The origin and reduction of switching noisein GaAs/AlGaAs lateral gated devices

Michel Pioro-Ladrière and Andy S Sachrajdaand

John H Davies and Andrew R Longand

P Zawadzki, J Lapointe, J Gupta, Z Wasilewski andS Studenikin

Supported by CIAR, NSERC and FQRNT.

The Ottawa–Glasgow collaboration was stimulated by the Canadian–European Research Initiative on Nanostructures CERION-2.

A paper will shortly appear in Physical Review B (cond-mat/0503602)

Outline

• Description of ‘switching’ or ‘telegraph’ noise and why it is so important in laterally gated nanoelectronic devices at low temperature

• Experience shows that cooling the sample with a positive bias on the gates (‘bias cooling’) can suppress this noise

• Model to explain the effect of bias cooling on the noise:

- noise arises from a leakage current from the gates, with some electrons being trapped close to the channel

- positive bias cooling effectively builds in a negative gate voltage so that a smaller voltage needs to be applied

- this suppresses tunnelling through the Schottky barrier under the gate, which reduces the leakage and noise

• Direct observation of tunnelling current into a quantum dot (10–20 A)

• Speculations on the nature of the traps close to the channel

Laterally gated structures

patterned gates on surface, Vg(negative)

random donors

electrons in 2DEG

‘source’

‘drain’

Based on GaAs–AlGaAs heterostructures with a two-dimensional electron gas (2DEG) of high mobility at low temperature due to remote doping.

Example: quantum point contact, a short constriction that is so narrow that only a small number of transverse modes can pass (electron waveguide)

The conductance rises by 2e2/h whenever another mode can pass, giving a staircase for G(Vg).

Noise in a quantum point contact

Vg / V

On average, the conductance shows steps of 2e2/h as expected.

The conductance at a fixed value of Vg fluctuates between two values with time: this is telegraph or switching noise.

It is particularly strong on the transitions between steps, where transmission of the ‘new’ mode is most sensitive to the potential landscape.

Random telegraph or switching noise

As the experiment shows, random telegraph or switching noise occurs when the characteristics of the device switch randomly between two states (sometimes more).

It has been well studied in many systems, notably MOSFETs, where it is found that telegraph signals from different traps blend together to become 1/f noise as the sample becomes larger.

Telegraph signals have also been studied in QPCs since the early days (1990). The general model is that an electron becomes trapped near the QPC, where its Coulomb potential raises the potential energy near the constriction and reduces the conductance.

• A QPC is most sensitive to fluctuations in its environment on the transition between quantized steps, where the highest mode is only partially transmitted

• Other modes are less sensitive because they would require back-scattering

Bias cooling

Devices are usually cooled to cryogenic temperature with all gates grounded to the substrate to protect against electrostatic effects.

Bias cooling means that a bias Vgc is applied between the gates and substrate while the device is cooled. It is removed at low temperature.

This is effective because of the non-ideal behaviour of donors in AlGaAs: electrons ‘freeze’ into deep traps – DX centres – below about 150 K. The occupation of donors is frozen at low temperature and cannot respond to the gate. (More on this later.)

Bias cooling is found to have two effects:

• the characteristics are shifted as a function of gate bias by Vg = –Vgc

• telegraph noise is suppressed by a positive bias cool, Vgc ≈ +0.3 V

The suppression of telegraph noise has been known for some years but not understood: our aim is to provide an explanation.

Vg / V

Effect of bias cooling on characteristics

∆Vg = –Vgc

increasing bias cool voltage

t / s

Effect of bias cooling on telegraph noise

incr

easi

ng b

ias

cool

vol

tage

Summary of experimental observations

These are the main experimental issues that we wish to explain.

• Bias cooling shifts the characteristics as a function of gate bias by Vg = –Vgc

• A positive bias during cooling suppresses telegraph noise, with an optimum value around Vgc ≈ +0.3 V

• Asymmetric bias on the gates tends to make the noise worse

We therefore need models for

• the effect of bias cooling

– this affects the donors, which are close to the surface

• the origin of the telegraph noise

– this presumably arises from traps that are close to the QPC

Look first at the detailed effect of bias cooling on the conduction band.

Construction of band diagrams

Consider the conduction band Ec as a function of depth z under a large gate.

The main ingredient is the solution of Poisson’s equation. Where does the charge come from?

• Surface states hold negative charge to produce the Schottky barrier Vb

• Electrons in the channel provide negative charge

• Positive charge to balance these comes from the donors. Typically there are far more donors than needed, so not all are ionized. A thick slab of donors separates into three layers:

– an ionized layer close to the surface, to balance the surface states

– a neutral layer in the middle (the band must be flat here)

– a thin, ionized layer next to the spacer, to balance the electrons

In AlGaAs the ‘neutral’ donors behave as deep levels (DX centres) at low temperature, where their occupation is frozen:

• pin the conduction band at EDD ≈ 0.12 eV above the Fermi level µs

EDD =0.12 eV

∆Ec =0.25 eV

µ

eVb =0.7 eV

cap doped layer spacer channel

ionized donors

2DEG

neutral

∆Ec

13 nm

Sample cooled without gate bias (Vgc = 0 V)

40 nm 40 nm 15 nm

GaAs AlGaAs AlGaAs GaAs

Sample during cooling with gate bias Vgc = +0.2 V

EDDµs

eVb =0.7 eV

µm

biaseVgc =

+0.20 eV

10 nm

2DEG

At room temperature, electrons in the the doped region are free to move in response to the bias on the gate. They ‘screen’ the 2DEG from the gate.

band diagram unchanged here

ionizedlayer

thinner

doped layer

Sample with bias removed after cool with Vgc = +0.2 V

µ

eVb =0.7 eV

eVgc =+0.20 eV

cap doped layer spacer channel

When the bias is released at low temperature, the occupation of the donors is frozen: the only charge that can move is in the 2DEG.

2DEG partly depleted

This has the same effect on the 2DEG as a gate bias of Vg = –Vgc = –0.2 V on layers that were cooled without a bias.

The thinner layer of ionized donors acts like a negative bias on the gate.

Effect of bias cooling on bands

At room temperature, the bias on the gate affects only the electrons in the neutral, middle region of the doped layer.

• positive bias attracts electrons into this region, reducing the thickness of the ionized layer near the surface

• electrons in the channel (2DEG) are unaffected

At low temperature, the electrons in the doped layer become trapped in DX centres and remain frozen for the duration of the experiment.

• the thinner layer of ionized donors is now fixed

Removing the bias Vgc applied during the cool is equivalent to applying an equal but opposite bias Vg = –Vgc to layers that were cooled without a bias

• confirmed by experiments shown earlier

Thus a positive bias cool builds in a negative effective gate voltage

• a smaller (less negative) ‘physical’ bias is needed to reach the same experimental conditions in the sample

Origin of noise

Our model for the noise is based on previous work by Cobden et al (1991):

• Electrons from the gate tunnel through the Schottky barrier underneath the gate into the conduction band

– this depends strongly on the potential barrier, which is influenced by bias cooling

• They travel towards the channel under the influence of the electric field, probably in the conduction band but possible through trapped

• Many enter the channel are have no visible effect but some become trapped in long-lived states near the QPC (active region)

• Their Coulomb potential raises the energy in the QPC, lowers the conductance, and causes telegraph noise

• Eventually these electrons escape into the channel and the conductance returns to its previous (higher) value

Bands under quantum point contacts

gate (negative)gate (negative)

Consider a quantum point contact, biased so that it is just about to cut off. Thus the conductance is on the first transition from 0 to 2e2/h.

electrons in channel(about to be cut off)

Plot conduction band along line indicated, which is no longer normal to the surface — the route that an electron might take for the leakage current.

Assume that a bias Vg = –0.4 V is needed to cut off the QPC

µs

channel just depleted

µm leakage of tunnelling electrons

QPC at cutoff without bias cool; Vg = –0.4 V applied

eVb

eVg =–0.40 eV

Electrons have to tunnel only through the cap and ionized layers, about 25 nm

– large leakage current

µs

channel just depleted

QPC with bias cool of Vgc = +0.2 V; Vg = –0.2 V

eVb

eVgc =+0.20 eV

eVg =–0.20 eV

µm tunnelling suppressed

Only Vg = –0.2 V need be applied to the gate to achieve the same effect on the channel because of the built-in effect of the bias cool.

Electrons must now tunnel all the way to the channel

– tiny leakage current

Tunnelling current

-60

-50

-40

-30

-20

-10

0

-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

lg (

curr

ent d

ensi

ty /

A m

–2)

bias cool voltage / V

through all layers, gate tochannel

intoneutraldopedlayer

intoionizeddopedlayer

The current is too small to be measured directly but it is possible to use a quantum dot as an electrometer. This accumulates charge, which in turn

Vp / V

Conductance through QPC near dot with Vp

The conductance of the QPC shows a step whenever an electron enters or leaves the dot. Gate p is swept but we suspect that electrons leak from d. (Unfortunately Vp has many effects.)

t / min

Conductance through QPC near dot with time

The bias Vp was changed abruptly from +0.26 V to 0 V at t = 0, which isolates the dot. Electrons leak into the dot until equilibrium is established.

What are the traps?

Our model shows how bias cool affects the leakage current through its effect on the Schottky barrier under the gate. However, this current does not give rise to noise unless some of the electrons are trapped near the active region of the device (e.g. QPC).

These traps must have a lifetime of very roughly 1 second and must be close enough to the QPC to modulate its conductance. What are they?

It is most likely that they are somewhere near the junction between the doped layer and the spacer layer, where there is a thin layer of ionized donors (needed to balance the charge of the 2DEG). Here are some possibilities:

• a wire has a natural potential well due to the gates and donors

• hydrogenic levels of donors, aided by the potential from the gates

• long-ranged fluctuations due to the layer of donors

• defects or unexpected impurities

Electrostatic potential under a gated wire at cutoff

gate (–ve)gate (–ve)gap between gates on surface

field lines thin, equipotentials thick

thin layer of ionized donors next to cap

plane of 2DEG(depleted)

potential wellfor electrons

The potential well arises from a combination of two fields:

• electrons are attracted by the thin, ionized layer of donors

• the gates repel electrons away from them, into the gap

Unfortunately this works only for wires — not for QPCs.

Conclusions

Our model explains many of the main features of the experiments:

• bias cooling shifts the characteristics by changing the ionization of donors frozen in at low temperature

• telegraph noise arises from electrons that tunnel from the gates

– direct evidence from experiments on quantum dots

• positive bias cooling suppresses telegraph noise because a smaller bias is needed on the gate to reach the same experimental conditions

– it also strengthens the barrier against tunnelling

Needless to say, there are plenty of unanswered questions:

• what exactly are the traps?

• some groups claim that there are large variations between wafers, and the ‘better’ wafers often show stronger telegraph noise

– does the ‘intrinsic potential well’ play a role here?