DE112011102156B4 - Cell state determination in phase change storage - Google Patents

Abstract

A method for determining the state of a phase change memory cell having a non-linear sub-threshold current/voltage characteristic, the method comprising:
Performing a variety of measurements dependent on the non-linear sub-threshold current/voltage characteristic of the cell;
Processing the measured values using differences (log R ₁ - log R ₂ ) to obtain a measure which depends on the slope of the current/voltage characteristic and is independent of the absolute cell resistance; and
Determine the state of the cell depending on the measurement value.

Description

This invention relates generally to phase change memories and, more particularly, to methods and apparatus for determining the state of phase change memory cells.

Phase-change memory (PCM) is a new non-volatile solid-state memory technology that utilizes the reversible switching of certain chalcogenide materials between at least two states with different electrical conductivity. PCMs are fast, have excellent retention and long-life properties, and have proven adaptable to future lithography nodes. For these reasons, they are believed to have the potential to either replace or complement flash memory in today's prevalent memory and storage applications.

In commercially available PCM devices, the elementary storage unit (the "cell") can be set to one of two states, crystalline or amorphous, by applying heat. In the amorphous state, which represents a binary 0, the cell's electrical resistance is high. When the chalcogenide material is heated to a temperature above its crystallization point and then cooled, it is converted to an electrically conductive, crystalline state. This low-resistance state represents a binary 1. If the cell is then heated to a temperature above the chalcogenide melting point, the chalcogenide material returns to its amorphous state upon rapid cooling. To write data to a PCM cell, a voltage or current pulse is applied to the cell to heat the chalcogenide material to a suitable temperature to induce the desired cell state upon cooling. To read a cell, the cell's state is determined using the cell resistance as a measure. Cell resistance is determined either by biasing the cell with a constant voltage and measuring the current flowing through it, or by passing a constant current and measuring the resulting voltage across the cell. This measurement is performed in the sub-threshold region of the cell's current/voltage characteristic, i.e., below the threshold switching voltage (i.e., the voltage at which the chalcogenide enters a conductive "ON" state, allowing current to flow through the cell to Joule heat it and potentially cause a phase change). In this sub-threshold region, the cell can be read without affecting the cell state, with a high-resistance reading indicating a binary 0 and a low-resistance reading indicating a binary 1.

Crucially, PCMs can only gain market acceptance in the form of multi-state cells (MLCs), which can reduce the cost per bit to levels competitive with MLC flash memory technology. Multi-state memory cells can be set to s different resistance values, where s>2, and thus allow the storage of more than one bit per cell. NOR flash memory, for example, can store four states, i.e., two bits per cell. Currently, MLC NAND flash memory chips are available in 43 nm process technology, which can store four data bits (i.e., sixteen states) per single flash cell. In PCM cells, MLC operation is achieved by utilizing partially amorphous states of the chalcogenide cell. Different cell states are set by changing the effective volume of the amorphous phase within the chalcogenide material. This, in turn, changes the cell resistance. Although commercially available PCM chips currently only store one bit per cell, the storage of four bits per cell in PCM chips has already been demonstrated experimentally.

One problem in PCM devices is a physical phenomenon known as short-term resistance drift or structural relaxation, often simply referred to as "drift." This problem is particularly significant in MLC devices and represents a significant technical obstacle to designing PCMs as MLCs. Structural relaxation is thought to be caused by local changes in the atomic arrangement in the amorphous phase of phase-change materials, which affect their electrical conductivity. In particular, the resistance of a PCM cell programmed to the amorphous state or semi-amorphous states in MLC-PCMs increases over time and is also affected by temperature. Therefore, the cell resistance measured at different times is observed to fluctuate, following an increasing trend with time. The events contributing to this resistance change are stochastic in nature and timing of their occurrence and consequently very difficult to predict and mitigate. Due to resistance drift, different resistance values corresponding to different cell states (configurations of amorphous/crystalline material phases within the active volume) may overlap at random times, resulting in random errors in the determination of the cell state.

A number of techniques have been proposed to address the problem of resistance drift. One technique requires the use of reference cells, whereby a specific portion of the memory cell array is reserved for drift mitigation. Each of these reference cells is programmed to a specific cell state, and the resistance of these cells is monitored at regular intervals to obtain an estimate of the resistance drift for other cells (i.e., those used for actual user data storage). The estimated drift is then removed from measured values of the user cells to obtain drift-free resistance values. The effectiveness of such reference-cell-based drift cancellation relies heavily on the assumption that states of similar cells have similar drift characteristics. However, due to the inevitable presence of significant cell-to-cell variances (caused by process variations, which increase with smaller cell dimensions) and parameter variations within cells (mainly caused by material variations), the validity of this assumption is questionable, resulting in inadequate drift cancellation.

Regarding drift, drift acceleration has also been proposed. During (or after) programming a memory cell, the cell is annealed at a specific (sufficiently low) temperature for a period of time to accelerate the drift effect according to an Arrhenius equation. It is assumed that the cell resistance does not drift noticeably after annealing. The effectiveness of this approach has not been adequately verified experimentally. Furthermore, since the phase change phenomenon is thermally activated, annealing cells can lead to undesirable perturbation of the cell state.

Coding techniques have also been proposed to combat drift. In these cases, memory cells are programmed and read in blocks of cells (codewords) rather than individually. Redundancy added to these codewords is intended to make codewords immune to drift and ensure error-free information retrieval during decoding. While drift coding can be a potentially powerful technique, its effectiveness typically varies with the redundancy of the code used. Higher redundancy detracts from the memory capacity available for storing the actual user data. Typically, only minimal redundancy is tolerated, and this can reduce the effectiveness of a code in combating drift.

The DE 10 2009 050 746 A1 describes a method for multilevel reading of a phase-change memory cell, in which a bit line and a PWS cell are first selected, and a first bias voltage is applied to the selected bit line. A first read current flowing through the selected bit line in response to the first bias voltage is compared to a first reference current. The first reference current is such that the first read current is less than the first reference current when the selected PWS cell is in a reset state and greater otherwise. It is then determined whether the selected PWS cell is in the reset state based on comparing the first read current with the first reference current. A second bias voltage, greater than the first bias voltage, is applied to the selected bit line when the selected PWS cell is not in the reset state.

US 2010/0 182 827 A1 describes an electronic device and method for programming for binary and multilevel memory operation. The active material of the device is a phase-change material. The method involves using the pulse duration of electrical pulses as a programming variable to program a phase-change device to two or more memory states that differ in the relative proportion and/or spatial arrangement of crystalline and amorphous phase regions. Pulse-width programming, in conjunction with an electrical contact of the device with a resistivity within a specific range, enables fine control of the crystalline-amorphous phase-change process by facilitating control of the spatial distribution of thermal energy generated by Joule heating. This degree of control over the phase-change process enables reliable multilevel memory operation by enabling reproducible programming of memory states that are well-resolved in both the resistance and the programming variable.

US 2008/0 019 163 A1 describes a method for reading a storage datum from a resistive memory cell having a selection transistor addressable via a control value. The method comprises detecting a cell current flowing through the resistive memory cell, setting the control value as a function of the detected cell current, and providing information associated with the control value as the storage datum.

• Ausführen einer Vielzahl von von der nichtlinearen unterschwelligen Strom/Spannungs-Kennlinie der Zelle abhängigen Messungen;
• Verarbeiten der Messwerte mittels Differenzen, um eine Maßzahl zu erhalten, welches von der Steigung der Strom/Spannungs-Kennlinie abhängig und vom absoluten Zellenwiderstand unabhängig ist; und
• Ermitteln des Zustands der Zelle in Abhängigkeit von der Maßzahl.

An embodiment of an aspect of the present invention provides a method for determining the state of a phase-change memory cell having a nonlinear subthreshold current/voltage characteristic. The method comprises:

• Performing a variety of measurements dependent on the non-linear sub-threshold current/voltage characteristic of the cell;
• Processing the measured values using differences to obtain a measure that depends on the slope of the current/voltage characteristic and is independent of the absolute cell resistance; and
• Determine the state of the cell depending on the measurement value.

In embodiments of this invention, a metric is used that depends on the slope of the cell's subthreshold current/voltage (I/V) characteristic, i.e., the slope of the I/V characteristic below the threshold switching voltage. The slope of the subthreshold I/V characteristic depends on resistance differentials, i.e., a derivative of resistance, but not on any absolute resistance value. While the cell resistance varies noticeably over time, as discussed above, the slope of the I/V characteristic in the subthreshold region remains almost unchanged over time. This is because the subthreshold I/V slope is a function of the effective volume of the amorphous phase within the cell. The effective amorphous volume, in turn, is a good measure of the cell state and, remarkably, a measure that is not susceptible to drift, since drift is known not to affect the geometry of the amorphous phase (drift is assumed to be due to defect annihilation within the amorphous phase but does not affect the total amorphous volume).

Methods embodying this invention utilize the subthreshold I/V slope to obtain a cell state metric that is substantially drift-independent. In particular, the metric used in embodiments of the invention is substantially unaffected by drift, i.e., it remains substantially constant over time, except for unavoidable noise fluctuations. Since the subthreshold I/V slope is a function of the effective amorphous volume within the cell and thus a measure of cell state, it follows that the above-mentioned metric is also indicative of the cell state and can thus be used to distinguish between different states in MLC-PCM. The validity of this statement and the suitability of this metric as a measure of cell state have been demonstrated by experimental results on actual PCM cell arrays, as described below. Thus, by using the described metric, embodiments of the invention provide methods for determining the state of PCM cells in a manner that retrieved information is robust to drift. Methods according to embodiments of the invention may not make assumptions regarding the nature of the drift itself and may not result in an inherent loss of user storage capacity. Thus, embodiments of the invention may provide improvements in cell state detection for PCM arrays, generally supporting better MLC capabilities and efficient operation of PCM devices.

The aforementioned metric may depend directly or indirectly on the slope of the subthreshold I/V characteristic curve, depending on this slope in various ways. The point is that the metric is somehow related to the subthreshold I/V slope and therefore not directly dependent on the absolute cell resistance, the latter being subject to drift as discussed above. In other words, according to embodiments of the invention, the PCM cell state may be determined based on a metric that is independent or substantially independent of the absolute cell resistance. According to embodiments of the invention, to derive the metric, at least two measurements are taken on the cell, these measurements depending (directly or indirectly) on the subthreshold I/V slope. More than two measurements may be taken to enable averaging and improve accuracy, as described further below. The resulting measurements may then be processed in various ways to obtain the final metric used to calculate the cell state. For example, some embodiments may include performing a plurality of measurements of the cell current at different cell bias voltages, wherein the measure depends on differences as a function of the measured cell current at the different bias voltages. Accordingly, the voltage across the cell may be measured for different applied cell currents, and the measure may depend on differences as a function of the measured cell voltages. Alternatively, for example, a plurality of measurements of the cell resistance may be performed at different points on the sub-threshold I/V characteristic curve, and the measure may depend on differences as a function of the measured cell resistance at the different points. In these examples, the specified function of the cell in question could measured value can simply be the measured value itself or it could be some more complex function, for example a logarithm of that value.

The specific manner in which the cell state is determined from the metric may also vary in different embodiments. The details of this step may depend on the cell type (number of states), the exact form of the metric itself, and any techniques that might be used in addition to the basic metric derivation method, e.g., any additional correction techniques to further enhance reading accuracy. In preferred embodiments, the cell state may be determined simply by comparing the derived metric (with or without any further processing) to one or more reference values corresponding to the different cell states. While embodiments of the invention can be applied to two-state PCM cells, application to multi-state cells is particularly advantageous, since drift is more problematic in MLC devices. When used to determine the state of a multi-state cell (i.e., an s-state cell with s>2), preferred methods may include determining the cell's state by comparing the derived measure with a plurality of reference values corresponding to the s states of the cell. Such reference values may define a cell state in various ways, e.g., as predefined thresholds that define boundaries for measurement ranges associated with the various readback states.

• eine Messschaltung zum Ausführen einer Vielzahl von von der nichtlinearen unterschwelligen Strom/Spannungs-Kennlinie der Zelle abhängigen Messungen; und
• eine Steuereinheit zum Verarbeiten der Messwerte mittels Differenzen, um eine Maßzahl zu erhalten, welche von der Steigung der Strom/Spannungs-Kennlinie abhängig und vom absoluten Zellenwiderstand unabhängig ist, wobei die Steuereinheit so eingerichtet ist, dass sie den Zustand der Zelle in Abhängigkeit der Maßzahl ermitteln kann.

An embodiment of a second aspect of the invention provides an apparatus for determining the state of a phase-change memory cell with a nonlinear sub-threshold current/voltage characteristic. The apparatus comprises:

• a measuring circuit for performing a plurality of measurements dependent on the non-linear sub-threshold current/voltage characteristic of the cell; and
• a control unit for processing the measured values by means of differences in order to obtain a measurement value which is dependent on the slope of the current/voltage characteristic curve and independent of the absolute cell resistance, wherein the control unit is designed in such a way that it can determine the state of the cell as a function of the measurement value.

According to a further embodiment of the invention, the PCM cell state is determined on the basis of a measure which is independent or substantially independent of the absolute cell resistance.

• einen Speicher, eine Vielzahl von Phasenwechselspeicherzellen mit einer nichtlinearen unterschwelligen Strom/Spannungs-Kennlinie aufweisend; und
• eine Lese/Schreib-Vorrichtung zum Lesen von Daten aus den und Schreiben von Daten in die Phasenwechselspeicherzellen, wobei die Lese/SchreibVorrichtung eine Vorrichtung gemäß dem zweiten Aspekt der Erfindung zum Ermitteln des Zustands einer Speicherzelle enthält.

An embodiment of a third aspect of the invention provides a phase change memory device comprising:

• a memory comprising a plurality of phase-change memory cells with a non-linear sub-threshold current/voltage characteristic; and
• a read/write device for reading data from and writing data to the phase change memory cells, the read/write device including a device according to the second aspect of the invention for determining the state of a memory cell.

In general, where features are described herein with respect to a method embodying the invention, corresponding features may be provided in an apparatus or device embodying the invention, and vice versa.

• 1 ist ein schematischer Blockschaltplan einer die Erfindung verkörpernden Phasenwechselspeicher-Einheit;
• 2 zeigt eine Mittelwert-Programmierkurve für PCM-Zellen mit acht Zuständen;
• 3 veranschaulicht die Zeitabhängigkeit des PCM-Zellenwiderstands bei verschiedenen angelegten Spannungen;
• 4 zeigt eine einfache Differenzmaßzahl-Berechnungsschaltung zum Erzeugen einer Zellenzustandsmaßzahl in der Einheit in 1;
• 5 zeigt die Ergebnisse aus 3 nach einem Mittelwertentfernungsprozess;
• Die 6a und 6b veranschaulichen die Zeitabhängigkeit einer in der Einheit in 1 verwendeten Differenzmaßzahl vor beziehungsweise nach Mittelwertentfernung;
• 7 vergleicht die Zeitabhängigkeit des Zellenwiderstands mit der Zeitabhängigkeit der Differenzmaßzahl;
• Die 8a und 8b veranschaulichen die Funktionsweise digitaler beziehungsweise analoger Ausführungen einer Messschaltung der Einheit in 1 ;
• 9 vergleicht die Wirkung von Drift auf Zellenzustandsmessungen bei verschiedenen Zuständen unter Verwendung einer Roh-Widerstandsmaßzahl und der Differenzmaßzahl der Einheit in 1;
• 10 zeigt, wie die mittlere Differenzmaßzahl sich mit dem gespeicherten Zellenzustand ändert; und
• 11 ist eine schematische Darstellung einer PCM-Zelle, welche die effektive amorphe Dicke der Zelle zeigt.

Preferred embodiments of the invention will now be described by way of example with reference to the following accompanying drawings.

• 1 is a schematic block diagram of a phase change memory unit embodying the invention;
• 2 shows a mean programming curve for eight-state PCM cells;
• 3 illustrates the time dependence of PCM cell resistance at different applied voltages;
• 4 shows a simple difference measure calculation circuit for generating a cell state measure in the unit in 1 ;
• 5 shows the results from 3 after a mean removal process;
• The 6a and 6b illustrate the time dependence of a unit in 1 used difference measure before or after mean removal;
• 7 compares the time dependence of the cell resistance with the time dependence of the difference measure;
• The 8a and 8b illustrate the functionality of digital or analog versions of a measuring circuit of the unit in 1 ;
• 9 compares the effect of drift on cell state measurements at different conditions using a raw resistance measure and the unit difference measure in 1 ;
• 10 shows how the mean difference measure changes with the stored cell state; and
• 11 is a schematic representation of a PCM cell showing the effective amorphous thickness of the cell.

1 is a schematic block diagram of a phase-change memory unit embodying the invention. The unit 1 contains a phase-change memory 2 for storing data in one or more integrated arrays of multi-state PCM cells. Although the memory 2 is shown in the figure as a single block, it may generally comprise any desired configuration of PCM memory units, for example, from a single chip to a plurality of memory banks, each containing multiple modules of memory chips. Reading and writing data to the memory 2 is performed by a read/write device 3. The device 3 contains a data read/write measurement circuit 4 for writing data to the PCM cells and for performing cell measurements that allow the cell state to be determined and, consequently, the stored data to be read back. By applying suitable voltages to an array of word and bit lines in the memory assembly 2, the circuit 4 can address individual PCM cells for writing and reading purposes. This process is carried out in a generally known manner, except as detailed below. A read/write control unit 5 generally controls the operation of the device 3 and includes the functionality for deriving a cell state metric from read measurements and using this metric for cell state determination, i.e., state detection, as described in more detail below. In general, the functionality of the control unit 5 could be implemented in hardware or software, or a combination thereof, although for reasons of speed of operation, the use of hard-wired logic circuits is usually preferred. Suitable implementations will be apparent to those skilled in the art from the description given herein. As indicated by block 6 in the figure, user data input to the unit 1 is usually subjected to some type of write processing, such as encoding for error correction purposes, before being supplied as write data to the read/write device 3. Accordingly, read-back data output by the device 3 is usually processed by a read processing module 7, which performs, for example, codeword detection and error correction operations to restore the original input user data. Such processing by modules 6 and 7 is independent of the cell state measurement system to be described and does not need to be discussed in detail here.

Each of the multi-state cells in memory 2 can be set to one of s predefined resistance values, where s>2, corresponding to different amorphous/crystalline states of the cell. The resistance values defining the different states are usually unevenly spaced and are usually represented logarithmically. In this particular example, s=8, allowing each cell to store eight states, providing three bits of storage per cell. To write data to a given cell, circuit 4 applies a voltage pulse to set the cell to the state corresponding to the appropriate resistance value. 2 illustrates how the cell resistance in PCM cells changes with the applied voltage. This figure shows the mean programming curve obtained for applied voltage pulses with increasing amplitude Vg for an array of sixty 8-state PCM cells as the logarithm of the (average) cell resistance R. The eight predefined resistance values R0 to R7 are represented in the figure by horizontal lines. The left side of the programming curve (left of the vertical dashed line at Vg = 1.5 volts) shows how the programmed resistance initially decreases as the voltage is increased, starting from 0 volts. This is attributable to increasing crystallization in the chalcogenide material of the cell. Here, Vg = 1.5 volts corresponds to a state of maximum crystallization. Thereafter, increasing voltage causes increasing melting, resulting in a larger effective volume of the amorphous phase within the cell. This causes the programmed resistance to increase along the right programming curve, as shown to the right of the vertical dashed line in the figure. In accordance with conventional practice Data is stored in cells in the unit in 1 written by placing the cells on the right programming slope of the curve in 2 be programmed.

Reading a memory cell requires determining the cell's state, i.e., identifying which of the predefined values R0 to R7 the cell is set to. In conventional units, this is done by performing a direct measurement of the cell resistance. Specifically, a measurement of the cell current is taken for a given applied voltage, and the cell resistance is calculated and used as a cell state metric, which is compared with the predefined values to determine the cell state. This measurement is performed in the sub-threshold region of the cell's current/voltage (I/V) characteristic so that the measurement does not affect the cell state. The I/V characteristic is highly non-linear in the sub-threshold region, resulting in different resistances being measured at different bias voltages. This can be seen from the plot of log R versus time in 3 which shows that the measured resistance of PCM cells decreases as the applied voltage is increased. This figure also clearly illustrates the effect of drift on resistance measurements. In particular, the resistance of the amorphous phase increases over time approximately according to the equation: R(t) = R ₀ (t/t ₀ ) ^v , where log R(t) = log R ₀ + vlog(t/t ₀ ), where v is the drift exponent, which is assumed to be proportional to the volume of the amorphous phase in the active region of the PCM cell. It has been shown that the drift exponent increases with increasing temperature. Drift is a stochastic phenomenon that can be treated as non-stationary noise and is therefore very difficult to predict.

Unit 1 in 1 uses a method for determining the cell state which uses a metric dependent on the slope of the subthreshold I/V characteristic. This can provide a metric that is independent of the absolute cell resistance. To read a cell, the read measurement circuit 4 performs a plurality of measurements dependent on the cell's subthreshold I/V characteristic. In this exemplary embodiment, a simple metric related to the subthreshold I/V slope is obtained as the difference between the logarithm of the cell resistance R ₁ at a certain bias voltage V ₁ and the logarithm of the resistance R ₂ at a different voltage V _2. Since the subthreshold I/V slope remains almost constant over time, the difference metric log R ₁ - log R ₂ has the same property. Although both log R ₁ and log R ₂ fluctuate appreciably and increase on average over time, their fluctuations are in fact so highly correlated that subtracting them removes their common component, which is attributable to drift. The remaining component is attributable to noise and other fluctuations that are largely uncorrelated and not caused by drift. Note that this approach makes no specific assumptions about the nature of the drift as a function of time. An arbitrary drift characteristic (seen as a function of time) can be effectively removed.

In a read operation of unit 1, measuring circuit 4 detects the current I _{1 flowing through a cell when a first (sub-threshold) voltage V 1 is} applied and the current I ₂ flowing when a second (sub-threshold) voltage V ₂ is applied. The resulting resistance measurements R ₁ = V ₁ /I ₁ and R ₂ = V ₂ /I ₂ are output to a control unit 5. The control unit 5 then calculates the difference measure log R ₁ - log R ₂ . This can be done in the control unit 5 either in the digital or in the analog domain by means of a simple differential amplifier circuit, as in 4 illustrated. Since the resulting metric depends on resistance differences, the metric depends on the slope of the I/V characteristic, but not on any absolute resistance (and therefore absolute current or voltage) value. The subthreshold I/V slope is a function of the effective amorphous volume within the cell and thus a measure of the cell state, as discussed previously. It follows that the difference metric is also indicative of the cell state. The difference metric can therefore be used to distinguish between different stored states, while being essentially unaffected by drift for the reasons explained above. This is demonstrated by the following discussion of experimental results.

First of all 3 Returning to the original, it can be observed that measurements of log (R(t)) at different stresses appear to differ only by a constant. Therefore, the structural relaxation of the material (drift) should be independent of stress, at least at low stresses (no annealing). The following model is chosen to explain the measurements: $$\text{r}\left(\text{t},{\text{V}}_{\text{i}}\right)={\text{R}}_{\text{i}}+\text{w}\left(\text{t}\right)$$ where w(t) is a function of time with mean zero, R _i depends only on V _i and r() is used to denote log(R()). Therefore: the mean value E taken with respect to time is given by $$\text{E}\left[\text{r}\left(\text{t},{\text{V}}_{\text{i}}\right)\right]=\text{Ri},$$ given, and consequently $$\text{r}\left(\text{t},{\text{V}}_{\text{i}}\right)-\text{E}\left[\text{r}\left(\text{t},{\text{V}}_{\text{i}}\right)\right]=\text{w}\left(\text{t}\right)\text{ f}\ddot{\text{u}}\text{r alle }\left(\text{i}\right).$$

This is done by 5 which supports the results from 3 after mean removal. If we now consider the difference DR(t,V _i,k ) between pairs of r(t) measured at different voltages V _i , V _{k ,} we get: $$\text{DR}\left(\text{t},{\text{V}}_{\text{i},\text{k}}\right)=\text{r}\left(\text{t},{\text{V}}_{\text{i}}\right)-\text{r}\left(\text{t},{\text{V}}_{\text{k}}\right)={\text{R}}_{\text{i}}-{\text{R}}_{\text{k}}$$ which is independent of (t), ie, constant over time. Therefore, all signal waveforms DR(t,V _i,k ) should be constants over time (slope = 0). It should be noted that this difference measure assumes no knowledge of drift characteristics (ie, w(t) can be arbitrary). These predictions are determined by the 6a and 6b clearly supported. In 6a the difference measure for different voltage pairs V _i , V _k is plotted against time in a logarithmic scale, and 6b shows the same results after mean removal (DR(t,V _i,k ) - E[DR(t,V _i,k )]).

7 shows a direct comparison between the difference measure D and the conventional raw resistance measurement (absolute resistance in logarithmic representation) as a function of time on a logarithmic scale. The solid lines provide a straightforward impression of the results for each curve. This most clearly demonstrates that the difference measure is less time-dependent than the raw measure. The difference measure can thus provide an essentially drift-independent measure, as well as one that functions without knowledge of the drift characteristics (e.g., whether logR(t) is proportional to log(t) or any other drift model).

While a simple model is used above to explain the measurements, a further refined model of R(t) measured at different voltages can be considered, which assumes a power-law behavior of R over time (the usual drift model). According to the standard drift model, log [R(t)] = α(R ₀ ) + vlogt, where R ₀ =R(0), v: drift power-law exponent, and assuming t ₀ =1, without loss of generality. Using a refined model, the following is: $$\text{log}\left[\text{R}\left(\text{t},{\text{V}}_{\text{i}}\right)\right]=\mathrm{\alpha }\left({\text{R}}_0,{\text{V}}_{\text{i}}\right)+\left(\text{v}+{\text{w}}_{\text{i}}\right)\text{log t}$$ where the mean value E _i {w _i } = 0, v depends on the R-value and w _i <<v, the difference measure then takes the following form: $$\text{log}\left[\text{R}\left(\text{t},{\text{V}}_{\text{i}}\right)\right]-\text{log}\left[\text{R}\left(\text{t},{\text{V}}_{\text{k}}\right)\right]=\left[\mathrm{\alpha }\left({\text{R}}_0,{\text{V}}_{\text{i}}\right)-\mathrm{\alpha }\left({\text{R}}_0,{\text{V}}_{\text{k}}\right)\right]+\left({\text{w}}_{\text{i}}+{\text{w}}_{\text{k}}\right)\text{log t}.$$

The first term in square brackets is a measure of R(0) and has a magnitude that increases with |V _i -V _k |. The second term is a weak function of time (w _i <<v). The quality of the measure (time independence, variance) can then be improved by averaging: $$\text{E}\left\{\text{log}\left[\text{R}\left(\text{t},{\text{V}}_{\text{i}}\right)\right]-\text{log}\left[\text{R}\left(\text{t},{\text{V}}_{\text{k}}\right)\right]\right\}=\text{E}\left[\mathrm{\alpha }\left({\text{R}}_0,{\text{V}}_{\text{i}}\right)-\mathrm{\alpha }\left({\text{R}}_0,{\text{V}}_{\text{k}}\right)\right]$$ which has no time dependence. The average value can be calculated over a number of different voltage pairs Vi, Vk. Such an averaging process can be expressed in the unit in 1 can be realized in a simple manner. During a cell read operation, the measuring circuit 4 detects the cell current at several different applied bit line (BL) voltages. This is shown in 8a for a digital circuit design and in 8b for an analog implementation. The resulting resistance measurements (V/I) at each voltage are fed to control unit 5, which calculates the difference between pairs of these resistance values and averages the results to obtain the final mean difference measure.

In 9 the slopes of the signal curves of the mean difference measure over time for different cell states are compared with the slopes of the corresponding signal curves for the raw (absolute) These slopes are an estimate of the drift exponent, and the results clearly demonstrate the superior performance of the mean difference measure.

Having presented the drift resistance of the difference metric as a measure of cell state, we now turn to the question of state discrimination. To be effective, the metric must, of course, be state-dependent and ideally allow state detection with a good margin. 10 shows how the mean difference metric varies with the stored resistance value, averaging over multiple voltage pairs as described above. This proves that the difference metric discriminates sufficiently between stored resistance values to be used as an effective measure of cell state. State detection can be performed in the control unit 5 of the unit 1 simply by comparing the mean difference metric obtained for a cell with a plurality of predefined reference values. The reference values may, for example, correspond to previously calculated metric values defining the various cell states or thresholds defining the boundaries between respective ranges of metric values considered to be associated with the various cell states. A simple comparison of the calculated metric with the reference values in the control unit 5 thus provides the stored cell state. The resulting read-back data is then output from the control unit 5 for further read processing to recover the user data, as discussed above.

It will be appreciated that by utilizing the described cell state metric, the above embodiment can implement a new technique for PCM cell state detection, whereby retrieved data is substantially resistant to drift. This technique arguably provides no insight into the nature of the drift itself, nor does it result in an inherent loss of user storage capacity. Unit 1 can thus constitute a new MLC PCM unit utilizing the new cell state metric technique to provide improved performance combined with simple implementation.

It will, of course, be appreciated that many changes and modifications can be made to the exemplary embodiment described above. For example, various other metrics dependent on the subthreshold IN characteristic of PCM cells can be envisaged. Another simple metric can be obtained as the difference between logarithms of the cell current at various bias voltages Vi, Vk, or, correspondingly, as the difference between logarithms of the measured voltage at various constant current values. While logarithms of the sensed quantity are used here, other functions of these quantities, or even the sensed values themselves, could be used to calculate a difference metric. Moreover, while a simple difference metric provides a rough numerical approximation of the I/V slope (which nevertheless has similar properties (time independence, R-value dependence) to the I/V slope), better numerical approximations can be used if desired, and these can provide improved accuracy. Numerical approximations of the derivative of a function are a well-researched topic, and those skilled in the art will recognize various possibilities here. Further possible measures related to the subliminal I/V slope can be seen from a consideration of the difference measure, which was suggested above in connection with analytical expressions of conduction in the subliminal region. Specific examples are given below using the 11 described.

11 is a schematic representation of a PCM cell in which the shaded hemisphere represents the effective volume of the amorphous phase in the active volume of thickness t _gst of the cell. The amorphous volume has an effective thickness u _a as indicated in the figure. Conduction in amorphous chalcogenides is thought to be attributable to the thermally activated hopping of carriers between local defect states (traps). The two main models for trap-limited conduction in the amorphous phase are Poole conduction (Ielmini-Zhang) for high defect concentrations and Poole-Frenkel conduction for low defect concentrations. These models express the dependence of the cell current I on the applied voltage V with respect to the temperature T, the effective amorphous thickness u _a , and various other parameters. Regarding the Poole conduction model, it can be shown that the difference measure $$\begin{array}{c}DIM=In\left(R_2\right)-ln\left(R_1\right)\\ =ln\left(I_2\right)-ln\left(I_1\right)+ln\left(V_2/V_1\right)\\ =\frac{qdz}{2k_{B}T{u}_a}*\left(V_1-V_2\right)+\text{ln}\left(V_2/V_1\right)\end{array}$$ where dz is the mean distance between traps, k _B is the Boltzmann constant, and q is the charge of an electron. Accordingly, u _a can be estimated as: $$u_a=\frac{qdz}{2k_{B}T{u}_a}*\left[\frac{V_1-V_2}{\text{ln}\left(I_1\right)-\text{ln}\left(I_2\right)}\right]$$

The effective amorphous thickness u _a estimated in this way could be used as a cell state metric in alternative embodiments of the invention.

A corresponding analysis for the Poole-Frenkel model shows that the difference measure $$\begin{array}{c}DIM=In\left(R_2\right)-ln\left(R_1\right)\\ =ln\left(I_2\right)-ln\left(I_1\right)+ln\left(V_2/V_1\right)\\ =\frac{q^{3\text{/}2}}{k_{B}T\sqrt{\pi \epsilon }\sqrt{u_a}}*\left(\sqrt{V_1}-\sqrt{V_2}\right)\end{array}$$ where ε is the effective dielectric constant. Accordingly, $\sqrt{u_a}$ be estimated as: $$\sqrt{u_a}=\frac{q^{3\text{/}2}}{k_{B}T\sqrt{\pi \epsilon }\sqrt{u_a}}*\left(\frac{\sqrt{V_1}-\sqrt{V_2}}{\text{ln}\left(I_1\right)-\text{ln}\left(I_2\right)-\text{ln}\left(V_1/V_2\right)}\right)$$

The parameter estimated in this way $\sqrt{u_a}$ could also be used as a cell health metric in alternative embodiments.

It should be noted that embodiments of the invention could, if desired, utilize other techniques to improve performance in conjunction with the cell state metric system described above. A clever combination of the cell state metric system with other techniques, such as coding to combat drift, may particularly provide improved performance. As another example, the reference values used in state detection may be updated on a dynamic basis, e.g., at regular time intervals, based on reference cell- or model-based correction techniques. Noise in the measurements that is uncorrelated may also be suppressed by averaging the results along the lines discussed above.

Many other changes and modifications may be made to the described exemplary embodiments without departing from the scope of the invention.

Claims (15)

A method for determining the state of a phase-change memory cell having a nonlinear sub-threshold current/voltage characteristic, the method comprising: performing a plurality of measurements dependent on the nonlinear sub-threshold current/voltage characteristic of the cell; processing the measured values by means of differences (log R ₁ - log R ₂ ) to obtain a metric that is dependent on the slope of the current/voltage characteristic and independent of the absolute cell resistance; and determining the state of the cell as a function of the metric. Procedure according to Claim 1 for determining the state of an s-state phase change memory cell with s>2, the method comprising determining the state of the cell by comparing the measure with a plurality of reference values corresponding to the s states of the cell. Procedure according to Claim 1 or Claim 2 , which involves performing a plurality of measurements of the cell current at different cell bias voltages, wherein the measure depends on differences in a function of the measured cell current at the different bias voltages. Procedure according to Claim 1 or Claim 2 , which involves performing a plurality of measurements of the voltage across the cell for different supplied cell currents, wherein the measure depends on differences in a function of the measured cell voltage at the different supplied currents. Procedure according to Claim 1 or Claim 2 , which involves performing a plurality of measurements of the cell resistance at different points on the current/voltage characteristic curve, the measure being dependent on differences in a function of the measured cell resistance at the different points. Procedure according to one of the Claims 3 until 5 , where the function of the measured value has a logarithm of this value. Method according to one of the preceding claims, wherein the measure depends on the effective amorphous thickness (u _a ) in the cell. Procedure according to Claim 7 , where an estimate of the effective amorphous thickness (u _a ) in the cell is used as a measure. A method according to any one of the preceding claims, which includes performing more than two measurements, wherein the processing includes an averaging process. A device for determining the state of a phase-change memory cell with a non-linear sub-threshold current/voltage characteristic, the device comprising: a measuring circuit (4) for carrying out a plurality of measurements dependent on the non-linear sub-threshold current/voltage characteristic of the cell; and a control unit (5) for processing the measured values by means of differences (log R ₁ - log R ₂ ) in order to obtain a metric which is dependent on the slope of the current/voltage characteristic and independent of the absolute cell resistance, the control unit (5) being configured to determine the state of the cell as a function of the metric. Device according to Claim 10 for determining the state of an s-state phase change memory cell with s>2, wherein the control unit (5) is arranged to determine the state of the cell by comparing the measure with a plurality of reference values which correspond to the s states of the cell. Device according to Claim 10 or Claim 11 , wherein the measuring circuit (4) is arranged to carry out a plurality of measurements of the cell current at different cell bias voltages, and wherein the measure depends on differences in a function of the measured cell current at the different bias voltages. Device according to Claim 10 or Claim 11 , wherein the measuring circuit (4) is arranged to carry out a plurality of measurements of the voltage across the cell for different applied cell currents, and wherein the measure depends on differences in a function of the measured cell voltage at the different applied currents. Device according to Claim 10 or Claim 11 , wherein the measuring circuit (4) is arranged to carry out a plurality of measurements of the cell resistance at different points on the current/voltage characteristic curve, and wherein the measure depends on differences in a function of the measured cell resistance at the different points. Phase change memory unit (1), comprising: a memory (2) which has a plurality of phase change memory cells with a non-linear sub-threshold current/voltage characteristic; and a read/write device (3) for reading data from and writing data into the phase change memory cells, wherein the read/write device (3) comprises a device according to one of the Claims 10 until 14 to determine the state of a memory cell.