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Semiconductors and NTC Thermistors

Key idea: Explain why semiconductor resistivity decreases with temperature and interpret the I–V characteristics of an NTC thermistor and semiconductor diode.

  • GCE A-Level H2 Physics 2027
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Learning objectives

  • Apply resistance and resistivity, interpret I–V characteristics and explain temperature effects.

1. Semiconductor temperature dependence

A semiconductor has a number density of mobile charge carriers that increases strongly with temperature. Heating also increases lattice vibration and collisions, but the rise in carrier number density is the dominant effect for a typical semiconductor:

T↑ ⇒ n↑ ⇒ ρ↓.

This contrasts with a typical metal, where carrier number density is approximately constant and increased collision frequency makes resistivity rise with temperature.

Use the required microscopic contrast

For a metal, explain the trend using reduced drift velocity from more frequent collisions. For a semiconductor, explain it using the increased number density of charge carriers.

2. NTC thermistor

An NTC thermistor is a semiconductor component with a negative temperature coefficient: its resistance decreases as its temperature increases.

If self-heating is negligible and temperature is held constant, a thermistor can have an approximately linear I–V characteristic over a small range. In a typical measurement over a wider range, current heats the thermistor, lowering its resistance and making the curve become steeper.

3. Semiconductor diode

A diode conducts readily in its forward direction after the applied p.d. becomes sufficiently positive, but carries negligible reverse current in the idealised syllabus model.

Semiconductor diode I–V characteristic

An illustrative diode characteristic with negligible reverse current and a rapidly increasing forward current after the knee region.

Scroll across the graph to read all labels.

An illustrative diode characteristic with negligible reverse current and a rapidly increasing forward current after the knee region.An illustrative diode characteristic with negligible reverse current and a rapidly increasing forward current after the knee region.
Illustrative values only: the required feature is strongly asymmetric conduction, not a universal fixed turn-on voltage.
Open full-size graph
View figure data
Values for Semiconductor diode I–V characteristic
Potential difference, V (V)Diode
-2-0.1
-1-0.05
00
0.30.1
0.50.7
0.63
0.79
0.818

The precise curve depends on the diode material and temperature. Avoid claiming that every diode switches suddenly at exactly 0.7 V.

4. Comparing required I–V characteristics

ComponentShape and symmetryPhysical reason
Ohmic resistor at constant temperaturestraight line through origin; symmetricconstant resistance
Filament lampcurve becomes less steep at large $V
NTC thermistor with self-heatingcurve becomes steeper at large $V
Semiconductor diodestrongly asymmetricconducts mainly in one direction

5. Common Mistakes

  • Explaining the semiconductor trend only as “electrons move faster”. The required cause is increased carrier number density.
  • Reversing the temperature trends for a metal and an NTC thermistor.
  • Treating an NTC thermistor as an ohmic resistor while its temperature is changing.
  • Drawing a diode curve symmetric about the origin.
  • Reading resistance directly as the gradient of an I–V graph; at a point, R = V/I.

6. Worked Examples

Modelled example 1

Compare a filament lamp and NTC thermistor

Core

Problem

Explain why the resistance of a filament lamp rises with temperature while that of an NTC thermistor falls.
Study the worked solution

  1. Explain the metal filament

    Method

    Link heating to greater resistance.

    Reason

    Increased lattice vibration causes more frequent collisions and reduces drift velocity for a given field; carrier number density is approximately constant.

    Working

    Metal: T↑ ⇒ collisions ↑ ⇒ ρ↑.

  2. Explain the NTC semiconductor

    Method

    Link heating to lower resistance.

    Reason

    The large increase in mobile-carrier number density dominates the additional collisions.

    Working

    NTC: T↑ ⇒ n↑ ⇒ ρ↓.

  3. Make the contrast explicit

    Method

    State that the dominant microscopic change differs.

    Reason

    The two trends cannot be explained by temperature alone.

    Working

    Metal: collision effect dominates; NTC: carrier-density effect dominates.

Guided practice 2

Identify a diode characteristic

About 4 min

Problem

An I–V graph shows negligible current for negative p.d. and a rapid current increase for positive p.d. Identify the component and explain the evidence.

Try this before viewing the solution

Component

Hints

Hint 1: inspect symmetry
Decide whether reversing p.d. produces a similar current magnitude.
Hint 2: name the bias states
Connect negligible negative-p.d. current to reverse bias and rapid positive-p.d. current to forward bias.
View solution step by step

  1. Use the reverse region

    Method

    Identify blocking under reverse bias.

    Reason

    The current is negligible for negative p.d.

    Working

    Reverse bias: I ≈ 0.

  2. Use the forward region

    Method

    Identify ready conduction under forward bias.

    Reason

    Current rises rapidly for positive p.d.

    Working

    Forward bias: rapid increase in I.

  3. Name the component

    Method

    Conclude semiconductor diode.

    Reason

    A diode’s I–V characteristic is strongly asymmetric.

    Working

    Component: diode.

Common misconception 3

Why an NTC curve becomes steeper

Find and correct the mistake

Learner claim

On an I-against-V graph, an NTC thermistor’s curve becomes steeper at larger |V|. A learner says this means its resistance is increasing. Diagnose the claim.

Try this before viewing the solution

Meaning of a steeper I-against-V curve

View solution step by step

  1. Read the axes

    Method

    Use R = V/I at the operating point.

    Reason

    On an I-against-V graph, I/V is conductance, not resistance.

    Working

    R = V/I = 1/(I/V)

  2. Explain self-heating

    Method

    Link larger current to a hotter thermistor.

    Reason

    Electrical power raises temperature during the measurement.

    Working

    I↑ ⇒ heating ↑ ⇒ T↑.

  3. Apply the NTC mechanism

    Method

    Conclude that resistance falls.

    Reason

    Heating greatly increases mobile-carrier number density.

    Working

    T↑ ⇒ n↑ ⇒ ρ↓.

Examiner practice 4

Compare three non-ohmic characteristics

4 marks

Examination question

Compare the symmetry and large-|V| shape of the I–V characteristics for a filament lamp, a self-heating NTC thermistor and a semiconductor diode. [4 marks]

Try this before viewing the solution

View solution step by step

  1. Describe the lamp

    1 mark

    Method

    State symmetric and less steep at large |V|.

    Reason

    Heating increases metal resistivity.

    Working

    Lamp: symmetric; I grows less than proportionally with V.

  2. Describe the NTC thermistor

    1 mark

    Method

    State symmetric and steeper at large |V|.

    Reason

    Heating increases carrier number density and lowers resistance.

    Working

    NTC: symmetric; I grows more than proportionally with V.

  3. Describe the diode

    1 mark

    Method

    State strongly asymmetric.

    Reason

    It blocks in reverse bias and conducts readily in forward bias.

    Working

    Diode: negligible reverse current; rapid forward rise.

  4. State the comparison boundary

    1 mark

    Method

    Avoid assigning one universal turn-on voltage.

    Reason

    The precise diode curve depends on material and temperature.

    Working

    Use the curve shown or the stated diode model.

Challenge 5

Point resistance from a diode graph

Minimal support

Independent transfer

The illustrative diode graph gives approximately I = 9.0 mA at V = 0.70 V. Calculate V/I at that point, then explain why this value does not make the diode an ohmic resistor.

Try this before viewing the solution

Hints

Hint 1: convert the current
Express 9.0 mA in amperes before using R = V/I.
View solution step by step

  1. Calculate the point ratio

    Method

    Divide voltage by current in amperes.

    Reason

    R = V/I defines the ratio at the selected operating point.

    Working

    V/I = 0.70/(9.0 × 10⁻³) = 78 Ω

  2. Interpret the curve

    Method

    Reject constant resistance.

    Reason

    The diode curve is not a straight line through the origin, so V/I changes with operating point.

    Working

    Different graph points give different V/I ratios.

7. Mind Stretchers

Mind stretcher 1: Temperature mechanisms without the comparison tableExtension

Explain, without referring back to the table, why heating makes a metal’s resistivity rise but a typical NTC semiconductor’s resistivity fall. State the microscopic quantity that dominates in each material.

Show Answer

In the metal, greater lattice vibration increases collision frequency and reduces drift velocity for a given field; carrier number density remains approximately constant, so resistivity rises. In the NTC semiconductor, the large increase in mobile-carrier number density dominates the additional collisions, so resistivity falls.

Next: Internal Resistance

Continue with the next resource in this course.

Course and syllabus information
Course
GCE A-Level H2 Physics
Edition
GCE A-Level H2 Physics 2027