Semiconductor Very Basics

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1 Semiconductor Very Basics Material (mostly) from Semiconductor Devices, Physics & Technology, S.M. Sze, John Wiley & Sons Semiconductor Detectors, H. Spieler (notes) July 3, 2003

2 Conductors, Semi-Conductors, Insulators Characterized by resistivity, ρ Conductor: Cu ρ ~ Ω-cm Semiconductor: Si ρ ~ Ω-cm Very dependent on impurities, T Insulator: Fused Quartz: ρ ~ 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) ~ Ω

3 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

4 Diamond lattice (Si & Ge too) Two interpenetrating fcc lattices with one sub-lattice displaced from the other by ¼ the distance along the diagonal each atom surrounded by 4-equidistant nearest-neighbors.

5 Miller Indeces Orientation of plane through lattice can be characterized by Miller Indeces: (1,0,0) (1,1,0) (2,1,0)

6 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)

7 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.

8 Bands Isolated atoms brought together to form lattice discrete atomic levels shift to form energy bands

9 Energy Bands (cont.) Insulator SemiConductor Conductor E g : band gap (1.12 ev for Si) Note: kt ~ ev at room temp.

10 Energy Bands (cont.) Probability that e - state of energy E is occupied is given by the Fermi-Dirac function: where E F is the Fermi energy. Remember: kt << E g

11 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 N c (N v ) is the density of states in the conduction (valence) band. For pure Si, n ~ cm -3 at 300 K, corresponds to ρ = 400 kω cm

12 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.

13 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

14 Aside: how do you dope? Diffusion Ion Implantation

15 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.

16 Mobility Mobility µ defined by V = µe V = carrier velocity E = applied electric field µ = eτ/m eff τ =mean time between collisions (~ psec) m eff = effective mass of electrons/holes The probability of collisions, and hence τ and µ, depend on the concentration of impurities and the temperature.

17 Mobility (cont.) In Silicon, hole mobility ~ 1/3 of electron mobility

18 Resistivity Not surprisingly, the resistivity is a function of the mobility and the density of charge carriers High impurity concentration low resistivity Where n = e-concentration p = hole-concentration µ e = electron mobility µ p = hole mobility

19 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 -- D ++ N Acceptor Ions Donor Ions Hole (+) Diffusion Electron (-) Diffusion The Depletion Zone (D) is a region with no charge carriers

20 The p-n junction no ext V Difference of potential V bi (built-in potential) Thin depletion region, length W where N A and N D are the acceptor and donor concentrations Typically: V bi ~ 0.7 Volts, W < 1 µm

21 p-n junction Forward bias P - + N + Volts - 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!

22 Diode IV characteristics Reverse Bias: almost no conduction Forward Bias: R=0 (almost)

23 A curiosity. The statement: The diode conducts when the applied voltage is greater than V min is an artifact of plotting I vs. V on a linear scale, see IV curves below:

24 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.

25 Width of depeletion region, reverse biased p-n junction In many cases, N A >> N D or N D >> N A ; then if N B is the smallest of the two: Or, in terms of resistivity: Numerically (V in Volts and ρ in Ωcm) for Si:

26 Basic structure for many Si strip detectors Real structures much more complicated, will see later P + N Few µm L= 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 V dep negligible Typical: L=300 µ m, ρ n = 5 kω-cm V dep ~ 70V

27 Basic structure for many Si strip detectors (cont.) P + N (depleted) 0 V dep or more Few µm L= µm x=0 x E(x) Electric Field With typical parameters from previous page, E max ~ 4800 V/cm x

28 Capacitance, like parallel plate: As the reverse-bias-voltage V bias is increased from 0, the depth of the depletion region increases, and the capacitance decreases as Until it reaches a constant value at V bias = V dep Measuring C vs. V bias is the standard way to find V dep (and from V dep, ρ and impurity concentration).

29 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.

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