1. 4.3.4 Photoconductive Devices
We have for a photoconductor the steady state excess carrier concentrations generated by an
optical generation rate gop:
n=ngOP and p=pgOP (n ≠p if trapping is present) (4-16)
The change in photoconductivity is:
∆ = qgOP(nn + pp) (4-17)
Considerations in choosing a photoconductor:
(1) sensitive wavelength range (determined by Eg)
(2) time response (, device geometry)
(3) optical sensitivity ( and )
Examples of photoconductors: InSb (0.18eV); Ge (0.67eV); Si(1.11eV); CdS (2.42eV)
Applications of photoconductive devices: light detectors that can be used in automatic night
lights, burglar systems, moving object counters…

2. 4.4 Diffusion of Carriers
4.4.1 Diffusion Processes
Two basic processes of current conduction:
Drift in an electric field
Diffusion due to a concentration gradient
Net flow of particles
Diffusion is the result of the random motion
the individual particles!

3. Figure 4—12
Spreading of a pulse of electrons by diffusion.

4. Figure 4—13
An arbitrary electron concentration gradient in one dimension: (a) division of n(x) into segments of length equal to a mean free path for the electrons; (b) expanded view of two of the segments centered at x0.

5. Diffusion Current Density
The electron and hole flux density (rate of flow per unit area) due to diffusion:
(4-22a)
(4-22b)
The electron and hole diffusion current density:
(4-23a)
(4-23b)
Dn and Dp are electron and hole diffusion coefficients, respectively.

6. Total Current Density
In the presence of both an electric field and a carrier gradient, the current density will each
have a drift component and a diffusion component:
(4-23a)
(4-23b)
The total current density is:
J(x)=Jn(x) +Jp(x) (4-24)
Minority carrier can contribute to current flow significantly by diffusion !

7. The Variation of Band Energy with E (x)
—Assume an electric field E (x) in x direction, we expect: (1) Electrons will drift;
(2) Electron potential energy U(x) will vary in x direction
—If the electrostatic potential due to electric field E (x) is V(x), we have:
V(x)=U(x)/(-q) Note: POTENTIAL=ENERGY/CHARGE
—The definition of electric field,
—Choose Ei as a convenient reference,
(4-25)
Fig. 4-15
(4-26)

8. Figure 4—14
Drift and diffusion directions for electrons and holes in a carrier gradient and an electric field. Particle flow directions are indicated by dashed arrows, and the resulting currents are indicated by solid arrows.

9. Figure 4—15
Energy band diagram of a semiconductor in an electric field %(x).

10. Einstein Relation—the relation between  and D
At equilibrium, if there is a diffusion current (e.g., due to doping gradient or band gap
variation), it must be balanced by a built-in field to give zero net current flow,
(4-27)
Use
Eq.(4-27) becomes:
(4-28)
Because
And that EF is constant at equilibrium, Eq. (4-28) reduces to:
Einstein relation
(4-29)
Valid for either carrier type!

11. 4.4.3 Diffusion and Recombination; The Continuity Equation
Consider both diffusion and recombination, we have:
(4-31a)
Continuity Equations
(4-31b)
If the current is strictly by diffusion:
(4-33a)
Diffusion Equations
(4-33b)

12. Figure 4—16
Current entering and leaving a volume ∆xA.

13. 4.4.4 Steady State Carrier Injection; Diffusion Length
In the steady state case the diffusion equations become
(4-34a)
Steady State Diffusion Equations
(4-34b)
diffusion length
Let us assume that excess holes are injected into a semi-infinite semiconductor bar at x=0,
and that at the injection point p(x=0) = p is constant. The solution to Eq. (4-34b)
has the form:
(4-35)

14. We expect p decay to zero for large x due to recombination, therefore C1=0. Similarly, the
condition p = p at x=0 gives C2=p, and the solution is:
(4-36)
The physical significance of Lp (or Ln)
p = (1/e) p at x = Lp (2) Lp is the average distance a hole diffuses before
recombining. <x>=Lp
(4-40a)
(4-40b)

15. Figure 4—17
Injection of holes at x = 0, giving a steady state hole distribution p(x) and a resulting diffusion current density Jp(x).

16. 4.4.6 Gradients in the Quasi-Fermi Levels
At equilibrium, there is no gradient in the Fermi level EF
In the steady state, there is a gradient in the quasi-Fermi level due to drift and diffusion
The total electron current becomes:
(4-51)
(4-52a)
Modified Ohm’s Law
(4-52b)

17. 4.4.5 The Haynes-Shockley Experiment
Figure 4—18
Drift and diffusion of a hole pulse in an n-type bar: (a) sample geometry; (b) position and shape of the pulse for several times during its drift down the bar.

18. Figure 4—19
Calculation of Dp from the shape of the dp distribution after time td. No drift or recombination is included

19. Figure 4—20
The Haynes–Shockley experiment: (a) circuit schematic; (b) typical trace on the oscilloscope screen.