a.carbone, r.introzzi and h.c. liu physics department and infm, politecnico di torino c.so duca...

A.Carbone, R.Introzzi and H.C. Liu

Physics Department and INFM, Politecnico di TorinoC.so Duca degli Abruzzi, 24 – 10129 – Torino, (Italy)

Institute for Microstructural Sciences, National Research Council, Ottawa, Ontario, K1A 0R6 (Canada)

Photocurrent Noise in QWIPs:Theory and Experiment

Vb

Lb Lb

Lw

Ve

Vc

I e

EE

Fqw

1

EFe

0

Vw

Emitter

Collector

Redistribution of potential in the presence of radiation

M.Ershov, H.C.Liu, M.Buchanan, Z.R.Wasileski, V. Ryzhii, Appl.Phys.Lett. , 70, 414 (1997).

V. Ryzhii, J.Appl. Phys. 86, 6586, (1997)

V.Letov, M.Ershov, S.G.Matsik, A.G.U.Perera, H.C.Liu, Z.R.Wasilewski and M.Buchanan, Appl.Phys. Lett. 79, 2094, (2001)

Redistribution of potential at different applied bias

Noise gain Si/4eI

Samples

AlGaAs/GaAs QWIPs with the same design except the number of wells N

Well number: N = 4, 8,16, 32 Barrier width: Lb=241Å Well width: Lw =62Å Area=240x240 m2

Dark-current noise

1 10 100 1000 100001E-22

1E-21

1E-20

1E-19

1E-18

1E-17 (a)

16 wells

8 wells

4 wells

I=1.0mAdark

32 wells

SI(f

) [A

2 /Hz]

f[Hz]

Photo-current noise

1 10 100 1000 100001E-22

1E-21

1E-20

1E-19

1E-18

1E-17 (a)

16 wells

32 wells

8 wells

I=1.0mAirradiated

4 wells

SI(f

) [A

2 /Hz]

f [Hz]

A.Carbone, R.Introzzi and H.C.Liu, Appl.Phys.Lett., 82, (2003)

Dark-current noise

1 10 100 1000 100001E-23

1E-22

1E-21

1E-20

1E-19

32 wells

16 wells

8 wells

4 wells

SI(f

) [A

2 /Hz]

I=0.2mAdark

f [Hz]

Photo-current noise

1 10 100 1000 100001E-23

1E-22

1E-21

1E-20

1E-19

32 wells

16 wells

4 wells

8 wells

(b)

I=0.2mAIrradiated

S I(f) [

A2 /Hz]

f[Hz]

Power spectra over 4eI/N

21

p1

NeI40S

c

I )(

0.2 0.4 0.6 0.8 1.0 1.21

10

100

SI/4

eI/N

(f=2

0Hz)

I[mA]

32 wells 16 wells 8 wells 4 wells dark

f=20Hz

Contents

Noise measurements (in the dark and in the presence of IR radiation) in QWIPs with different number of wells.

Limits of the noise models, based on the continuity equation valid for standard semiconductors (models proposed so far).

Necessity of a noise model based on the QWIP continuity equation (proposed in this work).

c

nxnv

tn

To calculate the spectral intensity of the fluctuations in homogeneous semiconductors, a white noise excitation source (x,t) is applied to the right side of the first-order continuity equation :

Under the assumption that the transit time is much longer than the carrier recombination time the well-known expression:

dc

2c

2

2c

0n 14S

)(

If the carriers are photogenerated, the above relationship still holds provided that the thermal generation rate is replaced by the photo-generation rate . JS

The responsivity is obtained by the same differential equation:

)(

PnRn

c

cn i1R

)(

0

Since each photogenerated carrier induces a current pulse , the current noise power spectral density and the responsivity are obtained:

dpeg /

)(IS )(IR

2c

2pI 11eIg4S

)(

cpI i1

1gheR

)(

21

p1

NeI40S

cI )(

If , taking into account the expression of the photoconductivity gain gp for QWIPs

c

ppi p

1ege0R

)(

Np

cp Np

1g 0

Since for QWIPs having identical growth sequence but different N, the quantum efficiency:

N

1k

ks kLx

txnv

tn )(

The transport and the generation-recombination of carriers in QWIPs are described by the equation:

In order to calculate the spectral intensity of the fluctuations, a white noise excitation source k(x,t) is applied to the right side of the previous relationship

)(tjep

t k0

N

1k

ck

kLx

0.01 0.1 1 100.1

1

10

32 wells 16 wells

8 wells 4 wells

Cur

rent

Noi

se P

ower

Spe

ctru

m (a

.u.)

(a.u.)

0.1 1 100.1

1

10

32 wells

16 wells

8 wells

Cur

rent

Noi

se P

ower

Spe

ctru

m (a

.u.)

(a.u.)

4 wells

J-E zoomc

pdarki p

1eP

EJEJR

)()()(

10 15 20 25 30 350.0

1.0

2.0

3.0

4.0

5.0N=8N=32 N=4N=16

T=90K

Cur

rent

[10-4

A]

Electric Field [kV/cm]

0.2 0.4 0.6 0.8 1.0 1.21

10

N=32 N=16 N=4 N=8

1/p

c

I[mA]

Conclusion• The photocurrent noise, measured in QWIPs having

the same growth sequence but different number of wells, shows features related to the discrete structure of the device.

• A noise model based on the continuity equation developed for QWIPs instead of that valid for homogeneous semiconductors, seems to be able to account for the experimental results.