External Photoemission - unipv · The total current in the photodiode is thus the sum of I ph. Basic diode equation is an approximant of such a sum. In particular, at high reverse

PHOTODIODES 1

External PhotoemissionExternal Photoemission

Steps of photodetection in semiconductors

• absorption of photons in the material ( α, P=P0 exp -αL)

• production of charge carriers ( hν>Eg

λs [µm] = hc/E = 1.24 / E[eV] ),

• drift of charge carriers under an internal electric field( junction, high µ)

• collection of charge carriers at the ohmic contacts

PHOTODIODES 2

MaterialsMaterials andand structuresstructures

• single semiconductors Si, Ge, Se, etc. • binary compounds GaAs, InSb, PbS, PbSe, etc., • ernary compounds GaAlAs, InGaP, HgCdTe, PbSnTe • quaternary compounds InGaAsP, etc. energy gap Eg: from several eV to a few 10meV, spectral range (or threshold λs): from the UV to the far IR.

Structures:

photodiodes (pn, pin, ms and avalanche), bipolar and unipolar phototransistors, photo-SCR, photoresistances

PHOTODIODES 3

Features of semiconductor detectorsFeatures of semiconductor detectors

PRO’s

•compact size and flexibility of geometry •low bias voltage •spectral range fromdeep UV to far IR• high peak quantum efficiency•uniformity of performance parameters• excellent ruggedness wide temperature range• excellent mean time to failure (MTTF)• space and hostile ambient qualification• generally low cost

CON’s

• very large areas difficult• no single-photon capability, GB not the best• temperature dependence

PHOTODIODES 4

PhotodiodePhotodiode’’ss familyfamily

A sample of popular semiconductor

photodetectors: single-element photodiodes in

metal and ceramic packages, linear arrays

of photodiodes and high frequency SMD

photodiodes with integrated preamplifier

PHOTODIODES 5

pnpn--junction Photodiodejunction Photodiode

Vbb+-

ANODE CATHODE

window

(SiO )2

depletion

layer

metallization

(Al)

p n

Φ

Eg

0

bbV

DRIFT

ELECTRON DIFFUSION

HOLE DIFFUSION

z0

P = P e0-αz

L

w

n pLW

energy

metallurgical

junction

hν

PHOTODIODES 6

Absorption coefficientAbsorption coefficient

200 300 400 600 800 1000 1400 2000

10

α (cm )

-110

10

10

10

10

1

2

3

4

5

66

0.01

0.1

1

10

100

1000

L (

µm)

abs

1.02345 1.5 0.8 0.6

hν (eV)

ZnS SiC

GaP

PbO

GaAs

Si

InP

Ge

InAs

InGaAsP

InSb

WAVELENGTH λ (nm)

Absorption coefficient α

(and Labs =1/ α) strongly varies with

λ in all semiconductors

(data for T=300 K)

PHOTODIODES 7

Refraction indexRefraction index ofof semiconductorssemiconductors

1.023456 0.8 0.6

200 300 400 600 800 1000 1400 2000

1

2

3

4

5

INDEX OF REFRACTION n

WAVELENGTH λ (nm)

GaP

SiO 2

Si N3 4

InSb

Si

Si

InP

Ge

GaAs

InAsGaSb

hν (eV)

refraction index of semiconductor

materials of typical photodiodes is fairly

high (usually >3), giving a large

reflection loss at entrance window

PHOTODIODES 8

Reflection lossReflection loss atat entranceentrance windowwindow

200 300 400 600 800 1000 1400 20000

0.2

0.4

0.6

REFLECTION COEFFICIENT R

GeInAs

GaAs

Si

InP

λ/4

SiO2Si

Si N3 4 Si

WAVELENGTH λ (nm)

1.023456 0.8 0.6hν (eV)

reflection R of vacuum-

semiconductor interfaces,

untreated (full lines) and single-

layer anti-reflection coated

PHOTODIODES 9

Spectral sensitivitySpectral sensitivity (UV .. NIR)(UV .. NIR)

spectral sensitivity

σ(λ) [A/W] = = I/P =

= ηeλ/hc = η λ[µm]/1.24

η=100%1.0

.1

.01

.001

SPECTRAL SENSITIVITY σ (A/W

)

2

5

3

4

6

8

2

5

3

4

6

8

2

5

3

4

6

8

200 300 400 500 600 800 1000 20001400

1

0.5

0.2

Si

ARC-ML

Si

(ext. UV)

Si

standard Si mis

Ga P

GaAsP

mis

Si

ARC-SL

GaAs

Si pn/pin

W=1000 µm 300

100

Ge

WAVELENGTH λ (nm)

In Ga As

on InP substrate

.53 .47

2

5

20

10

50

PHOTODIODES 10

Spectral sensitivitySpectral sensitivity (MIR .. FIR)(MIR .. FIR)

10

1.0

.1

.01

WAVELENGTH λ (mm)

2

5

3

4

6

8

2

5

3

4

6

8

2

5

3

4

6

8

2 3 4 5 6 8 10 20 2414

1

10

50

20

5

2

0.5

0.2

12 16

η=100%

Ge:Cu

4 K

InSb

77 K

HgCdTe

-70 °C

22°C -70°C 77 K

InAs

PbS

77 K

PbSe

77 K

Ge:Au

4 K

Si:As

4 K

SPECTRAL SENSITIVITY σ (A/W

)

Hg Cd Te

77 Kx 1-x

SiPt ms

300 K

PHOTODIODES 11

pnpn--junction Characteristicsjunction Characteristics

V0.5 1

-0.5-20-40-60-80

I (µA)

3

2

1

-1

-2

0

1

2

P = 3 µW

50 1

2

5

10

20

500

200

100

R Cs b

(Ω) (pF)

C

R

b

s

ak

(V)

-3

Iph =σP

I = Io [Iph eV/nkT)-1] -Iph

PHOTODIODES 12

DarkDark currentcurrent andand ideality factorideality factor((advanced topicadvanced topic))

From Shockley standard analysis of the pn-junction, ideality factor is unity (n=1) and reverse current Id is :

Id = A e ni2 [(Dp/LpND)+(Dn/LnNA)]

≈ A e ni2 (Dp/LpND) (for NA>>ND)

where A=PD active area, Dn,p=minority diffusion constants, Ln,p=diffusion lengths, ND,A=doping concentrations of donor/acceptor; ni, intrinsic concentration of charge carriers is:

ni2 = NC NV exp -Eg/kT ∝ T3 exp-Eg/kT,

Taking for (D/L) a dependence Tγ from temperature, it is:

Id ∝ T3+γ exp -Eg/kT, (independent from V)

The, temperature coefficient of the dark current Io=Id is:

dIo /Io dT = [3+γ +Eg/kT] / T ≈ 0.33 [3+γ +Eg/kT] (%/°C, 300 K)

These eqs. apply at weak current levels or when the intrinsic concentration of charge carrier ni is not too low.

PHOTODIODES 13

DarkDark currentcurrent andand ideality factorideality factor((advanced topicadvanced topic, 2), 2)

Another contribution is generation-recombination in the depleted region, through defect levels near bandgap middle, which give:

I = Ig-r [exp (eV/2kT) - 1],

it has an ideality factor n=2; in addition, the reverse saturation current is:

Ig-r = A e ni W / 2τwhere W=width of the depleted region, τ =1/(√3kT/m)σtNt is charge carriers lifetime, dependent on Nt and on cross-section σt of the g-r levels.The term Ig-r has (through W) a dependence Vβ upon voltage, with β=1/2 or 1/3 for abrupt or gradual junctions; its temperature coefficient is:

dIo /IodT = [2+Eg/2kT]/T ≈ 0.33[2+Eg/2kT] (%/°C at 300 K)The total current in the photodiode is thus the sum of Iph. Basic diode equation is an approximant of such a sum. In particular, at high reverse bias the dark current is the sum of the two-saturation terms:

I = - Io = - Id - Ig-r

Trend is that of diffusion (n=1) for ni (Dp/LpND)> W/2τ, and of g-r (n=2) in the opposite case.

PHOTODIODES 14

DarkDark currentcurrent andand saturationsaturation((advanced topicadvanced topic, 3), 3)

In direct or zero bias, we obtain an ideality factor n=1 for voltage

V > (2kT/e) ln [(W/2τ)/(niDp/LpND)], n=2 otherwise.A final contribution to I0 is from surface states, interfaces defects giving bangap levels. This is important only in PDs with very low I0.

PD saturation :at high Iph, saturation determines the maximum signal detectable with linearity (III quadrant), the logarithmic conformity, and the voltage in the photovoltaic mode (IV quadrant). A saturation is caused by storage of charge Q collected at the boundary of undepleted regions after drift in the junction. When Q= Iphτ, (τ=drift time) is comparable to charge (Q=CbV) supplied by ionized dopant atoms to sustain applied voltage V, junction field decreases and a reverse fields appear in undepleted regions, thus impeding increase of Iph with increasing P. For a p+n PD:

Iph(sat) = A e NA µ* V / 2W

where µ* =(1/µn+1/µp)-1 is effective mobility. If generation is in the neutrality region p+ (as, in the UV) the limit is lower [that of diffusion times (τ=Ln

2/Dn)]:

Iph(sat) = A e NADn / 2W Ln2

PHOTODIODES 15

Equivalent CircuitsEquivalent Circuits

R

R

RCg

phI

A

s

K

pCV

I u

R

C

(a)

(b)

(c)

Cg

pC Rnphi 2

nbi 4kTB____

sR

4kTB R s

R pRp

2

p

A

KC

-V bb

Vu

u

basic biasing scheme of a pn- PD

small-signals equivalent circuit

noise equivalent circuit

PHOTODIODES 16

Frequency responseFrequency response

PD frequency response results from:

- extrinsic cutoff due to the Z(ω) of the parasitics external to thejunction

- intrinsic cutoff inherent to the collection of photogenerated charges internal to junction

From the small-signal circuit:

Vu (ω) = Iph(ω) Z(ω) =

Iph(ω) Rp//(1/jωCg)//[Rs+(R//(1/jωCp)]/[1+Rs/(R//(1/jωCp)]where // is parallel operation,

Z(ω) = effective impedence seen by the PD (extrinsic cutoff)

Iph(ω) =f (ω) P(ω), signal current duplicating P(ω) with a tranferfunction f(ω) (intrinsic cutoff)

PHOTODIODES 17

Frequency responseFrequency response (2)(2)

Taking R>>Rs maximizes PD response (good for instrumen-tation applications with a modest B) and:

Vu(ω) /Vu(0) = [Iph(ω)/Iph(0)]/[1+jω(Cg+Cp)(Rp//R)]

and the 3-dB cutoff frequency is:

f2 = 1 / 2π(Rp//R)(Cg+Cp)

For maximum speed of response, R is taken small so Cp in is short-circuited (response is sacrificed). For R<Rs :

Iu(ω) /Iu(0) = [Iph(ω)/Iph(0)]/(1+jωCgRs)

and cutoff frequency:

f2 = 1 / 2πRsCg

PHOTODIODES 18

Frequency responseFrequency response (3)(3)

Mean transit time to collection by drift (and induced current duration):

τd(z) = (1/2) (τdn +τdp) =(1/2) [(W-z)/vn + z/vp]

integrating on z (uniform generation)

τd =(1/2) W(1/vn+1/vp) = (W2/2Vbb)(1/µn+1/µp)

= W2 / 2Vbb µ*

Frequency cutoff: f2d = 0.44 / τd

Mean diffusion time to collection from undepleted regions τDn,p = Ln,p

2/Dn,p

Frequency cutoff: f2d = 1 /2π τDn,p

A pole-zero frequency response is found (varies with λ)

PHOTODIODES 19

ZeroZero--pole in pole in pnpn--PDsPDs

1

.1

ff2D f2d

λ = 400 nm

600 nm

700 nm

800 nm

log

.01

relative response

I (

ω) / I (0)

ph

ph

In a pn-PD, intrinsic frequency response has a zero-pole region between f2D (diffusion) and f2d (drift), more markd at smaller λ. Typical values are f2D=1 MHz, f2d=200 MHz.

PHOTODIODES 20

pnpn and and pinpin junction PDsjunction PDs

A K+

depleted

region W

p n

W

i n

z

z

EE

d

NA

d

D

D

ND

E

z

zz

z

VV

0 0

0 0

dA

D

ND

N A

bb

bbV

0z

EB

V Vbb

0z

B

bbV

0 0

p

PHOTODIODES 21

designdesign nomogram fornomogram for SISI pnpn--junction PDsjunction PDs

C

(pF/mm )

5

2

2

10

1.0

1000

5

100

5

2

5

141010

1310

15 10

1610

17

1.0

0.1

10

100

5

5

5

2

2

2

W

(µm)

10 ps

100 ps

10 nsτ = 1 nsd

p n - Si+

1000 V

100 V

1 V

D-3N (cm )

10 V

5

P

Q Vbd

breakdown limit

b2

PHOTODIODES 22

designdesign nomogram fornomogram for Si pinSi pin--junction PDsjunction PDs

i-3N (cm )

5

2

2

0.01

0.001

5

0.1

5

2

5

τ (ns)d

pin - Si

1 10 100 1000

1.0

breakdown

limit

V (V)bb

2 C (pF/mm )2

b

1016

1015

1014

100

50

20

5

10

2 0.51

50

1

2

5

10

20

100

W =200 µm

PHOTODIODES 23

AdvantagesAdvantages of pin overof pin over pn PDspn PDs

• thickness W of the absorption region is independent from Vbb, (which has no influence on the spectral response; a goodη is got even at low bias Vbb near threshold λ≈λs)• with W>> dA,dD, diffusion contribution is small -(frequency response is independent of λ)• since E≈const in the active layer, intrinsic speed ofresponse is optimized (time τd);• reverse current (and g-r contribution) is nearly independent of Vbb, whence a very high value of Rp.

PHOTODIODES 24

SchottkySchottky (or metal(or metal--semiconductor)semiconductor) PDsPDs

V = 0

Em

m n

B

AV = +V

nm

bb

Eg

V = -Vbb

pm

V = 0

m p

Em B

AEF

PHOTODIODES 25

Heterojunction PDsHeterojunction PDs

+

A K

p n

A K

p i<

p n

P e - α z20

0 w z 0

power

energy

P e - α z20

g2E

g2Eg1E

g1E

g1E

g1Eg1Eg1Eg1E g2Eg2E g1E

z

PHOTODIODES 26

LatticeLattice matchingmatching inin heterostructuresheterostructures

a)

b)

c)

A material with a lattice size different from substrate (a)will produce a layer with

dislocation defects (b), but, if layer is very thin (c) , it is strained and layer has no

defects

PHOTODIODES 27

Lattice,Lattice, compositioncomposition andand energyenergy gapgap

d - lattice constant (nm)

0.64

0.62

0.60

0.58

0.56

0.54-0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2 2.2 2.4

semiconductor

semimetal

bandgap: direct - - - indirect

1.0 0.52310 4 1.5 0.60.8 0.7

Al SbGa Sb

Al As

In As

In P

Al P

Ga P

Cd TeHg Te

Sn Te Pb TeIn Sb

Ge

Sis-Ge . . . . . . . . . . . . .

Cd S

λ (µm)s

In Ga As.53 .47

Ga As

E (eV)gENERGY GAP

threshold wavelength

____

PHOTODIODES 28

Common PDCommon PD structuresstructures

R

p

n+

p+

A

K

G

(a)

Al

(b)

(c)

n+

n+

i

p+

A

K

p+

n

p+ p

A

n

K

m

A

K

(d)

(f)

p

A

In P p+

InP n

C

n

B

(e)

InP n+

InGaAs i

n

E

n+

i

p+

K

SiO2 V

bb

+

-