HIGHRESOLUTION ELECTRON MICROSCOPE IMAGES OF CRYSTAL LATTICEPLANES USING CONICAL ILLUMINATIONKlaus Heinemann and Helmut Poppa Citation: Applied Physics Letters 16, 515 (1970); doi: 10.1063/1.1653087 View online: http://dx.doi.org/10.1063/1.1653087 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/16/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Highresolution imaging with the stigmatic ion microscope J. Appl. Phys. 60, 1904 (1986); 10.1063/1.337240 Highresolution scanning transmission electron microscope at Johns Hopkins Rev. Sci. Instrum. 50, 403 (1979); 10.1063/1.1135840 Highvoltage, highresolution electron microscopes Phys. Today 27, 17 (1974); 10.1063/1.3128583 HighResolution Electron Microscopy of Crystal Lattice of TitaniumNiobium Oxide J. Appl. Phys. 42, 5891 (1971); 10.1063/1.1660042 A HighResolution Scanning Transmission Electron Microscope J. Appl. Phys. 39, 5861 (1968); 10.1063/1.1656079

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VOLUME 16, NUMBER 12 APPLIED PHYSICS LETTERS 15 JUNE 1970

HIGH-RESOLUTION ELECTRON MICROSCOPE IMAGES OF CRYSTAL LATTICE PLANES USING CONICAL ILLUMINATION

Klaus Heinemann* and Helmut Poppa

Ames Research Center, NASA, Moffett Field, California 94035 (Received 20 March 1970; in final form 4 May 1970)

The (111)-, (200)-, and (220)-lattice planes of small vapor-deposited gold crystals with 2.35-, 2.04-, and 1. 44-A respective interplanar lattice spacings were resolved by high-reso­lution transmission electron microscopy. The simultaneous resolution in one micrograph of the three different lattice spacings and the elimination of azimuthal orientation preferences of the imaged lattice planes were achieved by using conical instead of axial specimen illumina­tion methods.

For the analysis of very early stages of metal film growth, we have been faced with the problem of resolving directly some low-index lattice planes in small metal crystallites without prefer­ence to azimuthal direction. We have used a com­mercial Siemens Elmiskop 101 for our experi­ments and modified it slightly to improve beam stability and reduce the effective chromatical and spherical aberration coefficients of the normal objective lens. With this instrument we were able to resolve the (200)-lattice planes of gold (separa­tion of 2. 04 A) using paraxial illumination. Small lines of 1. l8-A separation, due to three-beam interference1,2 [half-spacings of (lll)-lattice planes of gold] could also be resolved in this mode of operation. This attests to the good mechanical stability and the sufficient shielding against 60-Hz magnetic stray fields provided by the manufacturer of the microscope. However, it was so far not pos­sible to resolve 1. 44A with paraxial illumination and even if these (220)-lattice planes could be imaged with paraxial illumination, they could not be resolved simultaneously with the (200)- and (11 I)-planes; the differences in defocus necessary to transfer all these space frequencies are prohi­bitive. 3

The tilted illumination method, as first pro­posed by DoweU4 and extended by Komoda, 5 im­proves the capability for the resolution of crystal lattice planes but does not allow one to image lattice planes of random azimuthal orientation. The method has significant advantages in that the influence of chromatic aberrations can be elimi­nated and lattice planes with a large spectrum of separations can be imaged, e. g., gold (200)- and (220)-planes, within one micrograph. 6

When utilizing a ring-shaped condensor aper­ture, one can combine the advantages of both axial- and tilted-illumination methods. With a con­denser aperture forming an illumination cone of an angle equal to the Bragg angle of (220)-lattice planes of gold, we were able to transfer not only the (220) but also the (111)- and (200)-lattice planes within one micrograph and in any azimuthal

direction. The micrograph shown (Fig. 1) was made with a half-cone of illumination which pre­serves the discussed principal advantages of the imaging technique and, at the same time, facil­itates somewhat proper instrument alignment. The micrograph was taken in bright field, and the objective aperture used was l. 8x 10-2 rad. Although the electron optical magnification of the microscope was already increased to 450 000 x, the quality of the micrograph shown is affected by the grain of the photographic mate­rial used; thus, even higher electron optical magnifications are clearly advantageous for studies of this nature, especially if even smaller separations are to be resolved, which should be possible with this technique. (Photographic copies of the micrograph which display the l. 44-A lat­tice planes more clearly than possible in the print can be obtained from the authors upon request. )

New experiments, using different sizes of ring­shaped condensor apertures and a higher electron optical magnification, are in progress.

We thank A. Green of the Naval Weapons Center, China Lake, Calif., for prOviding us with the par­ticular specimen used for the micrograph.

100 A

/ 2.351

FIG. 1. Transmission electron micrograph of vapor­deposited gold crystals grown on a NaCI substrate and prepared on a carbon support film.

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VOLUME 16, NUMBER 12 APPLIED PHYSICS LETTERS 15 JUNE 1970

*This work was performed under a National Research Council Postdoctoral Resident Research Associateship at the Ames Research Center.

1T . Komoda, Jap. J. Appl. Phys. 5, 1120 (1966). 2K. Yada and T. Hibi, Jap. J. AppI:' Phys. 2, 1007

(1967) .

3K. Yada and T. Hibi, J. Electr. Micr. 17, 97 (1968). 4W.C.T. Dowell, Optik 20,535 (1963). 5 -T. Komoda, Jap. J. Appl. Phys . .Q, 179, 603 (1966). 6T. Komoda, Jap. J. Appl. Phys . .Q. 452 (1966).

LONGITUDINAL PHOTON FLUX DISTRIBUTION IN LOW-Q SEMICONDUCTOR LASERS

R. Ulbrich and M. H. Pilkuhn * Physikalisches Institut, Universitiit Frankfurt a.M., Frankfurt a.M., Germany

(Received 26 February 1970; in final form 29 April 1970)

A nonuniform photon flux distribution over the length of the active region in semiconductor injection lasers has been found by investigating the scattered light perpendicular to the direc­tion of the stimulated light wave. This effect is present only in low-Q lasers.

The steady-state variation of photon flux with distance in the plane of the active layer of a semi­conductor laser is described by the gain coeffi­cient g that is related to the position of the quasi­Fermi levels of electrons and holes, i. e., the de­gree of population inversion in the active medi­um. 1,2 The longitudinal photon flux S(z) is defined as the number of stimulated photons (related to a unit area and unit time) propagating in the direc­tion of the laser beam. The significance of S(z), whose experimental measure is defined in connec­tion with Fig. 1, will be amplified later in the pa­per. For low photon flux S, one expects exponen­tial amplification of the light wave with the net gain coefficient g- a. a denotes the losses, for instance, due to scattering and diffraction (typical­ly a = 20 cm-1 for GaAs junction lasers3

). Under appropriate pumping conditions one can achieve high values of g-a (values of g-a = 188 cm-1 for a GaAs laser amplifier have been reported4

).

The following simple analysis can be made lead­ing to a photon flux distribution: The stimulated light wave in a Fabry-Perot type laser can be re­solved into forward and reverse traveling waves. Under steady-state conditions the relation

J+LI2 ] R exp[ (g - a) dz = 1 -LIZ

(1)

holds. R is the mirror reflectivity and L denotes the cavity length. The two exponentially ampli­fied waves contribute to the total photon flux 8 which has the form5,s

8(z) = ~80{exp[io" (g- a)db] + expeL 0 (g- a)db ]}. (2a)

If a constant average net gain coefficient is as­sumed, we obtain

516

8(z) =80 cosh[(lnR~ll2)z/~L]. (2b)

Under this assumption the photon flux at the la­ser ends should increase considerably in the case of low reflectivity, R« O. 1. For large values of R, 0.1 <R < 1, the distribution should remain near­ly uniform.

We report the first experimental observation of this longitudinal photon flux distribution by investi­gating the scattered light intensity perpendicular to the laser beam in the active region. The exper­iments were performed on conventional diffused and epitaxial GaAs laser diodes with two sides sawed and two sides cleaved. Average reflective coefficients R 0<0.06 were obtained by evaporating antireflective coatings. Furthermore, diodes

4 3

-1--.. __ ~-- -~i.-;ing ~ ,. ~ dirIPction '- lasIPr z 2 § bIPllm y ~ .Q '-... 2 <-

'" .. ' :, '- " Il..0

" 7 ct." ...... , ... '~ut Q.. .. .. .. .. , .. ....

0 _ .. ' , ..

0 0 2 4

Djod~ Curr~nt (AJ

FIG. 1. Current dependence of the integrated light intensity leaving the crystal in the y direction. The po­larized components Px (E-vector polarized perpendicu­lar to the junction plane) and P z (polarized parallel) are shown. Dashed line: total optical output power Pout of the stimulated emission in the z direction. Note the dif­ferent scales for Px , p z • and Pout·

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