Solar Cells, Sluggish Capacitance, and a Puzzling

Observation 

Tim GfroererDavidson College, Davidson, NC

with Mark WanlassNational Renewable Energy Lab, CO

~ Supported by Bechtel Bettis, Inc. and the American Chemical Society – Petroleum Research

Fund ~

Experiments by . . .

Kiril Simov (Davidson ’05)

Patten Priestley (Davidson ’03)and Malu Fairley (Spelman ’03)

Outline

• Semiconductors, defects, and solar cells• Diode capacitance and the DLTS

experiment• Our measurements and an unusual result• A new model for minority carrier

trapping/escape during DLTS

Semiconductors

PeriodicPotentialPhyslet

r

V(r) Energy levels

Spacing decreasing

n=3

n=2

n=1

a

a

--

f ree atoms atomic crystal

5.6 5.7 5.8 5.9 6.0 6.10.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

I nAs

GaAs

SevereMismatch

InPSubstrate

Band

gap

(eV)

Lattice parameter (Angstroms)

InGaAs Bandgap vs. Alloy Composition

Bandgapvs. LatticePhyslet

Semiconductor Defects

Lattice-Mismatch Applet

Defect Level Physlet(from the forthcoming Physlet Quantum Physics: An Interactive Introduction to Quantum Theory

by Mario Belloni et al., due out this Fall

Solar Cell Operation

Conduction Band

Valence Band

PHOTONEN

ER

GY

ELECTRON

E-Field

E-Field

HOLE

E-Field

E-Field

+ +

++

---

-

-

CURRENT

ABSORPTION

When a photon is absorbed, an electron is excited into the conduction band, leaving a hole behind in the valence band.  An internal electric field sweeps the electrons and holes away, creating electricity.

Defect-Related Trappingand Recombination

Conduction Band

Valence Band

EN

ER

GY Defect Level

-

+

PHONONS

PHONONS

But electrons can recombine with holes by hopping through defect levels and releasing phonons (heat). This loss mechanism reduces the efficiency of a solar cell.

Defect-Related Transition Probabilities

P ~ 10-

3

P ~ (0.5)10 ~ 10-3

P ~ 10-5

P ~ 10-1

P ~ (0.5)16 ~ 10-5

P ~ (0.5)4 ~ 10-1

The probability P of transitions involving phonon emission depends on the number of phonons required, which is determined by the position of the defect level in the gap.

-

+ + +

- -

p/n Junction Formation

NP+

++

+++++++

+

--

- -

-

+++++++

+++++

Depletion Layer

+-

+

+

-

-

+

+

+

-

-

-

+

+

+

-

-

-

+

Bias-Dependent Depletion

+

+-

- NP+

++

+++++++

+

-

-

-

+++++++

+++++

Depletion Layer

+-

+-

- +

+

+

-

-

+ -

-

With Bias

Diode Capacitance

No bias

Reverse bias

d1 Vbuilt-in

Vbuilt-in+Vapplied

d2

C = Q/V

~ 0A/d

Reverse bias increases the separation between the layers where free charge is added or taken away.

EN

ER

GY

Defect characterization via DLTS

+

+-

- NP+

++

+++++++

+

-

-

-

+++++++

+++++

Depletion Layer With Bias

+-

+-

- +

+

+

-

-

+

Temporary Reduced Bias

Depletion Layer With Bias

Depletion Layer With Bias

-

-

+

+ -

-

Temporary Reduced Bias

+

+

Typical DLTS Measurements

0.0 0.1 0.2 0.3 0.4 0.5

e-6

e-5

e-4

e-3

e-2

e-1

e0

T = 200K T = 180K T = 160K T = 140K

Capaci

tance

Change (

a.u

.)

Time (ms)

Pulsetowardzerobias

Return to steady-state reverse bias

free carriers

trapped carriers

DLTS Experimental Setup

Computer with LabVIEW

Temp Controller

Pulse GeneratorCryostat with sample

Digital Scope(Tektronix)

(1)(2)

(3)

(4)

(5)

Oxford77K

Agilent

Capacitance meter (Boonton)

Device Structure and Band Diagram

m (S) InP N = 3x10 cmD

18 -3

0.1 m (S) InP N = 1x10 cmD

19 -3

0.5 m (S) In Ga As N = 3x10 cm

0.53 0.47

D

16 -3

0.05 m (Zn) In Ga As N = 1x10 cm

0.53 0.47

A

19 -3

0.05 m (Zn) InP N = 2x10 cmA

18 -3

0.05 m (Zn) In Ga As N = 1x10 cm

0.53 0.47

A

19 -3

{ + + + - -- -+

Quasi EF,n

Conduction band

Valence bandp+/n Junction

-Quasi EF,p

Energy

Position

Depletionregion

W

Transient Capacitance: Escape

0.0 0.1 0.2 0.3 0.4 0.5

e-8

e-6

e-4

e-2

Steady-State Bias = -1.1VPulse = +0.1V

Cap

acita

nce

Cha

nge

(a.u

.)

Time (ms)

T = 130K T = 140K T = 145K T = 150K T = 160K

70 80 90 100e2

e4

e6

e8

e10

e12

esc

= 110 s

and SS Bias = -0.1Vand SS Bias = -1.1Vand SS Bias = -2.1V

Average Ea = 0.29 eV

Esc

ape

Rat

e (

s-1)

1 / kT (eV-1)

Pulse = +0.1V relative to SS

Filling Pulse Dependence: Capture

-200 0 200 400 600 800

e-7

e-6

e-5

e-4

e-3

e-2

e-1

T = 77K

Pulse Length: 10 s 30 s 100 s 200 s

Ca

pa

cita

nce

Ch

an

ge

(a

.u.)

Time (s)0 200 400 600

e-8

e-7

e-6

e-5

e-4

e-3

e-2

cap

= 113 +/- 2 s

Steady-State bias = -0.3VPulse: +0.2V (relative to SS)

C0 -

C

trap

s (a.

u.)

Pulse Length (s)

T = 77K

Proposed Model

+ + + - -- -+

Quasi EF,n

Conduction band

Valence band

Traps

p+/n Junction

-Quasi EF,p

Energy

Position

Depletionregion

d

W

Testing the Model

0.0 0.2 0.4 0.6e-10

e-8

e-6

e-4

e-2

Cap

acita

nce

chan

ge

C0

(a.u

.)

Time (ms)

Bias = -0.1V Bias = -1.1V Bias = -2.1V Bias = -3.1V

Pulse = +0.1VT = 77K

0 1 2 3

e-1

e0

e1

e2

e3

d W C

0 (a.u.)

Thi

ckne

ss (

nm)

Reverse Bias (V)

Variable-Bandgap Lattice-Mismatched Stuctures

Undoped InAsyP1-y, 30 nm

Undoped InxGa1-xAs, 1.5 μm

Undoped InAsyP1-y buffer, 1 μm

Undoped InAsyP1-y step-grade region:0.3 μm/step (~ -0.2% LMM/step), n

steps

Undoped InP substrate

Radiative Recombination

Conduction Band

Valence Band

PHOTON

EN

ER

GY

-

+

light in = heat + light out

radiative efficiency = light out / light in

heatlight in

light out

0.0 0.1 0.2 0.3 0.4 0.5 0.6100

104

108

1012

1016

Den

sity

of S

tate

s (c

m-3eV

-1)

Energy (eV)

Defect-Related Density of States

Valence Band

Conduction Band

EN

ER

GY

The distribution of defect levels within the bandgap can be represented by a density of states (DOS) function as shown above.

0

20

40

60

80

100

EV

EC

Energy

Log(

DO

S)

Eg = 0.80 eV

10231019 1021 1025

Ra

dia

tive

Eff

icie

ncy

(%

)

e-h Pair Generation and Recombination (cm-3s-1)

Radiative Efficiency Measurements

heat

light

1018 1020 1022 1024

0

20

40

60

80

100

EC

EV

EC

EV

Eg = 0.68 eV

Energy

Log(

DO

S)

Energy

Log(

DO

S)

Ra

dia

tive

Eff

icie

ncy

(%

)

e-h Pair Generation and Recombination (cm-3s-1)

Four Conclusions• 0.29eV hole trap is observed in n-type

InGaAs under reverse bias• Temperature-dependent capture and

escape rates are symmetrical• Rates level off at cold temperatures due to

tunneling• Device modeling points to defect states

near the p+/n junction

Two References• T.H. Gfroerer et al., APL 80, 4570 (2003).• T.H. Gfroerer et al., IPRM (2005).