More on HgCdTe detectors for Astronomy

M. Robberto

“P on N” design

Metallurgy

BASE LAYER

In-doped

CAP LAYER

undoped

IMPLANT

As-dopedGold

STOICHIOMETRY (Hg1-xCdxTe) vs. DOPING (In, As)

Geometry

~10 micron~1 micron

~1

mic

ron

REM

OV

ED

DLPH: Double Layer Planar

Heterostructure

DLPH: Double Layer Planar Heterostructure

- The CAP Layer has more Hg, wider band gap-Passivation is done with CdTe-Passivation needs protection (“overcoating”)

Heterostructure

REM

OV

ED

In concentration~1015 cm-3

As is “ion implanted”

Built-in field

REM

OV

ED

N-typeCathode

P-typeAnode

-0.05V +0.05V

( => direction of dark current)

Reverse bias

REM

OV

ED

N-typeP-type-0.250V

Vsub

Vreset

0.0V

Photogeneration

REM

OV

ED

N-typeP-type-0.250V

Vsub

Vreset

0.0V

Photogenation FORWARD biases the junction

REM

OV

ED

N-typeP-type-0.250V

Vsub

Vreset

0.0V

Reset

End of integration

The “unit cell equation”

Q C V

Differentiate:dQ CdV VdC

CCdV V dVV

CC V dVV

If :detdQ I dt

detIdVCdt C VV

Detector capacitance

And it is immediate to calculate also the derivative.

Detector currentdet dark photonI I I

, exp 1 + exp 12

b i bdark SAT diff

g

eE eWn eEI IKT KT

photI e

Iphot is negative because the convention is to assume Idark >0 under forward bias.

HEAT

HEAT HEAT

HEATHEAT

GR

DIFF

DIFF

Diffusion current

• Diffusion is a slow process;• Last only as long as the carrier lifetime.

Shockley Equation

2 exp forward biasexp 1

1 reverse bias

h ediff i

h d e

bb

a

eEeE

kTK

eD eDI n

TL N L N

,

, , , , ,

,

: detector biasD : minority carrier diffusion coefficient on the n,p side of the junction

L : diffusion lenght. It is L , with minority carrier lifetime

N : donor/acceptor concen

h e

h e h e h e h e h e

d a

V

D

trations

n : intrinsic carrier concentrationi

1/2 1/22

,

/ /h h e eSAT diff i

d a

I ekT nN N

(this is A/cm2)

• depends on mobility and recombination time scales (delicate to control)• depends on doping (easier to control)• proportional to ni

2

Generation-Recombination current

The Shockley equation neglects the current due to generation and recombination of charges in the depletion region. Both majority and minority charges are swept away by the electric field, become majority carrier in the neutral layer and generate a current that can be detected.

Generation-Recombination current

exp forward biasexp 1 2

21 reverse bias

iG R

g

bbeWn

eEeE

kTKT

I

20

0 0

: width of the depletion region: minority carrier lifetime in the depletion region

: built-in voltage = / ln /

: permittivity of the semiconductor material ( , = 8.854E

g

a d i

r

W

E kT e N N n

-12 F/m is the permittivity of the free space)

1

0

/22 1 1

(assumes abrupt junction)d a

bW E Ee N N

(this is A/cm2)

• similar to the expression for the diffusion current. G-R proportional to ni • Factor of 2 due to the detection of both majority and minority carriers• term E0 – Eb accounts for the size of the depletion region (in reverse bias Eb=-Erev)

Intrinsic Carrier ConcentrationFrom Hansen and Schmit (1983)

for T>50K.a)Calculate ni for the four cases of Eg (Ex.1).

Using ε=(20.5-15.5x+5.7x2) ε0, calculate

b) W (depletion width)c) Cjun (junction capacitance)

Assuming Vbuiltin =0, Vbias=-250mV, Nd=1E15cm-3, Na=1E19 cm-3, and 18micron pix.size.

Other dark current sources

• Band-to-band tunneling• Trap-assisted tunneling• Surface region tunneling• Surface leakage• Other leakages

a)Tunneling is independent on temperature.b)These phenomena dominate at low temperature.