Optoelectronically probing the density of nanowire surface trap states to the singlestate limitYaping Dan Citation: Applied Physics Letters 106, 053117 (2015); doi: 10.1063/1.4907882 View online: http://dx.doi.org/10.1063/1.4907882 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/106/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Hidden surface states at non-polar GaN ( 10 1 ¯ 0 ) facets: Intrinsic pinning of nanowires Appl. Phys. Lett. 103, 152101 (2013); 10.1063/1.4823723 Environmental sensitivity of n-i-n and undoped single GaN nanowire photodetectors Appl. Phys. Lett. 102, 213113 (2013); 10.1063/1.4808017 Electronic and structural properties of InAs/InP core/shell nanowires: A first principles study J. Appl. Phys. 111, 054315 (2012); 10.1063/1.3692440 Evidence for surface states in a single 3 nm diameter Co 3 O 4 nanowire Appl. Phys. Lett. 96, 262106 (2010); 10.1063/1.3457449 Surface states and origin of the Fermi level pinning on nonpolar GaN ( 1 1 ¯ 00 ) surfaces Appl. Phys. Lett. 93, 192110 (2008); 10.1063/1.3026743

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Optoelectronically probing the density of nanowire surface trap statesto the single state limit

Yaping Dana)

University of Michigan—Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University,Shanghai 200240, China

(Received 4 November 2014; accepted 19 January 2015; published online 5 February 2015)

Surface trap states play a dominant role in the optoelectronic properties of nanoscale devices.

Understanding the surface trap states allows us to properly engineer the device surfaces for better

performance. But characterization of surface trap states at nanoscale has been a formidable

challenge using the traditional capacitive techniques. Here, we demonstrate a simple but powerful

optoelectronic method to probe the density of nanowire surface trap states to the single state limit.

In this method, we choose to tune the quasi-Fermi level across the bandgap of a silicon nanowire

photoconductor, allowing for capture and emission of photogenerated charge carriers by surface

trap states. The experimental data show that the energy density of nanowire surface trap states is in

a range from 109 cm�2/eV at deep levels to 1012 cm�2/eV near the conduction band edge. This

optoelectronic method allows us to conveniently probe trap states of ultra-scaled nano/quantum

devices at extremely high precision. VC 2015 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4907882]

Highly sensitive photodetectors can find a wide range of

applications in, for instance, optical interconnect and dark

night vision. In recent years, planar black silicon and other

nanostructured photoconductors, induced by surface trap

states, have shown extraordinarily high photoconductivity

gain (up to 8 orders of magnitude higher than regular pn junc-

tion diodes).1–6 However, the application potential of these

photodetectors is often jeopardized by their slow response

that comes along with the high gain. Engineering the device

surface in a controllable way may allow for the development

of photodetectors with high gain and short response time. But

characterization of surface trap states at nanoscale has been a

formidable challenge using the traditional capacitive techni-

ques based on metal-insulator-semiconductor (MIS) capaci-

tors7 (Fig. 1(a)) and deep level transient spectroscopy

(DLTS),8–11 due to the ubiquitous nature of parasitic capaci-

tances. In this Letter, we demonstrate an optoelectronic

method that allows us to probe the surface trap-state density

of a silicon nanowire to the single state limit.

To understand this method, let us use p-type semicon-

ductors as an example. A highly doped p-type semiconductor

has an extremely high concentration of holes but a very low

concentration of electrons. Under illumination, excess elec-

trons and holes are generated in the conduction and valence

band, respectively. At small injection condition, these excess

carriers are negligibly low in concentration compared to the

majority holes, but often orders of magnitude larger than the

minority electrons. Consequently, the quasi-Fermi level of

electrons (EnF) shifts away significantly from the Fermi level

at equilibrium (EF), while the quasi-Fermi level of holes

(EpF) remains nearly unchanged as EF, as shown in Fig. 1(b).

In general, the shift of quasi-Fermi levels leads to filling the

trap states below EnF (but above EF) with electrons, and those

above EpF (but below EF) with holes. Clearly, for a highly

doped p-type semiconductor at small injection condition,

only the minority electrons get involved in the capture-

emission process of trap states. For every photogenerated

electron captured by trap states, there is one corresponding

hole remaining in the valence band to contribute to photo-

conductance. The shift of EnF will allow a large number of

electrons to be trapped if the density of trap states, at deep

levels in particular, is high, leading to the giant gain in pho-

toconductance that has been widely observed.1–3

When the illumination is turned off, the excess electrons

in the conduction band and those captured by the trap states

FIG. 1. Methods for probing the density of surface trap states. (a) Metal-

Insulator-Semiconductor (MIS) capacitor. The gate voltage drives the Fermi

level to sweep across the bandgap on the Si/SiO2 interface to allow for cap-

ture and emission of charges carriers by surface trap states. (b) Quasi-Fermi

level can be tuned across the bandgap by changing the intensity of optical

illumination. Dn is the excess electron concentration in the conduction band,

and Dnt is the excess electron concentration captured by the surface trap

states. The excess carriers in the valence band can be divided into two parts.

One part (Dp1) corresponds to the trapped electrons Dnt and the other (Dp2)

is equal to Dn. We have DntþDn¼Dp1þDp2.

a)Author to whom correspondence should be addressed. Electronic mail:

yaping.dan@sjtu.edu.cn

0003-6951/2015/106(5)/053117/5/$30.00 VC 2015 AIP Publishing LLC106, 053117-1

APPLIED PHYSICS LETTERS 106, 053117 (2015)

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will all recombine with the excess holes in the valence band

eventually, but the recombination processes are different. For

the electrons in the conduction band, the recombination

occurs almost immediately through surface recombination

centers (�100 ps for unpassivated nanowires12,13). In con-

trast, the electrons in the trap states are first emitted to the

conduction band at a much lower rate (milliseconds to tens of

seconds) and then recombine with the corresponding holes.

With this contrast in time domain, we can decouple these two

processes and separately extract photogenerated electrons in

the conduction band Dn and those in the trap states Dnt by

tuning the modulation frequency of illumination. At high fre-

quencies, for instance, Dnt will not be able to keep up the

pace of the modulation, leaving only Dn to contribute to the

photoconductance. The location of EnF can be found from Dn.

Differentiating Dnt with respect to EnF will allow us to obtain

information about the energy density of trap states.

Following the argument above, we first conduct

four-probe measurements on a single nanowire device

(L¼ 2.4 lm long and 80 nm in diameter) that is Ohmically

contacted by four microelectrodes (Fig. 2(a)). The nanowire

is p-type and the doping concentration is �1018 cm�3. Then

we place the nanowire device under illumination of a mono-

chromatic green light beam (k� 500 nm) that is modulated

on/off by a mechanical chopper. A lock-in amplifier is

employed to pick up the periodic ac photocurrent. For ex-

perimental details, please refer to our previous work.12 The

transient behavior of the nanowire conductance under the

periodic on/off illumination can be described by the red

curve in Fig. 2(b). During the first half period which is under

illumination, the conductance starts with an instantaneous

jump by rph followed by a relatively slow electron capture

process. During the second half period, the light is cut off.

The conductance immediately dips down by rph due to the

fast surface recombination, and then slowly decays by emit-

ting electrons from the surface trap states. Analytically, one

period of the red curve rðxtÞ in Fig. 2(b) can be described

by the equation given below

rðxtÞ ¼rT ½1� exp ð�t=sc � T=ð2scÞ þ u=scÞ� þ rph þ rd �T=2 � t < 0

rT exp ð�t=se þ v=seÞ þ rd 0 � t < T=2;

�(1)

where sc is the capture time constant, se is the emission time

constant, and the constants u and v (Ref. 14) are set to ensure

that the above equation is continuous. rT is contributed by Dp1

which is the excess holes left in the valence band after the cor-

responding electrons captured by trap states. rph is contributed

by Dn and Dp2 in equilibrium. rd is the nanowire conductance

in dark and x¼ 2p/T, with T as the chopping period.

According to advanced mathematics, any function can

be decomposed into an infinite summation of sine and cosine

functions in the following form, so can Eq. (1):

r xtð Þ ¼ a0

2þX1

n¼1an cos nxtð Þ þ bn sin nxtð Þ½ �: (2)

When the signal of above equation is fed into the lock-in am-

plifier, the amplifier multiplies the equation by 2 sinðxtÞ,where x¼ 2pf and f is the chopping frequency (¼ 1/T). All

the terms are still in a waveform after the multiplication,

except bn sinðnxtÞ with n¼ 1 which contains a dc compo-

nent b1. The internal filters inside the lock-in amplifier will

filter out all the wave terms, allowing for only b1, the ampli-

tude of the fundamental term sinðxtÞ, to be picked up. But

FIG. 2. (a) Diagram of experimental

setup. (b) Transient signal input to the

lock-in amplifier. (c) Nanowire ac pho-

toconductance as a function of chop-

ping frequency under illumination of

12.2 W/m2. (d) Frequency dependent

photoconductance under illumination

of different light intensity.

053117-2 Yaping Dan Appl. Phys. Lett. 106, 053117 (2015)

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the lock-in amplifier is designed to display the root mean

square (RMS) instead of the amplitude of this term, meaning

that the reading on the amplifier is jb1j=ffiffiffi2p

. After transform-

ing Eq. (1) into the form of Eq. (2), we find that b1 can be

expressed in the following form:14

b1 ¼1

prT f

T

2sc;

T

2se

� �þ f

T

2se;

T

2sc

� �� ��

2 rph þ rTð Þp

;

(3)

where f a; bð Þ ¼ 1�ea½ �½1þeb�½1�eaþb�½ b

pð Þ2þ1�

:

It is widely known that, for trap states in silicon,8 the

electron capture process is significantly faster than the elec-

tron emission process. In this case, we assume sc ! 0, lead-

ing to

b1 ¼

rT

p1þ exp � T

2se

� �� �

T

2pse

� �2

þ 1

�2 rph þ rTð Þ

p: (4)

By fitting jb1j=ffiffiffi2p

to the experimental data in Fig. 2(c), we

find rph¼ 0.8 nS, rT¼ 3.3 nS, and se¼ 0.4 ms. The photo-

conductance rph comes from both the photoexcited electrons

(Dn in Fig. 1(b)) and their counterpart holes (Dp2). But the

trap-induced photoconductance rT is only contributed by

part of the total excess holes (Dp1) in the valence band,

because the corresponding photoexcited electrons are cap-

tured by the surface trap states. This fact allows us to con-

clude that, under illumination of a light intensity 12.2 W/m2,

the electron quasi-Fermi level EnF of the nanowire shifts from

the original location 0.47 eV below to 0.23 eV above the

mid-bandgap energy level Ei, and that accordingly, a con-

centration 3.3 � 1015 cm�3 of electrons is captured by the

trap states within the range of EnF shift. The conclusion is

based on the fact that the hole mobility lp is estimated to be

�30 cm2/V s which is close to the hole mobilities of silicon

nanowires found in literature.15,16 The electron mobility ln

is assumed to be 3 times of this value.

To find the energy density of trap states, we sweep the

quasi-Fermi energy across the bandgap by tuning the illumi-

nation intensity. The ac photoconductance as a function of

the chopping frequency at different light intensity is illus-

trated in Fig. 2(d). All these curves are fitted by jb1j=ffiffiffi2p

of

Eq. (4) without any visible deviation, indicating that other

effects such as local heating by illumination are negligibly

small. From the fittings, we find a set of rph and rT, and plot

them in Figs. 3(a) and 3(b), respectively. rph is linear with

the light intensity, which shows that small injection condi-

tion is always maintained in the experiments. That is, Dn and

Dp are both negligibly small compared to the majority holes,

and therefore EpF remains almost the same as EF. Based on

this, we conclude that only electrons are involved in the cap-

ture and emission processes of the surface trap states. The

linearity of rph results in a logarithm dependence of EnF on

the illumination intensity, as shown in Fig. 3(a). It is evident

that a small injection of illumination will shift EnF over a

wide range in the bandgap. If the density of trap states in this

range is high, then a large number of carriers will potentially

be trapped to induce a high photocurrent gain. This could be

achieved by properly engineering the device surfaces.

Fig. 3(b) shows the trap-induced photoconductance rT,

which is a little nonlinear with the light intensity but always

remains approximately 4 times of rph for the whole range.

This photoconductance gain is mainly due to the fact that the

trap states on the nanowire surfaces capture a large number

of electrons. The same number of holes is left in the valence

band to contribute to the observed photoconductance. The

capture of electrons on the nanowire surfaces will change the

net surface charges and therefore inevitably modulate the

energy band bending of the silicon nanowire. Clearly, we

cannot exclude the possibility that this “gating effect”17 also

FIG. 3. (a) Photoconductance rph and

quasi-Fermi energy of electrons vs illu-

mination intensity. (b) Trap-states-

induced photoconductance rT as a

function of illumination intensity. (c)

Surface concentration of trapped elec-

trons as quasi Fermi level of electrons

moves up. Inset: a close-up of the first

four data points. (d) Calculated density

of surface trap states of our nanowire

device.

053117-3 Yaping Dan Appl. Phys. Lett. 106, 053117 (2015)

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plays a role in the photoconductance of our device. The non-

linearity of rT could be due to this effect. The “gating effect”

induced by surface trap states has two properties that need to

be pointed out. First, it has the same characteristics in time

domain as the red curve shown in Fig. 2(b). Second, how

strong the “gating effect” is depends on the density of sur-

face trap states, the initial net charge on the device surface

and the size of the device (surface-to-volume ratio),17 all of

which are part of device surface properties. These facts make

us believe that it is more appropriate to incorporate “the gat-

ing effect” as part of the surface properties. By doing so, we

can establish a unified model and quantitatively identify the

nominal density of surface trap states that reflects all the

properties of the device surfaces. The photoconductance gain

induced by the “gating effect” is equivalent to an amplifica-

tion of the density of surface trap states. The amplification

may be large for nanostructures and small for planar devices.

From Fig. 3(b), we calculate the number of excess holes

(Dp1) that contribute to the photoconductance rT.14 The same

number of electrons is captured by the surface trap states of

the silicon nanowire. We plot the surface concentration of the

trapped electrons as a function of EnF shown in Fig. 3(c). The

concentration follows an exponential curve. Amazingly, the

first data point (EnF � Ei ¼ 22meV) has a concentration

almost equal to the unit concentration as only one electron is

trapped on the nanowire surfaces, which is 1.66� 108 cm�2

for the nanowire under investigation (2.4 lm long and 80 nm

in diameter) as shown in the inset. The electron concentration

jumps up to only 3 times of this unit concentration (3 elec-

trons captured) after EnF increases by more than 110 meV

(>4kT, k the Boltzmann constant and T¼ 300 K) to the sec-

ond data point. This indicates that the captured electrons fol-

low the Fermi-Dirac distribution instead of Boltzmann

distribution. Clearly, there must be one trap state located

below or near EnF of the first data point. It is most likely that

one or two trap states are located within the gap between the

first and second data point. A gap of 110 meV is wide enough

to allow these trap states to be spaced far apart so that they

can be filled with electrons one by one. This is the reason

why we observed the quantization in the charge trapping. At

high energy levels, the trap states are located more closely

next to each other. The quantization of charge trapping

becomes increasingly less likely (see the inset).

We calculate the density of surface trap states by simply

differentiating the surface concentration of trapped electrons

with respect to the quasi Fermi energy, as shown in Fig.

3(d). The trend is the same with what is obtained by the C-V

characteristics of nanowire MIS capacitors,7 but our obtained

density is 2 orders of magnitude more precise. At deep lev-

els, the calculated density is accurate since the filling of trap

states is quantized. At higher energy levels where the energy

gaps between trap states are narrower, the density is some-

what overestimated since the electrons have high probabil-

ities to be captured by the states above EnF. We could find an

“accurate” solution of trap states that are distributed in the

full range of bandgap by taking into account the function of

Fermi distribution.14 The solution is accurate in mathematics

but not in physics, because it is known that trap-states at

shallow levels near the conduction band have short capture

and emission lifetimes.18 The highest modulation frequency

at 2000 Hz in our experiments might not be able to catch

those trap states. Therefore, it is not reliable to mathemati-

cally recover the density of trap states at shallow levels from

the existing data.

In conclusion, we have demonstrated a simple but

powerful method to probe the density of surface trap states

by measuring the photoconductance of a silicon nanowire

photoconductor. The photoconductance gain in the nanowire

device (and nanostructured devices in general) is due to the

capture of photogenerated carriers by surface trap states as

well as the consequent surface gating effect induced by the

carrier trapping. This method allows us to conveniently char-

acterize in situ the energy density of trap states in ultra-

scaled nano/quantum devices at very high precision. It opens

up the opportunity to design the density of surface trap states

for high-performance nanostructured photodetectors by engi-

neering the device surfaces.

We thank Professor Ali Javey for providing us silicon

nanowires, and Professor Abdelmadjid Mesli and Dr. Siew

Li Tan for useful discussions. The work reported here is

supported by the national “1000 Young Scholars” program

of the Chinese central government, the National Science

Foundation of China (61376001) and the “Pujiang Talent

Program” of the Shanghai municipal government.

The author declares no completing financial interests.

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