Experimental Verification of Pressure Enhancement by EncapsulationJames A. Corll Citation: Journal of Applied Physics 38, 2708 (1967); doi: 10.1063/1.1709990 View online: http://dx.doi.org/10.1063/1.1709990 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/38/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in An experimental verification of metamaterial coupled enhanced transmission for antennaapplications Appl. Phys. Lett. 104, 064102 (2014); 10.1063/1.4865763 Experimental verification of enhanced sound transmission from water to air at low frequencies J. Acoust. Soc. Am. 134, 3403 (2013); 10.1121/1.4822478 Experimental verification of enhancement of evanescent waves inside a wire medium Appl. Phys. Lett. 103, 051118 (2013); 10.1063/1.4817513 Experimental verification of enhanced sound transmission from water to air at low frequencies POMA 19, 070074 (2013); 10.1121/1.4800935 Experimental verification of enhanced sound transmission from water to air at low frequencies J. Acoust. Soc. Am. 133, 3528 (2013); 10.1121/1.4806352

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2708 COMMUNICATIONS

Squaring both sides, and using the definition for V,= L/r= 27r/TL, we obtain after some cancellation

(7)

Recognizing AL as the volume of the specimen, we have finally

(8)

where U is the energy density within the material. We see, therefore, that Eq. (1) is simply a restatement of the

energy-density conservation law for electrostatic fields, that is, the maximum electrostatic energy density which can be sustained by a material without breakdown is given by (8) in terms of the material constant E and the dielectric breakdown field E.

The fact that this, perhaps, is an obvious result should not detract from its implications, since Eq. (1) which is a consequence of it (as are the more familiar gain bandwidth relations) is quite useful in choosing among alternatives for investigation.

1 J. M. Early, IRE Trans. Electron Devices ED-6, 322 (1959). 'J. M. Early, IRE National Convention, Part 3, 60 (1962).

3 J. M. Goldey and P. M. Ryder, International Solid State Circuits Con-ference, February 1%3.

'E. O. Johnson and A. Rose, Proc. IRE. 47, 407 (1959). , E. O. Johnson, RCA Rev. 26, 163 (1965). 6 The derivation, which among other factors involves the computation of the

maximum current that can be sustained in a transistor, is open to some question since it assumes that base widening is the controlling factor. In that evaluation, the collector depletion-layer transit time i, set equal to the average transit time from emitter to collector, which along with some other asswnptions is far from the truth. However, it gives the correct form of the dependence if not the absolute value.

7 B. C. DeLoach, in Advances in Microwaves, Leo Young, Ed. (Academic Press Inc., New York), in press.

Experimental Verification of Pressure Enhancement by Encapsulation*

JAMES A. CORLL

Sandia Laboratory, Albuquerque, New Mexico

(Received 11 November 1966)

In this note we report experimental results which verify the pressure enhancement by encapsulation previously suggested! on theoretical grounds. The experiments consisted of comparing the occurrence of a pressure-induced change of state in encap­sulated and unencapsulated samples. The sample material chosen for this study was a ferroelectric ceramie,2 which undergoes a pressure-induced transition from the ferroelectric state to the antiferroelectric state at approximately 40000 psi.

Two spherical samples were ground from a single billet of the ceramic and electroded to form capacitors. One of the samples was encapsulated in an epoxy' sphere and the samples mounted in a hydrostatic pressure chamber for simultaneous testing. The samples were then poled in the ferroelectric state by the applica­tion of l000-V dc, which placed a bound charge of approximately 1 p.C on each sample. The fluid pressure in the chamber was then raised at about 800 psi/sec and the charge released by the pressure­induced transitions of the samples recorded on a dual-pen auto­graph. The horizontal axis of the autograph was driven by a trans­ducer monitoring the pressure in the chamber.

Figure 1 is a reproduction of the data recorded by the auto­graph during a typical experiment and displays a pressure en­hancement of approximately 15% due to the encapsulation. During the experiments, the zero points of the curves were arbitrarily displaced vertically for clarity and slightly displaced horizontally by the two-pen arrangement of the autograph. To verify that the effect observed was due to the encapsulation, sev­eral variations of this experiment were performed (including removing the epoxy from the encapsulated sample and encap-

1 "' '" 0: .. i5

zero f-------

1--+ 5000psi

---PRESSURE ---+

FIG. 1. Charge released from poled ferroelectric samples during the pressure­induced transition from the ferroelectric state to the antiferroelectric state. The encapsulated sample (dotted curve) depoled at.a lower pressure due to the pressure-enhancing effect of the encapsulation.

sulating the other sample). In all cases, the encapsulated sample discharged at lower applied pressures than the unencapsulated sample.

Although a numerical comparison between theory and experi­ment is limited by the lack of accurate data concerning the elastic parameters of the materials, calculations with estimated values4 predict the pressure enhancement should be between 10 and 20%. The Poisson's ratio of the encapsulating material is the controlling factor in the calculation of the expected enhancement [Ref. 1, Eq. (7)], and greater enhancement would have been encountered in these experiments if an encapsulating . material with a low Poisson's ratio had been used. The fact that a pressure enhancement of approximately 15% was observed even with a high Poisson's ratio encapsulating material such as epoxy, em­phasizes the potential importance of the effect to high-pressure experiments. Encapsulation effects are an inherent part of all experiments at very high pressures or low temperatures in which the pressure medium is a solid. Consideration of these effects should be included during the interpretation of the pressure­induced phenomena, as well as for an accurate pressure calibra­tion in such experiments.

The author gratefully acknowledges the technical assistance of B. E. Hammons throughout these experiments.

• This work was supported by the U.S. Atomic Energy Commission. 1 J. A. Corll and W. E. Warren, J. Appl. Phys. 36,3655 (1%5). 2 Pbo ... Nbo,02 [(Zro.80Sno.20)0."Tio.061 0 ... 0.. 3 The epoxy u,ed was a 100/20 mixture of Hysol6020 resin and AX hardener,

which cures at room temperature overnight. , Using the notation of Ref. 1: N=I; ~=0.24; '1=0.12; and 0.40<11<0.46.

These values were estimated from rough measurements on the epoxy and as~ suming the compressibility of the ceramic to be 6.0XlO-'/kbar.

Effect of Aluminum Doping on the Fluorescent Emission of CdS*

JICK H. YEE AND GEORGE A. CONDAS

Lawrence Radiation Laboratory, University of California, Livermore, California

(Received 5 December 1966; in final form 23 January 1967)

This communication deals with an examination of the low-tem­perature fluorescence of single crystals of CdS that were doped with small amounts of aluminum. Phosphors made by relatively heavy doping of CdS with aluminum, as well as other group III metals, have been investigated in the past.! However, doping

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COMMUNICATIONS 2709

I-

r-4820

UNDOPED

4867.1 I

.... .....

CdS

4920 4820 WAVELENGTH- ..

48S7.1 I

ALUMINUM DOPED CdS

4920

FIG. 1. The blue fluorescence of an undoped and aluminum-doped CdS crystal at 4.2°K.

with small amounts of aluminum allows the effect of this impurity on the fluorescent emission of "pure" CdS to be studied.

Since there is the possibility of a donor level being created by the introduction of small amounts of this group III impurity, an effect on the fluorescence of "pure" CdS was anticipated. This can be appreciated, since the most intense blue emission line (4867 1) of "pure" CdS crystals at low temperatures has been shown by Thomas and Hopfield2 to be due to the annihilation of an exciton bound to an unknown neutral donor. And since it is generally believed3- 5 that the green, low-temperature emissiiln arises from impurity levels, the controlled doping with aluminum mav also affect this emission.

Single crystals of CdS grown from the vapor phase by Harshaw Chemical Company from high-purity precipitated CdS were used. The crystals were high-purity n-type, and of the wurtzite form with a resistivity of approximately 1-5 fl·cm. Their total im­purities were less than 10 ppm with the exception of zinc, which appeared with a concentration of approximately 20 ppm. The doping with aluminum did not tend to change the crystals' resistivity.

The crystals were doped with aluminum by diffusion. The doping was accomplished by placing a l-cm cube of a single crystal in a vertical high-purity fused quartz tube which had an i.d. of 1.8 cm and a length of 9 em. The CdS was submerged in about 5 g of chips of 99.9999% pure aluminum. A quartz weight was placed on the CdS to keep it submerged during the doping process. The tube was evacuated to 10-5 Torr pressure and sealed off. The doping was accomplished by heating this crystal for 100 h at 900°C. Another technique was used in which the crystal was treated in a similar manner except that the aluminum was applied as a 300-1, high-purity, vacuum-deposited film to the surface of the crystal before processing. The immersion technique used first was more successful in obtaining a larger depth of doping.

An F/6.8 diffraction grating spectrometer with Kodak photo­graphic plates was used to examine the fluorescence. The samples were excited by a high-intensity mercury arc, 3650-1 light.

Prior to doping, the single crystals had a weak blue fluores­cent emission, but little or no perceptible green emission at low

FIG. 2. The green fluores­cence of an aluminum-doped CdS crystal at 4.2°K.

5100

5132.1 I

5200 5300 5400 WAVELENGTH -.8.

temperatures. The principal effect of the doping was to increase the intensity and the width of the main line of the blue fluores­cence, the bound exciton line, seen at 4867.1 1 here. Figure 1 shows a comparison of the blue emission for an undoped sample and a corresponding sample after doping.

The crystals doped by the immersion technique also tended to exhibit an intense green-edge fluorescence typical of CdS, the bands separated by 0.038 eV, which is characteristic of simul­taneous interactions with the 300 cm-] longitudinal optical phonons. However, a high-energy series6 typically seen at ~77°K for supposedly pure CdS was seen at 4.2°K. Figure 2 shows this emission seen in these doped crystals at 4.2°K, and Fig. 3 shows the emission at 77°K. The green-edge emission seen in these doped crystals at 4.2°K tended to increase slightly in wavelength at 77°K, indicating that the green-edge seen at these two tem­peratures can be considered to be due to the same high-energy series.

Spectroscopic analysis of filings from these crystals indicated that the aluminum concentration decreased as one went into the crystal from the surface. This analysis also indicated that this doping with aluminum increased the concentration of this im­purity from approximately 5 X 10]6 in the undoped samples to a maximum value of 1018 atoms cm-s in the doped samples. These blue and green emission effects were seen to decrease as the surface of the doped crystal was etched or polished away. This indicated that the effects were due not only to the heating but also to the presence of aluminum as an impurity.

This aluminum doping is consequently seen to have the effect of creating a high-energy green-edge emission in some CdS crystals. Some workers3•4 have seen a similar high-energy green­edge emission, in addition to the typical low-energy green-edge emission, at 4.2°K. And they have postulated that it is due to a free-to-bound transition. Other workers5 who have also seen a similar high-energy green-edge emission at 4.2°K have postulated that it is due to a bound-to-bound transition.

There seems to be some agreement at the present time that aluminum tends to act as a shallow donor in CdS.4 The appearance of an intense high-energy green-edge emission when aluminum is used as a dopant may be due to the creation of such shallow donor levels. The radiative recombination could then be explained as due to a bound-to-bound transition from these donors to cad­mium vacancies which would act as compensating deep acceptor levels.7

The 4867.1-1 bound exciton line of Fig. 1, as stated above, is known to arise from the annihilation of an exciton bound to a neutral donor.2 The doping obviously creates more bound ex­citons of slightly different bonding energies. This would explain

FIG. 3. The green fluorescence of the same aluminum-doped CdS crystal at 77°K.

~200 5300 5400 WAVEt...ENGTH - ,&

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2710 COMMUNICATIONS

the broadening and the intensity increase of this line with alumi­num doping.

The authors would like to thank K. R. Hermanson for the pre­paration of the samples and assistance in obtaining data.

* Work performed under the auspices of the U. S. Atomic Energy Commission. 1 W. Lehmann, Solid-State Electron. 9, 1107 (1966). 2 D. G. Thomas and J. J. Hopfield, Phys. Rev. Letters 7, 316 (1961). 3 L. S. Pedrotti and D. C. Reynolds, Phys. Rev. 120, 1664 (1960). 4 K. Colbow, Phys. Rev. 141, 742 (1966). 5 E. F. Gross, B. S. Razbirin, and S. A. Permogorov, Fiz. Tver. Tela. 7,

558 (1965) [English Trans!.: Soviet Phys.-Solid State 7, 444 (1965)1. 6 F. A. Kroger, Physica 7,1 (1940). 7 H. H. Woodbury, Phys. Rev. 134, A492 (1964).

Photoconductive Decay in n-Type Polycrystalline Films of Indium Arsenide

NIEVES A. JORDAN

Westingholtse Research Laboratori!?s, Churchill Borough, Pittsburgh, Pennsyl'l.!ania

(Received 14 December 1966; in final form 6 February 1967)

The electrical behavior of field-effect transistors fabricated on polycrystalline films of indium arsenide l seems to indicate that trapping of minority carriers takes place in these films. The existence of trapping would be a characteristic of the thin­film material, since in single crystal indium arsenide trapping was considered not to be important at room temperature.2

A useful method to demonstrate the existence of trapping and to provide information about the trapping kinetics is the analysis of the transient decay of photoconductivity. The transient decay problem has been discussed for the case of a single recom­bination level' and for trapping processes.'" In the photoconduc­tive decay experiments·, 7 a short pulse of light creates extra hole-electron pairs in the sample, the excess conductance of the sample being proportional to the total number of excess carriers. After turning off the light the hole-electron pair recombines, and the decay of the excess conductance can be monitored to assign a mean lifetime to the carriers.

The photoconductive decay was observed in indium arsenide films similar to those used in the fabrication of field-effect devices. The films are grown hy the simultaneous evaporation of indium and arsenic using the three-temperature technique.8 The films are n-type with carrier concentration in the range 5X 1017 to 1018 carriers/cm'.

The InAs films were etched into a bridge geometry, which is also convenient to perform Hall-effect measurements. It was found in the experiments that the signal-to-noise ratio improved when a pair of terminals were used to pass the dc current and a different one to extract the voltage. The Ohmic character of the current-carrying contacts was checked by reversing the polarity and observing no difference in the output. Measurements were made from liquid nitrogen to room temperature. The light SJurce was a FX-13 xenon flash tube. The light from the flash was focused on the sample by a lens. The flash duration was approximately 15 }Lsec. This time is smaller than the times in-

(a)

(b)

FIG. 1. Voltage decay of an InAs sample (a) T~

-18S c C, vertical scale=2 mV/div, horizontal scale=50 ,usec/div. (b) T~+25°C,

vertical scale=l mV/div, horizontal scale~50 }Lsec/div.

FIG. 2. Temperature de­pendence of the(1 /T) associ­ated with the first region of the decay.

volved in the experimental results which we have tried to in­terpret.

The average thickness of the indium arsenide films is 1000 ..t, and the electron mobility is of the order of 1000 cm2/V ·sec. Figure 1 shows oscillograms of the voltage decay of a sample at two different temperatures. The decay is not characterized by a simple exponential dependence on time, and the decay time increases as the temperature is lowered.

If the decay were to follow a simple exponential law, the semilogarithmic plot of signal amplitude taken from the oscil­lograms vs time would be a straight line with slope equal to -(l/T). When such plotting was carried out for the indium arsenide samples, we found that at least two segments of different slope could be resolved. A meaningful determination of the slope of the line amplitude vs time in the semilogarithmic plot can only be made for the first portion of the decay (approxi­mately the first 150 ,usee), since afterwards, within the resolution of our equipment, the signal amplitude variation with time is so small that determination of its value from the oscillograms is not accurate. For this reason, when trying to study the tem­perature dependence of (l/T) we have limited ourselves to the first region of the decay [initial straight-line segment up to approximately 150 ,usee in the plot In (signal) vs time]. Such a temperature dependence of (l/T) is shown in Fig. 2. From the graph it is seen that T falls exponentially with temperature from approximately -100°C to room temperature. From -100° down to -185°C, T does not change appreciably. This tempera­ture dependence of T has been observed in all the indium arsenide films used in the experiments. An activation energy of 0.082 eV can be associated with the process responsible for the exponential dependence of T on temperature.

Since the indium arsenide films are n-type with a high electron concentration, the Fermi level is very close to the conduction band. Most of the films used have carrier concentrations of the order of 1018 electrons/em', so that any existing electron traps would likely be filled at room temperature. We have additional evidence against electron trapping in the films from the fact that the value of field-effect mobility closely agrees with the measured Hall-effect mobility. If electron trapping would exist, the mobility determined from field-effect experiments would be much lower than that determined from Hall-effect measure­ments. It therefore appears that the trapping observed in the photoconductive decay experiments is minority carrier trapping. The different regions in the decay trace could be associated with the existence of more than one trapping level. The temperature dependence of (l/T) is similar to that which would be expected on the basis of the theory for a semiconductor where trapping and recombination levels exist. Detailed explanations of the effects of recombination and trapping in transient photoconduc­tive decay measurements are available in the literature.9 In the region where the dependence is exponential, the decay is dominated by the thermal release time T, from the traps, T fJ "" l/cp 'p" where Cp '= hole capture coefficient and

pl=Nvexp-(E,-Ev)/kT.

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