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Magnetic quantum oscillations in the photovoltaic effect of Cd0.24Hg0.76Te
Solid State Communications, Vol. 27, pp. 987-990. © Pergamon Press Ltd. 1978. Printed in Great Britain.
0038-1098/78/0908-0987 $02.00/0
MAGNETIC QUANTUM OSCILLATIONS IN THE PHOTOVOLTAIC EFFECT OF Cdo.24 Hgo.76Te* E. Dudziak, P. Becla, J. Brzezirlski and L. J~dral Institute of Physics, Wroclaw Technical University, St. Wyspiarlskiego 27, 50-370 Wroclaw, Poland
(Received 12 May 1978 by S. Lundqvist) The first experimental evidence of magnetic quantum oscillations in the photovoltaic effect is reported. Experiments were carried out with the p - n junction in Cdo.24 Hgo.76 Te placed in a quantizing magnetic field. The oscillations are related with the interband Ps ~ F6 magnetoabsorption transmissions. The discrepancy between experimental data and theory is explained by the effect of the p - n junction electric field on the magnetoabsorption behaviour.
THE INTERBAND magnetooptical transitions between Landau levels in CdxHg 1_:,Te have been extensively studied in recent years [ 1 - 7 ] . In the majority of works the classical methods of recording magnetoabsorption and magnetoreflection oscillations have been used. The oscillations in photoconductivity and in the photoelectromagnetic effect as a result of interband magnetooptical transitions have been measured in [2]. Recently magnetic quantum oscillations in the Auger-transition rate for Cd~Hgl _xTe have been also observed [6]. In this paper we report the first observations of the oscillations of the photovoltaic (PV) effect in Cdx Hgl -x Te p - n junctions placed in quantizing magnetic field. The p - n junctions have been produced by forming the thin n-type layer (about 5 pan thick) on the surface of the "as grown" p-type epitaxial graded-gap CdxHgl-~ Te layer. Some electrical and optical properties of these layers have been measured earlier and published in [8, 9]. Electrical Au and In contacts to p-type and to n-type, respectively, have been made by vacuum evaporation. The details of the technology and the properties of the p - n junction detectors used in experiments have been published in [ 1 0 - 1 2 ] . The samples with the p - n junction were placed in the superconducting solenoid of Spectro Mag 2 (Oxford Instruments) and the p - n junction was illuminated from the side of the n-type layer. The small size of the photo-sensitive surface (smaller than 1 mm 2) simplifies the satisfying of the homogeneity condition. The photo-sensitive surface was perpendicular to both the magnetic field and radiation beam (Faraday configuration). The measurements of spectral responsivity Rx were performed by means of a Zeiss SPM-2 monochromator with NaCI prism. These measurements
* This work was sponsored by the Wroclaw Technical University under contract 7/78 (IM-116). 987
were carried out at 7 K in a non-polarized radiation and in magnetic fields up to 6 T. Figure 1 shows the spectral characteristics of the responsivity of the p - n junction without magnetic field and in magnetic field of 5.5 T under the same illumination conditions. Two main features of the magnetic field effect on the spectral responsivity may be seen. The energy edge of the PV effect under magnetic field is shifted towards the higher energy because the effective energy gap (distance between two first Landau levels in valence and conduction bands) increases with increasing magnetic field. For photon energies above the energy gap responsivity oscillates in the vicinity of the responsivity curve for zero magnetic field. This behaviour is similar to that for the transmission oscillations in the magnetoabsorption spectrum of semiconductors. On this curve we can observe three peaks denoted A, B, C which we correlate with the electron transitions between three different pairs of Landau levels in valence and conduction bands at k = 0. All the other oscillation measurements have been made in another way: at fixed photon energy the spectral responsivity was recorded vs magnetic field B. The examples of the magneto-photovoltaic spectra measured in this way for a few photon energies are presented in Fig. 2. It is worth noting that the oscillation signals were strong with high signal-to-noise ratio. The lowest curve in Fig. 2 taken at 1O0 K proves that the PV oscillations with respectively smaller amplitudes at relatively high temperature can be recorded. The responsivity spectra Rx(B) are closely correlated with the magnetoabsorption behaviour t~(B). It has been found that the differences between the points where both ct(B) and Rx(B) have their maxima are within the error limits of our measurements. The positions of various responsivity maxima in terms of photon energy as a function of magnetic field
PHOTOVOLTAIC EFFECT OF Cdo.~ Hgo.76Te
988
Vol. 27, No. 10
~15 ¢-
B=0 :
:
B=55T
01 O O. 01
gs
A
U 0
0 120
140
160
180
200 Photon
220 energy [meV)
2i,0 ~-
Fig. 1. Spectral characteristics o f p - n junction in Cdo.24 Hgo.76Te at 7 K withc~at magnetic field and in magnetic field of 5.5 T. have been plotted in Fig. 3 and compared with transition energies between different pairs of theoretically calculated Landau levels. We have used the Pidgeon and Brown [ 13] model including the effects of the non-parabolicity of the conduction band and the quantum effect in the valence band. The energies of two sets "a" and "b" of Landau levels have been numerically calculated as a function of magnetic field. The same values of parameters as those accepted in paper [5] have been used, i.e. 71 = 4.5, 7 = 1,K = - - 1,Ep = 19eV, A = 1 eV. The energy gap value Eo was taken as equal to 0.138 eV. The energies of transitions allowed in paper [5] for Faraday geometry and for o ÷ and o- radiation polarization have been plotted in Fig. 3. The solid and dashed lines denote the transitions between the levels of "a"-set and "b"-set respectively. The number n of the Landau level in the conduction band is marked for the theoretical transition curves. These theoretical curves received from the Pidgeon and Brown model, except the lowest, have been experimentally verified by the magnetoabsorption measurements as reported in paper [5 ]. The transitions onto the lowest level in the conduction band have not been observed in paper [5] as the population of the lowest level presents such transitions. In our experiments in PV effect the electron transition onto the lowest level should be possible in the p - n junction region and in the p-type region as well. There exists a relatively great discrepancy between our experimental data taken from PV oscillations and theoretical curves. We believe that the principal reason for this discrepancy is the fact that in PV oscillations
the process of light absorption occurs not only in the magnetic field but also in the electric field built in the p - n junction. In our measurements the electric field is parallel to the magnetic field. Parallel fields act independently and produce two simultaneous motions: quantized cyclotron motion transverse to both fields and electric accelerating motion along the fields. The electric field parallel to the magnetic field cannot change the energy of Landau levels. The presence of electric field induces the optical interband transitions by means of photonassisted tunneling [ 1 4 - 1 6 ] . It induces, in turn, the exponential tails broadening the optical absorption processes. There is no appropriate theory of optical absorption in small-gap semiconductors placed in parallel electric and magnetic fields. It means there exists no theory similar to the Pidgeon and Brown model but taking account of the presence of electric field. In the simple two parabolic bands model, in the presence of parallel electric field E and magnetic field B, absorption coefficient a(E, B) is given by the Airy function. Based on this theory numerical calculations of ct(B) made by us for E = 2.7 x 10a V cm-l and fi)r examplary chosen point lying on the lowest theoretical curve and denoted by a cross (Fig. 3) give a broad peak similar to our PV oscillation peaks and shifted by about 1.25 T towards small magnetic field. The last value is equal to the difference between the theoretical value and our experimental datum. The electric field value E = 2.7 x l03 V cm -1 used in the fitting remains in satisfactory agreement with the p-n junction potential barrier of about 0.1 V and the p - n junction width of few tenths of micrometer estimated in another way.
Vol. 27, No. 10 I
PHOTOVOLTAIC EFFECT OF Cdo.~ Hgo.~ Te
989
210 •
7/
,.i
,','11
.I if*
./"
"
'
;71// y. /,,
> 200
:7//
E
tl(/ ,~
c 190
IJJ
//
,;
< j¢
.
s¢
el t
180
T
.
e o
7
Q?
~
.-"
/ / i ~I b
170 Z
st. J f f
iiiI / /
/' ~./
16C
. SS
".
sl "## ##
"'"
.,~- "0 /
0.4.
o. ~
ss S
15C;
ss
~ • f." *
140
1301 0
I 1
I r I 3 4 5 6 Magnetic field (T) =Fig. 2. Spectral responsivity vs magnetic field for p - n junction in Cdo.24 Hgo.76Te at 7 K for different photon energies (curves shifted vertically for separation). The lowest curve is taken at 100 K.
I 1
l 2
The above combining by us the two parabolic bands theory with the Pidgeon-Brown model is an inconsistency. Therefore one should treat the results received from parabolic bands theory as qualitative rather than a quantitative description of the parallel electric field effect on the a(B) behaviour. The oscillation broadening due to graded-gap structure of our CdxHg~ _xTe material seems not to be dominant. The changes of the molar composition x along the few micrometer thick optically active surface layer are not great in the region of the small composition region, where the composition gradient is small. In conclusion, we have presented experimental evidence of magnetic, quantum oscillations of PV effect. We believe that this new effect of the photoresponsivity oscillations of infrared detectors placed in the quantizing magnetic fields can become a useful tool for studying
I 2
I 3
I 4
Magnetic field (T)
I 5 =-
Fig. 3. Photon transition energies vs magnetic field. Solid lines and dashed lines denote the theoretical transitions between Landau levels of "a"-set and "b"-set, respectively, in Faraday geometry for o + and o- radiation polarization. Experimental dots and dot-dashed lines present the photon energies of the responsivity maxima vs magnetic field. The arrow shows the shift of the absorption peak in the presence of electric field parallel to magnetic field. the behaviour of electrons in small-gap semiconductors in a presence of electric and magnetic fields. The method should be better for homogenous, non-graded band-gap materials. Further experimental studies of this effect, including particularly the crossed fields geometry, are being carried out at present.
Acknowledgements - We are very obliged to Professor W. Zawadzki for his helpful discussions, and to Dr J.M. Pawlikowski for his friendly concern with our work. We are grateful too for technical assistance to E. Malek, M. Tomkiewicz and R. Polewski.
REFERENCES 1.
GROVES S.H., HARMAN T.C. & PIDGEON C.R., Solid State Commun. 9, 451 (1971).
2.
GEORGITSE E.I., IVANOW-OMSKII V.I., KOLOMIETS B.T., MALKOVA A.A. & SMEKALOVA K.P., Fiz. Tekh. Poluprov. 6,455 (1972).
3.
KIM R.S. & NARITA S., Phys. Status Solidi (b) 73,741 (1976).
990
PHOTOVOLTAIC EFFECT OF Cdo.24Hgo.76Te
Vol. 27, No. 10
4.
GULDNER Y., RIGAUX C., MYCIELSKI A. & COUDER Y., Phys. Stams Solidi (b) 81,615 (1977).
5.
GULDNER Y., RIGAUX C., MYCIELSKI A. & COUDER Y., Phys. Status Solidi (b) 82, 149 (1977).
6.
DORNHAUS R., MOLLER K.-H., NIMTZ G. & SCHIFFERDECKER M., Phys. Rev. Let. 37, 710 (1976).
7.
WEILER M.H.,AGGARWAL R.L. & LAX B.,Phys. Rev. BI6, 3603 (1977).
8.
SZATKOWSKIJ., SIERAI~SKI K., PAWLIKOWSKIJ.M., PLACZEK-POPKOE., BECLA P. & DUDZIAK E., Phys. Status Solidi (a) 42, 721 (1977).
9.
PAWLIKOWSKIJ.M., BECLA P. & DUDZIAK E., Optica Applicata 6, 3 (1976).
10.
BECLAP., DUDZIAK E. & PAWLIKOWSKIJ.M., Optica Applicata 4, 3 (1974).
11.
PAWLIKOWSKIJ.M. & BECLA P., Infrared Phys. 15,331 (1975).
12.
BECLAP. & PAWLIKOWSKIJ.M., Infrared Phys. 16,457 (1975).
13.
PIDGEONC.R. & BROWN E.L.,Phys. Rev. 146,575 (1966).
14. 15.
CIOBANUG.,Rev. Roum. Phys. 10, 109(1965). REINE M., VREHEN H.F. & LAX B.,Phys. Rev. 163,726 (1967).
16.
WEILER M.H., ZAWADZKIW. & LAX B.,Phys. Rev. 163,733 (1967).
0038-1098/78/0908-0987 $02.00/0
MAGNETIC QUANTUM OSCILLATIONS IN THE PHOTOVOLTAIC EFFECT OF Cdo.24 Hgo.76Te* E. Dudziak, P. Becla, J. Brzezirlski and L. J~dral Institute of Physics, Wroclaw Technical University, St. Wyspiarlskiego 27, 50-370 Wroclaw, Poland
(Received 12 May 1978 by S. Lundqvist) The first experimental evidence of magnetic quantum oscillations in the photovoltaic effect is reported. Experiments were carried out with the p - n junction in Cdo.24 Hgo.76 Te placed in a quantizing magnetic field. The oscillations are related with the interband Ps ~ F6 magnetoabsorption transmissions. The discrepancy between experimental data and theory is explained by the effect of the p - n junction electric field on the magnetoabsorption behaviour.
THE INTERBAND magnetooptical transitions between Landau levels in CdxHg 1_:,Te have been extensively studied in recent years [ 1 - 7 ] . In the majority of works the classical methods of recording magnetoabsorption and magnetoreflection oscillations have been used. The oscillations in photoconductivity and in the photoelectromagnetic effect as a result of interband magnetooptical transitions have been measured in [2]. Recently magnetic quantum oscillations in the Auger-transition rate for Cd~Hgl _xTe have been also observed [6]. In this paper we report the first observations of the oscillations of the photovoltaic (PV) effect in Cdx Hgl -x Te p - n junctions placed in quantizing magnetic field. The p - n junctions have been produced by forming the thin n-type layer (about 5 pan thick) on the surface of the "as grown" p-type epitaxial graded-gap CdxHgl-~ Te layer. Some electrical and optical properties of these layers have been measured earlier and published in [8, 9]. Electrical Au and In contacts to p-type and to n-type, respectively, have been made by vacuum evaporation. The details of the technology and the properties of the p - n junction detectors used in experiments have been published in [ 1 0 - 1 2 ] . The samples with the p - n junction were placed in the superconducting solenoid of Spectro Mag 2 (Oxford Instruments) and the p - n junction was illuminated from the side of the n-type layer. The small size of the photo-sensitive surface (smaller than 1 mm 2) simplifies the satisfying of the homogeneity condition. The photo-sensitive surface was perpendicular to both the magnetic field and radiation beam (Faraday configuration). The measurements of spectral responsivity Rx were performed by means of a Zeiss SPM-2 monochromator with NaCI prism. These measurements
* This work was sponsored by the Wroclaw Technical University under contract 7/78 (IM-116). 987
were carried out at 7 K in a non-polarized radiation and in magnetic fields up to 6 T. Figure 1 shows the spectral characteristics of the responsivity of the p - n junction without magnetic field and in magnetic field of 5.5 T under the same illumination conditions. Two main features of the magnetic field effect on the spectral responsivity may be seen. The energy edge of the PV effect under magnetic field is shifted towards the higher energy because the effective energy gap (distance between two first Landau levels in valence and conduction bands) increases with increasing magnetic field. For photon energies above the energy gap responsivity oscillates in the vicinity of the responsivity curve for zero magnetic field. This behaviour is similar to that for the transmission oscillations in the magnetoabsorption spectrum of semiconductors. On this curve we can observe three peaks denoted A, B, C which we correlate with the electron transitions between three different pairs of Landau levels in valence and conduction bands at k = 0. All the other oscillation measurements have been made in another way: at fixed photon energy the spectral responsivity was recorded vs magnetic field B. The examples of the magneto-photovoltaic spectra measured in this way for a few photon energies are presented in Fig. 2. It is worth noting that the oscillation signals were strong with high signal-to-noise ratio. The lowest curve in Fig. 2 taken at 1O0 K proves that the PV oscillations with respectively smaller amplitudes at relatively high temperature can be recorded. The responsivity spectra Rx(B) are closely correlated with the magnetoabsorption behaviour t~(B). It has been found that the differences between the points where both ct(B) and Rx(B) have their maxima are within the error limits of our measurements. The positions of various responsivity maxima in terms of photon energy as a function of magnetic field
PHOTOVOLTAIC EFFECT OF Cdo.~ Hgo.76Te
988
Vol. 27, No. 10
~15 ¢-
B=0 :
:
B=55T
01 O O. 01
gs
A
U 0
0 120
140
160
180
200 Photon
220 energy [meV)
2i,0 ~-
Fig. 1. Spectral characteristics o f p - n junction in Cdo.24 Hgo.76Te at 7 K withc~at magnetic field and in magnetic field of 5.5 T. have been plotted in Fig. 3 and compared with transition energies between different pairs of theoretically calculated Landau levels. We have used the Pidgeon and Brown [ 13] model including the effects of the non-parabolicity of the conduction band and the quantum effect in the valence band. The energies of two sets "a" and "b" of Landau levels have been numerically calculated as a function of magnetic field. The same values of parameters as those accepted in paper [5] have been used, i.e. 71 = 4.5, 7 = 1,K = - - 1,Ep = 19eV, A = 1 eV. The energy gap value Eo was taken as equal to 0.138 eV. The energies of transitions allowed in paper [5] for Faraday geometry and for o ÷ and o- radiation polarization have been plotted in Fig. 3. The solid and dashed lines denote the transitions between the levels of "a"-set and "b"-set respectively. The number n of the Landau level in the conduction band is marked for the theoretical transition curves. These theoretical curves received from the Pidgeon and Brown model, except the lowest, have been experimentally verified by the magnetoabsorption measurements as reported in paper [5 ]. The transitions onto the lowest level in the conduction band have not been observed in paper [5] as the population of the lowest level presents such transitions. In our experiments in PV effect the electron transition onto the lowest level should be possible in the p - n junction region and in the p-type region as well. There exists a relatively great discrepancy between our experimental data taken from PV oscillations and theoretical curves. We believe that the principal reason for this discrepancy is the fact that in PV oscillations
the process of light absorption occurs not only in the magnetic field but also in the electric field built in the p - n junction. In our measurements the electric field is parallel to the magnetic field. Parallel fields act independently and produce two simultaneous motions: quantized cyclotron motion transverse to both fields and electric accelerating motion along the fields. The electric field parallel to the magnetic field cannot change the energy of Landau levels. The presence of electric field induces the optical interband transitions by means of photonassisted tunneling [ 1 4 - 1 6 ] . It induces, in turn, the exponential tails broadening the optical absorption processes. There is no appropriate theory of optical absorption in small-gap semiconductors placed in parallel electric and magnetic fields. It means there exists no theory similar to the Pidgeon and Brown model but taking account of the presence of electric field. In the simple two parabolic bands model, in the presence of parallel electric field E and magnetic field B, absorption coefficient a(E, B) is given by the Airy function. Based on this theory numerical calculations of ct(B) made by us for E = 2.7 x 10a V cm-l and fi)r examplary chosen point lying on the lowest theoretical curve and denoted by a cross (Fig. 3) give a broad peak similar to our PV oscillation peaks and shifted by about 1.25 T towards small magnetic field. The last value is equal to the difference between the theoretical value and our experimental datum. The electric field value E = 2.7 x l03 V cm -1 used in the fitting remains in satisfactory agreement with the p-n junction potential barrier of about 0.1 V and the p - n junction width of few tenths of micrometer estimated in another way.
Vol. 27, No. 10 I
PHOTOVOLTAIC EFFECT OF Cdo.~ Hgo.~ Te
989
210 •
7/
,.i
,','11
.I if*
./"
"
'
;71// y. /,,
> 200
:7//
E
tl(/ ,~
c 190
IJJ
//
,;
< j¢
.
s¢
el t
180
T
.
e o
7
Q?
~
.-"
/ / i ~I b
170 Z
st. J f f
iiiI / /
/' ~./
16C
. SS
".
sl "## ##
"'"
.,~- "0 /
0.4.
o. ~
ss S
15C;
ss
~ • f." *
140
1301 0
I 1
I r I 3 4 5 6 Magnetic field (T) =Fig. 2. Spectral responsivity vs magnetic field for p - n junction in Cdo.24 Hgo.76Te at 7 K for different photon energies (curves shifted vertically for separation). The lowest curve is taken at 100 K.
I 1
l 2
The above combining by us the two parabolic bands theory with the Pidgeon-Brown model is an inconsistency. Therefore one should treat the results received from parabolic bands theory as qualitative rather than a quantitative description of the parallel electric field effect on the a(B) behaviour. The oscillation broadening due to graded-gap structure of our CdxHg~ _xTe material seems not to be dominant. The changes of the molar composition x along the few micrometer thick optically active surface layer are not great in the region of the small composition region, where the composition gradient is small. In conclusion, we have presented experimental evidence of magnetic, quantum oscillations of PV effect. We believe that this new effect of the photoresponsivity oscillations of infrared detectors placed in the quantizing magnetic fields can become a useful tool for studying
I 2
I 3
I 4
Magnetic field (T)
I 5 =-
Fig. 3. Photon transition energies vs magnetic field. Solid lines and dashed lines denote the theoretical transitions between Landau levels of "a"-set and "b"-set, respectively, in Faraday geometry for o + and o- radiation polarization. Experimental dots and dot-dashed lines present the photon energies of the responsivity maxima vs magnetic field. The arrow shows the shift of the absorption peak in the presence of electric field parallel to magnetic field. the behaviour of electrons in small-gap semiconductors in a presence of electric and magnetic fields. The method should be better for homogenous, non-graded band-gap materials. Further experimental studies of this effect, including particularly the crossed fields geometry, are being carried out at present.
Acknowledgements - We are very obliged to Professor W. Zawadzki for his helpful discussions, and to Dr J.M. Pawlikowski for his friendly concern with our work. We are grateful too for technical assistance to E. Malek, M. Tomkiewicz and R. Polewski.
REFERENCES 1.
GROVES S.H., HARMAN T.C. & PIDGEON C.R., Solid State Commun. 9, 451 (1971).
2.
GEORGITSE E.I., IVANOW-OMSKII V.I., KOLOMIETS B.T., MALKOVA A.A. & SMEKALOVA K.P., Fiz. Tekh. Poluprov. 6,455 (1972).
3.
KIM R.S. & NARITA S., Phys. Status Solidi (b) 73,741 (1976).
990
PHOTOVOLTAIC EFFECT OF Cdo.24Hgo.76Te
Vol. 27, No. 10
4.
GULDNER Y., RIGAUX C., MYCIELSKI A. & COUDER Y., Phys. Stams Solidi (b) 81,615 (1977).
5.
GULDNER Y., RIGAUX C., MYCIELSKI A. & COUDER Y., Phys. Status Solidi (b) 82, 149 (1977).
6.
DORNHAUS R., MOLLER K.-H., NIMTZ G. & SCHIFFERDECKER M., Phys. Rev. Let. 37, 710 (1976).
7.
WEILER M.H.,AGGARWAL R.L. & LAX B.,Phys. Rev. BI6, 3603 (1977).
8.
SZATKOWSKIJ., SIERAI~SKI K., PAWLIKOWSKIJ.M., PLACZEK-POPKOE., BECLA P. & DUDZIAK E., Phys. Status Solidi (a) 42, 721 (1977).
9.
PAWLIKOWSKIJ.M., BECLA P. & DUDZIAK E., Optica Applicata 6, 3 (1976).
10.
BECLAP., DUDZIAK E. & PAWLIKOWSKIJ.M., Optica Applicata 4, 3 (1974).
11.
PAWLIKOWSKIJ.M. & BECLA P., Infrared Phys. 15,331 (1975).
12.
BECLAP. & PAWLIKOWSKIJ.M., Infrared Phys. 16,457 (1975).
13.
PIDGEONC.R. & BROWN E.L.,Phys. Rev. 146,575 (1966).
14. 15.
CIOBANUG.,Rev. Roum. Phys. 10, 109(1965). REINE M., VREHEN H.F. & LAX B.,Phys. Rev. 163,726 (1967).
16.
WEILER M.H., ZAWADZKIW. & LAX B.,Phys. Rev. 163,733 (1967).