Multifunctional semiconductor micro-Hall devices for
magnetic, electric and photo-detection
A. M. Gilbertson,1 Hatef Sadeghi,2 V. Panchal,3 O. Kazakova,3 C. J. Lambert,2 S. A. Solin,1,4 L. F. Cohen1
1
Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BZ, UK
2
Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
3
National Physical Laboratory, Teddington, TW11 0LW, UK
4
Department of Physics and Institute for Materials Science and Engineering, Washington University in St.
Louis, St Louis, Missouri 63130, USA
Supporting Information
Scanning photovoltage microscopy (SPVM) and electrical scanning gate microscopy (SGM)
experiments were performed on different sized devices. The results from a 2 μm-wide InSb microHall device are presented in the manuscript. Data from a 1μm and 4 μm InSb micro-Hall device are
presented in Figs. S1 and S2, respectively. Here we display the perturbation induced changes in
resistance ΔR = ΔV/I0, where I0 is the bias current. For the 1μm device and 2 μm device excellent
correlation between the ΔRxx and ΔRxy maps generated from the SPVM and SGM techniques are
found. Notably, in the case of the 4 um device the electrical SGM data for the ΔRxy measurement
configuration does not exhibit the same symmetry as in the SPVM data. This is highlighted by the
large signal in the bottom right corner of the cross. Some correlation is found between the AFM
topography and the SGM data indicating that this feature may be related to the structural uniformity
of the device. This is supported by measurements taken with the current/voltage leads rotated by 90°,
which demonstrate that the region of high signal is not dependent on the bias current direction. We
also note that the electrical SGM images contain a small background offset, which is an artefact of the
technique and has been removed. No offset is observed in the SPVM data indicating that photocarriers
injected locally in the etched material outside of the 2DEG cross do no contribute to the measured
2DEG conductance changes due to the low mobility, which prohibits their transfer to the 2DEG.
Upon photoexcitation, the photovoltage generated in a photoconductor is related to the change in
resistance through ΔV = I0ΔR. This is applicable in the case of constant current conditions as in our
experiments. The change in resistance is due to photocarrier generation and can be expressed as
R  
L 
, where L and w are the length and width of the conductor, Δ =  – 0 is the photow  02
induced change in conductivity and 0 is the equilibrium conductivity. Therefore, for Δ > 0
corresponding to positive photoconductivity, a negative photovoltage is expected. In the longitudinal
measurements configuration the net photovoltage is negative for both the InSb 2DEG micro-Hall
devices and the macroscopic InSb 2DEG Hall bar (equivalent to spatially integrated photovoltage
images). In the simplest case of direct absorption in the 2DEG the photo-induced change in
conductivity is given by Δ = X Popt, where Popt is the incident optical power and X is a positive
coefficient involving the absorption efficiency, photon energy, excitation area and photocarrier
lifetime. Therefore the photovoltage takes the form V   I 0 Popt
L X
. In Fig. S3, we show that
w  02
photovoltage data from different sized devices exhibit a linear dependence on current and optical
power as expected from the simple model, confirming the photoconductive origin of the
photoresponse. No dependence of the photovoltage on chopper frequency was observed within our
experimental range (20-1000 Hz), indicating a fast relaxation process consistent with the positive
photoconductivity effect.
The photo-responsivity, charge responsivity and associated sensitivities deduced in the Johnson noise
limit are listed below in Table S1.
Table S1. Photo and charge detection properties of 1 m, 2 m and 4 m InSb 2DEG micro-Hall
devices.
Device size
1 m
2 m
4 m
Current (A)
10
10
70
Photoresponsivity
(V/W)
800
400
1200
Photosensitivity
(pW/√Hz)
13
20
7
Charge
responsivity
(nV/e)
480
240
260
Charge
sensitivity
(e/√Hz)
0.03
0.05
0.04
S1. (a) Scanning optical reflection image of a 1 μm InSb micro-Hall device. SPVM images of
longitudinal ΔRxx (b) and transverse ΔRxy (c) photovoltage [I0 = 10 μA; Popt = 20 nW; fchop = 512 Hz].
Electrical SGM images of ΔRxx (d) and ΔRxy (e) [I0 = 10 μA; VTip = 3.5 V; f = 2.5 kHz; lift height 20
nm].
S2. (a) Scanning optical reflection image of a 4 μm InSb micro-Hall device. SPVM images of
longitudinal ΔRxx (b) and transverse ΔRxy (c) photovoltage [I0 = 10 μA; Popt = 20 nW; fchop = 512 Hz].
Electrical SGM images of ΔRxx (d) and ΔRxy (e) [I0 = 10 μA; VTip = 3.5 V; f = 2.5 kHz; lift height 20
nm].
S3. Scaling of the photovoltage with current density and optical power. Results from different sized
devices fall onto the same curve.
S4. (a) Optical reflection image of the InSb macro-Hall bar. (b) ΔVxx photovoltage image for I0 = 0
μA showing a weak contribution from diffusion of photocarriers at POpt = 4 μW. (c) Line scan taken
from (b) along the dashed line. From the exponential decay of signal away from the lead we can
estimate a diffusion length of LD ≈ 15 μm.