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Submillimetre performance of photon-drag detectors
SUBMILLIMETRE PERFORMANCE PHOTON-DRAG DETECTORS
OF
M. F. KIMMITT and A. A. SERAFETINIDES Physics Department,
University of Essex, Colchester. England H. P. ROSER
Max-Planck Institute of Radioastronomy,
Bonn, Germany
D. A. HUCKRIDGE Culham Laboratory, Abingdon. Oxon. England Abstract-The submillimetre response of photon-drag detectors made from n- and p-type germanium is considered. Results at 385 and 337 pm are given and the usefulness of such detectors for both CW and pulsed submillimetre sources is discussed.
INTRODUCTION
The photon-drag effect has been exploited in the fabrication of high speed room temperature radiation detectors which are commercially available and widely used with CO2 lasers at 1Opm. The simplest description of photon drag is to ascribe it to radiation pressure on the mobile charge carriers in a semiconductor. On absorbing photons, the carriers acquire momentum as well as energy. If this description was adequate the photon-drag field F per unit intensity I would be determined by the incident momentum and given by F/I = a/et
(1)
where 0 is the absorption cross section of the dominant carriers, e the electronic charge and c the velocity of light. in the 2-l 1 pm However, it has been shown by Cameron et al. (l) that at wavelengths region the photon-drag effect in p-type germanium is extremely complicated. Not only is Eqn 1 not obeyed but holes can acquire momentum in a direction opposite to that of the photons at some wavelengths. The origin of this variation with wavelength is due to the complex band structure of p-type germanium, and Gibson and Montasser”’ have given a detailed theoretical description of the photon-drag spectrum. It has been appreciated for some time that there is an orientation dependence of the photon-drag effect which is described by a forth-rank tensor with, for germanium, two independent non-zero coefficients. By convention these coefficients are designated S and P and for propagation in a [loo] direction F is given by F”’ = SI. In Fig. 1, S/a is plotted against photon energy for [loo] p-type germanium. If Eqn 1 was obeyed there would be no wavelength dependence. In fact there is a wide variation with wavelength as indicated by the experimental points. However, this variation has been explained by Gibson and Montasser”’ and Gibson and Serafetinidesc3’ and the solid line is the theoretical prediction for S/a. PerThe theory of Gibson and Montasser’2’ requires a number of approximations. tinent to the discussion of photon drag at long wavelengths are the following: (a) that the only source of infrared absorption (b) that in p-type germanium the absorption transitions. Assumption (a) is not valid in p-type germanium intense lattice absorption. This does not, however, 675
is free charge carriers; by holes was due to direct,
intraband
in the range 2&50pm because of present a fundamental problem since
M.
F.
KIMMITTetul.
Wavelength, 25
12
6
pm
4
I
3
2
I
I
I
I
I
I
I
01
I
I
02
03
04
05
06
Photon
energy,
eV
Fig. I. Plot of Ku against photon energ) (wavelength) for [IOO] orientated p-type germanium. The points are expcrimcntal and the solid hnc the thcoretlcal prediction of Gibson and Montasser”’ and Gihson and Serafetinides.”
it is possible to increase the doping in order to make the free carrier contribution dominant. Assumption (b) is not valid for )I-type germanium, or for p-type germanium beyond about 40pm. In /l-type germanium absorption is by indirect, intraband transitions. Such transitions require the co-operation of a third particle, usually a phonon. to conserve energy and momentum simultaneously. This third particle will take up some of the radiation’s momentum and in consequence Sjci at IOpm. for example. is appreciably less for n-type than p-type germanium.‘“’ In P-type germanium beyond about 40/m indirect transitions become important and at longer wavelengths they dominate the absorption process. Thus at long wavelengths the photon-drag response of t?- and p-type germanium will become progressively more equal. At very long wavelengths the requirement to conserve energy and momentum simultaneously does not exist. The energy of an electron (hole) cannot be defined to better than an accuracy of h,‘t. and when this is equal to or greater than the photon energy IIW. and therefore ws < 1: intraband transitions can take place without phonon assistance. For both electrons and holes in germanium at room temperature T (the momentum relaxation time) = 3 x lo-l3 set and CWT-C 1 for i > 600 pm. At this wavelength and beyond all the radiation momentum should be given to the charge carriers. Qualitatively, at least, it is reasonable to expect that in the 1W1000~m region the value of S/a will be increasing with wavelength to reach a limiting value determined by the momentum of the radiation at wavelengths beyond about 6OOpm. However. germanium has a refractive index of approximately 4 throughout the infrared and submillimetre region and there is considerable dispute concerning the momentum of electromagnetic waves in non-dispersive dielectric media. Gibson and Montasser”’ argue that the ‘Minkowski’ approach is most appropriate in the present context and that in Eqn 1 c should therefore be the velocity of light in the medium. Assuming that this argument is correct the ‘classical’ value for S/a will be 8.3 x 10” m- I A- ‘.
1
Submillimetre
performance
of photon-drag
dctcctors
677
RESULTS
Although we have observed photon drag at various wavelengths between 118 and 1217pm using a CW optically pumped waveguide laser it has not yet been possible to obtain quantitative data from the results due to uncertainty in the calibration of the laser power. However, at 385pm, using a pulsed high power optically pumped D20 laser, and at 337pm with CW HCN lasers we have obtained meaningful results. The values of S/a obtained are plotted in Fig. 2 and it can be seen that for both n- and p-type germanium the S/a value is less than the classical value. At 385 pm is being taken up by the phonons and these cur z 1.5, so some part of the momentum results appear reasonable. At 337pm wz _ 1.8 and the S/a values are rather smaller as we expect. There appears to be no variation of S/a with resistivity. In practice, while it is the S/a values that are most useful in explaining the photon drag spectrum at various wavelengths, it is the responsivity of detectors which is important to the user. The relationship between S/a and the responsivity in V/W is given by V/W
= S,‘a[pcp:A][l
-
exp( -KL)l
(2)
where p is the resistivity of the material, p is its mobility and K the absorption coefficient. e is the electronic charge and L and A are the length and cross sectional area of the sample, respectively. The equation assumes no reflections in the detector material and no contribution from minority carriers. In the submillimetre region the absorption per carrier for p-type germanium is over 10 times greater than at 10.6,um. and that for n-type nearly 200 times greater.‘“’ With this information, inspection of Eqn 2 shows that we can use much higher resistivity material at long wavelengths, and still absorb most of the radiation, and therefore achieve significantly better responsivity than at 10.6pm. Using a fuller version of Eqn 2 which allows for reflections and the effect of minority carriers, we have calculated the parameters of two detectors using 25 ohm.cm n-type germanium at 385 pm. The parameters are shown in Table 1. In practice there are difficulties in producing high speed amplifiers without adding noise above that of the detector. However, pulsed powers of a few tens of watts should be detected reasonably easily. With CW HCN lasers we have measured powers of ~0.2 mW. At longer wavelengths the NEP values should improve. but at shorter wavelengths they will fall. The values at 385 ,um are an improvement by more than one order of magnitude over those at 10.6 pm for p-type germanium.
IO
_I=
-3
Classcalvalue
------------------~-_
a
n side
I 0
IO
I 20
30
40 - 40 Resrstrvlty,p, ohms cm
30
20
I IO
Fig. 2. Plot of S/a against resistivity for n-type germanium at 385 and 337itm and for p-type germanium at 385pm. The circles and squares are experimental points at 385 and 337pm. respectively. The crosses indicate the .!!‘a values that would have been obtained if the germanium had contained no minority carriers.
0
678
M. F. KIMMITT t’t ul. Table
I.
Source
Area
Resistance
Responsivity
CW Pulsed
0.1 cm2 I cm’
400 ohms 50 ohms
3Oj_lVW~’ 3 /IVW ’
NEP - 10m4 W (1 Hz bandwidth) - 3 W (10” Hz bandwidth)
CONCLUSIONS
Although the experimental results are rather limited it is already clear that photon drag detectors can be used to detect submillimetre radiation. Their detectivity is very low but they retain the advantages that have made them widely used at 10 pm. These are very high speed (- 10m9 set) reproducibility and convenience. Indeed. as the responsivity should vary much less than at short wavelengths they could provide a useful calibration standard for both CW and oulsed submillimetre sources. However, more results in the 5GlOOO pm region are required and experiments are being continued variety of sources. .4[.~n~,~/rt/ymlrnts_We wish to thank Dr A. F. Gibson for invaluable in germanium and on the momentum of radiation in dielectrics.
discussions
on absorption
REFERENCES I.
CAMERON. K.. A. F. GIBSON. J. GILES. C. B. HATCH. M. F. KIMMITT & S. SHAFIK. J. Ph~~s. C 8. 3137 (1975). 2. GIBSON. A. F. & S. MONTASSER. J. Phw C 8, 3147 (1975).
_ ^ 3. GIRSON. A. F. & A. A. SERAFETINIDES.J. Ph!,s. C 10. L107 (1977). 4. GIBSON. A. F.. M. F. KIMMITT & A. C. WALKER, Proc. /Ofh l~f. Co$ O!I Srj,lico,lducro,s. MA, 1970. p. 690. 5. BIKCH. J. R.. C. C. BRADLLY & M. F. KIMMITT. I~frarrtl Phw. 14. 189 (1974).
Cambridge.
OF
M. F. KIMMITT and A. A. SERAFETINIDES Physics Department,
University of Essex, Colchester. England H. P. ROSER
Max-Planck Institute of Radioastronomy,
Bonn, Germany
D. A. HUCKRIDGE Culham Laboratory, Abingdon. Oxon. England Abstract-The submillimetre response of photon-drag detectors made from n- and p-type germanium is considered. Results at 385 and 337 pm are given and the usefulness of such detectors for both CW and pulsed submillimetre sources is discussed.
INTRODUCTION
The photon-drag effect has been exploited in the fabrication of high speed room temperature radiation detectors which are commercially available and widely used with CO2 lasers at 1Opm. The simplest description of photon drag is to ascribe it to radiation pressure on the mobile charge carriers in a semiconductor. On absorbing photons, the carriers acquire momentum as well as energy. If this description was adequate the photon-drag field F per unit intensity I would be determined by the incident momentum and given by F/I = a/et
(1)
where 0 is the absorption cross section of the dominant carriers, e the electronic charge and c the velocity of light. in the 2-l 1 pm However, it has been shown by Cameron et al. (l) that at wavelengths region the photon-drag effect in p-type germanium is extremely complicated. Not only is Eqn 1 not obeyed but holes can acquire momentum in a direction opposite to that of the photons at some wavelengths. The origin of this variation with wavelength is due to the complex band structure of p-type germanium, and Gibson and Montasser”’ have given a detailed theoretical description of the photon-drag spectrum. It has been appreciated for some time that there is an orientation dependence of the photon-drag effect which is described by a forth-rank tensor with, for germanium, two independent non-zero coefficients. By convention these coefficients are designated S and P and for propagation in a [loo] direction F is given by F”’ = SI. In Fig. 1, S/a is plotted against photon energy for [loo] p-type germanium. If Eqn 1 was obeyed there would be no wavelength dependence. In fact there is a wide variation with wavelength as indicated by the experimental points. However, this variation has been explained by Gibson and Montasser”’ and Gibson and Serafetinidesc3’ and the solid line is the theoretical prediction for S/a. PerThe theory of Gibson and Montasser’2’ requires a number of approximations. tinent to the discussion of photon drag at long wavelengths are the following: (a) that the only source of infrared absorption (b) that in p-type germanium the absorption transitions. Assumption (a) is not valid in p-type germanium intense lattice absorption. This does not, however, 675
is free charge carriers; by holes was due to direct,
intraband
in the range 2&50pm because of present a fundamental problem since
M.
F.
KIMMITTetul.
Wavelength, 25
12
6
pm
4
I
3
2
I
I
I
I
I
I
I
01
I
I
02
03
04
05
06
Photon
energy,
eV
Fig. I. Plot of Ku against photon energ) (wavelength) for [IOO] orientated p-type germanium. The points are expcrimcntal and the solid hnc the thcoretlcal prediction of Gibson and Montasser”’ and Gihson and Serafetinides.”
it is possible to increase the doping in order to make the free carrier contribution dominant. Assumption (b) is not valid for )I-type germanium, or for p-type germanium beyond about 40pm. In /l-type germanium absorption is by indirect, intraband transitions. Such transitions require the co-operation of a third particle, usually a phonon. to conserve energy and momentum simultaneously. This third particle will take up some of the radiation’s momentum and in consequence Sjci at IOpm. for example. is appreciably less for n-type than p-type germanium.‘“’ In P-type germanium beyond about 40/m indirect transitions become important and at longer wavelengths they dominate the absorption process. Thus at long wavelengths the photon-drag response of t?- and p-type germanium will become progressively more equal. At very long wavelengths the requirement to conserve energy and momentum simultaneously does not exist. The energy of an electron (hole) cannot be defined to better than an accuracy of h,‘t. and when this is equal to or greater than the photon energy IIW. and therefore ws < 1: intraband transitions can take place without phonon assistance. For both electrons and holes in germanium at room temperature T (the momentum relaxation time) = 3 x lo-l3 set and CWT-C 1 for i > 600 pm. At this wavelength and beyond all the radiation momentum should be given to the charge carriers. Qualitatively, at least, it is reasonable to expect that in the 1W1000~m region the value of S/a will be increasing with wavelength to reach a limiting value determined by the momentum of the radiation at wavelengths beyond about 6OOpm. However. germanium has a refractive index of approximately 4 throughout the infrared and submillimetre region and there is considerable dispute concerning the momentum of electromagnetic waves in non-dispersive dielectric media. Gibson and Montasser”’ argue that the ‘Minkowski’ approach is most appropriate in the present context and that in Eqn 1 c should therefore be the velocity of light in the medium. Assuming that this argument is correct the ‘classical’ value for S/a will be 8.3 x 10” m- I A- ‘.
1
Submillimetre
performance
of photon-drag
dctcctors
677
RESULTS
Although we have observed photon drag at various wavelengths between 118 and 1217pm using a CW optically pumped waveguide laser it has not yet been possible to obtain quantitative data from the results due to uncertainty in the calibration of the laser power. However, at 385pm, using a pulsed high power optically pumped D20 laser, and at 337pm with CW HCN lasers we have obtained meaningful results. The values of S/a obtained are plotted in Fig. 2 and it can be seen that for both n- and p-type germanium the S/a value is less than the classical value. At 385 pm is being taken up by the phonons and these cur z 1.5, so some part of the momentum results appear reasonable. At 337pm wz _ 1.8 and the S/a values are rather smaller as we expect. There appears to be no variation of S/a with resistivity. In practice, while it is the S/a values that are most useful in explaining the photon drag spectrum at various wavelengths, it is the responsivity of detectors which is important to the user. The relationship between S/a and the responsivity in V/W is given by V/W
= S,‘a[pcp:A][l
-
exp( -KL)l
(2)
where p is the resistivity of the material, p is its mobility and K the absorption coefficient. e is the electronic charge and L and A are the length and cross sectional area of the sample, respectively. The equation assumes no reflections in the detector material and no contribution from minority carriers. In the submillimetre region the absorption per carrier for p-type germanium is over 10 times greater than at 10.6,um. and that for n-type nearly 200 times greater.‘“’ With this information, inspection of Eqn 2 shows that we can use much higher resistivity material at long wavelengths, and still absorb most of the radiation, and therefore achieve significantly better responsivity than at 10.6pm. Using a fuller version of Eqn 2 which allows for reflections and the effect of minority carriers, we have calculated the parameters of two detectors using 25 ohm.cm n-type germanium at 385 pm. The parameters are shown in Table 1. In practice there are difficulties in producing high speed amplifiers without adding noise above that of the detector. However, pulsed powers of a few tens of watts should be detected reasonably easily. With CW HCN lasers we have measured powers of ~0.2 mW. At longer wavelengths the NEP values should improve. but at shorter wavelengths they will fall. The values at 385 ,um are an improvement by more than one order of magnitude over those at 10.6 pm for p-type germanium.
IO
_I=
-3
Classcalvalue
------------------~-_
a
n side
I 0
IO
I 20
30
40 - 40 Resrstrvlty,p, ohms cm
30
20
I IO
Fig. 2. Plot of S/a against resistivity for n-type germanium at 385 and 337itm and for p-type germanium at 385pm. The circles and squares are experimental points at 385 and 337pm. respectively. The crosses indicate the .!!‘a values that would have been obtained if the germanium had contained no minority carriers.
0
678
M. F. KIMMITT t’t ul. Table
I.
Source
Area
Resistance
Responsivity
CW Pulsed
0.1 cm2 I cm’
400 ohms 50 ohms
3Oj_lVW~’ 3 /IVW ’
NEP - 10m4 W (1 Hz bandwidth) - 3 W (10” Hz bandwidth)
CONCLUSIONS
Although the experimental results are rather limited it is already clear that photon drag detectors can be used to detect submillimetre radiation. Their detectivity is very low but they retain the advantages that have made them widely used at 10 pm. These are very high speed (- 10m9 set) reproducibility and convenience. Indeed. as the responsivity should vary much less than at short wavelengths they could provide a useful calibration standard for both CW and oulsed submillimetre sources. However, more results in the 5GlOOO pm region are required and experiments are being continued variety of sources. .4[.~n~,~/rt/ymlrnts_We wish to thank Dr A. F. Gibson for invaluable in germanium and on the momentum of radiation in dielectrics.
discussions
on absorption
REFERENCES I.
CAMERON. K.. A. F. GIBSON. J. GILES. C. B. HATCH. M. F. KIMMITT & S. SHAFIK. J. Ph~~s. C 8. 3137 (1975). 2. GIBSON. A. F. & S. MONTASSER. J. Phw C 8, 3147 (1975).
_ ^ 3. GIRSON. A. F. & A. A. SERAFETINIDES.J. Ph!,s. C 10. L107 (1977). 4. GIBSON. A. F.. M. F. KIMMITT & A. C. WALKER, Proc. /Ofh l~f. Co$ O!I Srj,lico,lducro,s. MA, 1970. p. 690. 5. BIKCH. J. R.. C. C. BRADLLY & M. F. KIMMITT. I~frarrtl Phw. 14. 189 (1974).
Cambridge.