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Solid State Detectors

Astronomy 6525

Lecture 5

A6525 - Lecture 5Solid State Detectors 2

Outline Semiconductor Models Pure Semiconductors Doped semiconductors Bohr model for impurities Expected spectral response Photoconductivity

Unwanted impurities Photoelectron dynamics Photoconductive Gain

Supplemental Material References Photovoltaic detectors

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The Band Theory of Solids

Bring atoms together and the levels merge

The “valence states” and “conduction states” are analogous to the ground and excited states in the isolated atom.

BandGap

Tight binding approximation

Two levelAtoms

ConductionBand

ValenceBand

Metal, Insulator,or Semiconductor


Examples: H and He

Suppose we start with atomic hydrogen It forms a metallic solid since there are N e- and 2 N

levels for them in the 1s state.

An electron can migrate from one atom (proton) to the next with no additional energy.

If we start w/ helium The “broadened” 1s level is full because of the 2, 1s

electrons are present.

The e- cannot move an insulator

To move the e- must move up to the next (2s) level (Band)

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Semiconductors and Insulators

Valence Band

Band Gap

Conduction Band

Ev

Ec

Eg

Valence Band

Eg

Ec

Band Gap

Conduction Band

Ev Valence States

Conduction States

In a semiconductor or insulator, there is a threshold excitation requirement, Eg, for the e- to attain the conduction band

The filled band is called the valence band, while the unfilled one is called the conduction band The bandgap energy, Eg is the energy between the highest energy levels in the

valence band, and the lowest energy level in the conduction band For room temperature semiconductors: 0 < Eg < 3.5 eV

“metal”“semiconductor”

“insulator”


Band Gap

Si, Ge, InSb are “insulators” Have Eg = Eband gap ~ 20 kTroom

Thermal fluctuations (phonons) can excite an electron across the band gap.

Because there are many free (empty) levels, the electron and the hole left by it are free to move.

E

Valence Band

Band Gap Eg

Conduction Band

e-

hole (+)

ThermalExcitations

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Pure Semiconductors Pure semiconductors, i.e. Si and Ge, are called Intrinsic.

Material Eg(eV) λc(μm)Diamond 5.33 0.23Si 1.11 1.12Ge 0.67 1.85SiC 2.86 0.43

If the temperature of the material is low There will be few electrons in the conduction band.

A photon with Eph > Eg Eph (eV) = 1.24/λ(μm) can move an electron from the valence to the conduction band

Current can flow

We have a photon detector !!


Periodic TableH1

1s

Na11

3s

K19

4s

Rb37

5s

Cs55

6s

Mg12

3s2

Ca20

4s2

Sr38

5s2

Ba56

6s2

He2

1s2

Si14

3s23p2

P15

3s23p3

S16

3s23p4

Cl17

3s23p5

Ar18

3s23p6

Al13

3s23p

Ge32

4s24p2

As33

4s24p3

Se34

4s24p4

Br35

4s24p5

Kr36

4s24p6

Ga31

4s24p

Sn50

5s25p2

Sb51

5s25p3

Te52

5s25p4

I53

5s25p5

Xe54

5s25p6

In49

5s25p

Pb82

6s26p2

Bi83

6s26p3

Po84

6s26p4

At85

6s26p5

Rn86

6s26p6

Tl81

6s26p

Zn30

3d10

4s2

Cu29

3d9

4s2

Ni28

3d8

4s2

Co27

3d7

4s2

Fe26

3d6

4s2

Mn25

3d5

4s2

Cr24

3d4

4s2

V23

3d3

4s2

Ti22

3d2

4s2

Sc21

3d4s2

Outer electron configurations of neutral atoms in their ground states are shown.

Cd48

4d10

5s2

Ag47

4d9

5s2

Pd46

4d8

5s2

Rh45

4d7

5s2

Ru44

4d6

5s2

Tc43

4d5

5s2

Mo42

4d4

5s2

Nb41

4d3

5s2

Zr40

4d2

5s2

Y39

4d5s2

Hg80

5d10

6s2

Au79

5d9

6s2

Pt78

5d8

6s2

Ir77

5d7

6s2

Os76

5d6

6s2

Re75

5d5

6s2

W74

5d4

6s2

Ta73

5d3

6s2

Hf72

5d2

6s2

La57

5d6s2

IIb

Ib

VIIIb

VIIb

VIb

Vb

IVb

IIIb

Ia

IIa VIIaVIaVaIVaIIIaLi3

2s

Be4

2s2

C6

2s22p2

N7

2s22p3

O8

2s22p4

F9

2s22p5

Ne10

2s22p6

B5

2s22p

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More semiconductors Two-element compounds that symmetrically span column

IVa in the periodic table are often semiconductors.

Material Eg(eV) λc(μm)AlAs 2.16 0.57 III-VAlP 2.45 0.51AlSb 1.6 0.78GaAs 1.43 0.87GaP 2.26 0.55GaSb 0.7 1.8 InAs 0.36 3.45InP 1.35 0.92InSb 0.18 6.9

Material Eg(eV) λc(μm)CdS 2.42 0.51 II-VICdSe 1.73 0.72CdTe 1.58 0.79ZnSe 2.7 0.46ZnTe 2.25 0.55AgBr 2.81 0.44 I-VIIAgCl 3.33 0.37PbS 0.37 3.3 IV-VIPbSe 0.27 4.6 PbTe 0.29 4.3

Adapted from Rieke (1996)See http://en.wikipedia.org/wiki/List_of_semiconductor_materials for a comprehensive list of semiconductor materials.


Periodic TableH1

1s

Li3

2s

Na11

3s

K19

4s

Rb37

5s

Cs55

6s

Be4

2s2

Mg12

3s2

Ca20

4s2

Sr38

5s2

Ba56

6s2

C6

2s22p2

N7

2s22p3

O8

2s22p4

F9

2s22p5

Ne10

2s22p6

B5

2s22p

He2

1s2

Si14

3s23p2

P15

3s23p3

S16

3s23p4

Cl17

3s23p5

Ar18

3s23p6

Al13

3s23p

Ge32

4s24p2

As33

4s24p3

Se34

4s24p4

Br35

4s24p5

Kr36

4s24p6

Ga31

4s24p

Sn50

5s25p2

Sb51

5s25p3

Te52

5s25p4

I53

5s25p5

Xe54

5s25p6

In49

5s25p

Pb82

6s26p2

Bi83

6s26p3

Po84

6s26p4

At85

6s26p5

Rn86

6s26p6

Tl81

6s26p

Zn30

3d10

4s2

Cu29

3d9

4s2

Ni28

3d8

4s2

Co27

3d7

4s2

Fe26

3d6

4s2

Mn25

3d5

4s2

Cr24

3d4

4s2

V23

3d3

4s2

Ti22

3d2

4s2

Sc21

3d4s2

Outer electron configurations of neutral atoms in their ground states are shown.

Cd48

4d10

5s2

Ag47

4d9

5s2

Pd46

4d8

5s2

Rh45

4d7

5s2

Ru44

4d6

5s2

Tc43

4d5

5s2

Mo42

4d4

5s2

Nb41

4d3

5s2

Zr40

4d2

5s2

Y39

4d5s2

Hg80

5d10

6s2

Au79

5d9

6s2

Pt78

5d8

6s2

Ir77

5d7

6s2

Os76

5d6

6s2

Re75

5d5

6s2

W74

5d4

6s2

Ta73

5d3

6s2

Hf72

5d2

6s2

La57

5d6s2

IIb

Ib

VIIIb

VIIb

VIb

Vb

IVb

IIIb

Ia

IIa VIIaVIaVaIVaIIIa

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“Doped” semiconductors Doped semiconductors are called Extrinsic.

Photons of lower energy can ionize an electron or hole to produce a carrier.

C

V

Egelectronsholes Eg

Some combinations of elements may not be viable. Lattice structure breaks down at interesting concentration levels

Difficult to do the chemistry to make it


n-type doping Add electrons, e.g. Si:Sb, Si:P, and Si:As.

C

V

Egelectrons

C

V

Material Eg(eV) λc(μm)Si:Sb 0.039 31.8Si:P 0.045 27.6Si:As 0.054 23.0

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p-type doping Add holes, e.g. Si:In, Si:B, and Si:Ga.

C

V

Egholes

C

V

Material Eg(eV) λc(μm)Si:B 0.045 27.6Si:Ga 0.072 17.2

Ge:Ga 0.011 113.0Ge:Be 0.024 51.7


= Si

= Sb

e-

Bohr model for impurities

Angular momentum quantization: nh/2π = mvr

Effective mass: m → meff

Force equation:

2222

2

4n

m

mrn

em

hr

effo

eff

επ

ε ==

2

22

r

ermeff ε

ω =

ro = 0.53 A

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Energy levels

This is idealized. Not all impurities are the same!

Some actual values for λo.

Si:B ~ 30 μm

Ge:Ga ~ 120 μm

ε meff/m r(A) En=1(eV) λo(μm)Si 11.7 0.25 25 0.025 50Ge 15.8 0.12 70 0.0065 190

2

22

2 εεn

m

mR

r

eE eff

o−=−= Ro = 13.6 eV

λo = hc/E1


Ionization energies of impurities

.012 .013 .11.14.18.28 .30

.0096.0093

.01 .01 .01 .011 .011 .02.06

GAP CENTER

Li P As S Se TeSb

B Tl Ga In Be ZnAl

.035

.095

0.66eV

Ge

.045 .054 .21.14.069.039.033

.045 .067 .072.16

.3 .34

GAP CENTER

Li P As Bi Te TiSb

B Ga In Tl PdAl

1.12eV

Si

See Sze, Physics of Semiconductor Devices

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Photon Detector

For quasi-monochromatic radiation P/hν = # photons/sec (P = power)

If we have one electron per photon Current = (# e-/sec)·e = e·P/hν

Responsivity [Amps/Watt] Rmax = e / hν = 0.81·λ(μm) in Amps/Watt

The actual responsivity will be

R = ηG ·Rmax η = Quantum Efficiency

G = Photoconductive Gain


What is the spectral response?

No (or little) response for hν < EB.

Peak response for hν ~ EB.

Decreasing response for hν > EB. Ionization cross-section decreases for hν > EB.

(σν ∝ ν -3 like H-atom)

Only one e-/photon but more energy per photon

increases asdown goes watt

sec/ of No. ν−

e

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Expected spectral responsePeak

Cut-off wavelength

∝ ν -4

log λ

log

R (

amps

/wat

t)

For an optically thin detector


Absorption cross-sections of impurity dopants in Si and Ge

Peak optical absorption cross sections vs. cutoff wavelengths of impurity dopants.

After Rieke (1996)10 100

Si: Acceptors

Si: Donors

Ge: Acceptors

Ge: Donors

Pea

k ab

sorp

tion

cro

ss-s

ecti

on (

cm2 )

10-13

10-14

10-15

10-16

10-17

10-18

λCO (μm)

CuBe

In

GaAl Cu

As

SbBe Ga

SbAs

P

PB

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Photoconductivity

Photoconductor The electrical conductivity of

a semiconductor is increased by photons which promote electrons into the conduction band.

Photoconductors can be either intrinsic or extrinsic.

Expect the (photo)current, id, to depend on the photon flux.

Vb

id

id ∝ Nph (ph/sec)

C

V


Unwanted impurities

Real semiconductors have impurities both n-type (donors) and p-type (acceptors)

Consider a semiconductor with excess donors

C

V

Donors (some ionized)Acceptors (all ionized)

C

V

Which looks like

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Photoelectron dynamics

A photon can ionize one of the neutral donors.

C

V

Electron sits near its creation sight for some amount of time and then recombines with one of the D+s.

D+ holes are left by the ionization of donors by impurity acceptors in the detector.


Electron traps

The electron moves toward the positive electrode. It may be captured by any of the D+s and stop.

The presence of acceptors produces traps (D+s) that can terminate the motion of a photoelectron.

Applying an electric field, the e- drift toward the + end. The D+s stay in place since they cannot move.

-+

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Photoconductive Gain Photoconductive gain (G)

One typically defines the photoconductive gain by the product of the mobility, μe of the e- × lifetime of e- × electric field strength, εx, divided by the interelectrode spacing:

G = τe·μe·εx/d = vx·τe/d = e/d In practical terms this is the ratio of the distance traveled, e, to the

interelectrode spacing, d: G = e/d

If there are large numbers of acceptors (“dirty” semiconductor) then e << d and the detector is not very responsive. Note 1: The detector may still have a high quantum efficiency but

it just doesn’t produce any current. Note 2: G can be > 1 since electrons can leave the detector and be

replaced by e- from the - electrode. This will continue until the e-recombines with a D+.


Photoconductive detector model

Under the influence of an electric field, E, the electron-hole pair will each drift.

The drift velocities will be

vn = - μnEvp = μpE

where μn, μp = mobilities for negative and positive carriers.

At T ~ 290 K, μn ~ 102 - 104 cm2/V/sec and μp ~ μn/10

See Boyd, page 162

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PC Detector Model - (cont’d)

Suppose monochromatic light with power, P, at frequency, ν, falls onto the detector.

P

V i w

Let S be the surface density of conduction-band electrons (electrons/unit area of detector surface) due to both thermal & photo-electrons.

Let ΔS be the contribution from photo-excited electrons.


PC Detector Model - (cont’d)

τνη S

wh

P

t

S Δ−=ΔΔ

Let τ be the lifetime of the electron in the conduction band

Which in steady state giveswh

PS

ντη=Δ

If the bias voltage is V, then the drift velocity is

whereEnn μ−=v

VE =

νη

h

PGeweSi n =Δ−= vThe photocurrent is then

2

|v|

VG n μττ ==G, the photoconductive gain,

increases with applied voltage

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Limitations of Photoconductors Cannot dope too high because “dark current” increases due

to e- hopping towards + end (hopping current). ND ~ 1015 - 1016 cm-3

To get a high η must make this thick (> 100 μm) to geta high optical depth

aePabsτ−−= 1

For τa ~ 1 det ~ 100 μm

detDDa N στ =

ND = 1016 cm-3

σD = 10-14 cm-2

Show time constant effects (hook response, spiking, etc.)

Susceptible to ionizing radiation due to size


Blocked Impurity Band Detectors Many more donors than

for a photoconductor: ~1017 cm-3

Impurity levels < 1012 cm-3extrinsic (15-40μm thick)intrinsic (3-5μm thick)

Apply a bias Because of the high

doping levels the D+’s migrate towards the - end

Current cannot flow because of the blocking layer

+

-

Blocking layer

Depletion region

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BIB Detectors (cont’d) The photogenerated e-

moves towards the + end and can pass by the blocking layer.

No D+ to recombine with along the way so G = 1.

+

-

BIB is a “brand” name coined by Rockwell Inventor of the BIB (Rockwell/Boeing/DRS Tech)

IBC: Impurity Band Conduction Name used by other companies


BIB Advantages

High doping: good photon absorption

broader wavelength coverage

D+ depletion: good e- collection efficiency

Intrinsic layer: blocks dark current

Small size: easier to make arrays

less susceptible to ionizing radiation

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BIB Structure

Back-Illumination for arrays.

Si

TransparentContact

ReflectingContact

Intrinsic SiBlocking LayerIR Active

Region

Back-Illuminated Blocked-Impurity-Band -> BIBIB


Supplemental Info

References: Radiometry and the Detector of Optical Radiation (Boyd)

Excellent book on theory

Detection of light from UV to sub-mm (Rieke) detectors, readout, etc.

Photovoltaic Device See slides

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InSb Photoconductors: the Problem

For InSb it is not possible to simultaneously achieve both high G, and large resistance If G is small, signals are small likely dominated by

amplifier noise

If the resistance is small, the system will be dominated by Johnson noise (more later)

The situation is identical for Hg1-xCdxTe detectors, which are an alternative type in the near-IR

The situation is ameliorated by using the InSb or Hg1-xCdxTe materials as photodiodes


InSb Photoconductors: the Problem

Consider construction of an InSb intrinsic photoconductor for the 1-5 μm region The carrier lifetime, τe ≈ 10-7 s, μe ≈ 105 cm2V-1s-1

So that:G = τe·μe·εx/ ≈ 10-2 V/2

The breakdown voltage for InSb is small can only make G ~ 1 by making the physical size of

the device, , small. However, the detector resistance is:

Rd = /(σwd), where σ =qn0 μe Since the electron mobility in InSb is ~ 100 times that

of silicon, it is not possible to achieve high R, with small

Not shown in class

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Photovoltaic Detectors

Photovoltaic devices produce a photocurrent (or voltage) w/o a external bias.

C

V

p-type n-type

EF = Fermi level

EFdonors

acceptors

At room temperature most of the impurities will be ionized. (Fermi level => 1/2 occupancy)

E

p-n junction photodiode:


Photovoltaic Detectors When the two materials are brought into electrical contact,

the electrons and holes can diffuse: recombination occurs.

Depleted ofmobile charge

Not neutral

CB

VB

Depletion Region

Space Charge Region

EDevelopment of E-fieldstops diffusion.

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PV Detectors (cont’d) The electric field creates a potential difference, Vo,

between the p- and n-type materials.

current flows easilycurrent must overcome Vo

Electrons flow between the materials until the Fermi levels are in equilibrium

A diode

Vo

E

p-type n-typeCB

VB


Diode behavior – Reverse Bias

If we add to the contact potential (+ voltage applied to n-type material) this is termed reversed bias

The voltage drop appears across the depletion layer because this region has a large resistance (due to the depletion of mobile charges) The increased V increases the width of the

depletion zone, and Rjunction

Eventually the junction breaks down and becomes highly conducting

Vo - VaC

V

breakdown

reverse bias forward biasp

n

i

Va

Va

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Diode behavior – Reverse Bias, 2 At modest reverse biases, breakdown

can occurs via tunneling: If the conduction band in the n-type is

brought below the energy level of the valence band in the p-type material, and the width of the depletion region is small enough that the electron’s wave function can extend across it.

At high reverse biases, breakdown occurs by avalanching: The strong field accelerates a free

electron in the p-type region so strongly that it then can create additional conduction electrons through collisions Figure 4.3 in Reike:

tunneling through a junction

Not shown in class


Diode behavior – Forward Bias

If we subtract from the contact potential (+ voltage applied to the p-type material), this is termed forward bias This decreases the width of the depletion zone If the bias voltage is larger than Vo, then the

junction becomes strongly conducting.

Vo - VaC

V

breakdown

reverse bias forward biasp

n

i

Va

Va

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PV Depletion Region Size

Poisson’s eq’n:

)( 2 VEV −∇=−=∇ερ

Assume 1) junction at x = 02) NA = constant, x < 03) ND = constant, x > 0

Depletion Region

CB

VB

Space Charge Region

We also have

and

np xxdx

dVE ≥−≤=−= , 0

aopn VVVV −=−− )()(

NA = acceptor densityND = donor densityp = width of acceptor regionn = width of donor region


PV Depletion region size (cont’d)

=2

2

dx

Vd

0 << x-eN

pA

ε

nD x

eN<<− 0

εotherwise 0

Poisson’s Eq’nis then:

Solving gives:

=V( ) 0 2

22 <<+ x-xx

eNpp

A ε

( ) nnD xxx

eN <<−− 0 2

22

ε

( )2/1

/2

−

+= ao

DA

ADp VV

NN

NN

e

ε ( )

2/1/2

−

+= ao

DA

DAn VV

NN

NN

e

ε

where

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PV Depletion region size (cont’d)

nDpA NN =

Since the overall charge is neutral

The total width of the region is (p + n):

( )2/1

2

−+= ao

DA

DA VVNN

NN

ew

ε

Differentiating the voltage to get the electric field gives

=E

( ) 0 <<+− x-xeN

ppA

ε

( ) nnD xx

eN <<−− 0

ε


Plots of PV junction Parms

x

ρ(x)

ND

-NA

x

E(x)

p

-n

x

V(x)

( )w

VVE ao −−= 2

max

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Junction Capacitance Photodiodes have relatively high capacitance since the

distribution of oppositely charged particles across the junction forms a parallel plate capacitor with a small separation between the plates

This large capacitance limits the frequency response of the photodiode, and thereby drives the limiting noise of the readout electronics. Also, V = Q/C, higher C => lower voltage for a given charge. So

for a given voltage noise of the output amplifier (detector), this results in a higher (photoelectron) “read noise” [Q = CVoutput_noise]

A faster junction is a PIN diode p-type – intrinsic (insulator) – n-type junction


Junction Capacitance Stored charge per unit area

Q = eNAp in p-type region

-Q in n-type region

The p-n junction has a junction capacitance, which changes with voltage

For junction area, A, the differential capacitance is

w

A

VVNN

NNeA

dV

dAeN

dV

dQAC

aoDA

DA

pA

εε =

−+

=

==

2/11

2

Note that the capacitance decreases for an increasing negative bias.

Change of size of depletion region with bias change C

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Current flow through the p-n junction

Diffusion current, ind, electrons that enter the junction in the CB of the n-type material

with sufficient energy to overcome the potential barrier

kTeVondnd

aeii /,=

ind,o = electron diffusion current w/ no applied bias (Va)

ipd

Vo - VaCB

VB

p-type n-type

ind


Current flow through the p-n junction

Generation current, ing, that are generated via thermal excitation from the VB to the CB in

the p-type material.

There are analogous contributions from the motion of the positive carriers (holes).

Vo - VaCB

VB

p-type n-type

ing

ipg

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( ) ( )ngpgkTeV

ondopd

ngpgndpd

iieii

iiiii

a +−+=

−−+=/

,,

So that

Current flow (cont’d) The total current is the sum of each contribution

When the bias is zero, there can’t be any current flowing through the junction (isat = saturation current).

sat

ondopdngpg

i

iiii

≡

+=+ ,,

( )1/ −= kTeVsat

aeii

isat depends upon1) area of junction2) carrier mobilities3) recombination rates4) temperature

Typical isat ~ 10-7-10-9 A for Si photodiodes at room temp.


Adding photons

If hν > EB (band gap energy), the a photon will generate an electron-hole pair.

( )1/ −+−= kTeVsat

aeih

ePi

νη

Vo - VaCB

VB

p-type n-type

E

Want to keep isat small => less noise

Best to lower T rather than apply negative bias (keep small)

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Photodetection in a diode

Free carriers that are generated or recombine in either the n or the p-type regions produce little net current because of the low R in these regions

One needs creation of a charge carrier within or very near to a unbiased, or reverse-biased junction, so that it can be driven across the junction by the junction field to produce a net current

Charge carriers can be produced thermally or by photons –we presume that we can freeze out thermal electrons by cooling the device

Not shown in class


Photodetection in a diode – 2 The photodetection process is

illustrated to the right (Rieke F4.5): A photon is absorbed and excites and

e-/hole pair The hole drifts towards the negative

electrode or recombines The e- diffuses through the material

(remember the field drop only occurs across the depletion zone)

If it enters the depletion zone, it is accelerated across the region by the junction potential, creating the photocurrent

The process is the same if the n-type material is illuminated (with e-/hole role reversal)

Not shown in class

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Modes of operation

Photoconductive mode Bias detector negative so that the current is linear with photon flux. This is the usual mode: use constant voltage across the diode, and measure

the current If the voltage across the detector is held at zero, this suppresses certain

types of low frequency noise. Method – transimpedance amplifier – more later

i

VaDarkP0

P1

P0 < P1

P0,1 = incident power

Photovoltaic mode (no bias applied) Measure the output voltage at

fixed current (e.g. high impedance voltmeter)

But, V is non-linear in P:

+=

satcircuitopen ih

eP

e

kTV

νη

1ln

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