Lecture 3: Basic Concepts: Semiconductorsmech466/MECH466-Lecture-3.pdf · 7 Miller Indices, Planes Since atoms are symmetrical, similar planes have identical material properties.
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MECH 466Microelectromechanical Systems
University of VictoriaDept. of Mechanical Engineering
Step 3: Reduce these numbers to the smallest set of integers h,k and l, by multiplying all by a, which yields (1 0 0).Parentheses are used to denote a crystal plane.
Step 2: Take the reciprocals of the three numbers found in step 1.In this example: 1/a , 1/∞ (=0), and 1/∞ (=0).
Step 1: Identify the intercepts of the plane with the x, y and z axes. In this example, we have x = a, y = infinite, z = infinite.
x = a
y = ∞
z = ∞
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Miller Indices, Planes
Since atoms are symmetrical, similar planes have identical material properties.
z
x y
Families of similar planes are denoted with braces {}. Therefore, these three planes belong to the family of planes {100}.
Step 2: Reduce the three coordinates to the smallest set of integers [h,k and l]. For example, consider the vector originates at (0,0,0) and ends at (0,1,0). Therefore, the Miller Index direction is [0,1,0].
All collectively in direction family <100>.
[001]
Crystal Direction [001]
[010]
Crystal Direction [010]
Note that in a cubic lattice, such as Si, a vector with Miller Index [hkl] is always perpendicular to plane (hkl).
Image of Atomic Structure of Silicon Crystal along the {111} plane[image from Dept. of Synchrotron Radiation Research, in Lund]
Silicon Structural Properties
Image of Atomic Structure of Silicon Crystal along the {100} plane[image from Dept. of Synchrotron Radiation Research, in Lund]
We can view the actual atomic structure of a silicon crystal using SPM (Scanning Probe Microscopy) technology. Interestingly, the ‘probes’ used in SPM are made using ‘bulk micromachining’ of silicon crystal.
The conductivity of a semiconductor is determined by the number of ‘free charged particles’ in the bulk, and their ability to move through the bulk (mobility).
There are two types of charge carriers:
- electrons
- holes
An ‘intrinsic semiconductor’ is a perfect semiconductor crystal with no impurities or lattice defects.
For equilibrium conditions, for an intrinsic semiconductor:
Conductivity calculations are based on theory and experimentally determined coefficients.
We will not cover the details of ‘semiconductor conductivity theory’ in this course. However, some useful information and references are provided in the course textbook, pages 49-56.
Determining the conductivity parameters when fabricating semiconductors, or doping materials to create piezoresistive devices is critical.
For the remainder of the course, the ‘conductivity’ or ‘resistivity’ valves for semiconductors will be provided.
Diffusion doping is done using a deposition and baking process.
(a) A temporary mask is patterned onto the silicon.(b) A layer containing a high concentration of the desired dopant element is deposited onto the material (for example, PSG).(c) The chip is then baked at an elevated temperature, which promotes the diffusion of the dopant atoms into the exposed silicon surfaces.(d) The dopant layer is removed by chemical etching.(e) Finally, the mask layer is removed by chemical etching.
Ion implantation involves the ‘insertion’ of ions of one material, into another.
(a) The implant material is ‘energized’ to create charged ions (single atoms).(b) The ions are accelerated using an electric field toward the target.(c) (Optional) a ‘separation’ magnetic field can be applied to remove impurities.(d) (Optional) a deceleration electric field may be used to control the implant energy.(e) This mechanical implantation creates damage to the crystal structure, therefore, a thermal annealing process follows implantation to ‘heal’ some of these defects.
A concept used to determine the resistance of the doped paths in the silicon. The resistance of the tracks can be determined based on the track geometry and the resistivity.