscillator power. wc should get a photon noise limited photoconductive detector with a room temperature preamplifier. This detector was in operation on the JIPP T-II tokomak from February LO March IOXO.“” providing us with the electron density. Table 2 lists conditions under which wc observed the heterodyne signals in the beat modulated CH,OH laser interferomctcr system at I1X.S /lm. The responsivity of the detector including the preamplifier was I ‘x IO’ V’W at I I X.X/lrn. The output noise was observed to be 0.7 mV at the bandwidth of 5 x IO” Hz. The outpuL signal-to-noise ratio of plasma arm was 100 for 0.69 mW of source FIR laser and 0.073 mW of reference FIR laser. and that of reference arm was 250 for 0.049 mW source FIR laser and 0.33 rnW of’ reference FIR laser. In this experimental system. the FIR laser beams were not focused perfectly onto the detectot elements. The factor K was 0.015 for reference arm and 0.019 and 0.0016 for plasma arm, respectively. The correlation coefficient was 0.97 for reference arm and 0.87 for plasma arm. respectively. It is also clear that we could achieve a better signal-to-noise ratio if we optimized the optical system, viz. the focusing and the correlation of two FIR laser beams. Whenever we think of using a detector in a multi-channel interferometer system using one laser. a question arises as to how large a signal-to-noise ratio WCcan have by using such a detector. Table 2 provides an answer to this question. It can be easily seen from Table 2 that the detector system itself has a sufficiently low NEP for the above-mentioned purposes. Nevertheless, when we arrange an interferometer system, we must properly take care of the focusing of two beams on the detector element, the correlation between two beams on the detector element. the choice of the local oscillator power and the minimization of the induction noise frotn ;I tokamak. and 7. T\uhl\hlma li>r lhcir .?~~~~z~~~~letl~rrnrnt.v --The authors wsh to thank Professors S. Narlta. H. Yoshinaga encouragement. In particular they also thank Professors K. Mlxuno. J. FuJita. M. Yamanaka and Mr A. Nishi/,tha li)r helpful discussions. They would also like to express their appreciation to Professor K. Kawabata (‘or a crItIcal rcadlng 01 the manuscript. This work was carried out under the collaborating research program at the Institute 01‘ Plaw~n Ph?w~ Nagoy;a University. Nagoya 464, Japan. This work was supported in part by the Grant-In-Aid for Scicntilic Rewtrch I’rom the Mmistry of Education, Science and Culture. Japan.
REFERENCES
I Moore W. J. and Shenker H.. Ir~fi~~rrtl Ph~.s. 5, 99 (1965). 3. Wolfe S. M., Button K. J.. Waldman J. and Cohn R. Il.. ..I/>/~/_01”
15. 265-l (1’17h)
A heterodyne
3. 4. 5 6: 1. 8. 9.
IO. II.
detector
for plasma
255
diagnostics
Seib D. H.. fEEE J. Qurrnrum Electron. ()E-10, 130 (1974). Dodel G., Heppner J. and Holtzhauer E.. 5th Int. Conf: on i.r. und mm Wmes, p. 239 (1983). Dodel G.. Heppner J., Holtzhauer E. and Gornic E., 7th Int. Co@ on ir. and mm Wazw, p. 66 (1983). Nishizawa A., Noda N.. Yamanaka M.. Takeda Y., Okajima S., Makino S.. Nagasaka K.. Koizumi T., Yabusaki Y.. Takai T.. Murakami Y.. Nagashima A.. Tsunawaki Y. and Fujita .I., 5th Inr. Cmf: on ix. and mm Wuw.s, p. 179 (1980). Kido G.. Narita N., Kawauchi K., Ogura I. and Chikazumi S., .I. Phys. E. SC;. Instrum. 9, 587 (1976). Fritzshe H. and Cuevas M.. Phys. Rev. 199, 1238 (1960). Nishizawa A.. Noda N., Fujita J.. Yamanaka M.. Okajima S.. Takeda Y., Makino S., Nagasaka K.. Koizumi T., Yabusaki H.. Takai M.. Murakamt Y., Nagashima A.. Tsunawaki Y.. Kon S.. Kondo M. and Nakata S.. to be published. Yaric A., Inrroduction to Optical Ek/ronic.r, pp. 255. Holt, Rinehart & Winston, New York (1979). Blaney T. G.. .Sptrce Sr,;. Rrr. 17. 69 I (I 975).
APPENDIX
Noises in FIR Heterodyne
Detection”‘.“’
The dominant noises in heterodyne detection are (a) amplifier noise, (b) Johnson noise and (c) generation-recombination noise. The noise power from each of these at the input of a preamplifier is given below to facilitate a comparison of their magnitudes. (u) Ampl~fiw Amplifier
noise noise power can be written
as
JnA = I& (f)~If
= Ri, I’,,&= ys
(Al)
W
where &,(f’) is the noise energy at the input resistor R,,. Af the bandwidth, k the Boltzmann constant, T,% the amplifier’s noise temperature and M( 5 1) a factor expressing an impedance mismatch between the element and the load resistor and or an impedence mismatch between the load resistor and the amplifier. (h) Johnson Johnson
noise
noise power can be written
as
JnJ = E,,(f)Af
= R,,I;, = 4kTAf
W
(A2)
where E,,,(f) is the noise energy at the input resistor of the amplifier, lnJ the noise current and T the temperature. For the cooled detector element, this would be negligibly small compared with the noises of the load resistor and amplifier at room temperature. (c) Generution
recomhinution
The total radiation
noise
power which is absorbed
by the detector
PR = P, f P, + P,,
W
element
is (A3)
where P, is the signal radiation power, P, the background radiation power and P,, the local oscillator power, which is equal to zero in the video mode detection. The free carriers are excited from the impurities to the conductive band. and finally recombined into the ionized impurities (or the neutral impurities). These processes should produce a generation-recombination noise current while they can give rise to the photoconductive current. The noises are doubled due to fluctuations in the recombination of the carriers, or 2(r,/z,). Thus the noise power is given by
Jngr= E,,,,~/‘Mf = R,, It,, = 2R,,
(A4)
where &,(f’) is the noise energy, Zner the noise current, v] the quantum efficiency, ~~ the recombination life time, TVthe drift time, ho the photon energy, e the charge of carrier and x the current responsivity.