Surface Science 0 North-Holland
73 (1978) 207-216 Publishing Company
PHOTOCONDUCTIVITY MEASUREMENTS RELATED TO INTERSUBBAND TRANSITIONS IN SILICON MOSFET STRUCTURES * C.C. HU, J. PEARSE, KM. CHAM and R.G. WHEELER Department of Engheering Connecticut 06520. USA
and Applied Science, Becton Center, Yale University, New Haven,
We have confirmed reports that the observed differences in the subband spectroscopy of Si MOSFET devices have been associated with the establishment of electrostatic equilibrium of the depletion layer. Spectra have been obtained which varies in a continuous fashion from conditions of quasi-accumulation to strong inversion. Systematic differences in the nature of the photoresponse have been observed between the two conditions. At the lowest temperatures the sign of the photoresponse changes to conductive when operating in the thermally activated conduction regime. These results support a bolometric model.
Kamgar, Tsui and Sturge [l] have presented convincing evidence that at liquid helium temperatures the detailed nature of the electrostatic equilibrium, or lack thereof, in silicon MOSFET structures is the cause of the discrepancies in the intersubband spectroscopy as observed by absorption , photoconductivity  and emission techniques . We report on a series of experiments which confirm this explanation and extend the spectroscopy to other energies and provide more information on the nature of the photoconductive response. Some of the results reported here have also been reported by Neppl, Kotthaus, Koch and Shiraki [S]. First, in order to remove any lingering doubts that the photoresponse corresponds to subband absorption, direct absorption measurements were carried out on samples from the same wafer as used by Wheeler and Goldberg . These samples were fabricated such that the substrate contact and the contact to the n-source region were common, that is all the oxide was removed save for the gate and the aluminum pad overlays both the source and substrate on the front surface of the wafer. Fig. 1 shows the geometrical arrangement where the photoresistive measurements were made by chopping the laser radiation at 23 Hz. The direct absorption measurements followed where steady laser radiation was incident on the inversion layer. The gate voltage proportional to n, was slowly swept with a small superimposed 3 kHz voltage. The ac voltage serves to modulate the laser signal which is detected on the indium doped germanium photodetector at either 3 kHz for a deri* Work sponsored in part by the National Science Foundation under grant by the Office of Naval Research under contract N00014-76C-1083. 207
CC. Hu et al. / Photoconductivity
WINDOW E hw
Fig. 1. The geometrical plan of the experiment where the MOSFET is on the long surface (l e 2.5 mm) of the 90” prism. The beam width at the MOSFET surface is nearly Gaussian with a FWHM of 0.7 mm. The short wavelength cutoff of the cold sapphire window is approximately 25 pm or 49 meV . Fig. 2. (a) The photoresistive derivative of the absorption harmonic of the absorption old for this device is 0.4 V. bias.
response at 84 pm with the source-drain field +0.4 V/cm. (b) The obtained with a modulation voltage of 0.2 V rms. (c) The second obtained with a modulation voltage of 0.15 volts rms. The threshThe absorption results were invariant with or without source drain
vative or at 6 kHz for a second harmonic signal. A beam splitter in the laser emission path allowed monitoring and recording of the laser level with a similar detector. The detectors are linear over the range of intensities available and have a flat frequency response from 5 Hz to more than 100 kHz. The absolute laser signal falling on the absorption detector was measured before and after the absorption experiment, again by chopping the beam. A polarizer of about 90% efficiency was inserted in the beam, oriented such as to maximize the intensity of the electric vector normal to the inversion layer surface. Fig. 2 shows the raw data for the photoresistance, the first derivative and second derivative of the absorption as a function of gate voltage when illuminated with 84 pm radiation (L = 14.7 meV). Similar data, though not complete in each instance, has been obtained at 172 pm (7.2 meV), 118 nm (10.45 meV), 78 pm (15.8 meV),
C.C. HMet al. / Photoconductivity measurements
36 pm (34.1 meV) and 2&m (44.3 meV). As is apparent, the sharp peak occurs in both experiments at nearly the identical voltage position. Coincidence to within 0.02 V is obtained when the photoresistance is corrected for /bin, as the change in ~ondu~ti~ty is propo~ional to the number of electrons excited times the mobility which is a strong function of gate voltage i3]. The absolute absorption of this sharp peak was determined by measuring the ma~itude of the second harmonic signal as a function of ac modulation with gate voltage fixed at the line center. The Iine is nearly Lorentzian in shape, thus the maximum of the Fourier component of the second harmonic is (0.35/n)cwo,where o. is the peak absorption. When corrected for the measured beam size and shape the fraction adsorbed at the peak o. = 2.3 + 0.6 X IO-’ for the absorption of 14.7 meV radiation. We assume that this peak is due to the direct transition between the subband Eo and its excited state Er . For a single pass of radiation through the electron layer in this geometry with complete polarization of the electric vector, as in the plane of Ag. 1, the integrated fraction absorbed is a(o) R dti = 4n'fy
where f is the fine structure constant, n’ is the index of refraction of silicon, (Y>is the transition matrix element, n, is the electron density, and 8 is the angle between the device surface and the beam vector [3,6,7]. With reflection from the thick aluminum gate, since the oxide is much thinner than the wavelength in the silicon, the effective efectric field is doubled, hence in this geometry the fraction absorbed calculated from eq. (1) must be multiphed by 4 . With a Lorentzian line width of 1 meV FWHM, for n, = 0.9 X 1012 cm-* and estimates from Stern’s selfconsistent calculations for accumulation layers of the transition moment (rj2 = lo-l4 cm2 the fraction absorbed o. is 4 X I Ow2*in excellent agreement with experiment considering the uncertainties in (rJ2 and in the experiment. The initial broad peak observed in the photoresistive response can also be seen in the absorption, especially in the first derivative presentation. Due to the nature of the sweep in n,, that is the separation in energy levels increases as n, is increased; this absorption must be associated with a level or levels of larger energy than the El-E,.When the correction for mobility is made on the photoresistance the absorption peak and peak resistive response agree at ail wavelengths. Following these measurements and the report by Kamgar et al. [I] implying that this spectra is characteristic of accumulation layers, new advices were fabricated where the substrate contact was isolated from source. These samples fabricated on 15 ohm cm p-type [1001have the following characteristics measured by standard methods, at 4.2 K max~um /JFE = 25,000 cm2/V * s fured charge Q,, = 4.8 X lOi0 cmw2, surface state density IV,, = I A X 10” cm-’ eV_‘, oxide thickness -950 a, device area aO.45 X 0.5 mm. The gate, source and drain pads and the substrate contact on the reverse unpolished side of the 0.25 mm wafer were evaporated aluminum annealed at 440°C in a gas mixture of 15% H2 and 85% N,. The thresh-
C. C. Hu et al. / Photoconductivity
old was determined by capacity turn-on and Shubnikov-De Haas oscillations in the capacitance at 4.2 K. The agreement between these was better than 0.03 V corresponding to an uncertainty in the threshold value of n, to be <6 X IO9 electrons/ cm2. The threshold was +0.32 V with the substrate shorted to source and drain. The threshold shift with substrate bias was also checked with Shubnikov-De Haas measurements. The shifts agreed to better than 0.02 V. The absolute error in any tz, value is approximately 2% due to uncertainties in the capacitance measurements and the device area. In order to ascertain the electrostatic nature of the depletion layer in these devices we measured the threshold change as induced by substrate bias at 4.2 K. Comparison was made with the expected square root dependence upon substrate voltage; excellent agreement was found for negative voltages [lo]. Deviations occurred for positive polarity indicating a Schottky barrier contact which broke down with voltages greater than 1.5 V. Since these measurements indicated that the depletion charge could be changed by varying the substrate bias, infrared photoconductivity measurements were performed on the device. As now expected, continuous change in the spectra as a function of substrate voltage is obtained from that resembling accumulation to inversion [ 111. The spectra with a floating substrate is nearly identical with that observed with to.53 V substrate voltage. Thus we conclude that in the devices used by Wheeler and Goldberg the source-to-substrate contact was ineffective. We have extended measurements to higher photon energies where a photoconductance is the dominant feature. With +l .O V substrate bias at 28 pm the response depicts a smooth curve of similar shape to the field effect mobility as previously observed by Nichclas et al. [ 121. At zero or negative substrate bias significant photoresistive structure appears as shown in fig. 3 for 28 pm radiation. This structure
Fig. 3. The photoresponse spectra with -0.53 substrate bias induced by 28 pm (44.3 meV) radiation at 4.2 K. The broad photoconductance at +l.O V substrate bias is devoid of structure, but is a reproduction of the field effect mobility curve as a function of gate voltage. The small amplitude of the O-l response is related to the fact that the change in conductivity decreases as electron density increases.
C.C. Hu et al. / Photoconductivity
we associate with transitions to excited states 1 through 7. The disappearance of the structure at high positive bias is consistent with a shallow potential as one expects of quasi-accumulation. A number of experiments were carried out in order to further elucidate the nature of the photoconductivity. Since the substrate bias allowed us to investigate the quasi-accumulation and inversion regions, their differences and similarities may produce some clues. One of the most perplexing aspects of the Wheeler and Goldberg measurements was the long decay time of the photoresistance. We have repeated with signal averaging techniques this measurement. Fig. 4 is a sample of such data using 84 ,um radiation with a substrate bias corresponding to quasi accumulation such as to be able to distinguish three distinct peaks in the response spectrum. The decays are long, in the millisecond range, increasing as one proceeds to higher transitions. Application of negative substrate bias decreases the response time to less than 0.1 ms in the strong inversion region. This is also true of the response time for 28 pm radiation in the case of fig. 3. In this instance, the response time is less than 0.1 ms for the photo-conductance and for the case of signals at the photoresistance maximum for any value of n,. That there is a temperature dependence in the amplitude of response is clear, though its quantitative variation with temperature and laser intensity is imprecise. For the quasi-accumulation case, there is little temperature (<15’S) variation when one reduces the bath temperature below 5 K; however, the signal does decrease precipitously as the temperature is raised to 15 K, a factor of 50 in signal is observed. In the inversion case there is an increase in signal when one reduces the temperature of the bath as reported by Neppl et al. . In both cases our measuring sourcedrain field was 0.4 V/cm. This field does not produce a significant heating of the electrons with the sample immersed at 4.2 K, as deduced from the linearity of the photoresistive signal as a function of source drain field. At temperatures below 4.2 K significant heating due to the measurement field does occur. Fig. 5 is an illustration of the conductivity change with temperature and with source drain fields with the bath temperature at 4.2 and 1.55 K respectively for n, = 6.78 X 10’ ’ cm-*. At the lowest temperatures source-drain fields less than 20 mV/cm are necessary to insure insignificant heating [ 131. With the laser intensity we have available a change in conductivity do/a of the order of 10d3 has been obtained. In light of previous source-drain measurements we have tested the system as to whether the laser intensity is causing a significant temperature rise or whether a saturation phenomena is present. At 4.2 K a temperature increase of -0.3 K is induced with a 0.4 V/cm field, but any laser intensity induced temperature change is at least an order of magnitude smaller. Saturation effects in do/o with light intensity do occur, with a systematic variation in terminal level. These results are presented in table 1. As implied by fig. 5 at low temperatures very small source-drain fields are necessary to avoid heating the electron gas. When these conditions are satisfied the photoresponse of the system undergoes dramatic reversal in sign. Fig. 6 illustrates
C. C. flu
et al. / Photoconductivity
I 3 T(
Fig. 4. This figure is a composite description of the decay time measurements using 84 pm radi atron. All measurements shown were done w-ith a source-drain field of 0.4 V/cm and a substrate to source bias of +0.53 V, with the device immersed in 4.2 K liquid helium. (a) is the trace of the response of the indium doped germanium detector which is used as a monitor detector, and which shows the chopped laser beam incident on the device. (bf shows the trace of the O-1 photoresistive response, with deduced time constant 0.6 ms. (c) shows the trace of O-2 transition, time constant 1.1 ms (d) shows the trace of O-3 transition, time constant 1.5 ms. The increase in decay time from (b) to (d) is apparent. The error in these time constant measurements is less than 10%. In a separate experiment we searched for a delay between the time of illumination and the advent of the photoresistive response. There was none within a time resolution of about 50 PS. Fig. 5. The device conductance at izs = 6.78 X lo1 ’ cmv2 is shown as a function of temperature in the absence of a dc source-drain voltage (G-T at I/ 3~ = 0) and two plots where it is given as a function of applied dc source-drain field when the measurements were taken at two different bath temperatures, 1.55 and 4.2 K. To prevent heating the electron gas with the measuring field, the ac applied field was 4.5 mV/cm.
the change in the photoresponse from resistive to conductive as the source drain field is reduced. In this case we are always in the regime of thermally activated conductivity, the mobility edge is associated with n, = 7 X 10’ ’ cm-’ in this sample. The sample does not exhibit activated conductivity converging to a common minimum conductivity for all n, less than the mobility edge [ 141. The nature of this response is further illustrated in fig. 7 where at fvted source-drain field the substrate bias was changed such as to move the resonance across the mobility edge;
Substrate bias voltage
0 0.52 0.78
84Mm 84 Mm 84 Frn
1.2 x 10-S
3.2 X 1O-3
5 x10-4 1.1 x 10-S 8.52
*n, (Xl08 cm-q .-.--_____-____----
o-2 ~I-_~ do/o
$lslJ8 cmv2) ---. 2.82 3.09 1.83
4.1 x 10”” 1.7 x 10-4 2.0 x 10-J
2.0 x 10-3 2.4 x 1O-3
Table 1 This table lists the results of the saturation experiments where da is derived from the saturated value of the photoresistive signal and u is the channel conductivity in the presence of a source drain field; all measurements were done at 4.2 K with a 0.4 V/cm source-drain field and the accuracy in do/o is only 20%; assuming all photoexcited electrons do not conduct, then An, = n,(do/o)
w r.?. 2. Q 3 : E 2 9 6
C.. x 2
$ 2 g .
C.C. Hu e? al. / Photoconductivity
2 (vG-v,, Fig. 6. The photoresponse induced by 84 pm radiation as a function of source-drain bias with the bath temperature 1 SS K and substrate bias yielding inversion. The mobility edge occurs at a gate voltage of approximately 4 V. Reduction of the bias to I mV/cm only reduces the mag nitude of the signal in comparison with the 19 mV/cm example.
Fig. 7. The photoresponse induced by 84 Mm radiation with substrate voltage parameterization at 19.4 mV/cm source-drain field and bath temperature of 1.55 K. The a-to-f sequence of substrate voltages changes the depletion condition from quasi-accumulation to strong inversion. The dominant narrow peak corresponds to the O-l subband transition, while the structure in the conductive aspect of the a-to-c sequence corresponds to higher subband transitions.
C. C. Hu et al. / Photoconductivity
when the resonant response is above the mobility edge a resistive response is observed, when below a conductive response. The variation of the conductivity with temperature is illustrated in fig. 8. The two linear lines indicate qualitatively how the source drain field thermally biases the device. Two mechanisms have been proposed to account for the photoresponse associated with intersubband transitions. The first whereby the final state of the photoelectron has associated with it a different mobility than that in the initial state . Secondly, in this conference, Kotthaus et al. have proposed that the response is due to conversion of photon energy by the resonant electron into heating the system, a bolometric response [ 151. In our minds neither model as yet can be dismissed. The long response times, the high sensitivity at short wave length, the saturation phenomena and the photoresponse sign reversal at low temperatures are qualitatively consistent with the bolometric model. The response time variation by at least a factor of ten from the quasi-accumulation to strong inversion may be a manifestation of saturation, since the subband absorption decreases significantly as the system is changed to strong inversion. Conversely, a state dependent mobility model is consistent with the photoresponse sign reversal considering our present understanding of a localized thermally activated state below a mobility edge. However, this model depends upon the magnitude and variation of the electron mobility with state and temperature, and the long response time is still an enigma.
-MAX \ 3-
ns = 9.95~10”
Fig. 8. The conductivity as a function of temperature for the device biased to inversion with surface charge parameterization. The approximate position of the maximum in conductivity as a function of temperature is sketched. The source-drain bias changes the operating point of the device; this is qualitatively indicated.
C.C. Hu et al. 1 Photoconductivity
Acknowledgements We are grateful to Dr. D.C. Tsui and Professor J.F. Koch for their remission of preprints to us. We also express our appreciation to Mr. Stanley Mroczkowski for assistance
of our devices.
References [I] A. Kamgar, D.C. Tsui and M.D. Sturge,
to be published.
reported at the American Physical Society, San Diego, March (1977).  A. Kamgar, P. Kneschaurek, G. Dorda and J.F. Koch, Phys. Rev. Letters   [S]  
[lo] (111 [ 121  1141 
32 (1974) 1251. R.G. Wheeler and H. Goldberg, IEEE Trans. Electron Devices ED-22 (1975) 1001. E. Gornik and D.C. Tsui, Phys. Rev. Letters 37 (1976) 1425. F. Neppl, J.P. Kotthaus, J.F. Koch and Y. Shiraki, to be published. C.B. Duke, Phys. Rev. 177 (1969) 1394. F. Stern, Phys. Rev. Letters 33 (1974) 960. The calculation reported in this reference contains an error. Stern’s eq. (2) should read in mks units ~ij(E)/Sij(E) = (~*e*Q)*n&ij/fid) (u/E)~/*. This implies for the case therein treated amax = 30.2 m-l. One must point out parenthetically that the absorption coefficient and hence the Einstein coefficient deduced by Gornik and Tsui  is too small by a factor of 23. We wish to thank Dr. F. Stern for bringing this to our attention in a private communication. R.G. Wheeler and J.C. Hill, J. Opt. Sot. Am. 56 (1966) 657. A.S. Grove, Physics and Technology of Semiconductor Devices (Wiley, New York, 1967) p. 324. A. Kamgar, P. Kneschaurek, G. Dorda and J.F. Koch, Phys. Rev. 814 (1976) 1610. R.J. Nicholas, K. von Klitzing and R.A. Stradling, Solid State Commun. 19 (1976) 984. F.F. Fangand A.B. Fowler, Phys. Rev. 169 (1968) 619; J. Appl. Phys. 41 (1970) 1825. D.C. Tsui and S.J. Allen, Jr., Phys. Rev. Letters 20 (1975) 1293. F. Neppl, J.P. Kotthaus, J.F. Koch, Y. Shiraki and G. Dorda, presented at Intern. Conf. on the Electronic Properties of Two-Dimensional Systems, Berchtesgaden, 1977.