[Nonuniform primary photocurrent spreading [Nonuniform primary photocurrent spreading in quantum well infrared photoconductors]in quantum well infrared photoconductors]

M. CookM. Cook

Solid State PhysicsSolid State Physics

Phys 8510Phys 8510

$$ 25,000,000.0025,000,000.00

Even in the darkest caves, we can easily distinguish this man from

Mr. Laden

Probably no electricity in the caves of Tora Bora!

Background informationBackground information

Metal vs. Metal vs. Semiconductor Semiconductor

Drift-diffusion Drift-diffusion approximationapproximation

Analytical equations Analytical equations describing physical describing physical processes in QWIPprocesses in QWIP Rate equation(s)Rate equation(s) Continuity equationContinuity equation

Simplified model we incorporated:Simplified model we incorporated:

Assumed the Assumed the dark currentdark current could be made negligibly could be made negligibly small by making QWIP with large barrier width when small by making QWIP with large barrier width when compared with QW widthcompared with QW width

Neglected contact effects which have been shown to Neglected contact effects which have been shown to play important roles for QWIP performance. This is play important roles for QWIP performance. This is especially true for detectors having a relatively small especially true for detectors having a relatively small number of QWsnumber of QWs thermoionically assisted injection currentthermoionically assisted injection current

Only study steady state mode of operationOnly study steady state mode of operation this case is assumed to give threshold amount of this case is assumed to give threshold amount of

lateral spreading which would be present in any lateral spreading which would be present in any QWIP described by our model QWIP described by our model

Ershov et al., J. Appl. Phys. 82, 1446 (1997)

Physical Processes in QWIP

What is the lateral current distribution here?

0

.2 V

.5 V

.8 V

Bias V

oltage

Ershov et al., J. Appl. Phys. 82, 1446 (1997)

Ban

dedg

e pr

ofil

e

distance

Conduction band diagrams for different applied voltages

5 QWs GaAs / Al0.25Ga0.75As

“Band-bending”

Basic Equations (current density):Basic Equations (current density):

Assume current Assume current density:density:

--Drift-diffusion Drift-diffusion approximation approximation

neDEenzyxJ

),,(

EElectrostatic scalar potential

Diffusion coefficient

electrons per unit volume

electron mobility

Basic Eqns. of model (continuity equation for Basic Eqns. of model (continuity equation for continuum state electrons) – continuum state electrons) – steady statesteady state

jIJet

n

1

,jax

Source terms

If (exact locations of QWs)

What about when ?jax

0

.0jI

Source terms (continuum state Source terms (continuum state electrons)electrons)

when x is any multiple of the fundamental length a, i.e. exactly at a QW, the continuity equation is no longer homogeneous and must now be described by some Ij which is dependent on QW index

RGGI Toj

Optical excitation of bounded electrons

Thermal excitation of bounded electrons Capture of continuum

state electrons

-0.2

0

0.2

0.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Ds=103 cm2s-1

Ds=102 cm2s-1

Ds=10-1 cm2s-1

45 QWs

(10-5

cm)

Cur

rent

den

sity

(A

/cm

2 )

-0.1

0.0

0.1

0.2

0.3

0.0 0.5 1.0 1.5 2.0 2.5 3.0

45 QWs

Ds = 103 (cm2s-1)

Ds = 102 (cm2s-1)

J (

)

0.2

0.3

0.4

0.5

0.6

0.7

0 200 400 600 800

45 QWs

20 QWs

5 QWs

<

> (

10-5 c

m)

Ds (cm2s-1)

Plots of average lateral smearing vs. Ds for three separate systems

For systems with many periods, the performance of QWIP is a

strong function of

Ds

Spreading is more pronounced for Ds = 102 cm2s-1

Optimal performance of device for points of minima

on the graph

0.2

0.3

0.4

0.5

0 50 100 150 200

45 QWs

20 QWs

<

> (

10-5 c

m)

Ds (cm2s-1)