Progression of Ideas and Concept Summary for Introduction to
Semiconductor and Device Physics
Modern Physics of Solids
1. Lattices and Crystal Structure
2. Quantum Mechanics, particle in a potential energy well; electron tunneling, solid state
drives, optical communication (FIOS)
3. Hydrogen Atom and the Periodic Table
4. Quantum Mechanics of Crystalline Solids, Insulators, Metals and Semiconductors, band
structure and band gap.
Doping and Carrier Transport
5. Start with intrinsic semiconductor: n=p=ni
6. Dope semiconductor to be N-type (donors) or P-type.
7. Two types or current: Drift (from electric field) and Diffusion (from concentration
gradient driven by random motion)
8. Uniform doping: n-type: Nd is the same everywhere and Na = 0 or Nd >> Na (No
diffusion current).
9. Uniform doping: p-type Na is the same everywhere and Nd=0 or Na>> Nd) (No diffusion
current).
10. Jndrift=qunE, Jpdrift=qupE; mobility (u) is the proportionality constant between electric
field and average carrier velocity.
11. Jndiff=qDdn/dx, Jpdiff=-qDdp/dx; Diffusivity (D) is the proportionality constant between
the carrier concentration gradient and the current density.
12. Non-uniform doping at equilibrium: Drift Current is equal and opposite to Diffusion
Current and a Built-in Electric Field and Built-in Electric Potential is established.
13. Phi built in = ɸo = Vt ln(n1/n2) is approx. = Vt ln(Nd1/Nd2) for nonuniformly doped
N=type. Or n1 = n2 exp(ɸo/Vt)
PN Junction
14. A PN junction is a two terminal device that allows current to flow in on direction but not
the other.
15. PN Junction: Again have non-uniform doping, n-side with Nd (donors) and the p-side
with Na (acceptors).
16. PN Junction is by definition non-uniformly doped since one side is Na and the other is
Nd.
17. PN Junction at equilibrium: Drift and Diffusion balance each other and built-in potential
is established.
18. Phi built in = ɸo = Vt ln(NdNa/ni2)
19. Forward bias: Apply voltage to reduce electric field and built in potential (positive to Pside). This reduces amount of drift current so now diffusion is greater than drift and
current flows.
20. Reverse bias: Apply voltage in other direction, increases potential and field, but no
carriers to pull back since they have already all been pulled back during equilibrium.
21. Derivation of diode equation. Solve current and continuity equations in bulk regions for
minority carrier concentrations. Apply boundary conditions and take derivative to get
diffusion currents.
BJT (NPN or PNP), the following refers to an NPN
22. A BJT is a Three Terminal Device, where the input into the Base controls the flow of
current between the Collector and Emitter.
23. Composed of two PN Junctions back to back; the base length is very short; and the Nd
doping in the emitter is much greater than the Na doping is the base.
24. Analysis almost the same as PN junctions:
a. Base-Emitter Junction Forward biased,
b. Collector-Base Junction Reverse biased
25. Operation
c. Many electrons from Emitter diffuse through forward biased BE junction into
base and then swept into collector forming Ie1 & Ic.
d. A few electrons that diffuse from emitter recombine with holes in the base to give
rise to one component of the base current (Ie2 and Ib1)
e. Some holes from P-base diffuse to across F-B B-E junction to give rise to second
component of base current (Ie3 and Ib2). But since the N-type doping in the
emitter is much greater than the P-type doing in the base, this current is very small
compared to Ic and Ie1.
26. Beta = Ic/Ib.
f. Since the collector current due to electrons diffusing from the emitter and through
the base and then swept into the collector is much greater than either of the two
components of hole current, Beta is typically very large (about 100 or more).
27. The collector current into the BJT (Ic) is mainly controlled by the B-E voltage, (or the
base current)
MOSFET: Metal Oxide Semiconductor Field Effect Transistor
28. A MOSFET is a three terminal device where the voltage applied to the gate controls the
current flow between the drain and the source. (There is a fourth terminal, the body, but
that is fixed at ground or at the supply voltage, so don’t worry about it.)
29. The MOSFET structure is similar to a BJT, but these is an oxide between the gate contact
and the semiconductor.
30. The voltage between the gate and source inverts the surface and creates a conducting
channel of mobile electrons (N-channel MOSFET), those electrons are then swept into
the drain by the voltage between the drain and the source. This gives rise to the drain
current.