## Introduction and Theory....

The Scanning Tunneling Microscope (STM) was developed by Gerd Binnig and Heinrich Rohrer at the IBM Zurich Research Laboratory in the early 80's. Their accomplishment which won them a Nobel prize in 1986 utilized the everyday basics of quantum mechanics and produced a revolutionary method for determining surface structure atom by atom.1 Their apparatus consisted of a large cylindrical metal frame that suspended the microscope mechanism and used springs and magnets for damping vibrations.2 The entire apparatus was encased in a vacuum chamber and a fine tip was pushed close to the surface of a solid using a piezoelectric device. Applying a voltage across the tip and surface, Binnig and Rohrer were able to detect a tunneling current and thus map the surface atom by atom on a computer.3

Here is a crude schematic of the STM invented by Binnig and Rohrer that was published in the August 1985 ed. of Scientific American.

Today, the STM, in various sizes, can be used to produced high quality images of surface structure in the open laboratory. Furthermore, the advent of Binnig and Rohrer's apparatus opened a new field of science which has led to many advancements in science and technology.

Here are some interesting Web Site on current applications with the STM....

So how does the Tip to Surface tunneling work? Newton can't explain it?

Using classical mechanics, the idea of an electron passing from one metal across a barrier to another can not be explained. Thus, we must use the wave/particle nature of the electron asserted by quantum mechanics to solve our problem.

Consider two metals, one is a tip and the other is a surface, separated by a finite distance. The distance between the two metals represents a uniform potential barrier, U(x). Now let's consider the wave properties of an electron in the tip as governed by the time independent one-dimensional Shrödinger equation:

The wave function for the electron can be described by the equation:

Likewise, the wave function for an electron in the surface metal is of the same form with different coefficients (C and D, instead of A and B). Notice that the wave function does not go to zero when at the boundary of the metal. Therefore, there is some probability that the electron will penetrate the potential barrier.

Picture obtained from Buleigh Instructional STM Workbook.

Furthermore, if the separation between the metals is small enough (on the order of 10 angstroms), an electron from one metal may appear on the other side of the barrier. This probability is given by the relation that T(E) = e-2L where L is measured in angstroms.4 From this relation we can see that as the two metals move farther apart the probability of electrons tunneling the barrier decreases exponentially and as they move closer the tunneling increases.

Picture obtained from Buleigh Instructional STM Workbook.

So how can the tip be maintained approximately 10 angstroms from the surface?

As mentioned earlier, Binnig and Rohrer's apparatus consisted of a relatively large and elaborate mechanism for damping vibrations, and maintaining a 10 angstrom separation. Today, such a separation can be steadily maintained using similar devices in a much smaller apparatus. The example used for this experiment is a Burleigh Instructional STM.

External vibrations were reduced by placing the STM on a laser bench. Additional measures were taken by placing the microscope apparatus on a 100 lb. Weight which rested on a inner-tube. Internally, the tip and surface mounting is placed on stacked plates with Elastomer spacers. This measures proved to be adequate with two exceptions: when the phone rang, or when my lab partner and I were talking too loud.

The tip can be manually adjusted using both knobs and coarse movement buttons. Once the tip is within about 0.5-1.0 mm of the surface, a button for "fine" adjustments is used. The fine approach button invokes a piezoelectric device which both elongates and bends depending on how much potential is across the device.5 Since the amount of tunneling current is related to the separation, a negative feedback loop can move the tip via the piezoelectric device in atomically small increments depending on the tunneling current. Therefore, if no tunneling current is being detected the voltage across the piezoelectric device is increased pushing the tip closer until a specific tunneling current is reached. Once the specific tunneling current is reached, surface images may then be collected.