Semiconductor Very Basics
Material (mostly) from
• Semiconductor Devices, Physics & Technology,
S.M. Sze, John Wiley & Sons
• Semiconductor Detectors, H. Spieler (notes)
July 3, 2003
Conductors, Semi-Conductors, Insulators
• Characterized by resistivity, ρ
• Conductor: Cu ρ ~ 2 ¢ 10-6 Ω-cm
• Semiconductor: Si ρ ~ 105 – 10-2 Ω-cm
– Very dependent on impurities, T…
• Insulator: Fused Quartz: ρ ~ 1017 Ω-cm
• Wire of length L, x-sec A: R = ρ L/A
• L = 1 cm, A=π (1 mm)2:
– R(Cu) ~ 0.6 mΩ
– R(Si) ~ 3 MΩ (for ρ = 10 kΩ–cm)
– R(fused quartz) ~ 3 1019 Ω
Lattice = 3D periodic arrangement of atoms in crystal
Simple cubic lattice
polonium is only one
like this (I think).
Body-centered
cubic (bcc).
Sodium, tungsten
Face-centered
cubic (fcc).
Al, Cu, Au…
Lattice constant: length of the side of the cube, typically 5 A
Diamond lattice (Si & Ge too)
Two interpenetrating fcc lattices with one sub-lattice displaced
from the other by ¼ the distance along the diagonal à each
atom surrounded by 4-equidistant nearest-neighbors.
Miller Indeces
Orientation of plane through lattice can be
characterized by Miller Indeces:
(1,0,0)
(1,1,0)
(2,1,0)
Bonds
• Each atom in diamond lattice has 4 nearest
neighbors.
• Each atom has 4 e- in outer orbit.
• Each atom shares these e- with neighbors.
– Valence electrons, covalent bonding,
tetrahedron bond
• Valence e- spend most of their time
between the two nuclei.
(2D picture, easier to visualize than 3D)
Holes
• Low T: electrons bound in lattice.
• Higher T: thermal vibrations can break bonds.
– “Free” electron, can conduct current.
– “Missing electron”: hole.
• Think of a hole as a fictitious positive charge.
– Moves under electric field. Current from both e and holes.
• Like a bubble in a liquid: it is the liquid that moves, but it is
much easier to think of the bubble moving.
Bands
Isolated atoms brought together to
form lattice à discrete atomic levels
shift to form energy bands
Energy Bands (cont.)
Insulator SemiConductor Conductor
Eg: band gap (1.12 eV for Si)
Note: kT ~ 0.026 eV at room temp.
Energy Bands (cont.)
Probability that e - state of energy E is
occupied is given by the Fermi-Dirac function:
where EF is the Fermi energy. Remember: kT << Eg
Energy Bands (cont.)
• At finite T, some of the electrons move
from top of the valence band into the
bottom of the conduction band.
• Intrinsic carrier density:
where Nc (Nv) is the density of states in
the conduction (valence) band.
• For pure Si, n ~ 1010 cm -3 at 300 K,
corresponds to ρ = 400 kΩ cm
Impurities
• Intrinsic semiconductor = pure, no
impurities.
• Extrinsic semiconductor = impurities
added.
• Some impurities always present.
• Turns out to be extremely useful to
add impurities to control the
properties of the semiconductor.
Donors and Acceptors: Doping
• P or As impurities.
• 5 e- in outer shell.
• 4 e- for bonds, one
e- left-over (free).
• Donor impurity
• (donates e-)
• N-type silicon
• Al or B impurities.
• 3 e- in outer shell
• 3 e- for bonds, one
hole left-over (free)
• Acceptor impurity
• P-type silicon
Aside: how do you dope?
Diffusion
Ion Implantation
A bit of jargon that comes up a lot
• Often we have “pieces” of material
that are much more heavily-doped
than others.
• The heavily-doped pieces are called
n+-type or p+-type; the lightly-doped
pieces, simply n-type or p-type.
Mobility
• Mobility µ defined by V = µE
– V = carrier velocity E = applied electric field
• µ = eτ/meff
– τ =mean time between collisions (~ psec)
– meff = effective mass of electrons/holes
• The probability of collisions, and hence τ
and µ, depend on the concentration of
impurities and the temperature.
Mobility (cont.)
In Silicon, hole mobility ~ 1/3 of electron mobility
Resistivity
• Not surprisingly, the resistivity is a
function of the mobility and the
density of charge carriers
High impurity concentration
à low resistivity
Where
• n = e-concentration
• p = hole-concentration
• µe = electron mobility
• µp = hole mobility
The p-n junction (diode)
Bring p-type and n-type into contact:
P
N
0 Volts
Hole Diffusion
Electron Diffusion
A Depletion Zone (D) and a Barrier Field Form at the PN Junction:
Barrier Field
0 Volts
P
--
Acceptor Ions
D
++
N
Donor Ions
Hole (+) Diffusion
Electron (-) Diffusion
The Depletion Zone (D) is a region with no charge carriers
The p-n junction – no ext V
• Difference of potential Vbi (built-in potential)
• Thin “depletion region”, length W
where N A and N D are the acceptor and donor concentrations
Typically:
Vbi ~ 0.7 Volts, W < 1 µm
p-n junction – Forward bias
+ Volts
P
-
+
N
- Volts
Current
• External voltage reduces the barrier field
• Holes and electrons are “pushed” toward the
junction and the depletion zone shrinks in size
• Carriers are swept across the junction and the
depletion zone
• There is a net carrier flow in both the P and N
sides = current flow!
Diode IV characteristics
Forward Bias:
R=0 (almost)
Reverse Bias:
almost no conduction
A curiosity. The statement: “The diode conducts when the
applied voltage is greater than Vmin” is an artifact of
plotting I vs. V on a linear scale, see IV curves below:
Reverse-biased p-n junctions
• All of our detectors are based on reverse
biased p-n junctions.
• When the p-n junction is reverse-biased, the
current that flows is small (nA-µA).
• The most important thing that happens is that
the width of the depleted region, i.e., the
region with no free carriers, grows.
• We’ll understand why this is important later.
Width of depeletion region, reverse
biased p-n junction
In many cases, NA >> ND or ND >> NA; then if NB
is the smallest of the two:
Or, in terms of resistivity:
Numerically (V in Volts and ρ in Ωcm) for Si:
Basic structure for many Si strip detectors
Real structures much more complicated, will see later
P+
Few µm
N
L=300-500 µm
•As we apply a reverse bias voltage, the size of the
depletion region grows into the n-side.
•At some voltage the whole N region is depleted
• depletion voltage Vdep
negligible
•Typical: L=300 µ m, ρn= 5 kΩ-cm à Vdep ~ 70V
Basic structure for many Si strip detectors (cont.)
0
P+
Few µm
L=300-500 µm
x
x=0
E(x)
Vdep
or more
N (depleted)
Electric Field
x
With typical parameters from previous page, E max ~ 4800 V/cm
Capacitance, like parallel plate:
As the reverse-bias-voltage Vbias is increased from 0,
the depth of the depletion region increases, and the
capacitance decreases as
Until it reaches a constant value at Vbias = Vdep
Measuring C vs. Vbias is the standard way to find Vdep
(and from Vdep, ρ and impurity concentration).
A preview of things to come
• Charged particles going through Si make e-hole
pairs.
• In a depleted diode, e and h do not recombine
(much).
• The electric field pushes the charges (e and h)
to the opposite sides of the diodes.
• The carge from e and/or h is collected (not
literally!) on electrodes on the two sides.
• Collected charge is signature of charged
particles going through the diode.