Técnicas de Caracterização de Materiais

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Texto

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2º Semestre de 2016

Instituto de Física

Universidade de São Paulo

Professores:

Antonio Domingues dos Santos

Manfredo H. Tabacniks

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Energia / Momento Matéria

Propriedade

a ser

caracterizada

Interação matéria-matéria, (ou radiação-matéria) Detectam-se forças ou corrente elétrica (ou intensidade luminosa) Energia / Momento Matéria

•Microscopias de Sonda Local

(SPM)

Nature Nanotechnology, 1 (2006) 3

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Interação Ponta-Amostra

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Interação Ponta-Amostra

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Modo de Corrente Constante

The tunnel currents registered in the course of the measurement are sufficiently small - up to 0.03 nA (with a special STM head - up to 0.01 nA), so it is possible to investigate also low conductivity surfaces, in particular

biological objects.

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Modos de Operação

eletrônico (STM)

Modo de Altura Constante

In Constant Height mode (CHM) of operation the scanner of STM moves the tip only in plane, so that current between the tip and the sample surface visualizes the sample relief. Because in this mode the adjusting of the surface height is not needed a higher scan speed can be obtained. CHM can only be applied if the sample surface is very flat, because surface corrugations higher than 5-10 A will cause the tip to crash. The weak feedback is still present to maintain a constant average tip-sample distance. As the information on the surface structure is obtained via the current, a direct gauging of height

differences is no longer possible..

G. Binnig and H. Rohrer: Surf. Sci. 126 (1983) 236. Rep. Prog. Phys. 55, 1165-1240 (1992).

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Modo de Altura de Barreira

The LBH image is obtained by measuring point by point the logarithmic change in the tunneling current with respect to the change in the gap separation, that is, the slope of log I vs. z. In the LBH

measurement, the tip-sample distance is modulated sinusoidally by an additional AC voltage applied to the feedback signal for the z-axis piezodevice

attached to the tip. The modulation period is chosen to be much shorter than the time constant of the feedback loop in the STM.

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Modos de Operação

eletrônico (STM)

Modo de Densidade de Estados

LDOS determining can also help to distinguish chemical nature of the surface atoms. LDOS

acquisition is provided simultaneously with the STM images obtaining. During scanning the Bias Voltage is modulated on the value dU, the modulation period is chosen to be much shorter than the time constant of the feedback loop in the STM.

Suitable modulation of tunnel current dI is

measured, divided by dU and presented as LDOS image. On Example the topography and LDOS image of HOPG sample are presented.

G. Binnig and H. Rohrer: Surf. Sci. 126 (1983) 236. Rep. Prog. Phys. 55, 1165-1240 (1992).

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Modo de Espectroscopia I(z)

The I(z) Spectroscopy is related to LBH

spectroscopy and can be used for providing an information about the z-dependence of the microscopic work function of the surface. Next important use of the I(z) Spectroscopy is concerned with for testing of the STM tip quality.

The tunneling current IT in STM exponentially decays with the tip-sample separation z .

In the I(z) Spectroscopy, we measure the tunnel

current versus tip-sample separation at each pixel of an STM image. For Uav = 1 eV, 2k = 1.025 A-1eV-1. Sharp I(z) dependence helps in determining of tip quality. As is empirically established if tunnel current IT drop to one-half with Z < 3 A the tip is considered to be very good, if with Z < 10 A, then using this tip it is possible to have an atomic

resolution on HOPG. If this takes place with Z > 20 A this tip should not be used and must be replaced.

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Modos de Operação

eletrônico (STM)

Modo de Espectroscopia I(V) ou CITS

In I(V) Spectroscopy (or Current Imaging Tunneling Spectroscopy, CITS) a normal topographic image is acquired at fixed Io and Vo. At each point in the

image feedback loop is interrupted and the bias voltage is set to a series of voltages Vi and the tunneling current Ii is recorded. The voltage is then returned to Vo and the feedback loop is turned back on. Each I-V spectra can be acquired in a few

milliseconds so there is no appreciable drift in the tip position.

This procedure generates a complete current image Ii(x,y) at each voltage Vi in addition to the

topographic image z(x,y)|VoIo.

CITS data can be used to calculate a current

difference image DIVi,Vj(x,y) where Vi and Vj bracket a particular surface state, producing an atomic

resolved, real space image of a surface state. This technique, for example can be used in UHV to image filled ad-atom states or the dangling bond states for silicon reconstructions.

G. Binnig and H. Rohrer: Surf. Sci. 126 (1983) 236. Rep. Prog. Phys. 55, 1165-1240 (1992).

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Microscópio de tunelamento

eletrônico (STM)

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Microscópio de tunelamento

eletrônico (STM)

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O critério de Rayleigh estabelece para um microscópio ótico tradicional a

resolução:

0, 61

sin

x

n

 

onde, λ é o comprimento de onda da radiação, n é o

índice de refração do meio e θ é a semi-largura

angular definida pela abertura da lente objetiva.

Considerando –se que o módulo do vetor de onda é

dado por:

2 /

k

n

 

Sendo a variação da componente x do momento dada

por:

2 sin (2 / )

x

p

n

  

 

Assim, o critério de Rayleigh se assemelha ao Princípio da

Incerteza:

  

x p

x

h

Como, para uma onda homogênea, todas as suas componentes

de k serão inferiores ou iguais a n2π/λ.

Consequentemente, a resolução espacial em cada componente

fica limitada ao critério de Rayleigh.

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Mas, se tivermos a componente z da onda com carater evanescente, o

valor da componente de k nesta direção será imaginário.

Assim, podemos escrever que:

Com

2 2 2 2

2 /

x y z

k

 

k

k

n

 

e

O que permite uma melhor resolução lateral !!!

2

0

z

k

2 2 2

2 /

x y

k

k

n

 

Portanto, Δp

x

e Δp

y

e Δx e Δy ↓

Onda evanescente

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Como o critério de Rayleigh e o Princípio da incerteza de Heisenberg são

formalmente semelhantes, esperamos o mesmo comportamento para a

resolução de imagens construídas com elétrons.

Se os elétrons forem descritos por uma onda com uma

componente evanescente, teremos uma resolução lateral

melhor do que se trabalharmos com uma onda plana.

Esta condição é exatamente atendida na situação de

tunelamento eletrônico.

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Comprimento de onda para partículas

Não relativístico

Relativístico:

Desde 10

-14

m (raios

) até ~km (rádiofrequência)

/

hc E

/

h p

0

0

/ 2

(1

/ 2

)

h

m K

K

E

E (eV)

λ (nm)

1x10

6

0,00122

1x10

4

0,0122

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Accuracy and Calibration

Instrumental Factors. The performance of a scanning probe instrument is limited by a number of factors. One of these is the

resolution of the mechanical components used to move the tip and measure its position. The sharpness and stability of the probe tip determine the area of contact and the reproducibility of imaging. Obviously, environmental vibrations must be controlled to a high degree. In addition, most positioners depend on piezoelectric drive, which is subject to problems of non-linearity and to overshoot during rapid movements. The major manufacturers of SPM equipment have made substantial improvements in mechanical and electronic design. These improvements and advanced electronic calibration routines result in measurements that are more linear and accurate than the early models. Mark VanLandingham (University of Delaware) has published a discussion of instrumental

uncertainties on the Web. (http://www.me.udel.edu/~vanlandi/MTpaper.html)

Accurately nanofabricated gratings are the basis for two and three-dimensional calibrations. Such calibration gratings and calibration software are commercially available.

Probe-Related Image Distortions. At very high magnifications and high-relief sample surfaces, the mode of imaging and the geometry

of the probe tip can influence the scanned image. Knowledge of the probe geometry then becomes important for interpretation of the image.

To image individual atoms and molecules it is necessary for the tip-surface interaction to depend only on the nearest atom(s) of the

tip. This occurs in scanning tunneling microscopy because the tunneling current passes only through the nearest atom of the tip. Tunneling current falls off very steeply with distance from the surface. In atomic force microscopy the tip-surface interaction forces fall off less steeply with distance. Thus an AFM probe responds to the average force of interaction for a number of tip atoms, depending on the sharpness of the tip. An AFM image does not show individual atoms, but rather an averaged surface. For ordered surfaces this will reflect the average unit cell.

Probe Deconvolution (Image Restoration). Imaging very sharp vertical surfaces (surfaces with high relief) is also influenced by the

sharpness of the tip. Only a tip with sufficient sharpness can properly image a given z-gradient. Some gradients will be steeper or sharper than any tip can be expected to image without artifact. False images are generated that reflect the self-image of the tip surface, rather than the object surface. Mathematical methods of tip deconvolution can be employed for image restoration. The effectiveness of these methods will depend on the specific characteristics of the sample and the probe tip.

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1982

First atomic resolution

demonstrated by Binnig on Si(7x7)

1984 First Near-field Optical Microscope is invented

Omicron is founded

1985 Binnig, Gerber, and Quate develop the first AFM

1986 Binnig and Rohrer share half the

Nobel Prize in physics for the invention of the STM

1987

First Atomic resolution with the AFM demonstrated by T. Albrecht at Stanford

Noncontact AFM introduced

MFM invented

Digital Instruments is founded by Univ. of California - Santa Barbara researchers.

1988 First commercial AFM available

Park Scientific is founded by Stanford researchers

1989

Topometrix is founded

Burleigh Instruments offers SPM systems

State Univ. researchers.

1994 TappingMode® in fluids is first

introduced

1995 Nanonics is founded

1996 MACMode® is introduced

1997

ThermoSpectra acquires Park Scientific

WITec founded by Universität Ulm researchers

Nanosurf founded by Universität Basel researchers

Park Scientific Instruments Asia Founded (later renamed Park Systems)

1998

Veeco Instruments acquires Digital Instruments

1999

Asylum Research founded by former Digital Instruments employees

JPK founded

2001

Veeco acquires ThermoMicroscopes, renaming it TM Microscopes.

2002

Digital Instruments and TM Microscopes merged with Veeco Metrology Group. Nanoscience Instruments Founded

Imagem

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