Memristor

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Memristor

Memristor developed by the University of Illinois at Urbana-Champaign and National Energy Technology Laboratory
Invented	Leon Chua (1971)
Electronic symbol

A memristor (/ˈmɛmrɪstər/; a portmanteau of memory resistor) is a non-linear two-terminal electrical component relating electric charge and magnetic flux linkage. It was described and named in 1971 by Leon Chua, completing a theoretical quartet of fundamental electrical components which comprises also the resistor, capacitor and inductor.

Chua and Kang later generalized the concept to memristive systems. Such a system comprises a circuit, of multiple conventional components, which mimics key properties of the ideal memristor component and is also commonly referred to as a memristor. Several such memristor system technologies have been developed, notably ReRAM.

The identification of memristive properties in electronic devices has attracted controversy. Experimentally, the ideal memristor has yet to be demonstrated.

As a fundamental electrical component

Conceptual symmetries of resistor, capacitor, inductor, and memristor.

Chua in his 1971 paper identified a theoretical symmetry between the non-linear resistor (voltage vs. current), non-linear capacitor (voltage vs. charge), and non-linear inductor (magnetic flux linkage vs. current). From this symmetry he inferred the characteristics of a fourth fundamental non-linear circuit element, linking magnetic flux and charge, which he called the memristor. In contrast to a linear (or non-linear) resistor, the memristor has a dynamic relationship between current and voltage, including a memory of past voltages or currents. Other scientists had proposed dynamic memory resistors such as the memistor of Bernard Widrow, but Chua introduced a mathematical generality.

Derivation and characteristics

The memristor was originally defined in terms of a non-linear functional relationship between magnetic flux linkage Φ_m(t) and the amount of electric charge that has flowed, q(t):

${\displaystyle f(\mathrm {\Phi } _{\mathrm {m} }(t),q(t))=0}$

The magnetic flux linkage, Φ_m, is generalized from the circuit characteristic of an inductor. It does not represent a magnetic field here. Its physical meaning is discussed below. The symbol Φ_m may be regarded as the integral of voltage over time.

In the relationship between Φ_m and q, the derivative of one with respect to the other depends on the value of one or the other, and so each memristor is characterized by its memristance function describing the charge-dependent rate of change of flux with charge.

${\displaystyle M(q)={\frac {\mathrm {d} \Phi _{\rm {m}}}{\mathrm {d} q}}}$

Substituting the flux as the time integral of the voltage, and charge as the time integral of current, the more convenient forms are;

${\displaystyle M(q(t))={\cfrac {\mathrm {d} \Phi _{\rm {}}/\mathrm {d} t}{\mathrm {d} q/\mathrm {d} t}}={\frac {V(t)}{I(t)}}}$

To relate the memristor to the resistor, capacitor, and inductor, it is helpful to isolate the term M(q), which characterizes the device, and write it as a differential equation.

Device	Characteristic property (units)	Differential equation
Resistor (R)	Resistance (V / A, or ohm, Ω)	R = dV / dI
Capacitor (C)	Capacitance (C / V, or farad)	C = dq / dV
Inductor (L)	Inductance (Wb / A, or henry)	L = dΦm / dI
Memristor (M)	Memristance (Wb / C, or ohm)	M = dΦm / dq

The above table covers all meaningful ratios of differentials of I, q, Φ_m, and V. No device can relate dI to dq, or dΦ_m to dV, because I is the derivative of q and Φ_m is the integral of V.

It can be inferred from this that memristance is charge-dependent resistance. If M(q(t)) is a constant, then we obtain Ohm's Law R(t) = V(t)/I(t). If M(q(t)) is nontrivial, however, the equation is not equivalent because q(t) and M(q(t)) can vary with time. Solving for voltage as a function of time produces

${\displaystyle V(t)=\ M(q(t))I(t)}$

This equation reveals that memristance defines a linear relationship between current and voltage, as long as M does not vary with charge. Nonzero current implies time varying charge. Alternating current, however, may reveal the linear dependence in circuit operation by inducing a measurable voltage without net charge movement—as long as the maximum change in q does not cause much change in M.

Furthermore, the memristor is static if no current is applied. If I(t) = 0, we find V(t) = 0 and M(t) is constant. This is the essence of the memory effect.

Analogously, we can define a ${\displaystyle W(\phi (t))}$ as menductance.

${\displaystyle i(t)=W(\phi (t))v(t)}$

The power consumption characteristic recalls that of a resistor, I²R.

${\displaystyle P(t)=\ I(t)V(t)=\ I^{2}(t)M(q(t))}$

As long as M(q(t)) varies little, such as under alternating current, the memristor will appear as a constant resistor. If M(q(t)) increases rapidly, however, current and power consumption will quickly stop.

M(q) is physically restricted to be positive for all values of q (assuming the device is passive and does not become superconductive at some q). A negative value would mean that it would perpetually supply energy when operated with alternating current.

Modelling and validation

In order to understand the nature of memristor function, some knowledge of fundamental circuit theoretic concepts is useful, starting with the concept of device modeling.

Engineers and scientists seldom analyze a physical system in its original form. Instead, they construct a model which approximates the behaviour of the system. By analyzing the behaviour of the model, they hope to predict the behaviour of the actual system. The primary reason for constructing models is that physical systems are usually too complex to be amenable to a practical analysis.

In the 20th century, work was done on devices where researchers did not recognize the memristive characteristics. This has raised the suggestion that such devices should be recognised as memristors. Pershin and Di Ventra have proposed a test that can help to resolve some of the long-standing controversies about whether an ideal memristor does actually exist or is a purely mathematical concept.

The rest of this article primarily addresses memristors as related to ReRAM devices, since the majority of work since 2008 has been concentrated in this area.

Superconducting memristor component

Dr. Paul Penfield, in a 1974 MIT technical report mentions the memristor in connection with Josephson junctions. This was an early use of the word "memristor" in the context of a circuit device.

One of the terms in the current through a Josephson junction is of the form:

${\displaystyle {\begin{aligned}i_{M}(v)&=\epsilon \cos(\phi _{0})v\\&=W(\phi _{0})v\end{aligned}}}$

where ${\displaystyle \epsilon }$ is a constant based on the physical superconducting materials, ${\displaystyle v}$ is the voltage across the junction and ${\displaystyle i_{M}}$ is the current through the junction.

Through the late 20th century, research regarding this phase-dependent conductance in Josephson junctions was carried out. A more comprehensive approach to extracting this phase-dependent conductance appeared with Peotta and DiVentra's seminal paper in 2014.

Memristor circuits

Due to the practical difficulty of studying the ideal memristor, we will discuss other electrical devices which can be modelled using memristors. For a mathematical description of a memristive device (systems), see Theory.

A discharge tube can be modelled as a memristive device, with resistance being a function of the number of conduction electrons ${\displaystyle n_{e}}$.

${\displaystyle {\begin{aligned}v_{M}&=R(n_{e})i_{M}\\{\frac {dn_{e}}{dt}}&=\beta n+\alpha R(n_{e})i_{M}^{2}\end{aligned}}}$

${\displaystyle v_{M}}$ is the voltage across the discharge tube, ${\displaystyle i_{M}}$ is the current flowing through it and ${\displaystyle n_{e}}$ is the number of conduction electrons. A simple memristance function is ${\displaystyle R(n_{e})={\frac {F}{n_{e}}}}$. ${\displaystyle \alpha ,\beta }$ and ${\displaystyle F}$ are parameters depending on the dimensions of the tube and the gas fillings. An experimental identification of memristive behaviour is the "pinched hysteresis loop" in the ${\displaystyle v-i}$ plane. For an experiment that shows such a characteristic for a common discharge tube, see "A physical memristor Lissajous figure" (YouTube). The video also illustrates how to understand deviations in the pinched hysteresis characteristics of physical memristors.

Thermistors can be modelled as memristive devices.

${\displaystyle {\begin{aligned}v&=R_{0}(T_{0})\exp \left[\beta \left({\frac {1}{T}}-{\frac {1}{T_{0}}}\right)\right]i\\&\equiv R(T)i\\{\frac {dT}{dt}}&={\frac {1}{C}}\left[-\delta \cdot (T-T_{0})+R(T)i^{2}\right]\end{aligned}}}$

${\displaystyle \beta }$ is a material constant, ${\displaystyle T}$ is the absolute body temperature of the thermistor, ${\displaystyle T_{0}}$ is the ambient temperature (both temperatures in Kelvin), ${\displaystyle R_{0}(T_{0})}$ denotes the cold temperature resistance at ${\displaystyle T=T_{0}}$, ${\displaystyle C}$ is the heat capacitance and ${\displaystyle \delta }$ is the dissipation constant for the thermistor.

A fundamental phenomenon that has hardly been studied is memristive behaviour in pn-junctions. The memristor plays a crucial role in mimicking the charge storage effect in the diode base, and is also responsible for the conductivity modulation phenomenon (that is so important during forward transients).

Criticisms

In 2008, a team at HP Labs claimed to have found Chua's missing memristor based on an analysis of a thin film of titanium dioxide, thus connecting the operation of ReRAM devices to the memristor concept. According to HP Labs, the memristor would operate in the following way: the memristor's electrical resistance is not constant but depends on the current that had previously flowed through the device, i.e., its present resistance depends on how much electric charge has previously flowed through it and in what direction; the device remembers its history—the so-called non-volatility property. When the electric power supply is turned off, the memristor remembers its most recent resistance until it is turned on again.

The HP Labs result was published in the scientific journal Nature. Following this claim, Leon Chua has argued that the memristor definition could be generalized to cover all forms of two-terminal non-volatile memory devices based on resistance switching effects. Chua also argued that the memristor is the oldest known circuit element, with its effects predating the resistor, capacitor, and inductor. There are, however, some serious doubts as to whether a genuine memristor can actually exist in physical reality. Additionally, some experimental evidence contradicts Chua's generalization since a non-passive nanobattery effect is observable in resistance switching memory. A simple test has been proposed by Pershin and Di Ventra to analyze whether such an ideal or generic memristor does actually exist or is a purely mathematical concept. Up to now, there seems to be no experimental resistance switching device (ReRAM) which can pass the test.

These devices are intended for applications in nanoelectronic memory devices, computer logic, and neuromorphic/neuromemristive computer architectures. In 2013, Hewlett-Packard CTO Martin Fink suggested that memristor memory may become commercially available as early as 2018. In March 2012, a team of researchers from HRL Laboratories and the University of Michigan announced the first functioning memristor array built on a CMOS chip.

An array of 17 purpose-built oxygen-depleted titanium dioxide memristors built at HP Labs, imaged by an atomic force microscope. The wires are about 50 nm, or 150 atoms, wide. Electric current through the memristors shifts the oxygen vacancies, causing a gradual and persistent change in electrical resistance.

According to the original 1971 definition, the memristor is the fourth fundamental circuit element, forming a non-linear relationship between electric charge and magnetic flux linkage. In 2011, Chua argued for a broader definition that includes all 2-terminal non-volatile memory devices based on resistance switching. Williams argued that MRAM, phase-change memory and ReRAM are memristor technologies. Some researchers argued that biological structures such as blood and skin fit the definition. Others argued that the memory device under development by HP Labs and other forms of ReRAM are not memristors, but rather part of a broader class of variable-resistance systems, and that a broader definition of memristor is a scientifically unjustifiable land grab that favored HP's memristor patents.

In 2011, Meuffels and Schroeder noted that one of the early memristor papers included a mistaken assumption regarding ionic conduction. In 2012, Meuffels and Soni discussed some fundamental issues and problems in the realization of memristors. They indicated inadequacies in the electrochemical modeling presented in the Nature article "The missing memristor found" because the impact of concentration polarization effects on the behavior of metal−TiO_2−x−metal structures under voltage or current stress was not considered. This critique was referred to by Valov et al. in 2013.

In a kind of thought experiment, Meuffels and Soni furthermore revealed a severe inconsistency: If a current-controlled memristor with the so-called non-volatility property exists in physical reality, its behavior would violate Landauer's principle, which places a limit on the minimum amount of energy required to change "information" states of a system. This critique was finally adopted by Di Ventra and Pershin in 2013.

Within this context, Meuffels and Soni pointed to a fundamental thermodynamic principle: Non-volatile information storage requires the existence of free-energy barriers that separate the distinct internal memory states of a system from each other; otherwise, one would be faced with an "indifferent" situation, and the system would arbitrarily fluctuate from one memory state to another just under the influence of thermal fluctuations. When unprotected against thermal fluctuations, the internal memory states exhibit some diffusive dynamics, which causes state degradation. The free-energy barriers must therefore be high enough to ensure a low bit-error probability of bit operation. Consequently, there is always a lower limit of energy requirement – depending on the required bit-error probability – for intentionally changing a bit value in any memory device.

In the general concept of memristive system the defining equations are (see Theory):

${\displaystyle {\begin{aligned}y(t)&=g(\mathbf {x} ,u,t)u(t),\\{\dot {\mathbf {x} }}&=f(\mathbf {x} ,u,t),\end{aligned}}}$

where u(t) is an input signal, and y(t) is an output signal. The vector x represents a set of n state variables describing the different internal memory states of the device. ẋ is the time-dependent rate of change of the state vector x with time.

When one wants to go beyond mere curve fitting and aims at a real physical modeling of non-volatile memory elements, e.g., resistive random-access memory devices, one has to keep an eye on the aforementioned physical correlations. To check the adequacy of the proposed model and its resulting state equations, the input signal u(t) can be superposed with a stochastic term ξ(t), which takes into account the existence of inevitable thermal fluctuations. The dynamic state equation in its general form then finally reads:

${\displaystyle {\dot {\mathbf {x} }}=f(\mathbf {x} ,u(t)+\xi (t),t),}$

where ξ(t) is, e.g., white Gaussian current or voltage noise. On base of an analytical or numerical analysis of the time-dependent response of the system towards noise, a decision on the physical validity of the modeling approach can be made, e.g., would the system be able to retain its memory states in power-off mode?

Such an analysis was performed by Di Ventra and Pershin with regard to the genuine current-controlled memristor. As the proposed dynamic state equation provides no physical mechanism enabling such a memristor to cope with inevitable thermal fluctuations, a current-controlled memristor would erratically change its state in course of time just under the influence of current noise. Di Ventra and Pershin thus concluded that memristors whose resistance (memory) states depend solely on the current or voltage history would be unable to protect their memory states against unavoidable Johnson–Nyquist noise and permanently suffer from information loss, a so-called "stochastic catastrophe". A current-controlled memristor can thus not exist as a solid-state device in physical reality.

The above-mentioned thermodynamic principle furthermore implies that the operation of 2-terminal non-volatile memory devices (e.g. "resistance-switching" memory devices (ReRAM)) cannot be associated with the memristor concept, i.e., such devices cannot by itself remember their current or voltage history. Transitions between distinct internal memory or resistance states are of probabilistic nature. The probability for a transition from state {i} to state {j} depends on the height of the free-energy barrier between both states. The transition probability can thus be influenced by suitably driving the memory device, i.e., by "lowering" the free-energy barrier for the transition {i} → {j} by means of, for example, an externally applied bias.

A "resistance switching" event can simply be enforced by setting the external bias to a value above a certain threshold value. This is the trivial case, i.e., the free-energy barrier for the transition {i} → {j} is reduced to zero. In case one applies biases below the threshold value, there is still a finite probability that the device will switch in course of time (triggered by a random thermal fluctuation), but – as one is dealing with probabilistic processes – it is impossible to predict when the switching event will occur. That is the basic reason for the stochastic nature of all observed resistance-switching (ReRAM) processes. If the free-energy barriers are not high enough, the memory device can even switch without having to do anything.

When a 2-terminal non-volatile memory device is found to be in a distinct resistance state {j}, there exists therefore no physical one-to-one relationship between its present state and its foregoing voltage history. The switching behavior of individual non-volatile memory devices thus cannot be described within the mathematical framework proposed for memristor/memristive systems.

An extra thermodynamic curiosity arises from the definition that memristors/memristive devices should energetically act like resistors. The instantaneous electrical power entering such a device is completely dissipated as Joule heat to the surrounding, so no extra energy remains in the system after it has been brought from one resistance state x_i to another one x_j. Thus, the internal energy of the memristor device in state x_i, U(V, T, x_i), would be the same as in state x_j, U(V, T, x_j), even though these different states would give rise to different device's resistances, which itself must be caused by physical alterations of the device's material.

Other researchers noted that memristor models based on the assumption of linear ionic drift do not account for asymmetry between set time (high-to-low resistance switching) and reset time (low-to-high resistance switching) and do not provide ionic mobility values consistent with experimental data. Non-linear ionic-drift models have been proposed to compensate for this deficiency.

A 2014 article from researchers of ReRAM concluded that Strukov's (HP's) initial/basic memristor modeling equations do not reflect the actual device physics well, whereas subsequent (physics-based) models such as Pickett's model or Menzel's ECM model (Menzel is a co-author of that article) have adequate predictability, but are computationally prohibitive. As of 2014, the search continues for a model that balances these issues; the article identifies Chang's and Yakopcic's models as potentially good compromises.

Martin Reynolds, an electrical engineering analyst with research outfit Gartner, commented that while HP was being sloppy in calling their device a memristor, critics were being pedantic in saying that it was not a memristor.

Experimental tests

Chua suggested experimental tests to determine if a device may properly be categorized as a memristor:

• The Lissajous curve in the voltage-current plane is a pinched hysteresis loop when driven by any bipolar periodic voltage or current without respect to initial conditions.
• The area of each lobe of the pinched hysteresis loop shrinks as the frequency of the forcing signal increases.
• As the frequency tends to infinity, the hysteresis loop degenerates to a straight line through the origin, whose slope depends on the amplitude and shape of the forcing signal.

According to Chua all resistive switching memories including ReRAM, MRAM and phase-change memory meet these criteria and are memristors. However, the lack of data for the Lissajous curves over a range of initial conditions or over a range of frequencies complicates assessments of this claim.

Experimental evidence shows that redox-based resistance memory (ReRAM) includes a nanobattery effect that is contrary to Chua's memristor model. This indicates that the memristor theory needs to be extended or corrected to enable accurate ReRAM modeling.

Theory

In 2008, researchers from HP Labs introduced a model for a memristance function based on thin films of titanium dioxide. For R_ON ≪ R_OFF the memristance function was determined to be

${\displaystyle M(q(t))=R_{\mathrm {OFF} }\cdot \left(1-{\frac {\mu _{v}R_{\mathrm {ON} }}{D^{2}}}q(t)\right)}$

where R_OFF represents the high resistance state, R_ON represents the low resistance state, μ_v represents the mobility of dopants in the thin film, and D represents the film thickness. The HP Labs group noted that "window functions" were necessary to compensate for differences between experimental measurements and their memristor model due to non-linear ionic drift and boundary effects.

Operation as a switch

For some memristors, applied current or voltage causes substantial change in resistance. Such devices may be characterized as switches by investigating the time and energy that must be spent to achieve a desired change in resistance. This assumes that the applied voltage remains constant. Solving for energy dissipation during a single switching event reveals that for a memristor to switch from R_on to R_off in time T_on to T_off, the charge must change by ΔQ = Q_on−Q_off.

${\displaystyle E_{\mathrm {switch} }=\ V^{2}\int _{T_{\mathrm {off} }}^{T_{\mathrm {on} }}{\frac {\mathrm {d} t}{M(q(t))}}=\ V^{2}\int _{Q_{\mathrm {off} }}^{Q_{\mathrm {on} }}{\frac {\mathrm {d} q}{I(q)M(q)}}=\ V^{2}\int _{Q_{\mathrm {off} }}^{Q_{\mathrm {on} }}{\frac {\mathrm {d} q}{V(q)}}=\ V\Delta Q}$

Substituting V = I(q)M(q), and then ∫dq/V = ∆Q/V for constant VTo produces the final expression. This power characteristic differs fundamentally from that of a metal oxide semiconductor transistor, which is capacitor-based. Unlike the transistor, the final state of the memristor in terms of charge does not depend on bias voltage.

The type of memristor described by Williams ceases to be ideal after switching over its entire resistance range, creating hysteresis, also called the "hard-switching regime". Another kind of switch would have a cyclic M(q) so that each off-on event would be followed by an on-off event under constant bias. Such a device would act as a memristor under all conditions, but would be less practical.

Memristive systems

In the more general concept of an n-th order memristive system the defining equations are

${\displaystyle {\begin{aligned}y(t)&=g({\textbf {x}},u,t)u(t),\\{\dot {\textbf {x}}}&=f({\textbf {x}},u,t)\end{aligned}}}$

where u(t) is an input signal, y(t) is an output signal, the vector x represents a set of n state variables describing the device, and g and f are continuous functions. For a current-controlled memristive system the signal u(t) represents the current signal i(t) and the signal y(t) represents the voltage signal v(t). For a voltage-controlled memristive system the signal u(t) represents the voltage signal v(t) and the signal y(t) represents the current signal i(t).

The pure memristor is a particular case of these equations, namely when x depends only on charge (x = q) and since the charge is related to the current via the time derivative dq/dt = i(t). Thus for pure memristors f (i.e. the rate of change of the state) must be equal or proportional to the current i(t) .

Pinched hysteresis

Example of pinched hysteresis curve, V versus I

One of the resulting properties of memristors and memristive systems is the existence of a pinched hysteresis effect. For a current-controlled memristive system, the input u(t) is the current i(t), the output y(t) is the voltage v(t), and the slope of the curve represents the electrical resistance. The change in slope of the pinched hysteresis curves demonstrates switching between different resistance states which is a phenomenon central to ReRAM and other forms of two-terminal resistance memory. At high frequencies, memristive theory predicts the pinched hysteresis effect will degenerate, resulting in a straight line representative of a linear resistor. It has been proven that some types of non-crossing pinched hysteresis curves (denoted Type-II) cannot be described by memristors.

Extended systems

Some researchers have raised the question of the scientific legitimacy of HP's memristor models in explaining the behavior of ReRAM. and have suggested extended memristive models to remedy perceived deficiencies.

One example attempts to extend the memristive systems framework by including dynamic systems incorporating higher-order derivatives of the input signal u(t) as a series expansion

${\displaystyle {\begin{aligned}y(t)&=g_{0}({\textbf {x}},u)u(t)+g_{1}({\textbf {x}},u){\operatorname {d} ^{2}u \over \operatorname {d} t^{2}}+g_{2}({\textbf {x}},u){\operatorname {d} ^{4}u \over \operatorname {d} t^{4}}+\ldots +g_{m}({\textbf {x}},u){\operatorname {d} ^{2m}u \over \operatorname {d} t^{2m}},\\{\dot {\textbf {x}}}&=f({\textbf {x}},u)\end{aligned}}}$

where m is a positive integer, u(t) is an input signal, y(t) is an output signal, the vector x represents a set of n state variables describing the device, and the functions g and f are continuous functions. This equation produces the same zero-crossing hysteresis curves as memristive systems but with a different frequency response than that predicted by memristive systems.

Another example suggests including an offset value ${\displaystyle a}$ to account for an observed nanobattery effect which violates the predicted zero-crossing pinched hysteresis effect.

${\displaystyle {\begin{aligned}y(t)&=g_{0}({\textbf {x}},u)(u(t)-a),\\{\dot {\textbf {x}}}&=f({\textbf {x}},u)\end{aligned}}}$

Implementations

Titanium dioxide memristor

Interest in the memristor revived when an experimental solid-state version was reported by R. Stanley Williams of Hewlett Packard in 2007. The article was the first to demonstrate that a solid-state device could have the characteristics of a memristor based on the behavior of nanoscale thin films. The device neither uses magnetic flux as the theoretical memristor suggested, nor stores charge as a capacitor does, but instead achieves a resistance dependent on the history of current.

Although not cited in HP's initial reports on their TiO₂ memristor, the resistance switching characteristics of titanium dioxide were originally described in the 1960s.

The HP device is composed of a thin (50 nm) titanium dioxide film between two 5 nm thick electrodes, one titanium, the other platinum. Initially, there are two layers to the titanium dioxide film, one of which has a slight depletion of oxygen atoms. The oxygen vacancies act as charge carriers, meaning that the depleted layer has a much lower resistance than the non-depleted layer. When an electric field is applied, the oxygen vacancies drift (see Fast ion conductor), changing the boundary between the high-resistance and low-resistance layers. Thus the resistance of the film as a whole is dependent on how much charge has been passed through it in a particular direction, which is reversible by changing the direction of current. Since the HP device displays fast ion conduction at nanoscale, it is considered a nanoionic device.

Memristance is displayed only when both the doped layer and depleted layer contribute to resistance. When enough charge has passed through the memristor that the ions can no longer move, the device enters hysteresis. It ceases to integrate q=∫I dt, but rather keeps q at an upper bound and M fixed, thus acting as a constant resistor until current is reversed.

Memory applications of thin-film oxides had been an area of active investigation for some time. IBM published an article in 2000 regarding structures similar to that described by Williams. Samsung has a U.S. patent for oxide-vacancy based switches similar to that described by Williams. Williams also has a U.S. patent application related to the memristor construction.

In April 2010, HP labs announced that they had practical memristors working at 1 ns (~1 GHz) switching times and 3 nm by 3 nm sizes, which bodes well for the future of the technology. At these densities it could easily rival the current sub-25 nm flash memory technology.

Polymeric memristor

In 2004, Krieger and Spitzer described dynamic doping of polymer and inorganic dielectric-like materials that improved the switching characteristics and retention required to create functioning nonvolatile memory cells. They used a passive layer between electrode and active thin films, which enhanced the extraction of ions from the electrode. It is possible to use fast ion conductor as this passive layer, which allows a significant reduction of the ionic extraction field.

In July 2008, Erokhin and Fontana claimed to have developed a polymeric memristor before the more recently announced titanium dioxide memristor.

In 2010, Alibart, Gamrat, Vuillaume et al. introduced a new hybrid organic/nanoparticle device (the NOMFET : Nanoparticle Organic Memory Field Effect Transistor), which behaves as a memristor and which exhibits the main behavior of a biological spiking synapse. This device, also called a synapstor (synapse transistor), was used to demonstrate a neuro-inspired circuit (associative memory showing a pavlovian learning).

In 2012, Crupi, Pradhan and Tozer described a proof of concept design to create neural synaptic memory circuits using organic ion-based memristors. The synapse circuit demonstrated long-term potentiation for learning as well as inactivity based forgetting. Using a grid of circuits, a pattern of light was stored and later recalled. This mimics the behavior of the V1 neurons in the primary visual cortex that act as spatiotemporal filters that process visual signals such as edges and moving lines.

In 2012, Erokhin and co-authors have demonstrated a stochastic three-dimensional matrix with capabilities for learning and adapting based on polymeric memristor.

Layered memristor

In 2014, Bessonov et al. reported a flexible memristive device comprising a MoO_x/MoS₂ heterostructure sandwiched between silver electrodes on a plastic foil. The fabrication method is entirely based on printing and solution-processing technologies using two-dimensional layered transition metal dichalcogenides (TMDs). The memristors are mechanically flexible, optically transparent and produced at low cost. The memristive behaviour of switches was found to be accompanied by a prominent memcapacitive effect. High switching performance, demonstrated synaptic plasticity and sustainability to mechanical deformations promise to emulate the appealing characteristics of biological neural systems in novel computing technologies.

Atomristor

Atomristor is defined as the electrical devices showing memristive behavior in atomically thin nanomaterials or atomic sheets. In 2018, Ge and Wu et al. in the Akinwande group at the University of Texas, first reported a universal memristive effect in single-layer TMD (MX₂, M = Mo, W; and X = S, Se) atomic sheets based on vertical metal-insulator-metal (MIM) device structure. The work was later extended to monolayer hexagonal boron nitride, which is the thinnest memory material of around 0.33 nm. These atomristors offer forming-free switching and both unipolar and bipolar operation. The switching behavior is found in single-crystalline and poly-crystalline films, with various conducting electrodes (gold, silver and graphene). Atomically thin TMD sheets are prepared via CVD/MOCVD, enabling low-cost fabrication. Afterwards, taking advantage of the low "on" resistance and large on/off ratio, a high-performance zero-power RF switch is proved based on MoS₂ or h-BN atomristors, indicating a new application of memristors for 5G, 6G and THz communication and connectivity systems. In 2020, atomistic understanding of the conductive virtual point mechanism was elucidated in an article in nature nanotechnology.

Ferroelectric memristor

The ferroelectric memristor is based on a thin ferroelectric barrier sandwiched between two metallic electrodes. Switching the polarization of the ferroelectric material by applying a positive or negative voltage across the junction can lead to a two order of magnitude resistance variation: R_OFF ≫ R_ON (an effect called Tunnel Electro-Resistance). In general, the polarization does not switch abruptly. The reversal occurs gradually through the nucleation and growth of ferroelectric domains with opposite polarization. During this process, the resistance is neither R_ON or R_OFF, but in between. When the voltage is cycled, the ferroelectric domain configuration evolves, allowing a fine tuning of the resistance value. The ferroelectric memristor's main advantages are that ferroelectric domain dynamics can be tuned, offering a way to engineer the memristor response, and that the resistance variations are due to purely electronic phenomena, aiding device reliability, as no deep change to the material structure is involved.

Carbon nanotube memristor

In 2013, Ageev, Blinov et al. reported observing memristor effect in structure based on vertically aligned carbon nanotubes studying bundles of CNT by scanning tunneling microscope.

Later it was found that CNT memristive switching is observed when a nanotube has a non-uniform elastic strain ΔL0. It was shown that the memristive switching mechanism of strained СNT is based on the formation and subsequent redistribution of non-uniform elastic strain and piezoelectric field Edef in the nanotube under the influence of an external electric field E(x,t).

Biomolecular memristor

Biomaterials have been evaluated for use in artificial synapses and have shown potential for application in neuromorphic systems. In particular, the feasibility of using a collagen‐based biomemristor as an artificial synaptic device has been investigated, whereas a synaptic device based on lignin demonstrated rising or lowering current with consecutive voltage sweeps depending on the sign of the voltage furthermore a natural silk fibroin demonstrated memristive properties; spin-memristive systems based on biomolecules are also being studied.

In 2012, Sandro Carrara and co-authors have proposed the first biomolecular memristor with aims to realize highly sensitive biosensors. Since then, several memristive sensors have been demonstrated.

Spin memristive systems

Spintronic memristor

Chen and Wang, researchers at disk-drive manufacturer Seagate Technology described three examples of possible magnetic memristors. In one device resistance occurs when the spin of electrons in one section of the device points in a different direction from those in another section, creating a "domain wall", a boundary between the two sections. Electrons flowing into the device have a certain spin, which alters the device's magnetization state. Changing the magnetization, in turn, moves the domain wall and changes the resistance. The work's significance led to an interview by IEEE Spectrum. A first experimental proof of the spintronic memristor based on domain wall motion by spin currents in a magnetic tunnel junction was given in 2011.

Memristance in a magnetic tunnel junction

The magnetic tunnel junction has been proposed to act as a memristor through several potentially complementary mechanisms, both extrinsic (redox reactions, charge trapping/detrapping and electromigration within the barrier) and intrinsic (spin-transfer torque).

Extrinsic mechanism

Based on research performed between 1999 and 2003, Bowen et al. published experiments in 2006 on a magnetic tunnel junction (MTJ) endowed with bi-stable spin-dependent states (resistive switching). The MTJ consists in a SrTiO3 (STO) tunnel barrier that separates half-metallic oxide LSMO and ferromagnetic metal CoCr electrodes. The MTJ's usual two device resistance states, characterized by a parallel or antiparallel alignment of electrode magnetization, are altered by applying an electric field. When the electric field is applied from the CoCr to the LSMO electrode, the tunnel magnetoresistance (TMR) ratio is positive. When the direction of electric field is reversed, the TMR is negative. In both cases, large amplitudes of TMR on the order of 30% are found. Since a fully spin-polarized current flows from the half-metallic LSMO electrode, within the Julliere model, this sign change suggests a sign change in the effective spin polarization of the STO/CoCr interface. The origin to this multistate effect lies with the observed migration of Cr into the barrier and its state of oxidation. The sign change of TMR can originate from modifications to the STO/CoCr interface density of states, as well as from changes to the tunneling landscape at the STO/CoCr interface induced by CrOx redox reactions.

Reports on MgO-based memristive switching within MgO-based MTJs appeared starting in 2008 and 2009. While the drift of oxygen vacancies within the insulating MgO layer has been proposed to describe the observed memristive effects, another explanation could be charge trapping/detrapping on the localized states of oxygen vacancies and its impact on spintronics. This highlights the importance of understanding what role oxygen vacancies play in the memristive operation of devices that deploy complex oxides with an intrinsic property such as ferroelectricity or multiferroicity.

Intrinsic mechanism

The magnetization state of a MTJ can be controlled by Spin-transfer torque, and can thus, through this intrinsic physical mechanism, exhibit memristive behavior. This spin torque is induced by current flowing through the junction, and leads to an efficient means of achieving a MRAM. However, the length of time the current flows through the junction determines the amount of current needed, i.e., charge is the key variable.

The combination of intrinsic (spin-transfer torque) and extrinsic (resistive switching) mechanisms naturally leads to a second-order memristive system described by the state vector x = (x₁,x₂), where x₁ describes the magnetic state of the electrodes and x₂ denotes the resistive state of the MgO barrier. In this case the change of x₁ is current-controlled (spin torque is due to a high current density) whereas the change of x₂ is voltage-controlled (the drift of oxygen vacancies is due to high electric fields). The presence of both effects in a memristive magnetic tunnel junction led to the idea of a nanoscopic synapse-neuron system.

Spin memristive system

A fundamentally different mechanism for memristive behavior has been proposed by Pershin and Di Ventra. The authors show that certain types of semiconductor spintronic structures belong to a broad class of memristive systems as defined by Chua and Kang. The mechanism of memristive behavior in such structures is based entirely on the electron spin degree of freedom which allows for a more convenient control than the ionic transport in nanostructures. When an external control parameter (such as voltage) is changed, the adjustment of electron spin polarization is delayed because of the diffusion and relaxation processes causing hysteresis. This result was anticipated in the study of spin extraction at semiconductor/ferromagnet interfaces, but was not described in terms of memristive behavior. On a short time scale, these structures behave almost as an ideal memristor. This result broadens the possible range of applications of semiconductor spintronics and makes a step forward in future practical applications.

Self-directed channel memristor

In 2017, Dr Kris Campbell formally introduced the self-directed channel (SDC) memristor. The SDC device is the first memristive device available commercially to researchers, students and electronics enthusiast worldwide. The SDC device is operational immediately after fabrication. In the Ge₂Se₃ active layer, Ge-Ge homopolar bonds are found and switching occurs. The three layers consisting of Ge₂Se₃/Ag/Ge₂Se₃, directly below the top tungsten electrode, mix together during deposition and jointly form the silver-source layer. A layer of SnSe is between these two layers ensuring that the silver-source layer is not in direct contact with the active layer. Since silver does not migrate into the active layer at high temperatures, and the active layer maintains a high glass transition temperature of about 350 °C (662 °F), the device has significantly higher processing and operating temperatures at 250 °C (482 °F) and at least 150 °C (302 °F), respectively. These processing and operating temperatures are higher than most ion-conducting chalcogenide device types, including the S-based glasses (e.g. GeS) that need to be photodoped or thermally annealed. These factors allow the SDC device to operate over a wide range of temperatures, including long-term continuous operation at 150 °C (302 °F).

Potential applications

Memristors remain a laboratory curiosity, as yet made in insufficient numbers to gain any commercial applications. Despite this lack of mass availability, according to Allied Market Research the memristor market was worth $3.2 million in 2015 and will be worth $79.0 million by 2022.

A potential application of memristors is in analog memories for superconducting quantum computers.

Memristors can potentially be fashioned into non-volatile solid-state memory, which could allow greater data density than hard drives with access times similar to DRAM, replacing both components. HP prototyped a crossbar latch memory that can fit 100 gigabits in a square centimeter, and proposed a scalable 3D design (consisting of up to 1000 layers or 1 petabit per cm³). In May 2008 HP reported that its device reaches currently about one-tenth the speed of DRAM. The devices' resistance would be read with alternating current so that the stored value would not be affected. In May 2012, it was reported that the access time had been improved to 90 nanoseconds, which is nearly one hundred times faster than the contemporaneous Flash memory. At the same time, the energy consumption was just one percent of that consumed by Flash memory.

Memristor have applications in programmable logic signal processing, Super-resolution imaging physical neural networks, control systems, reconfigurable computing, in-memory computing, brain–computer interfaces and RFID. Memristive devices are potentially used for stateful logic implication, allowing a replacement for CMOS-based logic computation Several early works have been reported in this direction.

In 2009, a simple electronic circuit consisting of an LC network and a memristor was used to model experiments on adaptive behavior of unicellular organisms. It was shown that subjected to a train of periodic pulses, the circuit learns and anticipates the next pulse similar to the behavior of slime molds Physarum polycephalum where the viscosity of channels in the cytoplasm responds to periodic environment changes. Applications of such circuits may include, e.g., pattern recognition. The DARPA SyNAPSE project funded HP Labs, in collaboration with the Boston University Neuromorphics Lab, has been developing neuromorphic architectures which may be based on memristive systems. In 2010, Versace and Chandler described the MoNETA (Modular Neural Exploring Traveling Agent) model. MoNETA is the first large-scale neural network model to implement whole-brain circuits to power a virtual and robotic agent using memristive hardware. Application of the memristor crossbar structure in the construction of an analog soft computing system was demonstrated by Merrikh-Bayat and Shouraki. In 2011, they showed how memristor crossbars can be combined with fuzzy logic to create an analog memristive neuro-fuzzy computing system with fuzzy input and output terminals. Learning is based on the creation of fuzzy relations inspired from Hebbian learning rule.

In 2013 Leon Chua published a tutorial underlining the broad span of complex phenomena and applications that memristors span and how they can be used as non-volatile analog memories and can mimic classic habituation and learning phenomena.

Derivative devices

Memistor and memtransistor

The memistor and memtransistor are transistor based devices which include memristor function.

Memcapacitors and meminductors

In 2009, Di Ventra, Pershin, and Chua extended the notion of memristive systems to capacitive and inductive elements in the form of memcapacitors and meminductors, whose properties depend on the state and history of the system, further extended in 2013 by Di Ventra and Pershin.

Memfractance and memfractor, 2nd- and 3rd-order memristor, memcapacitor and meminductor

In September 2014, Mohamed-Salah Abdelouahab, Rene Lozi, and Leon Chua published a general theory of 1st-, 2nd-, 3rd-, and nth-order memristive elements using fractional derivatives.

History

Precursors

Sir Humphry Davy is said by some to have performed the first experiments which can be explained by memristor effects as long ago as 1808. However the first device of a related nature to be constructed was the memistor (i.e. memory resistor), a term coined in 1960 by Bernard Widrow to describe a circuit element of an early artificial neural network called ADALINE. A few years later, in 1968, Argall published an article showing the resistance switching effects of TiO₂ which was later claimed by researchers from Hewlett Packard to be evidence of a memristor.

Theoretical description

Leon Chua postulated his new two-terminal circuit element in 1971. It was characterized by a relationship between charge and flux linkage as a fourth fundamental circuit element. Five years later he and his student Sung Mo Kang generalized the theory of memristors and memristive systems including a property of zero crossing in the Lissajous curve characterizing current vs. voltage behavior.

Twenty-first century

On May 1, 2008, Strukov, Snider, Stewart, and Williams published an article in Nature identifying a link between the 2-terminal resistance switching behavior found in nanoscale systems and memristors.

On 23 January 2009, Di Ventra, Pershin, and Chua extended the notion of memristive systems to capacitive and inductive elements, namely capacitors and inductors, whose properties depend on the state and history of the system.

In July 2014, the MeMOSat/LabOSat group (composed of researchers from Universidad Nacional de General San Martín (Argentina), INTI, CNEA, and CONICET) put memory devices into orbit for their study at LEO. Since then, seven missions with different devices are performing experiments in low orbit, onboard Satellogic's Ñu-Sat satellites.

On 7 July 2015, Knowm Inc announced Self Directed Channel (SDC) memristors commercially. These devices remain available in small numbers.

On 13 July 2018, MemSat (Memristor Satellite) was launched to fly a memristor evaluation payload.

In 2021, Jennifer Rupp and Martin Bazant of MIT started a "Lithionics" research programme to investigate applications of lithium beyond their use in battery electrodes, including lithium oxide-based memristors in neuromorphic computing.

Implicit stereotype

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Implicit_stereotype

In social identity theory, an implicit bias or implicit stereotype, is the pre-reflective attribution of particular qualities by an individual to a member of some social out group.

Implicit stereotypes are thought to be shaped by experience and based on learned associations between particular qualities and social categories, including race and/or gender. Individuals' perceptions and behaviors can be influenced by the implicit stereotypes they hold, even if they are sometimes unaware they hold such stereotypes. Implicit bias is an aspect of implicit social cognition: the phenomenon that perceptions, attitudes, and stereotypes can operate prior to conscious intention or endorsement. The existence of implicit bias is supported by a variety of scientific articles in psychological literature. Implicit stereotype was first defined by psychologists Mahzarin Banaji and Anthony Greenwald in 1995.

Explicit stereotypes, by contrast, are consciously endorsed, intentional, and sometimes controllable thoughts and beliefs.

Implicit biases, however, are thought to be the product of associations learned through past experiences. Implicit biases can be activated by the environment and operate prior to a person's intentional, conscious endorsement. Implicit bias can persist even when an individual rejects the bias explicitly.

Bias, attitude, stereotype and prejudice

Attitudes, stereotypes, prejudices, and bias are all examples of psychological constructs. Psychological constructs are mental associations that can influence a person's behavior and feelings toward an individual or group. If the person is unaware of these mental associations the stereotypes, prejudices, or bias is said to be implicit.

Bias is defined as prejudice in favor of or against one thing, person, or group compared with another, usually in a way considered to be unfair. Bias can be seen as the overarching definition of stereotype and prejudice, because it is how we associate traits (usually negative) to a specific group of people. Our “implicit attitudes reflect constant exposure to stereotypical portrayals of members of, and items in, all kinds of different categories: racial groups, professions, women, nationalities, members of the LGBTQ community, moral and political values, etc.”

An attitude is an evaluative judgment of an object, a person, or a social group. An attitude is held by or characterizes a person. Implicit attitudes are evaluations that occur without conscious awareness towards an attitude object or the self.

A stereotype is the association of a person or a social group with a consistent set of traits. This may include both positive and negative traits, such as African Americans are great at sports or African Americans are more violent than any other race in the United States. There are many types of stereotypes that exists: racial, cultural, gender, group (i.e. college students), all being very explicit in the lives of many people.

Prejudice is defined as unfair negative attitude toward a social group or a member of that group. Prejudices can stem from many of the things that people observe in a different social group that include, but are not limited to, gender, sex, race/ethnicity, or religion. This is pertinent to stereotypes because a stereotype can influence the way people feel toward another group, hence prejudice.

Methods for investigation

There is a clear challenge in measuring the degree to which someone is biased. There are two different forms of bias: implicit and explicit. The two forms of bias are, however, connected. “Explicit bias encompasses our conscious attitudes which can be measured by self-report, but pose the potential of individuals falsely endorsing more socially desirable attitudes. Although implicit biases have been considered unconscious and involuntary attitudes which lie below the surface of consciousness, some people seem to be aware of their influence on their behavior and cognitive processes. The implicit-association test (IAT) is one validated tool used to measure implicit bias. The IAT requires participants to rapidly pair two social groups with either positive or negative attributes.”

Implicit-association test

The implicit-association test (IAT) alleges to predict prejudice an individual has toward different social groups. The test claims to do this by capturing the differences in the time it takes respondent to choose between two unassociated but related topics. Respondents are instructed to click one of two computer keys to categorize stimuli into associated categories. When the categories appear consistent to the respondent, the time taken to categorize the stimuli will be less than when the categories seem inconsistent. An implicit association is said to exist when respondents take longer to respond to a category-inconsistent pairing than a category-consistent pairing. The implicit-association test is used in psychology for a wide array of topics. These fields include gender, race, science, career, weight, sexuality, and disability. While acclaimed and highly influential, the implicit-association test falls short of a strong scientific consensus. Critics of the implicit-association test cite studies that counterintuitively link biased test scores with less discriminatory behavior. Studies have also asserted that the implicit-association test fails to measure unconscious thought.

Go/no-go association task (GNAT)

The GNAT is similar to the implicit-association test. Although the IAT reveals differential associations of two target concepts (e.g. male-female and weak-strong), the GNAT reveals associations within one concept (for example, whether female is associated more strongly with weak or strong).

Participants are presented with word pairs among distractors. Participants are instructed to indicate "go" if the words are target pairs, or "no-go" if they are not. For example, participants may be instructed to indicate "go" if the word pairs are female names and words that are related to strength. Then, participants are instructed to indicate "go" if the word pairs are female names and words that are related to weakness. This method relies on signal detection theory; participants' accuracy rates reveal endorsement of the implicit stereotype. For example, if participants are more accurate for female-weak pairs than for female-strong pairs, this suggests the subject more strongly associates weakness with females than strength.

Semantic priming and lexical decision task

Semantic priming measures the association between two concepts. In a lexical decision task, subjects are presented with pair of words, and asked to indicate whether the pair are words (for example, "butter") or non-words (for example, "tubter"). The theory behind semantic priming is that subjects are quicker to respond to a word if preceded by a word related to it in meaning (e.g. bread-butter vs. bread-dog). In other words, the word "bread" primes other words related in meaning, including butter. Psychologists utilize semantic priming to reveal implicit associations between stereotypic-congruent words. For instance, participants may be asked to indicate whether pronouns are male or female. These pronouns are either preceded by professions that are predominantly female ("secretary, nurse"), or male ("mechanic, doctor"). Reaction times reveal strength of association between professions and gender.

Sentence completion

In a sentence completion task, subjects may be presented with sentences that contain stereotypic black and white names (Jerome, Adam), positive and negative stereotypic black behaviors (easily made the team, blasted loud music in his car) and counter-stereotypic behaviors (got a job at Microsoft, refused to dance). Subjects are asked to add to the end of a sentence in any way that is grammatical, e.g. "Jerome got an A on his test..." could be completed with "because it was easy" (stereotypic-congruent) or "because he studied for months" (stereotypic-incongruent) or "and then he went out to celebrate" (non-explanatory). This task is used to measure stereotypic explanatory bias (SEB): participants have a larger SEB if they give more explanations for stereotype-congruent sentences than stereotype–incongruent sentences, and if they give more stereotypic-congruent explanations.

Differences between measures

The Implicit Association Test (IAT), sequential priming, and other implicit bias tests, are mechanisms for determining how susceptible we are to stereotypes. They are widely used in Social Psychology, although measuring response time to a question as a good measure of implicit biases is still up for debate. “Some theorists do question the interpretation of the scores from tests such as the IAT, but the debate is still going on and responses to the criticisms are certainly widespread.”

Findings

Gender bias

See also: Sexism § Gender stereotypes, and Gender role § Gender stereotypes

Gender biases are the stereotypical attitudes or prejudices that we have towards specific genders. "The concept of gender also refers to the constantly ongoing social construction of what is considered ‘feminine’ and ‘masculine’ and is based on power and sociocultural norms about women and men." Gender biases are the ways in which we judge men and women based on their hegemonically feminine and masculine assigned traits.

The category of male has been found to be associated with traits of strength and achievement. Both male and female subjects associate male category members more strongly than female category members with words like bold, mighty, and power. The strength of this association is not predicted by explicit beliefs, such as responses on a gender stereotype questionnaire (for example, one question asked if subjects endorsed the word feminist). In a test to reveal the false fame effect, non famous male names are more likely to be falsely identified as famous than non famous female names; this is evidence for an implicit stereotype of male achievement. Females are more associated with weakness. This is true for both male and female subjects, but female subjects only show this association when the weak words are positive, such as fine, flower and gentle; female subjects do not show this pattern when the weak words are negative, such as feeble, frail, and scrawny.

Particular professions are implicitly associated with genders. Elementary school teachers are implicitly stereotyped to be female, and engineers are stereotyped to be male.

Gender bias in science and engineering

Implicit-association tests reveal an implicit association for male with science and math, and females with arts and language. Girls as young as nine years old have been found to hold an implicit male-math stereotype and an implicit preference for language over math. Women have stronger negative associations with math than men do, and the stronger females associate with a female gender identity, the more implicit negativity they have towards math. For both men and women, the strength of these implicit stereotypes predicts both implicit and explicit math attitudes, belief in one's math ability, and SAT performance. The strength of these implicit stereotypes in elementary-aged girls predicts academic self-concepts, academic achievement, and enrollment preferences, even more than do explicit measures. Women with a stronger implicit gender-math stereotype were less likely to pursue a math-related career, regardless of their actual math ability or explicit gender-math stereotypes. This may be because women with stronger implicit gender-math stereotypes are more at risk for stereotype threat. Thus, women with strong implicit stereotypes perform much worse on a math test when primed with gender than women who have weak implicit stereotypes.

Though the number of women pursuing and earning degrees in engineering has increased in the last 20 years, women are below men at all degree levels in all fields of engineering. These implicit gender stereotypes are robust; in a study of more than 500,000 respondents from 34 nations, more than 70% of individuals held this implicit stereotype. The national strength of the implicit stereotype is related to national sex differences among 8th graders on the International TIMSS, a worldwide math &science standardized achievement exam. This effect is present even after statistically controlling for gender inequality in general. Additionally, for women across cultures, studies have shown individual differences in strength of this implicit stereotype is associated with interest, participation and performance in sciences. Extending to the professional world, implicit biases and subsequent explicit attitudes toward women can "negatively affect the education, hiring, promotion, and retention of women in STEM".

The effects of such implicit biases can be seen in across multiple studies including:

• Parents rate the math abilities of their daughters lower than parents with sons who perform identically well in school
• College faculty are less likely to respond to inquiries about research opportunities if the email appears to be from a woman as opposed to an identical email from a man
• Science faculty are less likely to hire or mentor students they believe are women as opposed to men

An interagency report from the Office of Science and Technology Policy and Office of Personnel Management has investigated systemic barriers including implicit biases that have traditionally inhibited particularly women and underrepresented minorities in science, technology, engineering, and mathematics (STEM) and makes recommendations for reducing the impact of bias. Research has shown that implicit bias training may improve attitudes towards women in STEM.

Racial bias

Racial bias can be used synonymously with "stereotyping and prejudice" because "it allows for the inclusion of both positive and negative evaluations related to perceptions of race." We begin to create racial biases towards other groups of people starting as young as age 3, creating an ingroup and outgroup view on members of various races, usually starting with skin color.

In lexical decision tasks, after subjects are subliminally primed with the word BLACK, they are quicker to react to words consistent with black stereotypes, such as athletic, musical, poor and promiscuous. When subjects are subliminally primed with WHITE, they are quicker to react to white stereotypes, such as intelligent, ambitious, uptight and greedy. These tendencies are sometimes, but not always, associated with explicit stereotypes.

People may also hold an implicit stereotype that associates black category members as violent. People primed with words like ghetto, slavery and jazz were more likely to interpret a character in a vignette as hostile. However, this finding is controversial; because the character's race was not specified, it is suggested that the procedure primed the race-unspecified concept of hostility, and did not necessarily represent stereotypes.

An implicit stereotype of violent black men may associate black men with weapons. In a video game where subjects were supposed to shoot men with weapons and not shoot men with ordinary objects, subjects were more likely to shoot a black man with an ordinary object than a white man with an ordinary object. This tendency was related to subjects' implicit attitudes toward black people. Similar results were found in a priming task; subjects who saw a black face immediately before either a weapon or an ordinary object more quickly and accurately identified the image as a weapon than when it was preceded by a white face.

Implicit race stereotypes affect behaviors and perceptions. When choosing between pairs of questions to ask a black interviewee, one of which is congruent with racial stereotype, people with a high stereotypic explanatory bias (SEB) are more likely to ask the racially congruent stereotype question. In a related study, subjects with a high SEB rated a black individual more negatively in an unstructured laboratory interaction.

In-group and out-group bias

Group prototypes define social groups through a collection of attributes that define both what representative group members have in common and what distinguishes the ingroup from relevant outgroups. In-group favoritism, sometimes known as in-group–out-group bias, in-group bias, or intergroup bias, is a pattern of favoring members of one's in-group over out-group members. This can be expressed in evaluation of others, in allocation of resources, and in many other ways. Implicit in-group preferences emerge very early in life, even in children as young as six years old. In-group bias wherein people who are ‘one of us’ (i.e., our ingroup) are favored compared to those in the outgroup, meaning those who differ from ourselves. Ingroup favoritism is associated with feelings of trust and positive regard for ingroup members and surfaces often on measures of implicit bias. This categorization (ingroup vs. outgroup) is often automatic and pre-conscious.

The reasons for having in-group and out-group bias could be explained by ethnocentrism, social categorization, oxytocin, etc. A research paper done by Carsten De Dreu reviewed that oxytocin enables the development of trust, specifically towards individuals with similar characteristics - categorized as ‘in-group’ members - promoting cooperation with and favoritism towards such individuals. People who report that they have strong needs for simplifying their environments also show more ingroup favoritism. The tendency to categorize into ingroups and outgroups and resulting ingroup favoritism is likely a universal aspect of human beings.

We generally tend to hold implicit biases that favor our own ingroup, though research has shown that we can still hold implicit biases against our ingroup. The most prominent example of negative affect towards an ingroup was recorded in 1939 by Kenneth and Mamie Clark using their now famous “Dolls Test”. In this test, African American children were asked to pick their favorite doll from a choice of otherwise identical black and white dolls. A high percentage of these African American children indicated a preference for the white dolls. Social identity theory and Freudian theorists explain in-group derogation as the result of a negative self-image, which they believe is then extended to the group.

Other stereotypes

Research on implicit stereotypes primarily focuses on gender and race. However, other topics, such as age, weight, and profession, have been investigated. IATs have revealed implicit stereotypes reflecting explicit stereotypes about adolescents. The results from these tests claim that adolescents are more likely to be associated with words like trendy and defiant than adults. In addition, one IAT study revealed that older adults had a higher preference for younger adults compared to older adults; and younger adults had a lower implicit preference for younger adults compared to older adults. The study also found that women and participants with more education had lower implicit preference for younger adults. IATs have also revealed implicit stereotypes on the relationship between obese individuals and low work performance. Words like lazy and incompetent are more associated with images of obese individuals than images of thin ones. This association is stronger for thin subjects than overweight ones. Like explicit stereotypes, implicit stereotypes may contain both positive and negative traits. This can be seen in examples of occupational implicit stereotypes where people perceive preschool teachers as both warm and incompetent, while lawyers are judged as both cold and competent.

Activation of implicit stereotypes

Implicit stereotypes are activated by environmental and situational factors. These associations develop over the course of a lifetime beginning at a very early age through exposure to direct and indirect messages. In addition to early life experiences, the media and news programming are often-cited origins of implicit associations. In the laboratory, implicit stereotypes are activated by priming. When subjects are primed with dependence by unscrambling words such as dependent, cooperative, and passive, they judge a target female as more dependent. When subjects are primed with aggression with words like aggressive, confident, argumentative, they judge a target male as more aggressive. The fact that females and words such as dependent, cooperative, and passive and males and words like aggressive, confident, argumentative are thought to be associated together suggest an implicit gender stereotype. Stereotypes are also activated by a subliminal prime. To exemplify, white subjects exposed to subliminal words which consist of a black stereotype (ghetto, slavery, jazz) interpret a target male as more hostile, consistent with the implicit stereotype of hostile black man. However, this finding is controversial because the character's race is not specified. Instead, it is suggested that the procedure primed the race-unspecified concept of hostility, and did not necessarily represent stereotypes. By getting to know people who differ from you on a real, personal level, you can begin to build new associations about the groups those individuals represent and break down existing implicit associations.

Malleability of implicit stereotypes

Implicit stereotypes can, at least temporarily, be reduced or increased. Most methods have been found to reduce implicit bias temporarily, and are largely based on context. Some evidence suggests that implicit bias can be reduced long-term, but it may require education and consistent effort. Some implicit bias training techniques designed to counteract implicit bias are stereotype replacement, counter-stereotypic imaging, individuation, perspective taking, and increasing opportunities for contact.

Stereotype replacement is when you replace a stereotypical response with a non-stereotypical response. Counter-stereotypic imagining is when you imagine others in a positive light and replace stereotypes with positive examples. Individuation is when you focus on specific details of a certain member of a group to avoid over-generalizing. Perspective taking is when you take the perspective of a member of a marginalized group. Increasing opportunities for contact is when you actively seek out opportunities to engage in interactions with members of marginalized groups.

Self and social motives

The activation of implicit stereotypes may be decreased when the individual is motivated to promote a positive self-image, either to oneself or to others in a social setting. There are two parts to this: internal and external motivation. Internal motivation is when an individual wants to be careful of what they say, and external motivation is when an individual has a desire to respond in a politically correct way.

Positive feedback from a black person decreases stereotypic sentence completion, while negative feedback from a black person increases it. Subjects also reveal lesser strength of race stereotypes when they feel others disagree with the stereotypes. Motivated self-regulation does not immediately reduce implicit bias. It raises awareness of discrepancies when biases stand in the way of personal beliefs.

Promote counterstereotypes

Implicit stereotypes can be reduced by exposure to counterstereotypes. Reading biographies of females in leadership roles (such as Meg Whitman, the CEO of eBay) increases females’ associations between female names and words like leader, determined, and ambitious in a gender stereotype IAT. Attending a women's college (where students are presumably more often exposed to women in leadership positions) reduces associations between leadership and males after one year of schooling. Merely imagining a strong woman reduces implicit association between females and weakness, and imagining storybook princesses increases the implicit association between females and weakness.

Focus of attention

Diverting a participant's focus of attention can reduce implicit stereotypes. Generally, female primes facilitate reaction time to stereotypical female traits when participants are instructed to indicate whether the prime is animate. When participants instead are instructed to indicate whether a white dot is present on the prime, this diverts their focus of attention from the primes’ feminine features. This successfully weakens the strength of the prime and thus weakening the strength of gender stereotypes.

Configuration of stimulus cues

Whether stereotypes are activated depends on the context. When presented with an image of a Chinese woman, Chinese stereotypes were stronger after seeing her use chopsticks, and female stereotypes were stronger after seeing her put on makeup.

Characteristics of individual category members

Stereotype activation may be stronger for some category members than for others. People express weaker gender stereotypes with unfamiliar than familiar names. Judgments and gut reactions that go along with implicit biases are based on how familiar something is.

Criticism

Some social psychology research has indicated that individuating information (giving someone any information about an individual group member other than category information) may eliminate the effects of stereotype bias.

Meta-analyses

Researchers from the University of Wisconsin at Madison, Harvard, and the University of Virginia examined 426 studies over 20 years involving 72,063 participants that used the IAT and other similar tests. They concluded two things:

1. The correlation between implicit bias and discriminatory behavior appears weaker than previously thought.
2. There is little evidence that changes in implicit bias correlate with changes in a person’s behavior.

In a 2013 meta-analysis of papers, Hart Blanton, et al. declared that, despite its frequent misrepresentation as a proxy for the unconscious, "the IAT provides little insight into who will discriminate against whom, and provides no more insight than explicit measures of bias."

News outlets

Heather Mac Donald, writing in the Wall Street Journal, noted that:

Few academic ideas have been as eagerly absorbed into public discourse lately as “implicit bias.” Embraced by Barack Obama, Hillary Clinton and most of the press, implicit bias has spawned a multimillion-dollar consulting industry, along with a movement to remove the concept of individual agency from the law. Yet its scientific basis is crumbling.

Mac Donald suggests there is still a political and economic drive to use the implicit bias paradigm as a political lever and to profit off entities which want to avoid litigation.

Psychometric Concerns

Edouard Machery has argued that “the use of [indirect measures like the implicit association test] is deeply problematic” because the tests do not exhibit the psychometric properties we would expect from measures of "attitudes". However, many have already admitted that these indirect tests "assess behavior" rather than attitudes. This is an example of how the debate about implicit bias can involve "talking past one another" based on "different expectations of indirect measures", views of (what) implicit bias (is), assumptions about which evidence is relevant, threshholds for scientific significance, psychometric standards, and even norms of science communication. So evaluating debates about tests of implicit bias requires one to pay careful attention to debators' background assumptions and whether (or how well) debators' justify those assumptions.

Statement by original authors

Where previously Greenwald and Banaji asserted in their book BlindSpot (2013).

Given the relatively small proportion of people who are overtly prejudiced and how clearly it is established that automatic race preference predicts discrimination, it is reasonable to conclude not only that implicit bias is a cause of Black disadvantage but also that it plausibly plays a greater role than does explicit bias.

The evidence presented by their peer researchers led them to concede in correspondence that:

1. The IAT does not predict biased behaviour(in laboratory settings)
2. It is "problematic to use [the IAT] to classify persons as likely to engage in discrimination".

However, they also stated, "Regardless of inclusion policy, both meta-analyses estimated aggregate correlational effect sizes that were large enough to explain discriminatory impacts that are societally significant either because they can affect many people simultaneously or because they can repeatedly affect single persons."

Summary

Implicit bias is thought to be the product of positive or negative mental associations about persons, things, or groups that are formed and activated pre-consciously or subconsciously. In 1995, researchers Banaji and Greenwald noted that someone’s social learning experiences, such as observing parents, friends, or others, could create this type of association and, therefore, trigger this type of bias. Many studies have found that culture is able to stimulate biases as well, both in a negative and positive way regardless someone’s personal experience with other cultures. As far as many people are concerned, implicit bias knows no age restriction and it can be held by anyone regardless of their age. In fact, implicit biases can be found in a person as young as six years old. Even though implicates bias may be difficult to catch, especially compared to explicit bias, it can be measured through a number of mechanisms, such as sequential priming, response competition, EDA, EMG, fMRI, ERP and ITA. Thus, once a person becomes aware of their own bias, they can take action to change it, if they wish.

The existence of implicitly biased behavior is supported by several articles in psychological literature. Adults- and even children- may hold implicit stereotypes of social categories, categories to which they may themselves belong to. Without intention, or even awareness, implicit stereotypes affect human behavior and judgments. This has wide-ranging implications for society, from discrimination and personal career choices to understanding others in social interactions each day.